new york city state standards alignment kindergarten...
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New York City State Standards Alignment Kindergarten through Grade Ten
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New York City State Standards Alignment
Standards List with Aligned Product Skills
The Standards list with Aligned Product Skills Report is a standards-oriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product.
Introduction Letter .....................................................iii
Kindergarten - Grade 4 ................................................. 1
Grades 5 - 8 ....................................................81
Grades 9 - 10 ..................................................157
Note to educator: Thank you for your interest in Renaissance Learning™ technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standard documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope that this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (877) 204-5058. Sincerely, Renaissance Sales and Funding Staff
Helping educators improve schools through technology, professional development and research
P.O. Box 8036 • Wisconsin Rapids, WI 54495-8036 • Phone: (715) 424-3636 • Fax: (715) 424-4242 • www.renlearn.com
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of arithmetic and number concepts; that is, the student:
NYC M1.a - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is:NYC M1.a.i - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: adds, i.e., joins things together, increases.
Topic 2 - Whole Numbers: Addition
Obj. 10 - Add using pictures to 12
Obj. 11 - Addition sentences to 12Obj. 12 - Add using number line to 12
Obj. 13 - Addition facts to 12, vertical
Obj. 14 - Addition facts to 12, horizontal
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 37 - Addition facts from 11 to 18, verticalObj. 38 - Addition facts from 11 to 18, horizontalObj. 43 - Add three 1-digit #sObj. 44 - Adding in any orderObj. 45 - Add 2-digit #s, no regroup
NYC M1.a.ii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: subtracts, i.e., takes away, compares, finds the difference.
Topic 3 - Whole Numbers: Subtraction
Obj. 16 - Subtract using pictures from 12
Obj. 17 - Subtraction sentences from 12Obj. 18 - Finish subtraction sentences from 12Obj. 19 - Subtract using number line from 12Obj. 20 - Subtraction facts from 12, verticalObj. 21 - Subtraction facts from 12, horizontal
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
Accelerated Math Kindergarten - Grade 4
091207Page 1 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 39 - Subtraction facts from 11 to 18, verticalObj. 40 - Subtraction facts from 11 to 18, horizontalObj. 46 - Subtract 2-digit #s, no regroup
NYC M1.a.iii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: multiplies, i.e., uses repeated addition, counts by multiples, combines things that come in groups, makes arrays, uses area models, computes simple scales, uses simple rates.
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 99 - Make equal groups of objects
Obj. 100 - Skip-counting & repeated additionObj. 102 - Use multiplication patterns to complete tables
NYC M1.a.iv - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: divides, i.e., puts things into groups, shares equally; calculates simple rates.
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 103 - Divide into equal groups
Obj. 104 - Divide into equal groups with left over
NYC M1.a.v - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: analyzes problem situations and contexts in order to figure out when to add, subtract, multiply, or divide.
Topic 2 - Whole Numbers: Addition
Obj. 15 - WP: Add, 1-step
Topic 3 - Whole Numbers: Subtraction
Obj. 22 - WP: Subtract, 1-step
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 41 - Determine add & subt in # sentenceObj. 47 - WP: Write number sentence, add & subtract (to 18)Obj. 48 - WP: Add & subtract, 1-step
Obj. 49 - WP: Add & subtract, 2-step
Topic 9 - Graphs, Data, and Probability
Obj. 80 - Add with graphs & tables (to 12)Obj. 81 - Subtract with graphs & tables (to 12)
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
Obj. 82 - Add & subtract with graphs (to 18)
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 101 - WP: Multiplication strategies
Obj. 105 - WP: Division strategiesNYC M1.a.vi - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: solves arithmetic problems by relating addition, subtraction, multiplication, and division to one another.
NYC M1.a.vii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: computes answers mentally, e.g., 27 + 45, 30 x 4.
Topic 2 - Whole Numbers: Addition
Obj. 13 - Addition facts to 12, vertical
Obj. 14 - Addition facts to 12, horizontal
Topic 3 - Whole Numbers: Subtraction
Obj. 20 - Subtraction facts from 12, verticalObj. 21 - Subtraction facts from 12, horizontal
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 37 - Addition facts from 11 to 18, verticalObj. 38 - Addition facts from 11 to 18, horizontalObj. 39 - Subtraction facts from 11 to 18, verticalObj. 40 - Subtraction facts from 11 to 18, horizontalObj. 43 - Add three 1-digit #s
NYC M1.a.viii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: uses simple concepts of negative numbers, e.g., on a number line, in counting, in temperature, "owing."NYC M1.b - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is:
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M1.b.i - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: counts 1, 10, 100, or 1,000 more than or less than, e.g., 1 less than 10,000, 10 more than 380, 1,000 more than 23,000, 100 less than 9,000.NYC M1.b.ii - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: uses knowledge about ones, tens, hundreds, and thousands to figure out answers to multiplication and division tasks, e.g., 36 x 10, 18 x 100, 7 x 1,000, 4,000 ÷ 4.
NYC M1.c - Estimates, approximates, rounds off, uses landmark numbers, or uses exact numbers, as appropriate, in calculations.
Topic 6 - Money Obj. 57 - Estimate coin value
NYC M1.d - Describes and compares quantities by using concrete and real world models of simple fractions; that is:NYC M1.d.i - Describes and compares quantities by using concrete and real world models of simple fractions; that is: finds simple parts of wholes.
Topic 10 - Geometry and Fractions
Obj. 95 - Equal parts
Obj. 96 - 1/2, 1/3, & 1/4 as parts of a whole
NYC M1.d.ii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes simple fractions as instructions to divide, e.g., 1/4 of something is the same as dividing something by 4.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M1.d.iii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes the place of fractions on number lines, e.g., in measurement.
NYC M1.d.iv - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses drawings, diagrams, or models to show what the numerator and denominator mean, including when adding like fractions, e.g., 1/8 + 5/8, or when showing that 3/4 is more than 3/8.
Topic 10 - Geometry and Fractions
Obj. 97 - Equivalent fractions
NYC M1.d.v - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses beginning proportional reasoning and simple ratios, e.g., "about half of the people."NYC M1.e - Describes and compares quantities by using simple decimals; that is:NYC M1.e.i - Describes and compares quantities by using simple decimals; that is: adds, subtracts, multiplies, and divides money amounts.NYC M1.e.ii - Describes and compares quantities by using simple decimals; that is: recognizes relationships among simple fractions, decimals, and percents, i.e., that 1/2 is the same as 0.5, and 1/2 is the same as 50%, with concrete materials, diagrams, and in real world situations, e.g., when discovering the chance of a coin landing on heads or tails.
NYC M1.f - Describes and compares quantities by using whole numbers up to 10,000; that is:
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M1.f.i - Describes and compares quantities by using whole numbers up to 10,000; that is: connects ideas of quantities to the real world, e.g., how many people fit in the school’s cafeteria; how far away is a kilometer.NYC M1.f.ii - Describes and compares quantities by using whole numbers up to 10,000; that is: finds, identifies, and sorts numbers by their properties, e.g., odd, even, multiple, square.
Topic 4 - Whole Number Concepts II
Obj. 34 - Odd & even numbers
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:NYC M2.a - Gives and responds to directions about location, e.g., by using words such as "in front of," "right," and "above."
Topic 10 - Geometry and Fractions
Obj. 92 - Proximity in space
NYC M2.b - Visualizes and represents two dimensional views of simple rectangular three dimensional shapes, e.g., by showing the front view and side view of a building made of cubes.NYC M2.c - Uses simple two dimensional coordinate systems to find locations on a map and to represent points and simple figures.
Topic 10 - Geometry and Fractions
Obj. 98 - Read a coordinate grid
NYC M2.d - Uses many types of figures (angles, triangles, squares, rectangles, rhombi, parallelograms, quadrilaterals, polygons, prisms, pyramids, cubes, circles, and spheres) and identifies the figures by their properties, e.g., symmetry, number of faces, two- or three-dimensionality, no right angles.
Topic 1 - Whole Number Concepts I
Obj. 7 - Classify by attributes
Topic 10 - Geometry and Fractions
Obj. 86 - Identify plane figures
Obj. 87 - Count sides & corners on a plane figure
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
Obj. 89 - Identify solidsObj. 90 - Lines of symmetry
NYC M2.e - Solves problems by showing relationships between and among figures, e.g., using congruence and similarity, and using transformations including flips, slides, and rotations.
Topic 10 - Geometry and Fractions
Obj. 91 - Congruent figures
Obj. 93 - Slides, flips, and turnsObj. 94 - Combine & take apart shapes
NYC M2.f - Extends and creates geometric patterns using concrete and pictorial models.
Topic 1 - Whole Number Concepts I
Obj. 8 - Picture patterns
NYC M2.g - Uses basic ways of estimating and measuring the size of figures and objects in the real world, including length, width, perimeter, and area.
Topic 8 - Measurement Obj. 74 - Use tiles to estimate area
NYC M2.h - Uses models to reason about the relationship between the perimeter and area of rectangles in simple situations.NYC M2.i - Selects and uses units, both formal and informal as appropriate, for estimating and measuring quantities such as weight, length, area, volume, and time.
NYC M2.j - Carries out simple unit conversions, such as between cm and m, and between hours and minutes.NYC M2.k - Uses scales in maps, and uses, measures, and creates scales for rectangular scale drawings based on work with concrete models and graph paper.NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Uses linear patterns to solve problems; that is:
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M3.a.i - Uses linear patterns to solve problems; that is: shows how one quantity determines another in a linear ("repeating") pattern, i.e., describes, extends, and recognizes the linear pattern by its rule, such as, the total number of legs on a given number of horses can be calculated by counting by fours.
Topic 1 - Whole Number Concepts I
Obj. 9 - Number patterns
NYC M3.a.ii - Uses linear patterns to solve problems; that is: shows how one quantity determines another quantity in a functional relationship based on a linear pattern, e.g., for the "number of people and total number of eyes," figure out how many eyes 100 people have all together.
Topic 12 - Problem Solving Obj. 109 - WP: Patterns
NYC M3.b - Builds iterations of simple non-linear patterns, including multiplicative and squaring patterns (e.g., "growing" patterns) with concrete materials, and recognizes that these patterns are not linear.
NYC M3.c - Uses the understanding that an equality relationship between two quantities remains the same as long as the same change is made to both quantities.
NYC M3.d - Uses letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations with concrete materials, i.e., demonstrates understanding and use of a beginning concept of a variable.
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 42 - Solve equations for symbol
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts in the following areas; that is, the student:
Accelerated Math Kindergarten - Grade 4
091207Page 8 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M4.a - Collects and organizes data to answer a question or test a hypothesis by comparing sets of data.
Topic 9 - Graphs, Data, and Probability
Obj. 79 - Record data and answer questions
NYC M4.b - Displays data in line plots, graphs, tables, and charts.NYC M4.c - Makes statements and draws simple conclusions based on data; that is:NYC M4.c.i - Makes statements and draws simple conclusions based on data; that is: reads data in line plots, graphs, tables, and charts.
Topic 9 - Graphs, Data, and Probability
Obj. 76 - Tally charts
Obj. 77 - PictographsObj. 78 - Bar graphsObj. 83 - Money with graphs
NYC M4.c.ii - Makes statements and draws simple conclusions based on data; that is: compares data in order to make true statements, e.g., "seven plants grew at least 5 cm".
NYC M4.c.iii - Makes statements and draws simple conclusions based on data; that is: identifies and uses the mode necessary for making true statements, e.g., "more people chose red".NYC M4.c.iv - Makes statements and draws simple conclusions based on data; that is: makes true statements based on a simple concept of average (median and mean), for a small sample size and where the situation is made evident with concrete materials or clear representations.NYC M4.c.v - Makes statements and draws simple conclusions based on data; that is: interprets data to determine the reasonableness of statements about the data, e.g., "twice as often," "three times faster".
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M4.c.vi - Makes statements and draws simple conclusions based on data; that is: uses data, including statements about the data, to make a simple concluding statement about a situation, e.g., "This kind of plant grows better near sunlight because the seven plants that were near the window grew at least 5 cm."
NYC M4.d - Gathers data about an entire group or by sampling group members to understand the concept of sample, i.e., that a large sample leads to more reliable information, e.g., when flipping coins.
NYC M4.e - Predicts results, analyzes data, and finds out why some results are more likely, less likely, or equally likely.
Topic 9 - Graphs, Data, and Probability
Obj. 85 - Identify more likely events
NYC M4.f - Finds all possible combinations and arrangements within certain constraints involving a limited number of variables.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates logical reasoning throughout work in mathematics, i.e., concepts and skills, problem solving, and projects; demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow; and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion.
- FORMULATIONNYC M5.a - Given the basic statement of a problem situation, the student:
Accelerated Math Kindergarten - Grade 4
091207Page 10 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M5.a.i - Given the basic statement of a problem situation, the student: makes the important decisions about the approach, materials, and strategies to use, i.e., does not merely fill in a given chart, use a pre-specified manipulative, or go through a predetermined set of steps.NYC M5.a.ii - Given the basic statement of a problem situation, the student: uses previously learned strategies, skills, knowledge, and concepts to make decisions.
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 47 - WP: Write number sentence, add & subtract (to 18)
Obj. 48 - WP: Add & subtract, 1-step
Obj. 49 - WP: Add & subtract, 2-step
Obj. 50 - WP: Too much or little info, 1- & 2-dig add & subt
Topic 6 - Money Obj. 58 - WP: Add & subtract money expressions
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 101 - WP: Multiplication strategies
Obj. 105 - WP: Division strategiesNYC M5.a.iii - Given the basic statement of a problem situation, the student: uses strategies, such as using manipulatives or drawing sketches, to model problems.
Topic 2 - Whole Numbers: Addition
Obj. 15 - WP: Add, 1-step
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 101 - WP: Multiplication strategies
Topic 12 - Problem Solving Obj. 106 - Draw pictures to solve problemsObj. 107 - Guess and check to solve problemsObj. 108 - Use lists to solve problems
- IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes up and uses a variety of strategies and approaches to solving problems and uses or learns approaches that other people use, as appropriate.
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes connections among concepts in order to solve problems.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves problems in ways that make sense and explains why these ways make sense, e.g., defends the reasoning, explains the solution.
- CONCLUSIONNYC M5.c - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student:NYC M5.c.i - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains a pattern that can be used in similar situations.
NYC M5.c.ii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem is similar to other problems he or she has solved.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M5.c.iii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the mathematics used in the problem is like other concepts in mathematics.
NYC M5.c.iv - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem solution can be applied to other school subjects and in real world situations.NYC M5.c.v - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: makes the solution into a general rule that applies to other circumstances.NYC M6 - MATHEMATICAL SKILLS AND TOOLSNYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, books, or other students, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Adds, subtracts, multiplies, and divides whole numbers correctly; that is:NYC M6.a.i - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: knows single digit addition, subtraction, multiplication, and division facts.
Topic 2 - Whole Numbers: Addition
Obj. 15 - WP: Add, 1-step
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 43 - Add three 1-digit #s
Accelerated Math Kindergarten - Grade 4
091207Page 13 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M6.a.ii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: adds and subtracts numbers with several digits.
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 45 - Add 2-digit #s, no regroup
Obj. 46 - Subtract 2-digit #s, no regroup
NYC M6.a.iii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides numbers with one or two digits.NYC M6.a.iv - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides three digit numbers by one digit numbers.NYC M6.b - Estimates numerically and spatially.
Topic 4 - Whole Number Concepts II
Obj. 33 - Estimate # in group (2 dig)
Topic 6 - Money Obj. 57 - Estimate coin valueTopic 8 - Measurement Obj. 66 - Estimate length in non-
standard unitsNYC M6.c - Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems.
Topic 8 - Measurement Obj. 68 - Measure length in cm with ruler
NYC M6.d - Computes time (in hours and minutes) and money (in dollars and cents).
Topic 6 - Money Obj. 55 - Add & subtract with coins
NYC M6.e - Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid.
Topic 10 - Geometry and Fractions
Obj. 86 - Identify plane figures
Obj. 89 - Identify solidsNYC M6.f - Uses +, -, x, ÷, /, long division symbol, $, ¢, %, and . (decimal point) correctly in number sentences and expressions.
Topic 5 - Whole Numbers: Addition and Subtraction
Obj. 41 - Determine add & subt in # sentence
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M6.g - Reads, creates, and represents data on line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs.
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the 1/8 inch; metric to the millimeter), graph paper (customary to the inch or half-inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound or ounce; metric to the kilogram or gram).
Topic 8 - Measurement Obj. 68 - Measure length in cm with ruler
Obj. 70 - Capacity in cups, pints, quarts, & gallons
NYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work.NYC M7.b - Shows mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models.
Topic 2 - Whole Numbers: Addition
Obj. 10 - Add using pictures to 12
Topic 3 - Whole Numbers: Subtraction
Obj. 16 - Subtract using pictures from 12
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
Topic 12 - Problem Solving Obj. 106 - Draw pictures to solve problems
NYC M7.c - Explains solutions to problems clearly and logically, and supports solutions with evidence, in both oral and written work.NYC M7.d - Considers purpose and audience when communicating about mathematics.NYC M7.e - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale project each year, beginning in fourth grade, drawn from the following kinds and, over the course of elementary school, conducts projects drawn from at least two of the kinds. A single project may draw on more than one kind.
NYC M8.a - Data study, in which the student:NYC M8.a.i - Data study, in which the student: develops a question and a hypothesis in a situation where data could help make a decision or recommendation.NYC M8.a.ii - Data study, in which the student: decides on a group or groups to be sampled and makes predictions of the results, with specific percents, fractions, or numbers.NYC M8.a.iii - Data study, in which the student: collects, represents, and displays data in order to help make the decision or recommendation; compares the results with the predictions.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M8.a.iv - Data study, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.b - Science study, in which the student:NYC M8.b.i - Science study, in which the student: decides on a specific science question to study and identifies the mathematics that will be used, e.g., measurement.NYC M8.b.ii - Science study, in which the student: develops a prediction (a hypothesis) and develops procedures to test the hypothesis.NYC M8.b.iii - Science study, in which the student: collects and records data, represents and displays data, and compares results with predictions.NYC M8.b.iv - Science study, in which the student: writes a report that compares the results with the hypothesis; supports the results with diagrams, charts, and graphs; acknowledges assistance received from parents, peers, and teachers.NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: decides on a structure to design, the size and budget constraints, and the scale of design.NYC M8.c.ii - Design of a physical structure, in which the student: makes a first draft of the design, and revises and improves the design in response to input from peers and teachers.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M8.c.iii - Design of a physical structure, in which the student: makes a final draft and report of the design, drawn and written so that another person could make the structure; acknowledges assistance received from parents, peers, and teachers.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: decides on what to manage or plan, and the criteria to be used to see if the plan worked.NYC M8.d.ii - Management and planning, in which the student: identifies unexpected events that could disrupt the plan and further plans for such contingencies.NYC M8.d.iii - Management and planning, in which the student: identifies resources needed, e.g., materials, money, time, space, and other people.NYC M8.d.iv - Management and planning, in which the student: writes a detailed plan and revises and improves the plan in response to feedback from peers and teachers.
NYC M8.d.v - Management and planning, in which the student: carries out the plan (optional).NYC M8.d.vi - Management and planning, in which the student: writes a report on the plan that includes resources, budget, and schedule, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.d.vii - Management and planning, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 1
NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: decides on the area of mathematics to investigate, e.g., numbers, shapes, patterns.NYC M8.e.ii - Pure mathematics investigation, in which the student: describes a question or concept to investigate.NYC M8.e.iii - Pure mathematics investigation, in which the student: decides on representations that will be used, e.g., numbers, symbols, diagrams, shapes, or physical models.NYC M8.e.iv - Pure mathematics investigation, in which the student: carries out the investigation.NYC M8.e.v - Pure mathematics investigation, in which the student: writes a report that includes any generalizations drawn from the investigation, and acknowledges assistance received from parents, peers, and teachers.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of arithmetic and number concepts; that is, the student:
NYC M1.a - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is:NYC M1.a.i - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: adds, i.e., joins things together, increases.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 11 - Addition facts to 10
Obj. 12 - Addition facts from 11 to 18
Obj. 13 - Add three 1-digit #sObj. 14 - Add multiples of tenObj. 15 - Add 1- & 2-digit #s, no regroupObj. 16 - Add 1- & 2-digit #s, regroup
Obj. 17 - Add 2-digit #s, regroupObj. 18 - Add three #s, regroup (1 & 2 dig)
Topic 10 - Whole Number Addition and Subtraction II
Obj. 115 - Use doubles to add
Obj. 116 - Use compensation to add 2-digit numbersObj. 117 - Add 3-digit #s, no regroup
Obj. 118 - Add 3-digit #s, regroupObj. 119 - Add 3-digit money expressions
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 128 - Repeated addition
NYC M1.a.ii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: subtracts, i.e., takes away, compares, finds the difference.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 19 - Subtraction facts from 10
Obj. 20 - Subtraction facts from 11 to 18Obj. 21 - Subtract multiples of ten
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
Obj. 22 - Subtract 1- & 2-digit #s, no regroupObj. 23 - Subtract 1-dig from 2-dig #s, regroupObj. 24 - Subtract 2-digit #s, regroup
Topic 3 - Whole Number Concepts II
Obj. 44 - Compare #s to 1000 using <, >, =
Topic 10 - Whole Number Addition and Subtraction II
Obj. 120 - Subtract 3-digit #s, no regroupObj. 121 - Subtract 3-digit #s, regroupObj. 122 - Subtract 3-digit money expressions
NYC M1.a.iii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: multiplies, i.e., uses repeated addition, counts by multiples, combines things that come in groups, makes arrays, uses area models, computes simple scales, uses simple rates.
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 127 - Identify equal groups
Obj. 128 - Repeated additionObj. 130 - Multiplication facts, to 5s
Obj. 133 - Multiply with graphs (1 dig)
NYC M1.a.iv - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: divides, i.e., puts things into groups, shares equally; calculates simple rates.
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 134 - Divide into equal groups
Obj. 135 - Divide into equal groups with left overObj. 137 - Divide money
NYC M1.a.v - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: analyzes problem situations and contexts in order to figure out when to add, subtract, multiply, or divide.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 29 - WP: Add 1-digit #s, one-step
Obj. 30 - WP: Subtract 1-digit #s, one-stepObj. 31 - WP: Add 2-digit #s, one-step
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
Obj. 32 - WP: Subtract 2-digit #s, one-step
Topic 10 - Whole Number Addition and Subtraction II
Obj. 123 - WP: Add & subtract, 2-step
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 132 - WP: Multiplication
Obj. 138 - WP: DivisionNYC M1.a.vi - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: solves arithmetic problems by relating addition, subtraction, multiplication, and division to one another.
NYC M1.a.vii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: computes answers mentally, e.g., 27 + 45, 30 x 4.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 11 - Addition facts to 10
Obj. 12 - Addition facts from 11 to 18
Obj. 13 - Add three 1-digit #sObj. 14 - Add multiples of ten
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 130 - Multiplication facts, to 5s
NYC M1.a.viii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: uses simple concepts of negative numbers, e.g., on a number line, in counting, in temperature, "owing."NYC M1.b - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M1.b.i - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: counts 1, 10, 100, or 1,000 more than or less than, e.g., 1 less than 10,000, 10 more than 380, 1,000 more than 23,000, 100 less than 9,000.
Topic 10 - Whole Number Addition and Subtraction II
Obj. 116 - Use compensation to add 2-digit numbers
NYC M1.b.ii - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: uses knowledge about ones, tens, hundreds, and thousands to figure out answers to multiplication and division tasks, e.g., 36 x 10, 18 x 100, 7 x 1,000, 4,000 ÷ 4.
NYC M1.c - Estimates, approximates, rounds off, uses landmark numbers, or uses exact numbers, as appropriate, in calculations.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 35 - Estimate # in group (2 dig)
Obj. 36 - Estimate sum & diff, front digits only (2 dig)Obj. 37 - Round to nearest ten (2 dig)
Obj. 38 - Estimate sum & diff, round (2 dig)
NYC M1.d - Describes and compares quantities by using concrete and real world models of simple fractions; that is:NYC M1.d.i - Describes and compares quantities by using concrete and real world models of simple fractions; that is: finds simple parts of wholes.
Topic 9 - Fractions Obj. 105 - Equal parts
Obj. 106 - Meaning of a fraction's partsObj. 107 - Fractional parts of a whole
Obj. 108 - Fractional parts equal to a wholeObj. 109 - Fractional parts of a set
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M1.d.ii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes simple fractions as instructions to divide, e.g., 1/4 of something is the same as dividing something by 4.
NYC M1.d.iii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes the place of fractions on number lines, e.g., in measurement.
NYC M1.d.iv - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses drawings, diagrams, or models to show what the numerator and denominator mean, including when adding like fractions, e.g., 1/8 + 5/8, or when showing that 3/4 is more than 3/8.
Topic 9 - Fractions Obj. 111 - Compare & order fractions
NYC M1.d.v - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses beginning proportional reasoning and simple ratios, e.g., "about half of the people."NYC M1.e - Describes and compares quantities by using simple decimals; that is:NYC M1.e.i - Describes and compares quantities by using simple decimals; that is: adds, subtracts, multiplies, and divides money amounts.
Topic 10 - Whole Number Addition and Subtraction II
Obj. 119 - Add 3-digit money expressions
Obj. 122 - Subtract 3-digit money expressions
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M1.e.ii - Describes and compares quantities by using simple decimals; that is: recognizes relationships among simple fractions, decimals, and percents, i.e., that 1/2 is the same as 0.5, and 1/2 is the same as 50%, with concrete materials, diagrams, and in real world situations, e.g., when discovering the chance of a coin landing on heads or tails.
NYC M1.f - Describes and compares quantities by using whole numbers up to 10,000; that is:
NYC M1.f.i - Describes and compares quantities by using whole numbers up to 10,000; that is: connects ideas of quantities to the real world, e.g., how many people fit in the school’s cafeteria; how far away is a kilometer.
Topic 7 - Measurement Obj. 79 - Estimate capacity in customary & metric units
NYC M1.f.ii - Describes and compares quantities by using whole numbers up to 10,000; that is: finds, identifies, and sorts numbers by their properties, e.g., odd, even, multiple, square.
Topic 1 - Whole Number Concepts I
Obj. 8 - Odd & even numbers
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:NYC M2.a - Gives and responds to directions about location, e.g., by using words such as "in front of," "right," and "above."
Topic 8 - Geometry Obj. 102 - Use positional words
NYC M2.b - Visualizes and represents two dimensional views of simple rectangular three dimensional shapes, e.g., by showing the front view and side view of a building made of cubes.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M2.c - Uses simple two dimensional coordinate systems to find locations on a map and to represent points and simple figures.
Topic 8 - Geometry Obj. 103 - Coordinate graphs
NYC M2.d - Uses many types of figures (angles, triangles, squares, rectangles, rhombi, parallelograms, quadrilaterals, polygons, prisms, pyramids, cubes, circles, and spheres) and identifies the figures by their properties, e.g., symmetry, number of faces, two- or three-dimensionality, no right angles.
Topic 8 - Geometry Obj. 91 - Count faces, edges, & corners
NYC M2.e - Solves problems by showing relationships between and among figures, e.g., using congruence and similarity, and using transformations including flips, slides, and rotations.
Topic 8 - Geometry Obj. 97 - Identify symmetry
Obj. 99 - Flips, slides, and turnsNYC M2.f - Extends and creates geometric patterns using concrete and pictorial models.
Topic 4 - Graphs and Patterns Obj. 51 - Picture patterns
Topic 8 - Geometry Obj. 104 - Geometric patternsNYC M2.g - Uses basic ways of estimating and measuring the size of figures and objects in the real world, including length, width, perimeter, and area.
Topic 7 - Measurement Obj. 73 - Measure length in cm & m
NYC M2.h - Uses models to reason about the relationship between the perimeter and area of rectangles in simple situations.NYC M2.i - Selects and uses units, both formal and informal as appropriate, for estimating and measuring quantities such as weight, length, area, volume, and time.
Topic 7 - Measurement Obj. 71 - Measure length in non-standard units
Obj. 72 - Measure length in in., ft, & ydObj. 73 - Measure length in cm & m
Obj. 74 - Estimate length & heightObj. 78 - Capacity in litersObj. 82 - Weight in grams & kilograms
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
Obj. 83 - Estimate weight in cust & metric unitsObj. 84 - Compare weights
Topic 8 - Geometry Obj. 94 - Find area by counting squaresObj. 96 - Find volume of a box by counting cubes
NYC M2.j - Carries out simple unit conversions, such as between cm and m, and between hours and minutes.NYC M2.k - Uses scales in maps, and uses, measures, and creates scales for rectangular scale drawings based on work with concrete models and graph paper.NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Uses linear patterns to solve problems; that is:NYC M3.a.i - Uses linear patterns to solve problems; that is: shows how one quantity determines another in a linear ("repeating") pattern, i.e., describes, extends, and recognizes the linear pattern by its rule, such as, the total number of legs on a given number of horses can be calculated by counting by fours.
Topic 4 - Graphs and Patterns Obj. 52 - Number patterns
Obj. 53 - Complete patterns in tables
Obj. 54 - WP: Number patternsNYC M3.a.ii - Uses linear patterns to solve problems; that is: shows how one quantity determines another quantity in a functional relationship based on a linear pattern, e.g., for the "number of people and total number of eyes," figure out how many eyes 100 people have all together.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M3.b - Builds iterations of simple non-linear patterns, including multiplicative and squaring patterns (e.g., "growing" patterns) with concrete materials, and recognizes that these patterns are not linear.
NYC M3.c - Uses the understanding that an equality relationship between two quantities remains the same as long as the same change is made to both quantities.
NYC M3.d - Uses letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations with concrete materials, i.e., demonstrates understanding and use of a beginning concept of a variable.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 26 - Find missing addend in addition sentence
Obj. 27 - Find missing parts in subtraction sentence
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts in the following areas; that is, the student:
NYC M4.a - Collects and organizes data to answer a question or test a hypothesis by comparing sets of data.NYC M4.b - Displays data in line plots, graphs, tables, and charts.NYC M4.c - Makes statements and draws simple conclusions based on data; that is:NYC M4.c.i - Makes statements and draws simple conclusions based on data; that is: reads data in line plots, graphs, tables, and charts.
Topic 4 - Graphs and Patterns Obj. 45 - Tally charts
Obj. 46 - PictographsObj. 47 - Bar graphs
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M4.c.ii - Makes statements and draws simple conclusions based on data; that is: compares data in order to make true statements, e.g., "seven plants grew at least 5 cm".
Topic 4 - Graphs and Patterns Obj. 48 - Compare graphs
NYC M4.c.iii - Makes statements and draws simple conclusions based on data; that is: identifies and uses the mode necessary for making true statements, e.g., "more people chose red".NYC M4.c.iv - Makes statements and draws simple conclusions based on data; that is: makes true statements based on a simple concept of average (median and mean), for a small sample size and where the situation is made evident with concrete materials or clear representations.NYC M4.c.v - Makes statements and draws simple conclusions based on data; that is: interprets data to determine the reasonableness of statements about the data, e.g., "twice as often," "three times faster".
NYC M4.c.vi - Makes statements and draws simple conclusions based on data; that is: uses data, including statements about the data, to make a simple concluding statement about a situation, e.g., "This kind of plant grows better near sunlight because the seven plants that were near the window grew at least 5 cm."
NYC M4.d - Gathers data about an entire group or by sampling group members to understand the concept of sample, i.e., that a large sample leads to more reliable information, e.g., when flipping coins.
NYC M4.e - Predicts results, analyzes data, and finds out why some results are more likely, less likely, or equally likely.
Topic 12 - Problem Solving Obj. 140 - Identify most likely/least likely event
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M4.f - Finds all possible combinations and arrangements within certain constraints involving a limited number of variables.
Topic 12 - Problem Solving Obj. 145 - Use lists to solve problems
NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates logical reasoning throughout work in mathematics, i.e., concepts and skills, problem solving, and projects; demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow; and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion.
Topic 12 - Problem Solving Obj. 146 - Explain reasoning, evaluate reasonableness
- FORMULATIONNYC M5.a - Given the basic statement of a problem situation, the student:NYC M5.a.i - Given the basic statement of a problem situation, the student: makes the important decisions about the approach, materials, and strategies to use, i.e., does not merely fill in a given chart, use a pre-specified manipulative, or go through a predetermined set of steps.NYC M5.a.ii - Given the basic statement of a problem situation, the student: uses previously learned strategies, skills, knowledge, and concepts to make decisions.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 28 - WP: Find the correct equation
Obj. 33 - WP: Too much or little info, 2-dig add or subt
Topic 4 - Graphs and Patterns Obj. 54 - WP: Number patternsTopic 5 - Money Obj. 63 - WP: Add & subt money
expressionsTopic 7 - Measurement Obj. 76 - WP: Find length using cust
& metric unitsTopic 8 - Geometry Obj. 93 - WP: Perimeter
Obj. 95 - WP: Area
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M5.a.iii - Given the basic statement of a problem situation, the student: uses strategies, such as using manipulatives or drawing sketches, to model problems.
Topic 9 - Fractions Obj. 112 - WP: Fractions, draw pictures
Topic 12 - Problem Solving Obj. 141 - Draw a picture to solve a problem
- IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes up and uses a variety of strategies and approaches to solving problems and uses or learns approaches that other people use, as appropriate.
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes connections among concepts in order to solve problems.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves problems in ways that make sense and explains why these ways make sense, e.g., defends the reasoning, explains the solution.
- CONCLUSIONNYC M5.c - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student:
Accelerated Math Kindergarten - Grade 4
091207Page 31 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M5.c.i - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains a pattern that can be used in similar situations.
NYC M5.c.ii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem is similar to other problems he or she has solved.NYC M5.c.iii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the mathematics used in the problem is like other concepts in mathematics.
NYC M5.c.iv - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem solution can be applied to other school subjects and in real world situations.NYC M5.c.v - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: makes the solution into a general rule that applies to other circumstances.NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Kindergarten - Grade 4
091207Page 32 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, books, or other students, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Adds, subtracts, multiplies, and divides whole numbers correctly; that is:NYC M6.a.i - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: knows single digit addition, subtraction, multiplication, and division facts.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 11 - Addition facts to 10
Obj. 13 - Add three 1-digit #sObj. 19 - Subtraction facts from 10
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 128 - Repeated addition
Obj. 130 - Multiplication facts, to 5s
Obj. 131 - Multiply money expressions
NYC M6.a.ii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: adds and subtracts numbers with several digits.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 12 - Addition facts from 11 to 18
Obj. 14 - Add multiples of tenObj. 15 - Add 1- & 2-digit #s, no regroupObj. 16 - Add 1- & 2-digit #s, regroup
Obj. 17 - Add 2-digit #s, regroupObj. 18 - Add three #s, regroup (1 & 2 dig)Obj. 20 - Subtraction facts from 11 to 18Obj. 21 - Subtract multiples of tenObj. 23 - Subtract 1-dig from 2-dig #s, regroup
Accelerated Math Kindergarten - Grade 4
091207Page 33 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
Obj. 24 - Subtract 2-digit #s, regroup
NYC M6.a.iii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides numbers with one or two digits.
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 130 - Multiplication facts, to 5s
Obj. 131 - Multiply money expressions
NYC M6.a.iv - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides three digit numbers by one digit numbers.NYC M6.b - Estimates numerically and spatially.
Topic 2 - Whole Number Addition and Subtraction I
Obj. 35 - Estimate # in group (2 dig)
Obj. 36 - Estimate sum & diff, front digits only (2 dig)Obj. 38 - Estimate sum & diff, round (2 dig)Obj. 39 - WP: Estimate sum & diff, round (2 dig)
Topic 7 - Measurement Obj. 74 - Estimate length & heightTopic 10 - Whole Number Addition and Subtraction II
Obj. 125 - Estimate sum & diff, front digits only (3 dig)Obj. 126 - WP: Estimate sum & diff, front digits (2-3 dig)
NYC M6.c - Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems.
Topic 7 - Measurement Obj. 72 - Measure length in in., ft, & yd
Obj. 73 - Measure length in cm & m
Topic 8 - Geometry Obj. 96 - Find volume of a box by counting cubes
NYC M6.d - Computes time (in hours and minutes) and money (in dollars and cents).
Topic 5 - Money Obj. 61 - Add money expressions
Obj. 62 - Subtract money expressionsObj. 63 - WP: Add & subt money expressions
Topic 6 - Time Obj. 69 - Calculate elapsed time
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M6.e - Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid.
Topic 8 - Geometry Obj. 88 - Identify plane figures
Obj. 89 - Count sides & cornersObj. 90 - Identify solidsObj. 91 - Count faces, edges, & corners
NYC M6.f - Uses +, -, x, ÷, /, long division symbol, $, ¢, %, and . (decimal point) correctly in number sentences and expressions.
Topic 5 - Money Obj. 56 - Cent, dollar, & decimal symbols
Topic 11 - Exploring Multiplication and Division of Whole Numbers
Obj. 129 - Multiplication sentences
NYC M6.g - Reads, creates, and represents data on line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs.
Topic 4 - Graphs and Patterns Obj. 45 - Tally charts
Obj. 47 - Bar graphsObj. 49 - Add with graphs (2 dig)Obj. 50 - Subtract with graphs (2 dig)
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the 1/8 inch; metric to the millimeter), graph paper (customary to the inch or half-inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound or ounce; metric to the kilogram or gram).
Topic 7 - Measurement Obj. 72 - Measure length in in., ft, & yd
Obj. 80 - Read scales & estimate in poundsObj. 86 - Read thermometers
NYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work.NYC M7.b - Shows mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models.
Topic 9 - Fractions Obj. 112 - WP: Fractions, draw pictures
Topic 12 - Problem Solving Obj. 141 - Draw a picture to solve a problem
NYC M7.c - Explains solutions to problems clearly and logically, and supports solutions with evidence, in both oral and written work.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M7.d - Considers purpose and audience when communicating about mathematics.NYC M7.e - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale project each year, beginning in fourth grade, drawn from the following kinds and, over the course of elementary school, conducts projects drawn from at least two of the kinds. A single project may draw on more than one kind.
NYC M8.a - Data study, in which the student:NYC M8.a.i - Data study, in which the student: develops a question and a hypothesis in a situation where data could help make a decision or recommendation.NYC M8.a.ii - Data study, in which the student: decides on a group or groups to be sampled and makes predictions of the results, with specific percents, fractions, or numbers.NYC M8.a.iii - Data study, in which the student: collects, represents, and displays data in order to help make the decision or recommendation; compares the results with the predictions.NYC M8.a.iv - Data study, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.b - Science study, in which the student:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M8.b.i - Science study, in which the student: decides on a specific science question to study and identifies the mathematics that will be used, e.g., measurement.NYC M8.b.ii - Science study, in which the student: develops a prediction (a hypothesis) and develops procedures to test the hypothesis.NYC M8.b.iii - Science study, in which the student: collects and records data, represents and displays data, and compares results with predictions.NYC M8.b.iv - Science study, in which the student: writes a report that compares the results with the hypothesis; supports the results with diagrams, charts, and graphs; acknowledges assistance received from parents, peers, and teachers.NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: decides on a structure to design, the size and budget constraints, and the scale of design.NYC M8.c.ii - Design of a physical structure, in which the student: makes a first draft of the design, and revises and improves the design in response to input from peers and teachers.NYC M8.c.iii - Design of a physical structure, in which the student: makes a final draft and report of the design, drawn and written so that another person could make the structure; acknowledges assistance received from parents, peers, and teachers.NYC M8.d - Management and planning, in which the student:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M8.d.i - Management and planning, in which the student: decides on what to manage or plan, and the criteria to be used to see if the plan worked.NYC M8.d.ii - Management and planning, in which the student: identifies unexpected events that could disrupt the plan and further plans for such contingencies.NYC M8.d.iii - Management and planning, in which the student: identifies resources needed, e.g., materials, money, time, space, and other people.NYC M8.d.iv - Management and planning, in which the student: writes a detailed plan and revises and improves the plan in response to feedback from peers and teachers.
NYC M8.d.v - Management and planning, in which the student: carries out the plan (optional).NYC M8.d.vi - Management and planning, in which the student: writes a report on the plan that includes resources, budget, and schedule, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.d.vii - Management and planning, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: decides on the area of mathematics to investigate, e.g., numbers, shapes, patterns.NYC M8.e.ii - Pure mathematics investigation, in which the student: describes a question or concept to investigate.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 2
NYC M8.e.iii - Pure mathematics investigation, in which the student: decides on representations that will be used, e.g., numbers, symbols, diagrams, shapes, or physical models.NYC M8.e.iv - Pure mathematics investigation, in which the student: carries out the investigation.NYC M8.e.v - Pure mathematics investigation, in which the student: writes a report that includes any generalizations drawn from the investigation, and acknowledges assistance received from parents, peers, and teachers.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of arithmetic and number concepts; that is, the student:
NYC M1.a - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is:NYC M1.a.i - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: adds, i.e., joins things together, increases.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 15 - Addition facts
Obj. 16 - Add 2 whole #s, no regroup (1-3 dig)Obj. 17 - Add 3 whole #s, no regroup (1-3 dig)Obj. 19 - Add 2 whole #s, regroup (1-4 dig)Obj. 21 - Add 3 whole #s, regroup (1-4 dig)Obj. 28 - Add & subtract multiples of ten & hundred
NYC M1.a.ii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: subtracts, i.e., takes away, compares, finds the difference.
Topic 1 - Whole Number Concepts I
Obj. 6 - Compare whole #s (to 4 dig)
Topic 2 - Whole Numbers: Add and Subtract
Obj. 23 - Subtraction facts
Obj. 24 - Subtract whole #s, no regroup (1-4 dig)Obj. 26 - Subtract whole #s, regroup (2-4 dig)Obj. 28 - Add & subtract multiples of ten & hundred
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M1.a.iii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: multiplies, i.e., uses repeated addition, counts by multiples, combines things that come in groups, makes arrays, uses area models, computes simple scales, uses simple rates.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 40 - Use strategies to solve mult problems (to 12 x 12)
Obj. 41 - Multiplication as repeated additionObj. 42 - Arrays and multiplicationObj. 45 - DoublesObj. 46 - Multiply by multiples of ten (1 dig)Obj. 47 - Multiply by 1-digit, no regroup (3 dig)Obj. 48 - Multiply by 1-digit, regroup (2-3 dig)
Topic 4 - Whole Number Concepts II
Obj. 67 - Count with multiples
NYC M1.a.iv - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: divides, i.e., puts things into groups, shares equally; calculates simple rates.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 52 - Divide into equal groups
Obj. 53 - Use manipulatives to solve division problemsObj. 54 - Divide by 1-digit, 1-digit quotient, remainderObj. 55 - Divide multiple of ten or hundred by 1-digitObj. 56 - Divide by 1-digit, 2-digit quotient, no remainderObj. 57 - Divide by 1-digit, 2-digit quotient, remainder
NYC M1.a.v - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: analyzes problem situations and contexts in order to figure out when to add, subtract, multiply, or divide.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 18 - WP: Add whole #s, no regroup (1-2 dig)
Obj. 20 - WP: Add 2 whole #s, regroup (2-3 dig)Obj. 22 - WP: Add 3 whole #s, regroup (1-3 dig)
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Obj. 25 - WP: Subtract whole #s, no regroup (1-3 dig)Obj. 27 - WP: Subtract whole #s, regroup (1-4 dig)
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 49 - WP: Multiply by 1-digit (2-3 dig)Obj. 58 - WP: Divide by 1-digit divisor, 2-digit dividendObj. 65 - WP: Solve multi-step problems
NYC M1.a.vi - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: solves arithmetic problems by relating addition, subtraction, multiplication, and division to one another.
NYC M1.a.vii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: computes answers mentally, e.g., 27 + 45, 30 x 4.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 15 - Addition facts
Obj. 23 - Subtraction factsTopic 3 - Whole Numbers: Multiply and Divide
Obj. 38 - Multiplication basic facts to 5sObj. 39 - Multiplication facts from 6s to 9sObj. 50 - Division facts, horizontalObj. 51 - Division facts, vertical
NYC M1.a.viii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: uses simple concepts of negative numbers, e.g., on a number line, in counting, in temperature, "owing."NYC M1.b - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M1.b.i - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: counts 1, 10, 100, or 1,000 more than or less than, e.g., 1 less than 10,000, 10 more than 380, 1,000 more than 23,000, 100 less than 9,000.NYC M1.b.ii - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: uses knowledge about ones, tens, hundreds, and thousands to figure out answers to multiplication and division tasks, e.g., 36 x 10, 18 x 100, 7 x 1,000, 4,000 ÷ 4.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 46 - Multiply by multiples of ten (1 dig)
Obj. 55 - Divide multiple of ten or hundred by 1-digit
NYC M1.c - Estimates, approximates, rounds off, uses landmark numbers, or uses exact numbers, as appropriate, in calculations.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 29 - Estimate sums, round (2-4 dig)
Obj. 31 - Estimate sums, front digits only (2-4 dig)Obj. 33 - Estimate differences, round (2-4 dig)
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 59 - Estimate products, round (1-3 dig)Obj. 60 - Estimate products, front digits only (1-3 dig)Obj. 63 - Estimate quotients, compatible #s (1-2 dig)
NYC M1.d - Describes and compares quantities by using concrete and real world models of simple fractions; that is:NYC M1.d.i - Describes and compares quantities by using concrete and real world models of simple fractions; that is: finds simple parts of wholes.
Topic 5 - Fractions Obj. 76 - Name unit fractions
Obj. 77 - Model & name proper fractions as part of a wholeObj. 78 - Model & name proper fractions as part of a set
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Obj. 79 - Model fractions on number linesObj. 80 - Compare unit fractions (1/2 to 1/6 & 1/10)Obj. 83 - Equivalent proper fractions with models
NYC M1.d.ii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes simple fractions as instructions to divide, e.g., 1/4 of something is the same as dividing something by 4.
NYC M1.d.iii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes the place of fractions on number lines, e.g., in measurement.
Topic 5 - Fractions Obj. 79 - Model fractions on number lines
NYC M1.d.iv - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses drawings, diagrams, or models to show what the numerator and denominator mean, including when adding like fractions, e.g., 1/8 + 5/8, or when showing that 3/4 is more than 3/8.
Topic 5 - Fractions Obj. 82 - Compare & order proper fractions
Obj. 83 - Equivalent proper fractions with models
NYC M1.d.v - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses beginning proportional reasoning and simple ratios, e.g., "about half of the people."NYC M1.e - Describes and compares quantities by using simple decimals; that is:NYC M1.e.i - Describes and compares quantities by using simple decimals; that is: adds, subtracts, multiplies, and divides money amounts.
Topic 7 - Money Obj. 98 - WP: Add money expressions
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Obj. 101 - WP: Subtract money expressions
NYC M1.e.ii - Describes and compares quantities by using simple decimals; that is: recognizes relationships among simple fractions, decimals, and percents, i.e., that 1/2 is the same as 0.5, and 1/2 is the same as 50%, with concrete materials, diagrams, and in real world situations, e.g., when discovering the chance of a coin landing on heads or tails.
NYC M1.f - Describes and compares quantities by using whole numbers up to 10,000; that is:
NYC M1.f.i - Describes and compares quantities by using whole numbers up to 10,000; that is: connects ideas of quantities to the real world, e.g., how many people fit in the school’s cafeteria; how far away is a kilometer.
Topic 8 - Measurement, Time, and Temperature
Obj. 105 - Estimate customary length
Obj. 106 - Estimate customary weight
Obj. 111 - Estimate metric lengthObj. 112 - Estimate metric weight
NYC M1.f.ii - Describes and compares quantities by using whole numbers up to 10,000; that is: finds, identifies, and sorts numbers by their properties, e.g., odd, even, multiple, square.
Topic 1 - Whole Number Concepts I
Obj. 1 - Count with base-ten number blocks
Obj. 4 - Expanded to standard form (2-6 dig)Obj. 12 - Odd & even numbers
Topic 4 - Whole Number Concepts II
Obj. 67 - Count with multiples
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M2.a - Gives and responds to directions about location, e.g., by using words such as "in front of," "right," and "above."
Topic 9 - Geometry Obj. 129 - Use compass directions
NYC M2.b - Visualizes and represents two dimensional views of simple rectangular three dimensional shapes, e.g., by showing the front view and side view of a building made of cubes.NYC M2.c - Uses simple two dimensional coordinate systems to find locations on a map and to represent points and simple figures.
Topic 9 - Geometry Obj. 128 - Coordinate graphs
NYC M2.d - Uses many types of figures (angles, triangles, squares, rectangles, rhombi, parallelograms, quadrilaterals, polygons, prisms, pyramids, cubes, circles, and spheres) and identifies the figures by their properties, e.g., symmetry, number of faces, two- or three-dimensionality, no right angles.
Topic 9 - Geometry Obj. 124 - Classify shapes & count sides & corners
Obj. 132 - Faces of 3-D solidsNYC M2.e - Solves problems by showing relationships between and among figures, e.g., using congruence and similarity, and using transformations including flips, slides, and rotations.NYC M2.f - Extends and creates geometric patterns using concrete and pictorial models.
Topic 11 - Patterns, Expressions and Equations
Obj. 153 - Complete geometric patterns
NYC M2.g - Uses basic ways of estimating and measuring the size of figures and objects in the real world, including length, width, perimeter, and area.
Topic 9 - Geometry Obj. 135 - WP: Perimeter
NYC M2.h - Uses models to reason about the relationship between the perimeter and area of rectangles in simple situations.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M2.i - Selects and uses units, both formal and informal as appropriate, for estimating and measuring quantities such as weight, length, area, volume, and time.
Topic 8 - Measurement, Time, and Temperature
Obj. 104 - Appropriate unit of customary length
Obj. 105 - Estimate customary length
Obj. 106 - Estimate customary weight
Obj. 107 - Measure cust length with rulerObj. 108 - Measure customary weight
Obj. 109 - Customary units of capacityObj. 110 - Appropriate unit of metric lengthObj. 112 - Estimate metric weightObj. 113 - Measure metric length with rulerObj. 115 - Tell time to hour & minute
Obj. 116 - Tell time to quarter hourTopic 9 - Geometry Obj. 136 - Area with a grid
NYC M2.j - Carries out simple unit conversions, such as between cm and m, and between hours and minutes.NYC M2.k - Uses scales in maps, and uses, measures, and creates scales for rectangular scale drawings based on work with concrete models and graph paper.
Topic 9 - Geometry Obj. 138 - Use scales in maps & drawings
NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Uses linear patterns to solve problems; that is:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M3.a.i - Uses linear patterns to solve problems; that is: shows how one quantity determines another in a linear ("repeating") pattern, i.e., describes, extends, and recognizes the linear pattern by its rule, such as, the total number of legs on a given number of horses can be calculated by counting by fours.
Topic 4 - Whole Number Concepts II
Obj. 68 - Missing terms in number patterns
NYC M3.a.ii - Uses linear patterns to solve problems; that is: shows how one quantity determines another quantity in a functional relationship based on a linear pattern, e.g., for the "number of people and total number of eyes," figure out how many eyes 100 people have all together.
Topic 10 - Graphs, Probability, and Statistics
Obj. 148 - Make predictions and inferences from data display
NYC M3.b - Builds iterations of simple non-linear patterns, including multiplicative and squaring patterns (e.g., "growing" patterns) with concrete materials, and recognizes that these patterns are not linear.
NYC M3.c - Uses the understanding that an equality relationship between two quantities remains the same as long as the same change is made to both quantities.
NYC M3.d - Uses letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations with concrete materials, i.e., demonstrates understanding and use of a beginning concept of a variable.
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts in the following areas; that is, the student:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M4.a - Collects and organizes data to answer a question or test a hypothesis by comparing sets of data.NYC M4.b - Displays data in line plots, graphs, tables, and charts.
Topic 10 - Graphs, Probability, and Statistics
Obj. 143 - Construct frequency tables
Obj. 144 - Create pictographs & bar graphs
Topic 12 - Problem Solving Obj. 157 - Use lists to solve problems
NYC M4.c - Makes statements and draws simple conclusions based on data; that is:NYC M4.c.i - Makes statements and draws simple conclusions based on data; that is: reads data in line plots, graphs, tables, and charts.
Topic 10 - Graphs, Probability, and Statistics
Obj. 139 - Tally charts
Obj. 140 - PictographsObj. 141 - Bar graphsObj. 142 - Line plotsObj. 145 - Compare pictographs & bar graphs
NYC M4.c.ii - Makes statements and draws simple conclusions based on data; that is: compares data in order to make true statements, e.g., "seven plants grew at least 5 cm".
Topic 10 - Graphs, Probability, and Statistics
Obj. 148 - Make predictions and inferences from data display
NYC M4.c.iii - Makes statements and draws simple conclusions based on data; that is: identifies and uses the mode necessary for making true statements, e.g., "more people chose red".NYC M4.c.iv - Makes statements and draws simple conclusions based on data; that is: makes true statements based on a simple concept of average (median and mean), for a small sample size and where the situation is made evident with concrete materials or clear representations.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M4.c.v - Makes statements and draws simple conclusions based on data; that is: interprets data to determine the reasonableness of statements about the data, e.g., "twice as often," "three times faster".
NYC M4.c.vi - Makes statements and draws simple conclusions based on data; that is: uses data, including statements about the data, to make a simple concluding statement about a situation, e.g., "This kind of plant grows better near sunlight because the seven plants that were near the window grew at least 5 cm."
NYC M4.d - Gathers data about an entire group or by sampling group members to understand the concept of sample, i.e., that a large sample leads to more reliable information, e.g., when flipping coins.
NYC M4.e - Predicts results, analyzes data, and finds out why some results are more likely, less likely, or equally likely.
Topic 10 - Graphs, Probability, and Statistics
Obj. 146 - Identify likelihood of events
NYC M4.f - Finds all possible combinations and arrangements within certain constraints involving a limited number of variables.
Topic 12 - Problem Solving Obj. 157 - Use lists to solve problems
NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates logical reasoning throughout work in mathematics, i.e., concepts and skills, problem solving, and projects; demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow; and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
- FORMULATIONNYC M5.a - Given the basic statement of a problem situation, the student:NYC M5.a.i - Given the basic statement of a problem situation, the student: makes the important decisions about the approach, materials, and strategies to use, i.e., does not merely fill in a given chart, use a pre-specified manipulative, or go through a predetermined set of steps.
Topic 12 - Problem Solving Obj. 155 - Eliminate possiblities to solve problems
Obj. 156 - Draw a picture to solve a problemObj. 159 - Evaluate reasonableness of solution from context
NYC M5.a.ii - Given the basic statement of a problem situation, the student: uses previously learned strategies, skills, knowledge, and concepts to make decisions.
Topic 12 - Problem Solving Obj. 155 - Eliminate possiblities to solve problems
Obj. 156 - Draw a picture to solve a problemObj. 159 - Evaluate reasonableness of solution from context
NYC M5.a.iii - Given the basic statement of a problem situation, the student: uses strategies, such as using manipulatives or drawing sketches, to model problems.
Topic 12 - Problem Solving Obj. 156 - Draw a picture to solve a problem
Obj. 157 - Use lists to solve problems
- IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes up and uses a variety of strategies and approaches to solving problems and uses or learns approaches that other people use, as appropriate.
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes connections among concepts in order to solve problems.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves problems in ways that make sense and explains why these ways make sense, e.g., defends the reasoning, explains the solution.
- CONCLUSIONNYC M5.c - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student:NYC M5.c.i - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains a pattern that can be used in similar situations.
NYC M5.c.ii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem is similar to other problems he or she has solved.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M5.c.iii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the mathematics used in the problem is like other concepts in mathematics.
NYC M5.c.iv - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem solution can be applied to other school subjects and in real world situations.NYC M5.c.v - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: makes the solution into a general rule that applies to other circumstances.NYC M6 - MATHEMATICAL SKILLS AND TOOLSNYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, books, or other students, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Adds, subtracts, multiplies, and divides whole numbers correctly; that is:NYC M6.a.i - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: knows single digit addition, subtraction, multiplication, and division facts.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 15 - Addition facts
Obj. 23 - Subtraction factsTopic 3 - Whole Numbers: Multiply and Divide
Obj. 38 - Multiplication basic facts to 5s
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Obj. 39 - Multiplication facts from 6s to 9sObj. 50 - Division facts, horizontalObj. 51 - Division facts, vertical
NYC M6.a.ii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: adds and subtracts numbers with several digits.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 16 - Add 2 whole #s, no regroup (1-3 dig)
Obj. 17 - Add 3 whole #s, no regroup (1-3 dig)Obj. 19 - Add 2 whole #s, regroup (1-4 dig)Obj. 21 - Add 3 whole #s, regroup (1-4 dig)Obj. 24 - Subtract whole #s, no regroup (1-4 dig)Obj. 26 - Subtract whole #s, regroup (2-4 dig)Obj. 28 - Add & subtract multiples of ten & hundred
NYC M6.a.iii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides numbers with one or two digits.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 46 - Multiply by multiples of ten (1 dig)
Obj. 47 - Multiply by 1-digit, no regroup (3 dig)Obj. 48 - Multiply by 1-digit, regroup (2-3 dig)Obj. 54 - Divide by 1-digit, 1-digit quotient, remainderObj. 55 - Divide multiple of ten or hundred by 1-digitObj. 56 - Divide by 1-digit, 2-digit quotient, no remainderObj. 57 - Divide by 1-digit, 2-digit quotient, remainder
NYC M6.a.iv - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides three digit numbers by one digit numbers.NYC M6.b - Estimates numerically and spatially.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 59 - Estimate products, round (1-3 dig)Obj. 60 - Estimate products, front digits only (1-3 dig)Obj. 63 - Estimate quotients, compatible #s (1-2 dig)
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Topic 7 - Money Obj. 102 - Estimate sum & diff of money
NYC M6.c - Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems.
Topic 8 - Measurement, Time, and Temperature
Obj. 107 - Measure cust length with ruler
Obj. 108 - Measure customary weight
Obj. 113 - Measure metric length with ruler
NYC M6.d - Computes time (in hours and minutes) and money (in dollars and cents).
Topic 8 - Measurement, Time, and Temperature
Obj. 117 - Calculate elapsed time
Obj. 118 - Read calendarsNYC M6.e - Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid.
Topic 9 - Geometry Obj. 121 - Points, lines, segments, rays, & angles
Obj. 124 - Classify shapes & count sides & cornersObj. 130 - SolidsObj. 132 - Faces of 3-D solidsObj. 133 - Perimeter of rectangles & squaresObj. 134 - Perimeter of polygons
NYC M6.f - Uses +, -, x, ÷, /, long division symbol, $, ¢, %, and . (decimal point) correctly in number sentences and expressions.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 43 - Write multiplication sentences
NYC M6.g - Reads, creates, and represents data on line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs.
Topic 9 - Geometry Obj. 128 - Coordinate graphs
Topic 10 - Graphs, Probability, and Statistics
Obj. 139 - Tally charts
Obj. 141 - Bar graphsObj. 142 - Line plotsObj. 143 - Construct frequency tables
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Obj. 144 - Create pictographs & bar graphs
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the 1/8 inch; metric to the millimeter), graph paper (customary to the inch or half-inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound or ounce; metric to the kilogram or gram).
Topic 8 - Measurement, Time, and Temperature
Obj. 107 - Measure cust length with ruler
Obj. 108 - Measure customary weight
Obj. 113 - Measure metric length with ruler
NYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work.
Topic 8 - Measurement, Time, and Temperature
Obj. 104 - Appropriate unit of customary length
NYC M7.b - Shows mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models.
Topic 1 - Whole Number Concepts I
Obj. 5 - Read & write whole #s (3-6 dig)
Obj. 6 - Compare whole #s (to 4 dig)
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 43 - Write multiplication sentences
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
Topic 5 - Fractions Obj. 77 - Model & name proper fractions as part of a wholeObj. 78 - Model & name proper fractions as part of a setObj. 79 - Model fractions on number linesObj. 80 - Compare unit fractions (1/2 to 1/6 & 1/10)Obj. 83 - Equivalent proper fractions with models
Topic 6 - Decimals Obj. 88 - Model decimals (tenths)Topic 9 - Geometry Obj. 122 - Intersecting, parallel, &
perpendicular linesObj. 124 - Classify shapes & count sides & cornersObj. 126 - Lines of symmetryObj. 127 - Flips, turns, & slides
Topic 10 - Graphs, Probability, and Statistics
Obj. 143 - Construct frequency tables
Obj. 144 - Create pictographs & bar graphs
NYC M7.c - Explains solutions to problems clearly and logically, and supports solutions with evidence, in both oral and written work.NYC M7.d - Considers purpose and audience when communicating about mathematics.NYC M7.e - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale project each year, beginning in fourth grade, drawn from the following kinds and, over the course of elementary school, conducts projects drawn from at least two of the kinds. A single project may draw on more than one kind.
NYC M8.a - Data study, in which the student:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M8.a.i - Data study, in which the student: develops a question and a hypothesis in a situation where data could help make a decision or recommendation.NYC M8.a.ii - Data study, in which the student: decides on a group or groups to be sampled and makes predictions of the results, with specific percents, fractions, or numbers.NYC M8.a.iii - Data study, in which the student: collects, represents, and displays data in order to help make the decision or recommendation; compares the results with the predictions.NYC M8.a.iv - Data study, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.b - Science study, in which the student:NYC M8.b.i - Science study, in which the student: decides on a specific science question to study and identifies the mathematics that will be used, e.g., measurement.NYC M8.b.ii - Science study, in which the student: develops a prediction (a hypothesis) and develops procedures to test the hypothesis.NYC M8.b.iii - Science study, in which the student: collects and records data, represents and displays data, and compares results with predictions.NYC M8.b.iv - Science study, in which the student: writes a report that compares the results with the hypothesis; supports the results with diagrams, charts, and graphs; acknowledges assistance received from parents, peers, and teachers.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: decides on a structure to design, the size and budget constraints, and the scale of design.NYC M8.c.ii - Design of a physical structure, in which the student: makes a first draft of the design, and revises and improves the design in response to input from peers and teachers.NYC M8.c.iii - Design of a physical structure, in which the student: makes a final draft and report of the design, drawn and written so that another person could make the structure; acknowledges assistance received from parents, peers, and teachers.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: decides on what to manage or plan, and the criteria to be used to see if the plan worked.NYC M8.d.ii - Management and planning, in which the student: identifies unexpected events that could disrupt the plan and further plans for such contingencies.NYC M8.d.iii - Management and planning, in which the student: identifies resources needed, e.g., materials, money, time, space, and other people.NYC M8.d.iv - Management and planning, in which the student: writes a detailed plan and revises and improves the plan in response to feedback from peers and teachers.
NYC M8.d.v - Management and planning, in which the student: carries out the plan (optional).
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 3
NYC M8.d.vi - Management and planning, in which the student: writes a report on the plan that includes resources, budget, and schedule, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.d.vii - Management and planning, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: decides on the area of mathematics to investigate, e.g., numbers, shapes, patterns.NYC M8.e.ii - Pure mathematics investigation, in which the student: describes a question or concept to investigate.NYC M8.e.iii - Pure mathematics investigation, in which the student: decides on representations that will be used, e.g., numbers, symbols, diagrams, shapes, or physical models.NYC M8.e.iv - Pure mathematics investigation, in which the student: carries out the investigation.NYC M8.e.v - Pure mathematics investigation, in which the student: writes a report that includes any generalizations drawn from the investigation, and acknowledges assistance received from parents, peers, and teachers.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of arithmetic and number concepts; that is, the student:
NYC M1.a - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is:NYC M1.a.i - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: adds, i.e., joins things together, increases.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 13 - WP: Add 2 whole #s, no regroup (1-3 dig)
Obj. 15 - WP: Add 3 whole #s, no regroup (1-3 dig)Obj. 17 - WP: Add 2 whole #s (2-4 dig)Obj. 19 - WP: Add 3 whole #s (2-4 dig)
NYC M1.a.ii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: subtracts, i.e., takes away, compares, finds the difference.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 27 - WP: Subtract whole #s, no regroup (1-3 dig)
Obj. 29 - WP: Subtract whole #s (2-5 dig)
NYC M1.a.iii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: multiplies, i.e., uses repeated addition, counts by multiples, combines things that come in groups, makes arrays, uses area models, computes simple scales, uses simple rates.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 38 - WP: Multiply by 2-digit (2-3 dig)
NYC M1.a.iv - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: divides, i.e., puts things into groups, shares equally; calculates simple rates.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 48 - WP: Divide whole #s by 1-digit
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M1.a.v - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: analyzes problem situations and contexts in order to figure out when to add, subtract, multiply, or divide.NYC M1.a.vi - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: solves arithmetic problems by relating addition, subtraction, multiplication, and division to one another.
NYC M1.a.vii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: computes answers mentally, e.g., 27 + 45, 30 x 4.NYC M1.a.viii - Adds, subtracts, multiplies, and divides whole numbers, with and without calculators; that is: uses simple concepts of negative numbers, e.g., on a number line, in counting, in temperature, "owing."NYC M1.b - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is:NYC M1.b.i - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: counts 1, 10, 100, or 1,000 more than or less than, e.g., 1 less than 10,000, 10 more than 380, 1,000 more than 23,000, 100 less than 9,000.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M1.b.ii - Demonstrates understanding of the base ten place value system and uses this knowledge to solve arithmetic tasks; that is: uses knowledge about ones, tens, hundreds, and thousands to figure out answers to multiplication and division tasks, e.g., 36 x 10, 18 x 100, 7 x 1,000, 4,000 ÷ 4.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 39 - Multiply by multiples of ten (2-4 dig)
Obj. 40 - Multiply by powers of ten (2-3 dig)Obj. 51 - Divide by a multiple of ten (2-4 dig)
NYC M1.c - Estimates, approximates, rounds off, uses landmark numbers, or uses exact numbers, as appropriate, in calculations.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 23 - Estimate sums, 2 #s: front digits only (2-4 dig)
Obj. 24 - Estimate sums, 3 #s: front digits only (2-4 dig)Obj. 25 - WP: Estimate sums, front digits only (2-3 dig)Obj. 30 - Estimate differences, round (2-4 dig)Obj. 31 - WP: Estimate differences, round (2-4 dig)
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 41 - Estimate products, round (1-4 dig)Obj. 42 - WP: Estimate products, round (1-4 dig)Obj. 55 - Estimate quotients, compatible #s (2-3 dig)Obj. 56 - WP: Estimate whole quotients (2-3 dig)
NYC M1.d - Describes and compares quantities by using concrete and real world models of simple fractions; that is:NYC M1.d.i - Describes and compares quantities by using concrete and real world models of simple fractions; that is: finds simple parts of wholes.
Topic 4 - Fractions Obj. 63 - Model & name proper fractions as part of a whole
Obj. 64 - Model & name proper fractions as part of a setObj. 67 - Model equivalent fractions
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M1.d.ii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes simple fractions as instructions to divide, e.g., 1/4 of something is the same as dividing something by 4.
NYC M1.d.iii - Describes and compares quantities by using concrete and real world models of simple fractions; that is: recognizes the place of fractions on number lines, e.g., in measurement.
Topic 4 - Fractions Obj. 65 - Model fractions & mixed #s on number lines
NYC M1.d.iv - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses drawings, diagrams, or models to show what the numerator and denominator mean, including when adding like fractions, e.g., 1/8 + 5/8, or when showing that 3/4 is more than 3/8.NYC M1.d.v - Describes and compares quantities by using concrete and real world models of simple fractions; that is: uses beginning proportional reasoning and simple ratios, e.g., "about half of the people."NYC M1.e - Describes and compares quantities by using simple decimals; that is:NYC M1.e.i - Describes and compares quantities by using simple decimals; that is: adds, subtracts, multiplies, and divides money amounts.
Topic 6 - Money Obj. 93 - Add money expressions
Obj. 95 - Subtract money expressionsObj. 100 - Multiply money expressions by whole #s
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M1.e.ii - Describes and compares quantities by using simple decimals; that is: recognizes relationships among simple fractions, decimals, and percents, i.e., that 1/2 is the same as 0.5, and 1/2 is the same as 50%, with concrete materials, diagrams, and in real world situations, e.g., when discovering the chance of a coin landing on heads or tails.
NYC M1.f - Describes and compares quantities by using whole numbers up to 10,000; that is:
NYC M1.f.i - Describes and compares quantities by using whole numbers up to 10,000; that is: connects ideas of quantities to the real world, e.g., how many people fit in the school’s cafeteria; how far away is a kilometer.NYC M1.f.ii - Describes and compares quantities by using whole numbers up to 10,000; that is: finds, identifies, and sorts numbers by their properties, e.g., odd, even, multiple, square.
Topic 1 - Whole Number Concepts
Obj. 7 - Odd & even numbers
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:NYC M2.a - Gives and responds to directions about location, e.g., by using words such as "in front of," "right," and "above."NYC M2.b - Visualizes and represents two dimensional views of simple rectangular three dimensional shapes, e.g., by showing the front view and side view of a building made of cubes.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M2.c - Uses simple two dimensional coordinate systems to find locations on a map and to represent points and simple figures.
Topic 8 - Geometry Obj. 137 - Plot & name ordered pairs (first quadrant)
NYC M2.d - Uses many types of figures (angles, triangles, squares, rectangles, rhombi, parallelograms, quadrilaterals, polygons, prisms, pyramids, cubes, circles, and spheres) and identifies the figures by their properties, e.g., symmetry, number of faces, two- or three-dimensionality, no right angles.
Topic 8 - Geometry Obj. 129 - Identify polygons
NYC M2.e - Solves problems by showing relationships between and among figures, e.g., using congruence and similarity, and using transformations including flips, slides, and rotations.
Topic 8 - Geometry Obj. 130 - Congruent & similar figures
Obj. 134 - Flips, turns, & slidesNYC M2.f - Extends and creates geometric patterns using concrete and pictorial models.
Topic 11 - Patterns, Expressions, and Equations
Obj. 165 - Complete geometric patterns
NYC M2.g - Uses basic ways of estimating and measuring the size of figures and objects in the real world, including length, width, perimeter, and area.
Topic 9 - Perimeter, Area, and Volume
Obj. 142 - Area with a grid
NYC M2.h - Uses models to reason about the relationship between the perimeter and area of rectangles in simple situations.
Topic 9 - Perimeter, Area, and Volume
Obj. 138 - Model perimeter of rectangles
NYC M2.i - Selects and uses units, both formal and informal as appropriate, for estimating and measuring quantities such as weight, length, area, volume, and time.
Topic 7 - Measurement, Time, and Temperature
Obj. 102 - Appropriate unit of customary length
Obj. 109 - Select appropriate unit to measure mass, kg/gObj. 110 - Select appropriate units to measure capacity, mL/L
NYC M2.j - Carries out simple unit conversions, such as between cm and m, and between hours and minutes.
Topic 7 - Measurement, Time, and Temperature
Obj. 107 - Convert customary units of length
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
Obj. 117 - Convert metric units of length
NYC M2.k - Uses scales in maps, and uses, measures, and creates scales for rectangular scale drawings based on work with concrete models and graph paper.
Topic 7 - Measurement, Time, and Temperature
Obj. 118 - Use scales in maps and scale drawings
NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Uses linear patterns to solve problems; that is:NYC M3.a.i - Uses linear patterns to solve problems; that is: shows how one quantity determines another in a linear ("repeating") pattern, i.e., describes, extends, and recognizes the linear pattern by its rule, such as, the total number of legs on a given number of horses can be calculated by counting by fours.
Topic 11 - Patterns, Expressions, and Equations
Obj. 172 - Find the rule, given table or input/output box
NYC M3.a.ii - Uses linear patterns to solve problems; that is: shows how one quantity determines another quantity in a functional relationship based on a linear pattern, e.g., for the "number of people and total number of eyes," figure out how many eyes 100 people have all together.
Topic 10 - Graphs, Probability, and Statistics
Obj. 157 - Predictions from graphs
NYC M3.b - Builds iterations of simple non-linear patterns, including multiplicative and squaring patterns (e.g., "growing" patterns) with concrete materials, and recognizes that these patterns are not linear.
NYC M3.c - Uses the understanding that an equality relationship between two quantities remains the same as long as the same change is made to both quantities.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M3.d - Uses letters, boxes, or other symbols to stand for any number, measured quantity, or object in simple situations with concrete materials, i.e., demonstrates understanding and use of a beginning concept of a variable.
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts in the following areas; that is, the student:
NYC M4.a - Collects and organizes data to answer a question or test a hypothesis by comparing sets of data.NYC M4.b - Displays data in line plots, graphs, tables, and charts.NYC M4.c - Makes statements and draws simple conclusions based on data; that is:NYC M4.c.i - Makes statements and draws simple conclusions based on data; that is: reads data in line plots, graphs, tables, and charts.
Topic 10 - Graphs, Probability, and Statistics
Obj. 148 - Tally charts
Obj. 149 - PictographsObj. 150 - Bar graphsObj. 151 - Line graphsObj. 152 - Circle graphsObj. 153 - Frequency tablesObj. 155 - WP: Graphs
NYC M4.c.ii - Makes statements and draws simple conclusions based on data; that is: compares data in order to make true statements, e.g., "seven plants grew at least 5 cm".
NYC M4.c.iii - Makes statements and draws simple conclusions based on data; that is: identifies and uses the mode necessary for making true statements, e.g., "more people chose red".
Topic 10 - Graphs, Probability, and Statistics
Obj. 159 - Modes of data sets
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M4.c.iv - Makes statements and draws simple conclusions based on data; that is: makes true statements based on a simple concept of average (median and mean), for a small sample size and where the situation is made evident with concrete materials or clear representations.
Topic 10 - Graphs, Probability, and Statistics
Obj. 160 - Averages (means) of data sets
Obj. 161 - Medians of data setsNYC M4.c.v - Makes statements and draws simple conclusions based on data; that is: interprets data to determine the reasonableness of statements about the data, e.g., "twice as often," "three times faster".
NYC M4.c.vi - Makes statements and draws simple conclusions based on data; that is: uses data, including statements about the data, to make a simple concluding statement about a situation, e.g., "This kind of plant grows better near sunlight because the seven plants that were near the window grew at least 5 cm."
NYC M4.d - Gathers data about an entire group or by sampling group members to understand the concept of sample, i.e., that a large sample leads to more reliable information, e.g., when flipping coins.
NYC M4.e - Predicts results, analyzes data, and finds out why some results are more likely, less likely, or equally likely.NYC M4.f - Finds all possible combinations and arrangements within certain constraints involving a limited number of variables.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M5-1 - The student demonstrates logical reasoning throughout work in mathematics, i.e., concepts and skills, problem solving, and projects; demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow; and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion.
Topic 12 - Problem solving Obj. 173 - Guess & check to solve problems
Obj. 174 - Eliminate possibilities to solve problems
- FORMULATIONNYC M5.a - Given the basic statement of a problem situation, the student:NYC M5.a.i - Given the basic statement of a problem situation, the student: makes the important decisions about the approach, materials, and strategies to use, i.e., does not merely fill in a given chart, use a pre-specified manipulative, or go through a predetermined set of steps.NYC M5.a.ii - Given the basic statement of a problem situation, the student: uses previously learned strategies, skills, knowledge, and concepts to make decisions.
NYC M5.a.iii - Given the basic statement of a problem situation, the student: uses strategies, such as using manipulatives or drawing sketches, to model problems. - IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes up and uses a variety of strategies and approaches to solving problems and uses or learns approaches that other people use, as appropriate.
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: makes connections among concepts in order to solve problems.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves problems in ways that make sense and explains why these ways make sense, e.g., defends the reasoning, explains the solution.
- CONCLUSIONNYC M5.c - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student:NYC M5.c.i - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains a pattern that can be used in similar situations.
NYC M5.c.ii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem is similar to other problems he or she has solved.
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M5.c.iii - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the mathematics used in the problem is like other concepts in mathematics.
NYC M5.c.iv - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: explains how the problem solution can be applied to other school subjects and in real world situations.NYC M5.c.v - The student moves beyond a particular problem by making connections, extensions, and/or generalizations; for example, the student: makes the solution into a general rule that applies to other circumstances.NYC M6 - MATHEMATICAL SKILLS AND TOOLSNYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, books, or other students, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Adds, subtracts, multiplies, and divides whole numbers correctly; that is:NYC M6.a.i - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: knows single digit addition, subtraction, multiplication, and division facts.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 34 - Multiplication facts
Obj. 43 - Division facts
Accelerated Math Kindergarten - Grade 4
091207Page 73 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M6.a.ii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: adds and subtracts numbers with several digits.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 12 - Add 2 whole #s, no regroup (1-3 dig)
Obj. 14 - Add 3 whole #s, no regroup (1-3 dig)Obj. 16 - Add 2 whole #s (2-6 dig)Obj. 18 - Add 3 or more whole #s (2-5 dig)Obj. 26 - Subtract whole #s, no regroup (1-3 dig)Obj. 28 - Subtract whole #s (2-5 dig)
NYC M6.a.iii - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides numbers with one or two digits.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 36 - WP: Multiply by 1-digit (2-4 dig)
Obj. 39 - Multiply by multiples of ten (2-4 dig)
NYC M6.a.iv - Adds, subtracts, multiplies, and divides whole numbers correctly; that is: multiplies and divides three digit numbers by one digit numbers.
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 35 - Multiply by 1-digit (2-4 dig)
Obj. 45 - Divide 3-digit by 1-digit, no borrow, no remainderObj. 46 - Divide 3-digit by 1-digit, borrow, no remainderObj. 47 - Divide 3-digit by 1-digitObj. 48 - WP: Divide whole #s by 1-digit
NYC M6.b - Estimates numerically and spatially.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 20 - Estimate sums, round (2-4 dig)Obj. 21 - Estimate sums, round to 10 or 100Obj. 23 - Estimate sums, 2 #s: front digits only (2-4 dig)Obj. 24 - Estimate sums, 3 #s: front digits only (2-4 dig)Obj. 25 - WP: Estimate sums, front digits only (2-3 dig)Obj. 30 - Estimate differences, round (2-4 dig)Obj. 31 - WP: Estimate differences, round (2-4 dig)
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 41 - Estimate products, round (1-4 dig)
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
Obj. 42 - WP: Estimate products, round (1-4 dig)Obj. 55 - Estimate quotients, compatible #s (2-3 dig)Obj. 56 - WP: Estimate whole quotients (2-3 dig)
Topic 6 - Money Obj. 97 - Estimate sums & differences of moneyObj. 98 - WP: Estimate sums & differences of money
Topic 7 - Measurement, Time, and Temperature
Obj. 103 - Estimate customary length
Obj. 105 - Estimate customary capacityObj. 111 - Estimate metric lengthObj. 113 - Estimate metric capacity
NYC M6.c - Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems.
Topic 7 - Measurement, Time, and Temperature
Obj. 106 - Measure customary length
Obj. 114 - Measure metric lengthNYC M6.d - Computes time (in hours and minutes) and money (in dollars and cents).
Topic 6 - Money Obj. 93 - Add money expressions
Obj. 95 - Subtract money expressionsObj. 99 - Count money & figure changeObj. 100 - Multiply money expressions by whole #s
Topic 7 - Measurement, Time, and Temperature
Obj. 123 - Calculate elapsed time
NYC M6.e - Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid.
Topic 8 - Geometry Obj. 126 - Points, lines, segments, rays, & angles
Obj. 128 - Classify quadrilateralsObj. 135 - Solids
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M6.f - Uses +, -, x, ÷, /, long division symbol, $, ¢, %, and . (decimal point) correctly in number sentences and expressions.NYC M6.g - Reads, creates, and represents data on line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs.
Topic 10 - Graphs, Probability, and Statistics
Obj. 148 - Tally charts
Obj. 149 - PictographsObj. 150 - Bar graphsObj. 151 - Line graphsObj. 152 - Circle graphsObj. 153 - Frequency tablesObj. 154 - Stem-and-leaf plotsObj. 158 - Organize data to answer a question
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the 1/8 inch; metric to the millimeter), graph paper (customary to the inch or half-inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound or ounce; metric to the kilogram or gram).
Topic 7 - Measurement, Time, and Temperature
Obj. 106 - Measure customary length
Obj. 114 - Measure metric lengthNYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M7.a - Uses appropriate mathematical terms, vocabulary, and language, based on prior conceptual work.
Topic 11 - Patterns, Expressions, and Equations
Obj. 167 - Equations to word sentences
NYC M7.b - Shows mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models.NYC M7.c - Explains solutions to problems clearly and logically, and supports solutions with evidence, in both oral and written work.NYC M7.d - Considers purpose and audience when communicating about mathematics.NYC M7.e - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale project each year, beginning in fourth grade, drawn from the following kinds and, over the course of elementary school, conducts projects drawn from at least two of the kinds. A single project may draw on more than one kind.
NYC M8.a - Data study, in which the student:NYC M8.a.i - Data study, in which the student: develops a question and a hypothesis in a situation where data could help make a decision or recommendation.NYC M8.a.ii - Data study, in which the student: decides on a group or groups to be sampled and makes predictions of the results, with specific percents, fractions, or numbers.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M8.a.iii - Data study, in which the student: collects, represents, and displays data in order to help make the decision or recommendation; compares the results with the predictions.NYC M8.a.iv - Data study, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.
NYC M8.b - Science study, in which the student:NYC M8.b.i - Science study, in which the student: decides on a specific science question to study and identifies the mathematics that will be used, e.g., measurement.NYC M8.b.ii - Science study, in which the student: develops a prediction (a hypothesis) and develops procedures to test the hypothesis.NYC M8.b.iii - Science study, in which the student: collects and records data, represents and displays data, and compares results with predictions.NYC M8.b.iv - Science study, in which the student: writes a report that compares the results with the hypothesis; supports the results with diagrams, charts, and graphs; acknowledges assistance received from parents, peers, and teachers.NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: decides on a structure to design, the size and budget constraints, and the scale of design.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M8.c.ii - Design of a physical structure, in which the student: makes a first draft of the design, and revises and improves the design in response to input from peers and teachers.NYC M8.c.iii - Design of a physical structure, in which the student: makes a final draft and report of the design, drawn and written so that another person could make the structure; acknowledges assistance received from parents, peers, and teachers.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: decides on what to manage or plan, and the criteria to be used to see if the plan worked.NYC M8.d.ii - Management and planning, in which the student: identifies unexpected events that could disrupt the plan and further plans for such contingencies.NYC M8.d.iii - Management and planning, in which the student: identifies resources needed, e.g., materials, money, time, space, and other people.NYC M8.d.iv - Management and planning, in which the student: writes a detailed plan and revises and improves the plan in response to feedback from peers and teachers.
NYC M8.d.v - Management and planning, in which the student: carries out the plan (optional).NYC M8.d.vi - Management and planning, in which the student: writes a report on the plan that includes resources, budget, and schedule, and acknowledges assistance received from parents, peers, and teachers.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade K-4, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 4
NYC M8.d.vii - Management and planning, in which the student: writes a report that includes recommendations supported by diagrams, charts, and graphs, and acknowledges assistance received from parents, peers, and teachers.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: decides on the area of mathematics to investigate, e.g., numbers, shapes, patterns.NYC M8.e.ii - Pure mathematics investigation, in which the student: describes a question or concept to investigate.NYC M8.e.iii - Pure mathematics investigation, in which the student: decides on representations that will be used, e.g., numbers, symbols, diagrams, shapes, or physical models.NYC M8.e.iv - Pure mathematics investigation, in which the student: carries out the investigation.NYC M8.e.v - Pure mathematics investigation, in which the student: writes a report that includes any generalizations drawn from the investigation, and acknowledges assistance received from parents, peers, and teachers.
Accelerated Math Kindergarten - Grade 4
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Consistently and accurately adds, subtracts, multiplies, and divides rational numbers using appropriate methods (e.g., the student can add (1/2) + (5/6) mentally or on paper but may opt to add (13/24) + (57/68) on a calculator) and raises rational numbers to whole number powers. (Students should have facility with the different kinds and forms of rational numbers, i.e., integers, both whole numbers and negative integers; and other positive and negative rationals, written as decimals, as percents, or as proper, improper, or mixed fractions. Irrational numbers, i.e., those that cannot be written as a ratio of two integers, are not required content but are suitable for introduction, especially since the student should be familiar with the irrational number (pi).)
Topic 2 - Whole Numbers: Add and Subtract
Obj. 17 - Add 2 whole #s
Obj. 18 - Add 3 or more whole #sObj. 26 - Subtract whole #s (3-6 dig)
Obj. 27 - Subtract 3 or more whole #s
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 33 - Multiply by 1-digit
Obj. 34 - Multiply by 2 or more digObj. 36 - Multiply by a multiple of 10
Obj. 37 - Multiply by a power of 10Obj. 42 - Divide by 1-digit, no remainderObj. 43 - Divide by 1-digit, remainder
Obj. 45 - Divide by 2-digitObj. 47 - Divide by multiple of 10
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Accelerated Math Grades 5 - 8
091207Page 81 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Obj. 51 - Use calculator to solve problems
Topic 5 - Decimals: Add and Subtract
Obj. 59 - Add money expressions
Obj. 61 - Add same-place decimals (to thousandths)Obj. 62 - Add varied-place decimals (to thousandths)Obj. 64 - Subtract money expressionsObj. 66 - Subtract same-place decimals (to thousandths)Obj. 67 - Subtract varied-place decimals (to thousandths)
Topic 6 - Decimals: Multiply and Divide
Obj. 73 - Multiply money expressions by whole # (1-2 dig)Obj. 75 - Multiply decimals by whole #s (1-2 dig)Obj. 76 - Multiply decimals (to thousandths)Obj. 77 - Multiply decimals by powers of 10Obj. 81 - Divide money expressions by whole # (1-2 dig)Obj. 83 - Divide decimals by 1-digit whole #s
Topic 8 - Fractions: Add and Subtract
Obj. 98 - Add like fractions
Obj. 99 - Add like mixed #sObj. 101 - Add unlike fractionsObj. 102 - Add unlike mixed #sObj. 104 - Subtract like fractionsObj. 105 - Subtract like mixed #sObj. 106 - Subtract unlike fractionsObj. 107 - Subtract mixed #s from whole #sObj. 108 - Subtract unlike mixed #s, no regroupObj. 109 - Subtract mixed #s, regroup
Topic 9 - Fractions: Multiply and Divide
Obj. 111 - Multiply fractions
Obj. 112 - Multiply fractions by whole #sObj. 114 - Multiply mixed #s by fractionsObj. 116 - Multiply mixed #sObj. 117 - Divide whole #s by fractions
Accelerated Math Grades 5 - 8
091207Page 82 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Topic 14 - Fractions, Decimals, Percents, and Ratios
Obj. 184 - Percent of a number
NYC M1.b - Uses and understands the inverse relationships between addition and subtraction, multiplication and division, and exponentiation and root-extraction (e.g., squares and square roots, cubes and cube roots); uses the inverse operation to determine unknown quantities in equations.NYC M1.c - Consistently and accurately applies and converts the different kinds and forms of rational numbers.
Topic 7 - Introduction to Fractions
Obj. 92 - Mixed #s to improper fractions
Obj. 93 - Improper fractions to mixed #s
Topic 14 - Fractions, Decimals, Percents, and Ratios
Obj. 180 - Fractions to decimals
Obj. 181 - Decimals to fractionsObj. 182 - Mixed #s to decimalsObj. 186 - Convert decimals & percentsObj. 187 - Fractions to percentsObj. 189 - Write ratios as fractions
NYC M1.d - Is familiar with characteristics of numbers (e.g., divisibility, prime factorization) and with properties of operations (e.g., commutativity and associativity), short of formal statements.
Topic 1 - Whole Number Concepts
Obj. 11 - Prime & composite numbers
Obj. 12 - Factors of composite numbersObj. 13 - Prime factorizationObj. 14 - Greatest common factorObj. 15 - Multiples of whole #sObj. 16 - Least common multiple
Topic 2 - Whole Numbers: Add and Subtract
Obj. 19 - Properties of addition
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 38 - Properties of multiplication
NYC M1.e - Interprets percent as part of 100 and as a means of comparing quantities of different sizes or changing sizes.
Topic 14 - Fractions, Decimals, Percents, and Ratios
Obj. 183 - Find percents with models
Accelerated Math Grades 5 - 8
091207Page 83 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M1.f - Uses ratios and rates to express "part-to-part" and "whole-to-whole" relationships, and reasons proportionally to solve problems involving equivalent fractions, equal ratios, or constant rates, recognizing the multiplicative nature of these problems in the constant factor of change.
Topic 14 - Fractions, Decimals, Percents, and Ratios
Obj. 188 - Identify ratios
Obj. 191 - Equivalent ratios, same form
NYC M1.g - Orders numbers with the > and < relationships and by location on a number line; estimates and compares rational numbers using sense of the magnitudes and relative magnitudes of numbers and of base-ten place values (e.g., recognizes relationships to "benchmark" numbers 1/2 and 1 to conclude that the sum 1/2)+ 5/6 must be between 1 and 1 (1/2) (likewise, (13/24) + (1/4)).
Topic 1 - Whole Number Concepts
Obj. 6 - Compare whole #s (2+ dig)
Topic 4 - Introduction to Decimals
Obj. 57 - Compare decimals using <, >, =
Topic 7 - Introduction to Fractions
Obj. 86 - Model fractions & mixed #s on number linesObj. 94 - Compare fractions
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts in the following areas; that is, the student:
NYC M2.a - Is familiar with assorted two- and three-dimensional objects, including squares, triangles, other polygons, circles, cubes, rectangular prisms, pyramids, spheres, and cylinders.
Topic 11 - Geometry Obj. 140 - Identify polygons
Obj. 141 - Classify quadrilateralsObj. 148 - SolidsObj. 149 - Count faces, edges, & verticesObj. 150 - Parts of a circle
Accelerated Math Grades 5 - 8
091207Page 84 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M2.b - Identifies similar and congruent shapes and uses transformations in the coordinate plane, i.e., translations, rotations, and reflections.
Topic 11 - Geometry Obj. 143 - Congruent & similar figures
Obj. 145 - Similar trianglesObj. 147 - Flips, turns, & slides
NYC M2.c - Identifies three dimensional shapes from two dimensional perspectives; draws two dimensional sketches of three dimensional objects that preserve significant features.
Topic 12 - Perimeter, Area, and Volume
Obj. 163 - Identify nets (patterns) of solids
NYC M2.d - Determines and understands length, area, and volume (as well as the differences among these measurements), including perimeter and surface area; uses units, square units, and cubic units of measure correctly; computes areas of rectangles, triangles, and circles; computes volumes of prisms.
Topic 10 - Measurement, Time, Money, and Temperature
Obj. 120 - Measure customary length
Obj. 125 - Measure metric lengthObj. 126 - Measure to nearest centimeter
Topic 12 - Perimeter, Area, and Volume
Obj. 154 - Perimeter of rectangles
Obj. 155 - Perimeter of polygonsObj. 157 - Area by countingObj. 158 - Area of rectanglesObj. 159 - Area of parallelogramsObj. 161 - Volume of rectangular prisms & cubes
NYC M2.e - Recognizes similarity and rotational and bilateral symmetry in two- and three-dimensional figures.
Topic 11 - Geometry Obj. 146 - Lines of symmetry
NYC M2.f - Analyzes and generalizes geometric patterns, such as tessellations and sequences of shapes.
Topic 15 - Number Patterns Obj. 194 - Analyze geometric patterns
NYC M2.g - Measures angles, weights, capacities, times, and temperatures using appropriate units.
Topic 10 - Measurement, Time, Money, and Temperature
Obj. 132 - Read thermometers
Topic 11 - Geometry Obj. 139 - Measure anglesTopic 13 - Graphs, Probability, and Statistics
Obj. 171 - Time schedules
Accelerated Math Grades 5 - 8
091207Page 85 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M2.h - Chooses appropriate units of measure and converts with ease between like units, e.g., inches and miles, within a customary or metric system. (Conversions between customary and metric are not required.)
Topic 10 - Measurement, Time, Money, and Temperature
Obj. 121 - Convert customary length
Obj. 122 - Convert customary weight
Obj. 123 - Convert customary capacityObj. 127 - Convert metric lengthObj. 128 - Convert metric weightObj. 129 - Convert metric capacity
NYC M2.i - Reasons proportionally in situations with similar figures.
Topic 11 - Geometry Obj. 145 - Similar triangles
NYC M2.j - Reasons proportionally with measurements to interpret maps and to make smaller and larger scale drawings.NYC M2.k - Models situations geometrically to formulate and solve problems.
Topic 12 - Perimeter, Area, and Volume
Obj. 156 - WP: Perimeter
Obj. 160 - WP: AreaObj. 162 - WP: Volume of rectangular solids
Topic 16 - Problem Solving Obj. 204 - Draw a picture to solve a problem
NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Discovers, describes, and generalizes patterns, including linear, exponential, and simple quadratic relationships, i.e., those of the form f(n)=n^2 or f(n)=cn^2, for constant c, including A = (pi)r^2, and represents them with variables and expressions.
Topic 15 - Number Patterns Obj. 192 - Missing terms in number patterns
Obj. 193 - Terms in described number patternsObj. 194 - Analyze geometric patternsObj. 195 - Determine function rule
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Obj. 197 - Translate verbal expressions
NYC M3.b - Represents relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules.
Topic 16 - Problem Solving Obj. 203 - Everyday situations to math sentences
NYC M3.c - Analyzes tables, graphs, and rules to determine functional relationships.
Topic 15 - Number Patterns Obj. 195 - Determine function rule
NYC M3.d - Finds solutions for unknown quantities in linear equations and in simple equations and inequalities.
Topic 15 - Number Patterns Obj. 199 - Solve add/subtr equations, whole # facts
Obj. 200 - Solve mult/div equations, whole # factsObj. 201 - Solve 1-step equations, whole numbersObj. 202 - Determine perimeter, given formula
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts; that is, the student:NYC M4.a - Collects data, organizes data, and displays data with tables, charts, and graphs that are appropriate, i.e., consistent with the nature of the data.
NYC M4.b - Analyzes data with respect to characteristics of frequency and distribution, including mode and range.
Topic 13 - Graphs, Probability, and Statistics
Obj. 173 - Means of data sets
Obj. 174 - Medians of data setsObj. 175 - Modes of data setsObj. 176 - Ranges of data sets
NYC M4.c - Analyzes appropriately central tendencies of data by considering mean and median.
Topic 13 - Graphs, Probability, and Statistics
Obj. 173 - Means of data sets
Obj. 174 - Medians of data setsNYC M4.d - Makes conclusions and recommendations based on data analysis.NYC M4.e - Critiques the conclusions and recommendations of others’ statistics.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M4.f - Considers the effects of missing or incorrect information.NYC M4.g - Formulates hypotheses to answer a question and uses data to test hypotheses.NYC M4.h - Represents and determines probability as a fraction of a set of equally likely outcomes; recognizes equally likely outcomes, and constructs sample spaces (including those described by numerical combinations and permutations).
Topic 13 - Graphs, Probability, and Statistics
Obj. 177 - Find possible outcomes
Obj. 178 - Probability of single events
NYC M4.i - Makes predictions based on experimental or theoretical probabilities.
Topic 13 - Graphs, Probability, and Statistics
Obj. 179 - Predict based on experimental probability
NYC M4.j - Predicts the result of a series of trials once the probability for one trial is known.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion. - FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: formulates and solves a variety of meaningful problems.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 20 - WP: Add whole #s
Obj. 28 - WP: Subtract whole #sTopic 3 - Whole Numbers: Multiply and Divide
Obj. 35 - WP: Multiply whole #s
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Obj. 44 - WP: Divide by 1-digitObj. 46 - WP: Divide by 2-digitObj. 50 - WP: 2-step with whole #s
Topic 5 - Decimals: Add and Subtract
Obj. 60 - WP: Add money expressionsObj. 63 - WP: Add decimalsObj. 65 - WP: Subtract money expressionsObj. 68 - WP: Subtract decimals
Topic 6 - Decimals: Multiply and Divide
Obj. 74 - WP: Multiply money expressions by whole #sObj. 78 - WP: Multiply decimalsObj. 82 - WP: Divide money expressionsObj. 84 - WP: Divide decimals by whole #s
Topic 7 - Introduction to Fractions
Obj. 87 - WP: Name fraction of a whole or set
Topic 8 - Fractions: Add and Subtract
Obj. 100 - WP: Add like fractions & mixed #sObj. 103 - WP: Add unlike fractions & mixed #sObj. 110 - WP: Subtract fractions
Topic 9 - Fractions: Multiply and Divide
Obj. 113 - WP: Multiply fractions by whole #sObj. 115 - WP: Multiply mixed #s by whole #s, fractionsObj. 118 - WP: Divide whole #s by fractions
Topic 10 - Measurement, Time, Money, and Temperature
Obj. 134 - WP: 2-step with money
Topic 12 - Perimeter, Area, and Volume
Obj. 156 - WP: Perimeter
Obj. 160 - WP: AreaObj. 162 - WP: Volume of rectangular solids
Topic 14 - Fractions, Decimals, Percents, and Ratios
Obj. 185 - WP: Percent of a number
NYC M5.a.ii - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: extracts pertinent information from situations and figures out what additional information is needed.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 31 - WP: Too much information
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Obj. 32 - WP: Not enough information
- IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: uses and invents a variety of approaches and understands and evaluates those of others.NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: invokes problem solving strategies, such as illustrating with sense-making sketches to clarify situations or organizing information in a table.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: determines, where helpful, how to break a problem into simpler parts.NYC M5.b.iv - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves for unknown or undecided quantities using algebra, graphing, sound reasoning, and other strategies.
Topic 16 - Problem Solving Obj. 215 - Arguments and conclusions
Obj. 216 - Think visually to solve a problemObj. 218 - Use diagrams/tables to solve a problem
NYC M5.b.v - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: integrates concepts and techniques from different areas of mathematics.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M5.b.vi - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: works effectively in teams when the nature of the task or the allotted time makes this an appropriate strategy.
- CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: verifies and interprets results with respect to the original problem situation.NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: generalizes solutions and strategies to new problem situations.
- MATHEMATICAL REASONINGNYC M5.d - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student:NYC M5.d.i - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: formulates conjectures and argues why they must be or seem true.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M5.d.ii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes sensible, reasonable estimates.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 23 - WP: Estimate sums, round (3-5 dig)
Obj. 25 - WP: Estimate sums, front-end with adjustmentObj. 30 - WP: Estimate differences, round
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 40 - WP: Estimate products, round (2-4 dig)Obj. 49 - WP: Estimate quotients, compatible #s (2-4 dig)
Topic 5 - Decimals: Add and Subtract
Obj. 70 - WP: Estimate decimal sums, roundObj. 72 - WP: Estimate decimal differences, round
Topic 6 - Decimals: Multiply and Divide
Obj. 80 - WP: Estimate decimal products, round
Topic 16 - Problem Solving Obj. 206 - Evaluate reasonableness using estimationObj. 208 - Guess and check to solve a problem
NYC M5.d.iii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes justified, logical statements.
Topic 15 - Number Patterns Obj. 195 - Determine function rule
NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task (perhaps referring to notes, or books, perhaps working to reconstruct a method); that is, the student:
NYC M6.a - Computes accurately with arithmetic operations on rational numbers.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 17 - Add 2 whole #s
Obj. 18 - Add 3 or more whole #sObj. 26 - Subtract whole #s (3-6 dig)
Obj. 27 - Subtract 3 or more whole #s
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 33 - Multiply by 1-digit
Obj. 34 - Multiply by 2 or more digObj. 36 - Multiply by a multiple of 10
Obj. 37 - Multiply by a power of 10Obj. 42 - Divide by 1-digit, no remainderObj. 43 - Divide by 1-digit, remainder
Obj. 45 - Divide by 2-digitObj. 47 - Divide by multiple of 10
Topic 5 - Decimals: Add and Subtract
Obj. 59 - Add money expressions
Obj. 61 - Add same-place decimals (to thousandths)Obj. 62 - Add varied-place decimals (to thousandths)Obj. 64 - Subtract money expressionsObj. 66 - Subtract same-place decimals (to thousandths)Obj. 67 - Subtract varied-place decimals (to thousandths)
Topic 6 - Decimals: Multiply and Divide
Obj. 73 - Multiply money expressions by whole # (1-2 dig)Obj. 75 - Multiply decimals by whole #s (1-2 dig)
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Obj. 76 - Multiply decimals (to thousandths)Obj. 77 - Multiply decimals by powers of 10Obj. 81 - Divide money expressions by whole # (1-2 dig)Obj. 83 - Divide decimals by 1-digit whole #s
Topic 8 - Fractions: Add and Subtract
Obj. 98 - Add like fractions
Obj. 99 - Add like mixed #sObj. 101 - Add unlike fractionsObj. 102 - Add unlike mixed #sObj. 104 - Subtract like fractionsObj. 105 - Subtract like mixed #sObj. 106 - Subtract unlike fractionsObj. 107 - Subtract mixed #s from whole #sObj. 108 - Subtract unlike mixed #s, no regroupObj. 109 - Subtract mixed #s, regroup
Topic 9 - Fractions: Multiply and Divide
Obj. 111 - Multiply fractions
Obj. 112 - Multiply fractions by whole #sObj. 114 - Multiply mixed #s by fractionsObj. 116 - Multiply mixed #sObj. 117 - Divide whole #s by fractions
NYC M6.b - Knows and uses the correct order of operations for arithmetic computations.NYC M6.c - Estimates numerically and spatially.
Topic 2 - Whole Numbers: Add and Subtract
Obj. 21 - Estimate sums, round to greatest (3-5 dig)Obj. 22 - Estimate sums, round to 10,100,1000Obj. 24 - Estimate sums, front-end with adjustmentObj. 29 - Estimate differences, round
Topic 3 - Whole Numbers: Multiply and Divide
Obj. 39 - Estimate products, round (2-4 dig)Obj. 48 - Estimate quotients, compatible #s (2-4 dig)
Topic 5 - Decimals: Add and Subtract
Obj. 69 - Estimate decimal sums, round
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
Obj. 71 - Estimate decimal differences, round
Topic 6 - Decimals: Multiply and Divide
Obj. 79 - Estimate decimal products, round
Topic 10 - Measurement, Time, Money, and Temperature
Obj. 119 - Estimate customary measure
NYC M6.d - Measures length, area, volume, weight, time, and temperature accurately.
Topic 10 - Measurement, Time, Money, and Temperature
Obj. 120 - Measure customary length
Obj. 125 - Measure metric lengthObj. 132 - Read thermometers
Topic 12 - Perimeter, Area, and Volume
Obj. 157 - Area by counting
Obj. 158 - Area of rectanglesObj. 159 - Area of parallelogramsObj. 161 - Volume of rectangular prisms & cubes
NYC M6.e - Refers to geometric shapes and terms correctly.
Topic 11 - Geometry Obj. 137 - Classify angles
Obj. 140 - Identify polygonsObj. 141 - Classify quadrilateralsObj. 148 - SolidsObj. 150 - Parts of a circle
NYC M6.f - Uses equations, formulas, and simple algebraic notation appropriately.
Topic 15 - Number Patterns Obj. 196 - Identify algebraic terms
Obj. 197 - Translate verbal expressions
NYC M6.g - Reads and organizes data on charts and graphs, including scatter plots, bar, line, and circle graphs, and Venn diagrams; calculates mean and median.
Topic 13 - Graphs, Probability, and Statistics
Obj. 165 - Bar graphs
Obj. 166 - Line graphsObj. 169 - Circle graphsObj. 173 - Means of data setsObj. 174 - Medians of data sets
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions.
NYC M7 - MATHEMATICAL COMMUNICATION
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Uses mathematical language and representations with appropriate accuracy, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagrams.NYC M7.b - Organizes work, explains facets of a solution orally and in writing, labels drawings, and uses other techniques to make meaning clear to the audience.NYC M7.c - Uses mathematical language to make complex situations easier to understand.NYC M7.d - Exhibits developing reasoning abilities by justifying statements and defending work.NYC M7.e - Shows understanding of concepts by explaining ideas not only to teachers and assessors but to fellow students or younger children.
NYC M7.f - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of middle school, conducts investigations or projects drawn from three of the kinds. A single investigation or project may draw on more than one kind.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M8.a - Data study based on civic, economic, or social issues, in which the student:NYC M8.a.i - Data study based on civic, economic, or social issues, in which the student: selects an issue to investigate.NYC M8.a.ii - Data study based on civic, economic, or social issues, in which the student: makes a hypothesis on an expected finding, if appropriate.NYC M8.a.iii - Data study based on civic, economic, or social issues, in which the student: gathers data.
NYC M8.a.iv - Data study based on civic, economic, or social issues, in which the student: analyzes the data using concepts from Standard 4, e.g., considering mean and median, and the frequency and distribution of the data.
NYC M8.a.v - Data study based on civic, economic, or social issues, in which the student: shows how the study’s results compare with the hypothesis.NYC M8.a.vi - Data study based on civic, economic, or social issues, in which the student: uses pertinent statistics to summarize.NYC M8.a.vii - Data study based on civic, economic, or social issues, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.b - Mathematical model of physical phenomena, often used in science studies, in which the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M8.b.i - Mathematical model of physical phenomena, often used in science studies, in which the student: carries out a study of a physical system using a mathematical representation of the structure.
NYC M8.b.ii - Mathematical model of physical phenomena, often used in science studies, in which the student: uses understanding from Standard 3, particularly with respect to the determination of the function governing behavior in the model.
NYC M8.b.iii - Mathematical model of physical phenomena, often used in science studies, in which the student: generalizes about the structure with a rule, i.e., a function, that clearly applies to the phenomenon and goes beyond statistical analysis of a pattern of numbers generated by the situation.
NYC M8.b.iv - Mathematical model of physical phenomena, often used in science studies, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: generates a plan to build something of value, not necessarily monetary value.NYC M8.c.ii - Design of a physical structure, in which the student: uses mathematics from Standard 2 to make the design realistic or appropriate, e.g., areas and volumes in general and of specific geometric shapes.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M8.c.iii - Design of a physical structure, in which the student: summarizes the important features of the structure.NYC M8.c.iv - Design of a physical structure, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: determines the needs of the event to be managed or planned, e.g., cost, supply, scheduling.NYC M8.d.ii - Management and planning, in which the student: notes any constraints that will affect the plan.NYC M8.d.iii - Management and planning, in which the student: determines a plan.NYC M8.d.iv - Management and planning, in which the student: uses concepts from any of Standards 1 to 4, depending on the nature of the project.NYC M8.d.v - Management and planning, in which the student: considers the possibility of a more efficient solution.NYC M8.d.vi - Management and planning, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the plan.NYC M8.e - Pure mathematics investigation, in which the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 5
NYC M8.e.i - Pure mathematics investigation, in which the student: extends or "plays with," as with mathematical puzzles, some mathematical feature, e.g., properties and patterns in numbers.
NYC M8.e.ii - Pure mathematics investigation, in which the student: uses concepts from any of Standards 1 to 4, e.g., an investigation of Pascal’s triangle would have roots in Standard 1 but could tie in concepts from geometry, algebra, and probability; investigations of derivations of geometric formulas would be rooted in Standard 2 but could require algebra.
NYC M8.e.iii - Pure mathematics investigation, in which the student: determines and expresses generalizations from patterns.NYC M8.e.iv - Pure mathematics investigation, in which the student: makes conjectures on apparent properties and argues, short of formal proof, why they seem true.NYC M8.e.v - Pure mathematics investigation, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Consistently and accurately adds, subtracts, multiplies, and divides rational numbers using appropriate methods (e.g., the student can add (1/2) + (5/6) mentally or on paper but may opt to add (13/24) + (57/68) on a calculator) and raises rational numbers to whole number powers. (Students should have facility with the different kinds and forms of rational numbers, i.e., integers, both whole numbers and negative integers; and other positive and negative rationals, written as decimals, as percents, or as proper, improper, or mixed fractions. Irrational numbers, i.e., those that cannot be written as a ratio of two integers, are not required content but are suitable for introduction, especially since the student should be familiar with the irrational number (pi).)
Topic 2 - Whole Number Concepts Part 2
Obj. 15 - Add whole #s
Obj. 18 - Subtract whole #sObj. 21 - Multiply by 2 or more digObj. 23 - Multiply by a multiple of 10
Obj. 24 - Multiply by a power of 10Obj. 27 - Exponential notationObj. 28 - Evaluate exponentsObj. 29 - Multiply with exponentsObj. 30 - Divide whole #s (2+ dig divisor)
Topic 4 - Decimals: Add and Subtract
Obj. 50 - Add decimals
Obj. 54 - Subtract decimalsTopic 5 - Decimals: Multiply and Divide
Obj. 64 - Multiply decimals by whole #s (2-3 dig)Obj. 65 - Multiply decimals (to thousandths)
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
Obj. 67 - Multiply decimals by a power of 10Obj. 71 - Divide decimals by 1- & 2-digit whole #sObj. 73 - Divide whole #s by powers of 10 (decimal answer)Obj. 74 - Divide decimals by powers of 10Obj. 76 - Divide whole #s by decimalsObj. 78 - Divide decimals by decimals
Topic 7 - Fractions: Add and Subtract
Obj. 97 - Add like fractions
Obj. 98 - Add like fractions & mixed #sObj. 100 - Add unlike fractionsObj. 101 - Add unlike mixed #sObj. 105 - Subtract like fractionsObj. 106 - Subtract like mixed #sObj. 107 - Subtract unlike fractionsObj. 108 - Subtract unlike mixed #s, no regroupObj. 109 - Subtract mixed #s from whole #sObj. 110 - Subtract mixed #s, regroup
Topic 8 - Fractions: Multiply, Divide, and Combined Operations
Obj. 114 - Multiply fractions
Obj. 115 - Multiply fractions by whole #sObj. 117 - Multiply mixed #s by fractionsObj. 118 - Multiply mixed #sObj. 120 - Divide fractionsObj. 121 - Divide mixed #s by fractionsObj. 122 - Divide mixed #sObj. 123 - Divide whole #s & fractions
Topic 15 - Integers Obj. 232 - Add integersObj. 234 - Subtract positive integers
Obj. 235 - Subtract integersTopic 17 - Problem Solving Obj. 249 - Solve problems using
calculator
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M1.b - Uses and understands the inverse relationships between addition and subtraction, multiplication and division, and exponentiation and root-extraction (e.g., squares and square roots, cubes and cube roots); uses the inverse operation to determine unknown quantities in equations.
Topic 16 - Patterns, Expressions and Equations
Obj. 243 - Solve addition & subtraction equations
NYC M1.c - Consistently and accurately applies and converts the different kinds and forms of rational numbers.
Topic 13 - Fractions, Percents, and Decimals
Obj. 205 - Fractions to decimals, terminating
Obj. 206 - Decimals to fractionsObj. 207 - Decimals to mixed #sObj. 208 - Mixed #s to decimalsObj. 209 - Decimals to percentsObj. 210 - Percents to decimalsObj. 211 - Percents to fractionsObj. 212 - Fractions to percentsObj. 213 - Fractions to decimals, repeating
NYC M1.d - Is familiar with characteristics of numbers (e.g., divisibility, prime factorization) and with properties of operations (e.g., commutativity and associativity), short of formal statements.
Topic 1 - Whole Number Concepts Part 1
Obj. 9 - Prime & composite numbers
Obj. 11 - Prime factorizationTopic 2 - Whole Number Concepts Part 2
Obj. 16 - Properties of addition
Obj. 34 - Divisibility rulesNYC M1.e - Interprets percent as part of 100 and as a means of comparing quantities of different sizes or changing sizes.
Topic 14 - Percents, Ratios, and Proportions
Obj. 218 - Ratio as percent
NYC M1.f - Uses ratios and rates to express "part-to-part" and "whole-to-whole" relationships, and reasons proportionally to solve problems involving equivalent fractions, equal ratios, or constant rates, recognizing the multiplicative nature of these problems in the constant factor of change.
Topic 14 - Percents, Ratios, and Proportions
Obj. 215 - Ratio as fraction, lowest terms
Obj. 216 - WP: RatiosObj. 224 - Ratios as proportionsObj. 225 - Solve proportions
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
Obj. 226 - Write proportion representing situationObj. 227 - WP: Solve proportions
NYC M1.g - Orders numbers with the > and < relationships and by location on a number line; estimates and compares rational numbers using sense of the magnitudes and relative magnitudes of numbers and of base-ten place values (e.g., recognizes relationships to "benchmark" numbers 1/2 and 1 to conclude that the sum 1/2)+ 5/6 must be between 1 and 1 (1/2) (likewise, (13/24) + (1/4)).
Topic 1 - Whole Number Concepts Part 1
Obj. 7 - Compare whole #s (4+ dig)
Topic 6 - Introduction to Fractions
Obj. 88 - Model fractions & mixed #s on number linesObj. 95 - Compare fractions
Topic 15 - Integers Obj. 228 - Graph integers on number linesObj. 229 - Compare & order integers
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts in the following areas; that is, the student:
NYC M2.a - Is familiar with assorted two- and three-dimensional objects, including squares, triangles, other polygons, circles, cubes, rectangular prisms, pyramids, spheres, and cylinders.
Topic 10 - Geometry Obj. 147 - Identify polygons
Obj. 148 - Classify quadrilateralsObj. 154 - Name 3-dimensional object
NYC M2.b - Identifies similar and congruent shapes and uses transformations in the coordinate plane, i.e., translations, rotations, and reflections.
Topic 10 - Geometry Obj. 150 - Congruent & similar figures
Obj. 158 - Flips, turns, & slides
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M2.c - Identifies three dimensional shapes from two dimensional perspectives; draws two dimensional sketches of three dimensional objects that preserve significant features.
Topic 10 - Geometry Obj. 156 - Nets and 3-d figures
Obj. 157 - Orthographic drawingsNYC M2.d - Determines and understands length, area, and volume (as well as the differences among these measurements), including perimeter and surface area; uses units, square units, and cubic units of measure correctly; computes areas of rectangles, triangles, and circles; computes volumes of prisms.
Topic 11 - Perimeter, Area, and Volume
Obj. 164 - Perimeter of rectangles
Obj. 165 - Perimeter of polygonsObj. 166 - WP: PerimeterObj. 170 - Area of rectangles & squaresObj. 171 - WP: Area of rectangles & squaresObj. 173 - Area of trianglesObj. 174 - WP: Area of trianglesObj. 176 - Area of circlesObj. 179 - Find volume of rectangular prismsObj. 180 - Volume of rectangular prisms & cubesObj. 181 - WP: VolumeObj. 182 - Surface area of rectangular prisms
NYC M2.e - Recognizes similarity and rotational and bilateral symmetry in two- and three-dimensional figures.
Topic 10 - Geometry Obj. 152 - Lines of symmetry
Obj. 153 - Rotational symmetryNYC M2.f - Analyzes and generalizes geometric patterns, such as tessellations and sequences of shapes.
Topic 16 - Patterns, Expressions and Equations
Obj. 240 - Extend & generalize geometric patterns
NYC M2.g - Measures angles, weights, capacities, times, and temperatures using appropriate units.
Topic 9 - Measurement, Time, and Temperature
Obj. 129 - Measure length (customary & metric)
Topic 10 - Geometry Obj. 146 - Measure angles
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M2.h - Chooses appropriate units of measure and converts with ease between like units, e.g., inches and miles, within a customary or metric system. (Conversions between customary and metric are not required.)
Topic 9 - Measurement, Time, and Temperature
Obj. 130 - Convert customary length
Obj. 131 - Convert customary weight
Obj. 132 - Convert customary capacityObj. 133 - WP: Customary measurementObj. 134 - Convert metric lengthObj. 135 - Convert metric weightObj. 136 - Convert metric capacityObj. 137 - Mixed units of lengthObj. 138 - WP: Metric measurement
NYC M2.i - Reasons proportionally in situations with similar figures.NYC M2.j - Reasons proportionally with measurements to interpret maps and to make smaller and larger scale drawings.NYC M2.k - Models situations geometrically to formulate and solve problems.
Topic 17 - Problem Solving Obj. 248 - Model situations geometrically
NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Discovers, describes, and generalizes patterns, including linear, exponential, and simple quadratic relationships, i.e., those of the form f(n)=n^2 or f(n)=cn^2, for constant c, including A = (pi)r^2, and represents them with variables and expressions.
Topic 16 - Patterns, Expressions and Equations
Obj. 238 - Missing terms in number patterns
Obj. 239 - Terms in described number patternsObj. 240 - Extend & generalize geometric patterns
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M3.b - Represents relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules.
NYC M3.c - Analyzes tables, graphs, and rules to determine functional relationships.
Topic 16 - Patterns, Expressions and Equations
Obj. 247 - Equations and graphs
NYC M3.d - Finds solutions for unknown quantities in linear equations and in simple equations and inequalities.
Topic 16 - Patterns, Expressions and Equations
Obj. 243 - Solve addition & subtraction equations
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts; that is, the student:NYC M4.a - Collects data, organizes data, and displays data with tables, charts, and graphs that are appropriate, i.e., consistent with the nature of the data.
Topic 12 - Graphs, Probability and Statistics
Obj. 194 - Choose best type of graph
NYC M4.b - Analyzes data with respect to characteristics of frequency and distribution, including mode and range.
Topic 12 - Graphs, Probability and Statistics
Obj. 203 - Modes of data sets
Obj. 204 - Ranges of data setsNYC M4.c - Analyzes appropriately central tendencies of data by considering mean and median.
Topic 12 - Graphs, Probability and Statistics
Obj. 201 - Means of data sets
Obj. 202 - Medians of data setsNYC M4.d - Makes conclusions and recommendations based on data analysis.NYC M4.e - Critiques the conclusions and recommendations of others’ statistics.NYC M4.f - Considers the effects of missing or incorrect information.NYC M4.g - Formulates hypotheses to answer a question and uses data to test hypotheses.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M4.h - Represents and determines probability as a fraction of a set of equally likely outcomes; recognizes equally likely outcomes, and constructs sample spaces (including those described by numerical combinations and permutations).
Topic 12 - Graphs, Probability and Statistics
Obj. 195 - Find possible outcomes
Obj. 196 - Probability of single events
Obj. 198 - List outcomes for compound events
NYC M4.i - Makes predictions based on experimental or theoretical probabilities.
Topic 12 - Graphs, Probability and Statistics
Obj. 197 - Predict using probability, theor/exper
NYC M4.j - Predicts the result of a series of trials once the probability for one trial is known.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion. - FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: formulates and solves a variety of meaningful problems.
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M5.a.ii - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: extracts pertinent information from situations and figures out what additional information is needed.
Topic 2 - Whole Number Concepts Part 2
Obj. 37 - WP: Not enough information
Obj. 38 - WP: Too much information
- IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: uses and invents a variety of approaches and understands and evaluates those of others.NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: invokes problem solving strategies, such as illustrating with sense-making sketches to clarify situations or organizing information in a table.
Topic 17 - Problem Solving Obj. 248 - Model situations geometrically
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: determines, where helpful, how to break a problem into simpler parts.NYC M5.b.iv - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves for unknown or undecided quantities using algebra, graphing, sound reasoning, and other strategies.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M5.b.v - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: integrates concepts and techniques from different areas of mathematics.
NYC M5.b.vi - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: works effectively in teams when the nature of the task or the allotted time makes this an appropriate strategy.
- CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: verifies and interprets results with respect to the original problem situation.NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: generalizes solutions and strategies to new problem situations.
- MATHEMATICAL REASONINGNYC M5.d - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M5.d.i - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: formulates conjectures and argues why they must be or seem true.NYC M5.d.ii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes sensible, reasonable estimates.
Topic 2 - Whole Number Concepts Part 2
Obj. 26 - WP: Estimate products, round (2+ dig)
Obj. 33 - WP: Estimate quotients, compatible #s
Topic 4 - Decimals: Add and Subtract
Obj. 57 - WP: Round decimal sum & diff to nearest whole #Obj. 59 - WP: Round decimal sum & diff to greatest placeObj. 61 - WP: Front-end estimate decimal sums w/adjustment
Topic 5 - Decimals: Multiply and Divide
Obj. 81 - WP: Estimate decimal products, roundObj. 83 - WP: Estimate decimal quotients, compatible #s
Topic 7 - Fractions: Add and Subtract
Obj. 104 - WP: Estimate fraction sums, roundObj. 113 - WP: Estimate fraction differences, round
Topic 17 - Problem Solving Obj. 258 - Make/identify reasonable estimates
NYC M5.d.iii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes justified, logical statements.
NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task (perhaps referring to notes, or books, perhaps working to reconstruct a method); that is, the student:
NYC M6.a - Computes accurately with arithmetic operations on rational numbers.
Topic 2 - Whole Number Concepts Part 2
Obj. 15 - Add whole #s
Obj. 18 - Subtract whole #sObj. 21 - Multiply by 2 or more digObj. 23 - Multiply by a multiple of 10
Obj. 24 - Multiply by a power of 10Obj. 27 - Exponential notationObj. 28 - Evaluate exponentsObj. 29 - Multiply with exponentsObj. 30 - Divide whole #s (2+ dig divisor)
Topic 4 - Decimals: Add and Subtract
Obj. 48 - Add money expressions
Obj. 50 - Add decimalsObj. 52 - Subtract money expressionsObj. 54 - Subtract decimals
Topic 5 - Decimals: Multiply and Divide
Obj. 62 - Multiply money expressions by whole #sObj. 64 - Multiply decimals by whole #s (2-3 dig)Obj. 65 - Multiply decimals (to thousandths)Obj. 67 - Multiply decimals by a power of 10Obj. 69 - Divide money expressions by 2-digit whole #sObj. 71 - Divide decimals by 1- & 2-digit whole #sObj. 73 - Divide whole #s by powers of 10 (decimal answer)Obj. 74 - Divide decimals by powers of 10Obj. 76 - Divide whole #s by decimals
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
Obj. 78 - Divide decimals by decimals
Topic 7 - Fractions: Add and Subtract
Obj. 97 - Add like fractions
Obj. 98 - Add like fractions & mixed #sObj. 100 - Add unlike fractionsObj. 101 - Add unlike mixed #sObj. 105 - Subtract like fractionsObj. 106 - Subtract like mixed #sObj. 107 - Subtract unlike fractionsObj. 108 - Subtract unlike mixed #s, no regroupObj. 109 - Subtract mixed #s from whole #sObj. 110 - Subtract mixed #s, regroup
Topic 8 - Fractions: Multiply, Divide, and Combined Operations
Obj. 114 - Multiply fractions
Obj. 115 - Multiply fractions by whole #sObj. 117 - Multiply mixed #s by fractionsObj. 118 - Multiply mixed #sObj. 120 - Divide fractionsObj. 121 - Divide mixed #s by fractionsObj. 122 - Divide mixed #sObj. 123 - Divide whole #s & fractions
Topic 15 - Integers Obj. 232 - Add integersObj. 234 - Subtract positive integers
Obj. 235 - Subtract integersNYC M6.b - Knows and uses the correct order of operations for arithmetic computations.
Topic 2 - Whole Number Concepts Part 2
Obj. 29 - Multiply with exponents
Obj. 35 - Order of operationsObj. 36 - Simplify with grouping symbols
Topic 5 - Decimals: Multiply and Divide
Obj. 84 - Order of operations with decimals
NYC M6.c - Estimates numerically and spatially.
Topic 2 - Whole Number Concepts Part 2
Obj. 20 - Estimate whole # sums & differences, roundObj. 25 - Estimate products, round (3+ dig)Obj. 32 - Estimate quotients, compatible #s
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
Topic 4 - Decimals: Add and Subtract
Obj. 60 - Front-end estimate decimal sums w/adjustment
Topic 5 - Decimals: Multiply and Divide
Obj. 80 - Estimate decimal products, roundObj. 82 - Estimate decimal quotients, compatible #s
Topic 7 - Fractions: Add and Subtract
Obj. 103 - Estimate fraction sums, roundObj. 112 - Estimate fraction differences, round
Topic 8 - Fractions: Multiply, Divide, and Combined Operations
Obj. 125 - Estimate fraction products & quotients
Topic 17 - Problem Solving Obj. 258 - Make/identify reasonable estimates
NYC M6.d - Measures length, area, volume, weight, time, and temperature accurately.NYC M6.e - Refers to geometric shapes and terms correctly.
Topic 10 - Geometry Obj. 143 - Points, lines, segments, rays, & anglesObj. 144 - Intersecting, parallel, & perpendicular linesObj. 145 - Classify anglesObj. 147 - Identify polygonsObj. 148 - Classify quadrilateralsObj. 149 - Classify triangles by angles & sidesObj. 154 - Name 3-dimensional objectObj. 159 - Parts of a circle
NYC M6.f - Uses equations, formulas, and simple algebraic notation appropriately.
Topic 16 - Patterns, Expressions and Equations
Obj. 245 - Translate sentence to expression/equation
NYC M6.g - Reads and organizes data on charts and graphs, including scatter plots, bar, line, and circle graphs, and Venn diagrams; calculates mean and median.
Topic 12 - Graphs, Probability and Statistics
Obj. 184 - Bar graphs
Obj. 185 - Line graphsObj. 186 - Double bar graphsObj. 187 - Double line graphsObj. 188 - Circle graphsObj. 201 - Means of data setsObj. 202 - Medians of data sets
Topic 17 - Problem Solving Obj. 259 - Create Venn diagrams to solve problems
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions.
Topic 17 - Problem Solving Obj. 249 - Solve problems using calculator
NYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Uses mathematical language and representations with appropriate accuracy, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagrams.
Topic 16 - Patterns, Expressions and Equations
Obj. 241 - Variable expressions to word phrases
Obj. 242 - Equations to word sentencesObj. 245 - Translate sentence to expression/equation
NYC M7.b - Organizes work, explains facets of a solution orally and in writing, labels drawings, and uses other techniques to make meaning clear to the audience.NYC M7.c - Uses mathematical language to make complex situations easier to understand.NYC M7.d - Exhibits developing reasoning abilities by justifying statements and defending work.NYC M7.e - Shows understanding of concepts by explaining ideas not only to teachers and assessors but to fellow students or younger children.
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M7.f - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of middle school, conducts investigations or projects drawn from three of the kinds. A single investigation or project may draw on more than one kind.NYC M8.a - Data study based on civic, economic, or social issues, in which the student:NYC M8.a.i - Data study based on civic, economic, or social issues, in which the student: selects an issue to investigate.NYC M8.a.ii - Data study based on civic, economic, or social issues, in which the student: makes a hypothesis on an expected finding, if appropriate.NYC M8.a.iii - Data study based on civic, economic, or social issues, in which the student: gathers data.
NYC M8.a.iv - Data study based on civic, economic, or social issues, in which the student: analyzes the data using concepts from Standard 4, e.g., considering mean and median, and the frequency and distribution of the data.
NYC M8.a.v - Data study based on civic, economic, or social issues, in which the student: shows how the study’s results compare with the hypothesis.NYC M8.a.vi - Data study based on civic, economic, or social issues, in which the student: uses pertinent statistics to summarize.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M8.a.vii - Data study based on civic, economic, or social issues, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.b - Mathematical model of physical phenomena, often used in science studies, in which the student:
NYC M8.b.i - Mathematical model of physical phenomena, often used in science studies, in which the student: carries out a study of a physical system using a mathematical representation of the structure.
NYC M8.b.ii - Mathematical model of physical phenomena, often used in science studies, in which the student: uses understanding from Standard 3, particularly with respect to the determination of the function governing behavior in the model.
NYC M8.b.iii - Mathematical model of physical phenomena, often used in science studies, in which the student: generalizes about the structure with a rule, i.e., a function, that clearly applies to the phenomenon and goes beyond statistical analysis of a pattern of numbers generated by the situation.
NYC M8.b.iv - Mathematical model of physical phenomena, often used in science studies, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
NYC M8.c - Design of a physical structure, in which the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M8.c.i - Design of a physical structure, in which the student: generates a plan to build something of value, not necessarily monetary value.NYC M8.c.ii - Design of a physical structure, in which the student: uses mathematics from Standard 2 to make the design realistic or appropriate, e.g., areas and volumes in general and of specific geometric shapes.NYC M8.c.iii - Design of a physical structure, in which the student: summarizes the important features of the structure.NYC M8.c.iv - Design of a physical structure, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: determines the needs of the event to be managed or planned, e.g., cost, supply, scheduling.NYC M8.d.ii - Management and planning, in which the student: notes any constraints that will affect the plan.NYC M8.d.iii - Management and planning, in which the student: determines a plan.NYC M8.d.iv - Management and planning, in which the student: uses concepts from any of Standards 1 to 4, depending on the nature of the project.NYC M8.d.v - Management and planning, in which the student: considers the possibility of a more efficient solution.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 6
NYC M8.d.vi - Management and planning, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the plan.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: extends or "plays with," as with mathematical puzzles, some mathematical feature, e.g., properties and patterns in numbers.
NYC M8.e.ii - Pure mathematics investigation, in which the student: uses concepts from any of Standards 1 to 4, e.g., an investigation of Pascal’s triangle would have roots in Standard 1 but could tie in concepts from geometry, algebra, and probability; investigations of derivations of geometric formulas would be rooted in Standard 2 but could require algebra.
NYC M8.e.iii - Pure mathematics investigation, in which the student: determines and expresses generalizations from patterns.NYC M8.e.iv - Pure mathematics investigation, in which the student: makes conjectures on apparent properties and argues, short of formal proof, why they seem true.NYC M8.e.v - Pure mathematics investigation, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Consistently and accurately adds, subtracts, multiplies, and divides rational numbers using appropriate methods (e.g., the student can add (1/2) + (5/6) mentally or on paper but may opt to add (13/24) + (57/68) on a calculator) and raises rational numbers to whole number powers. (Students should have facility with the different kinds and forms of rational numbers, i.e., integers, both whole numbers and negative integers; and other positive and negative rationals, written as decimals, as percents, or as proper, improper, or mixed fractions. Irrational numbers, i.e., those that cannot be written as a ratio of two integers, are not required content but are suitable for introduction, especially since the student should be familiar with the irrational number (pi).)
Topic 1 - Whole Number Concepts
Obj. 9 - Multiply with exponents
Obj. 12 - Divide whole #s by a power of 10
Topic 2 - Decimals Obj. 33 - Multiply decimalsObj. 34 - Multiply decimals by a power of 10Obj. 35 - Multiply money expressions by whole #sObj. 37 - Divide decimals by whole #sObj. 38 - Divide decimals by a power of 10Obj. 39 - Divide money expressions by whole #sObj. 41 - Divide decimals by decimalsObj. 42 - Divide whole #s by decimals
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Obj. 46 - Add pos and neg decimals
Obj. 47 - Subtract pos and neg decimalsObj. 48 - Multiply pos and neg decimalsObj. 49 - Divide pos and neg decimals
Topic 3 - Fractions Obj. 56 - Add unlike fractionsObj. 57 - Add unlike mixed #sObj. 59 - Subtract unlike fractionsObj. 60 - Subtract unlike mixed #sObj. 61 - Subtract mixed #s from whole #sObj. 65 - Multiply fractionsObj. 66 - Multiply mixed #s by fractionsObj. 67 - Multiply mixed #sObj. 68 - Multiply fractions by whole #sObj. 70 - Divide fractionsObj. 71 - Divide mixed #s
Topic 10 - Integers Obj. 194 - Add integers using models
Obj. 195 - Add integersObj. 196 - Subtract integers using modelsObj. 197 - Subtract positive integers
Obj. 198 - Subtract integersObj. 200 - Multiply integersObj. 201 - Divide integers
NYC M1.b - Uses and understands the inverse relationships between addition and subtraction, multiplication and division, and exponentiation and root-extraction (e.g., squares and square roots, cubes and cube roots); uses the inverse operation to determine unknown quantities in equations.
Topic 1 - Whole Number Concepts
Obj. 10 - Square root of perfect squares
Topic 12 - Patterns, Functions, Expressions, and Equations
Obj. 220 - Solve addition & subtraction equations
NYC M1.c - Consistently and accurately applies and converts the different kinds and forms of rational numbers.
Topic 8 - Fractions, Percents, and Decimals
Obj. 161 - Decimals to mixed #s & fractions
Obj. 162 - Mixed #s to decimals
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Obj. 163 - Fractions to repeating decimals
Topic 11 - Number Representation
Obj. 204 - Negative/zero exponents as fraction/decimal
NYC M1.d - Is familiar with characteristics of numbers (e.g., divisibility, prime factorization) and with properties of operations (e.g., commutativity and associativity), short of formal statements.
Topic 1 - Whole Number Concepts
Obj. 1 - Prime & composite numbers
Obj. 2 - Factors of composite numbersObj. 3 - Divisibility rulesObj. 4 - Prime factorizationObj. 7 - Properties of addition & multiplication
NYC M1.e - Interprets percent as part of 100 and as a means of comparing quantities of different sizes or changing sizes.
Topic 9 - Percents, Ratios, and Proportions
Obj. 171 - Ratios as percents
Obj. 181 - Percent of decreaseObj. 182 - Percent of increaseObj. 183 - Percent of a number
NYC M1.f - Uses ratios and rates to express "part-to-part" and "whole-to-whole" relationships, and reasons proportionally to solve problems involving equivalent fractions, equal ratios, or constant rates, recognizing the multiplicative nature of these problems in the constant factor of change.
Topic 9 - Percents, Ratios, and Proportions
Obj. 169 - Ratios as fractions, lowest terms
Obj. 170 - Ratios as rates, lowest termsObj. 171 - Ratios as percentsObj. 173 - Unit ratesObj. 175 - Ratios as proportionsObj. 176 - Write ratios
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M1.g - Orders numbers with the > and < relationships and by location on a number line; estimates and compares rational numbers using sense of the magnitudes and relative magnitudes of numbers and of base-ten place values (e.g., recognizes relationships to "benchmark" numbers 1/2 and 1 to conclude that the sum 1/2)+ 5/6 must be between 1 and 1 (1/2) (likewise, (13/24) + (1/4)).
Topic 2 - Decimals Obj. 17 - Compare & order decimals
Topic 3 - Fractions Obj. 50 - Compare & order fractions
Topic 11 - Number Representation
Obj. 207 - Compare #s in scientific notation
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts in the following areas; that is, the student:
NYC M2.a - Is familiar with assorted two- and three-dimensional objects, including squares, triangles, other polygons, circles, cubes, rectangular prisms, pyramids, spheres, and cylinders.
Topic 5 - Geometry Obj. 89 - Identify polygons
Obj. 90 - Classify quadrilateralsObj. 91 - Classify triangles by angles & sidesObj. 99 - Classify plane or solid figuresObj. 101 - Solids
NYC M2.b - Identifies similar and congruent shapes and uses transformations in the coordinate plane, i.e., translations, rotations, and reflections.
Topic 5 - Geometry Obj. 92 - Congruent & similar figures
Obj. 107 - TranslationsObj. 108 - ReflectionsObj. 109 - Rotations
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M2.c - Identifies three dimensional shapes from two dimensional perspectives; draws two dimensional sketches of three dimensional objects that preserve significant features.NYC M2.d - Determines and understands length, area, and volume (as well as the differences among these measurements), including perimeter and surface area; uses units, square units, and cubic units of measure correctly; computes areas of rectangles, triangles, and circles; computes volumes of prisms.
Topic 6 - Perimeter, Area, and Volume
Obj. 113 - Perimeter of polygons
Obj. 114 - WP: Perimeter of polygons
Obj. 119 - Area of rectangles & squaresObj. 120 - WP: Areas of rectangles & squaresObj. 121 - Area of trapezoidsObj. 122 - Area of trianglesObj. 123 - Area of parallelogramsObj. 124 - Area of circlesObj. 125 - WP: Area of circlesObj. 127 - Volume of rectangular prisms & cubesObj. 128 - WP: Volume of rectangular prisms & cubesObj. 129 - Volume of triangular prismsObj. 132 - Surface area of triangular prismsObj. 133 - Surface area of cylinders
Obj. 134 - Surface area of rectangular prisms
NYC M2.e - Recognizes similarity and rotational and bilateral symmetry in two- and three-dimensional figures.
Topic 5 - Geometry Obj. 104 - Lines of symmetry
NYC M2.f - Analyzes and generalizes geometric patterns, such as tessellations and sequences of shapes.
Topic 12 - Patterns, Functions, Expressions, and Equations
Obj. 210 - Extend geometric patterns
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M2.g - Measures angles, weights, capacities, times, and temperatures using appropriate units.
Topic 5 - Geometry Obj. 87 - Measure angles
Topic 7 - Graphs, Probability, and Statistics
Obj. 143 - Time schedules
NYC M2.h - Chooses appropriate units of measure and converts with ease between like units, e.g., inches and miles, within a customary or metric system. (Conversions between customary and metric are not required.)
Topic 4 - Measurement Obj. 78 - Convert customary length
Obj. 79 - Convert customary weight
Obj. 80 - Convert customary capacity
Obj. 81 - Convert metric lengthObj. 82 - Convert metric weightObj. 83 - Convert metric capacity
Topic 9 - Percents, Ratios, and Proportions
Obj. 178 - Convert Currency
NYC M2.i - Reasons proportionally in situations with similar figures.NYC M2.j - Reasons proportionally with measurements to interpret maps and to make smaller and larger scale drawings.
Topic 9 - Percents, Ratios, and Proportions
Obj. 179 - Scale drawings
Obj. 180 - Use map scale to calculate distance
NYC M2.k - Models situations geometrically to formulate and solve problems.NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Discovers, describes, and generalizes patterns, including linear, exponential, and simple quadratic relationships, i.e., those of the form f(n)=n^2 or f(n)=cn^2, for constant c, including A = (pi)r^2, and represents them with variables and expressions.
Topic 12 - Patterns, Functions, Expressions, and Equations
Obj. 216 - Interpret graphs of linear functions
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M3.b - Represents relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules.
Topic 12 - Patterns, Functions, Expressions, and Equations
Obj. 212 - Function tables
NYC M3.c - Analyzes tables, graphs, and rules to determine functional relationships.NYC M3.d - Finds solutions for unknown quantities in linear equations and in simple equations and inequalities.
Topic 12 - Patterns, Functions, Expressions, and Equations
Obj. 219 - Identify solutions to equations
Obj. 220 - Solve addition & subtraction equationsObj. 221 - Solve multiplication & division equationsObj. 222 - Solve 2-step equationsObj. 223 - Solve multi-step equations
Obj. 224 - Solve inequalities, pos integer coefficientsObj. 225 - Solve inequalities, pos rational coefficientsObj. 226 - Solve inequalities, neg coefficients
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts; that is, the student:NYC M4.a - Collects data, organizes data, and displays data with tables, charts, and graphs that are appropriate, i.e., consistent with the nature of the data.
NYC M4.b - Analyzes data with respect to characteristics of frequency and distribution, including mode and range.
Topic 7 - Graphs, Probability, and Statistics
Obj. 155 - Means of data sets
Obj. 156 - Medians of data setsObj. 157 - Modes of data setsObj. 158 - Ranges of data sets
NYC M4.c - Analyzes appropriately central tendencies of data by considering mean and median.
Topic 7 - Graphs, Probability, and Statistics
Obj. 159 - Identify best measure of central tendency
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M4.d - Makes conclusions and recommendations based on data analysis.
Topic 7 - Graphs, Probability, and Statistics
Obj. 160 - Critique conclusions
NYC M4.e - Critiques the conclusions and recommendations of others’ statistics.
Topic 7 - Graphs, Probability, and Statistics
Obj. 160 - Critique conclusions
NYC M4.f - Considers the effects of missing or incorrect information.NYC M4.g - Formulates hypotheses to answer a question and uses data to test hypotheses.NYC M4.h - Represents and determines probability as a fraction of a set of equally likely outcomes; recognizes equally likely outcomes, and constructs sample spaces (including those described by numerical combinations and permutations).NYC M4.i - Makes predictions based on experimental or theoretical probabilities.
Topic 7 - Graphs, Probability, and Statistics
Obj. 148 - Probability of single events
Obj. 149 - Probability of complements of eventsObj. 150 - Probability of independent & dependent eventsObj. 151 - Probability of compound eventsObj. 152 - Odds of an event
NYC M4.j - Predicts the result of a series of trials once the probability for one trial is known.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion.
Topic 1 - Whole Number Concepts
Obj. 15 - WP: 2-step with whole #s
Topic 2 - Decimals Obj. 24 - WP: Round decimal sum & diff to nearest whole #Obj. 26 - WP: Round decimal sum & diff to greatest place
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Obj. 28 - WP: Front-end estimate decimal sums w/adjustmentObj. 30 - WP: Estimate decimal products, round
Topic 9 - Percents, Ratios, and Proportions
Obj. 184 - WP: Percent of a number
Obj. 186 - WP: Find total when percent is knownObj. 188 - WP: Find percent when total is knownObj. 189 - WP: DiscountsObj. 190 - WP: Simple interest
Topic 10 - Integers Obj. 199 - WP: Add & subtract integersObj. 202 - WP: Multiply & divide integers
- FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: formulates and solves a variety of meaningful problems.NYC M5.a.ii - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: extracts pertinent information from situations and figures out what additional information is needed. - IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: uses and invents a variety of approaches and understands and evaluates those of others.
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: invokes problem solving strategies, such as illustrating with sense-making sketches to clarify situations or organizing information in a table.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: determines, where helpful, how to break a problem into simpler parts.NYC M5.b.iv - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves for unknown or undecided quantities using algebra, graphing, sound reasoning, and other strategies.
NYC M5.b.v - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: integrates concepts and techniques from different areas of mathematics.
NYC M5.b.vi - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: works effectively in teams when the nature of the task or the allotted time makes this an appropriate strategy.
- CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: verifies and interprets results with respect to the original problem situation.NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: generalizes solutions and strategies to new problem situations.
- MATHEMATICAL REASONINGNYC M5.d - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student:NYC M5.d.i - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: formulates conjectures and argues why they must be or seem true.NYC M5.d.ii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes sensible, reasonable estimates.
NYC M5.d.iii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes justified, logical statements.
Topic 12 - Patterns, Functions, Expressions, and Equations
Obj. 209 - Missing terms in number patterns
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Obj. 210 - Extend geometric patterns
Topic 13 - Problem Solving Obj. 231 - Support conjecturesNYC M6 - MATHEMATICAL SKILLS AND TOOLSNYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task (perhaps referring to notes, or books, perhaps working to reconstruct a method); that is, the student:
NYC M6.a - Computes accurately with arithmetic operations on rational numbers.
Topic 1 - Whole Number Concepts
Obj. 9 - Multiply with exponents
Obj. 12 - Divide whole #s by a power of 10
Topic 2 - Decimals Obj. 33 - Multiply decimalsObj. 34 - Multiply decimals by a power of 10Obj. 35 - Multiply money expressions by whole #sObj. 37 - Divide decimals by whole #sObj. 38 - Divide decimals by a power of 10Obj. 39 - Divide money expressions by whole #sObj. 40 - WP: Divide money expressionsObj. 41 - Divide decimals by decimalsObj. 42 - Divide whole #s by decimalsObj. 43 - WP: Divide decimalsObj. 46 - Add pos and neg decimals
Obj. 47 - Subtract pos and neg decimalsObj. 48 - Multiply pos and neg decimalsObj. 49 - Divide pos and neg decimals
Topic 3 - Fractions Obj. 56 - Add unlike fractions
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Obj. 57 - Add unlike mixed #sObj. 58 - WP: Add fractions & mixed #sObj. 59 - Subtract unlike fractionsObj. 60 - Subtract unlike mixed #sObj. 61 - Subtract mixed #s from whole #sObj. 62 - WP: Subtract fractions & mixed #sObj. 65 - Multiply fractionsObj. 66 - Multiply mixed #s by fractionsObj. 67 - Multiply mixed #sObj. 68 - Multiply fractions by whole #sObj. 69 - WP: Multiply fractions & mixed #sObj. 70 - Divide fractionsObj. 71 - Divide mixed #sObj. 72 - WP: Divide fractions
Topic 10 - Integers Obj. 195 - Add integersObj. 196 - Subtract integers using modelsObj. 197 - Subtract positive integers
Obj. 198 - Subtract integersObj. 199 - WP: Add & subtract integersObj. 200 - Multiply integersObj. 201 - Divide integersObj. 202 - WP: Multiply & divide integers
NYC M6.b - Knows and uses the correct order of operations for arithmetic computations.
Topic 2 - Decimals Obj. 45 - Order of operations with decimals
NYC M6.c - Estimates numerically and spatially.
Topic 2 - Decimals Obj. 27 - Front-end estimate decimal sums w/adjustmentObj. 28 - WP: Front-end estimate decimal sums w/adjustmentObj. 29 - Estimate decimal products, roundObj. 30 - WP: Estimate decimal products, roundObj. 31 - Estimate decimal quotients, compatible #sObj. 32 - WP: Estimate decimal quotients, compatible #s
Topic 3 - Fractions Obj. 53 - Estimate fraction sum & diff, round
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
Obj. 54 - WP: Estimate fraction sums, roundObj. 55 - WP: Estimate fraction differences, roundObj. 63 - Estimate fraction products & quotientsObj. 64 - WP: Estimate fraction products & quotients
NYC M6.d - Measures length, area, volume, weight, time, and temperature accurately.NYC M6.e - Refers to geometric shapes and terms correctly.
Topic 5 - Geometry Obj. 86 - Classify angles
Obj. 89 - Identify polygonsObj. 90 - Classify quadrilateralsObj. 91 - Classify triangles by angles & sidesObj. 100 - Identify parts of right triangleObj. 103 - Count faces, edges, & vertices
NYC M6.f - Uses equations, formulas, and simple algebraic notation appropriately.NYC M6.g - Reads and organizes data on charts and graphs, including scatter plots, bar, line, and circle graphs, and Venn diagrams; calculates mean and median.
Topic 7 - Graphs, Probability, and Statistics
Obj. 135 - Bar graphs
Obj. 136 - Double line graphsObj. 137 - Circle graphsObj. 138 - Frequency tablesObj. 139 - Line plotsObj. 140 - HistogramsObj. 141 - Stem-and-leaf plotsObj. 142 - Box-and-whisker plotsObj. 155 - Means of data setsObj. 156 - Medians of data sets
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions.
NYC M7 - MATHEMATICAL COMMUNICATION
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Uses mathematical language and representations with appropriate accuracy, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagrams.NYC M7.b - Organizes work, explains facets of a solution orally and in writing, labels drawings, and uses other techniques to make meaning clear to the audience.NYC M7.c - Uses mathematical language to make complex situations easier to understand.NYC M7.d - Exhibits developing reasoning abilities by justifying statements and defending work.NYC M7.e - Shows understanding of concepts by explaining ideas not only to teachers and assessors but to fellow students or younger children.
NYC M7.f - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of middle school, conducts investigations or projects drawn from three of the kinds. A single investigation or project may draw on more than one kind.
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M8.a - Data study based on civic, economic, or social issues, in which the student:NYC M8.a.i - Data study based on civic, economic, or social issues, in which the student: selects an issue to investigate.NYC M8.a.ii - Data study based on civic, economic, or social issues, in which the student: makes a hypothesis on an expected finding, if appropriate.NYC M8.a.iii - Data study based on civic, economic, or social issues, in which the student: gathers data.
NYC M8.a.iv - Data study based on civic, economic, or social issues, in which the student: analyzes the data using concepts from Standard 4, e.g., considering mean and median, and the frequency and distribution of the data.
NYC M8.a.v - Data study based on civic, economic, or social issues, in which the student: shows how the study’s results compare with the hypothesis.NYC M8.a.vi - Data study based on civic, economic, or social issues, in which the student: uses pertinent statistics to summarize.NYC M8.a.vii - Data study based on civic, economic, or social issues, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.b - Mathematical model of physical phenomena, often used in science studies, in which the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M8.b.i - Mathematical model of physical phenomena, often used in science studies, in which the student: carries out a study of a physical system using a mathematical representation of the structure.
NYC M8.b.ii - Mathematical model of physical phenomena, often used in science studies, in which the student: uses understanding from Standard 3, particularly with respect to the determination of the function governing behavior in the model.
NYC M8.b.iii - Mathematical model of physical phenomena, often used in science studies, in which the student: generalizes about the structure with a rule, i.e., a function, that clearly applies to the phenomenon and goes beyond statistical analysis of a pattern of numbers generated by the situation.
NYC M8.b.iv - Mathematical model of physical phenomena, often used in science studies, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: generates a plan to build something of value, not necessarily monetary value.NYC M8.c.ii - Design of a physical structure, in which the student: uses mathematics from Standard 2 to make the design realistic or appropriate, e.g., areas and volumes in general and of specific geometric shapes.
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M8.c.iii - Design of a physical structure, in which the student: summarizes the important features of the structure.NYC M8.c.iv - Design of a physical structure, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: determines the needs of the event to be managed or planned, e.g., cost, supply, scheduling.NYC M8.d.ii - Management and planning, in which the student: notes any constraints that will affect the plan.NYC M8.d.iii - Management and planning, in which the student: determines a plan.NYC M8.d.iv - Management and planning, in which the student: uses concepts from any of Standards 1 to 4, depending on the nature of the project.NYC M8.d.v - Management and planning, in which the student: considers the possibility of a more efficient solution.NYC M8.d.vi - Management and planning, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the plan.NYC M8.e - Pure mathematics investigation, in which the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 7
NYC M8.e.i - Pure mathematics investigation, in which the student: extends or "plays with," as with mathematical puzzles, some mathematical feature, e.g., properties and patterns in numbers.
NYC M8.e.ii - Pure mathematics investigation, in which the student: uses concepts from any of Standards 1 to 4, e.g., an investigation of Pascal’s triangle would have roots in Standard 1 but could tie in concepts from geometry, algebra, and probability; investigations of derivations of geometric formulas would be rooted in Standard 2 but could require algebra.
NYC M8.e.iii - Pure mathematics investigation, in which the student: determines and expresses generalizations from patterns.NYC M8.e.iv - Pure mathematics investigation, in which the student: makes conjectures on apparent properties and argues, short of formal proof, why they seem true.NYC M8.e.v - Pure mathematics investigation, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Consistently and accurately adds, subtracts, multiplies, and divides rational numbers using appropriate methods (e.g., the student can add (1/2) + (5/6) mentally or on paper but may opt to add (13/24) + (57/68) on a calculator) and raises rational numbers to whole number powers. (Students should have facility with the different kinds and forms of rational numbers, i.e., integers, both whole numbers and negative integers; and other positive and negative rationals, written as decimals, as percents, or as proper, improper, or mixed fractions. Irrational numbers, i.e., those that cannot be written as a ratio of two integers, are not required content but are suitable for introduction, especially since the student should be familiar with the irrational number (pi).)
Topic 1 - Integers Obj. 5 - Add integers
Obj. 7 - Subtract integersObj. 11 - Multiply integersObj. 12 - Divide integers
Topic 3 - Rational Number Operations
Obj. 30 - Add decimals
Obj. 31 - Add fractions & mixed #sObj. 32 - Subtract decimalsObj. 33 - Subtract fractions & mixed #sObj. 34 - Multiply decimalsObj. 35 - Multiply fractions & mixed #sObj. 36 - Divide decimalsObj. 37 - Divide fractions & mixed #s
Obj. 38 - Operations w/fractions & mixed-numbers, pos/neg
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
Topic 7 - Roots and Exponents Obj. 94 - Square integersObj. 95 - Raise integers to power
NYC M1.b - Uses and understands the inverse relationships between addition and subtraction, multiplication and division, and exponentiation and root-extraction (e.g., squares and square roots, cubes and cube roots); uses the inverse operation to determine unknown quantities in equations.
Topic 1 - Integers Obj. 6 - Write a difference as a sum
Topic 5 - Linear Equations Obj. 59 - Solve 1-step eqns, add & subtract (integers)Obj. 60 - Solve 1-step eqns, add & subt (decimal & fraction)Obj. 63 - Solve 1-step eqns, multiply & divide by reciprocalObj. 64 - Solve 1-step eqns, multiply & divide (decimals)Obj. 66 - Solve 2-step eqns (integers)
Obj. 67 - Solve 2-step eqns (decimal & fraction)Obj. 69 - Solve multi-step equations
Topic 7 - Roots and Exponents Obj. 110 - Use square roots to solve equations
NYC M1.c - Consistently and accurately applies and converts the different kinds and forms of rational numbers.
Topic 1 - Integers Obj. 10 - WP: Add & subtract integers
Obj. 13 - WP: Multiply & divide integers
Topic 3 - Rational Number Operations
Obj. 41 - WP: Multiply & divide rational #sObj. 43 - WP: Add & subtract rational #s
Topic 8 - Ratio, Proportion, and Percent
Obj. 114 - WP: Proportions
Obj. 115 - Decimals to percentsObj. 116 - Fractions to percentsObj. 117 - Percents to decimalsObj. 118 - Percents to fractionsObj. 119 - Greater and lesser percentsObj. 121 - WP: Percents and taxes
Obj. 125 - WP: Percent
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
Obj. 126 - WP: Discount or markup
Obj. 127 - WP: Percent changeObj. 128 - WP: Simple interestObj. 129 - WP: Commission, Interest, Gratuities
NYC M1.d - Is familiar with characteristics of numbers (e.g., divisibility, prime factorization) and with properties of operations (e.g., commutativity and associativity), short of formal statements.
Topic 1 - Integers Obj. 3 - Opposites of integers
Topic 2 - Number Theory Obj. 15 - Divisibility rulesObj. 16 - Prime & composite numbersObj. 17 - Prime factorizationObj. 18 - Greatest common factorObj. 19 - Least common multiple
Topic 4 - Variables, Expressions, and Functions
Obj. 46 - Properties of addition & multiplicationObj. 47 - Distributive property with variables
NYC M1.e - Interprets percent as part of 100 and as a means of comparing quantities of different sizes or changing sizes.NYC M1.f - Uses ratios and rates to express "part-to-part" and "whole-to-whole" relationships, and reasons proportionally to solve problems involving equivalent fractions, equal ratios, or constant rates, recognizing the multiplicative nature of these problems in the constant factor of change.
Topic 8 - Ratio, Proportion, and Percent
Obj. 111 - Ratios as fractions, lowest terms
Obj. 112 - Word statements to proportionsObj. 113 - Solve proportionsObj. 114 - WP: Proportions
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M1.g - Orders numbers with the > and < relationships and by location on a number line; estimates and compares rational numbers using sense of the magnitudes and relative magnitudes of numbers and of base-ten place values (e.g., recognizes relationships to "benchmark" numbers 1/2 and 1 to conclude that the sum 1/2)+ 5/6 must be between 1 and 1 (1/2) (likewise, (13/24) + (1/4)).
Topic 1 - Integers Obj. 1 - Graph integers on number lines
Obj. 2 - Compare & order integersTopic 3 - Rational Number Operations
Obj. 27 - Compare & order decimals
Obj. 29 - Compare & order fractions
Topic 8 - Ratio, Proportion, and Percent
Obj. 123 - WP: Estimate the percent of a quantity
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts in the following areas; that is, the student:
NYC M2.a - Is familiar with assorted two- and three-dimensional objects, including squares, triangles, other polygons, circles, cubes, rectangular prisms, pyramids, spheres, and cylinders.
Topic 11 - Geometry Obj. 162 - Identify polygons & quadrilaterals
Obj. 163 - SolidsObj. 164 - Nets for solidsObj. 173 - Classify angles & triangles
NYC M2.b - Identifies similar and congruent shapes and uses transformations in the coordinate plane, i.e., translations, rotations, and reflections.
Topic 11 - Geometry Obj. 166 - Transl, rot, refl, & dilations
Obj. 174 - Similarity & congruence
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M2.c - Identifies three dimensional shapes from two dimensional perspectives; draws two dimensional sketches of three dimensional objects that preserve significant features.
Topic 11 - Geometry Obj. 164 - Nets for solids
Obj. 165 - Isometric & orthographic drawings
NYC M2.d - Determines and understands length, area, and volume (as well as the differences among these measurements), including perimeter and surface area; uses units, square units, and cubic units of measure correctly; computes areas of rectangles, triangles, and circles; computes volumes of prisms.
Topic 13 - Perimeter, Area, and Volume
Obj. 183 - Perimeter of quadrilaterals
Obj. 184 - WP: PerimeterObj. 185 - Circumference of circlesObj. 187 - Area of rectangles & squaresObj. 188 - Area of parallelogramsObj. 189 - Area of trianglesObj. 191 - Area of circlesObj. 192 - Surface area of prismsObj. 195 - Volume of rectangular solids
NYC M2.e - Recognizes similarity and rotational and bilateral symmetry in two- and three-dimensional figures.
NYC M2.f - Analyzes and generalizes geometric patterns, such as tessellations and sequences of shapes.
Topic 2 - Number Theory Obj. 23 - Write expression describing a pattern
NYC M2.g - Measures angles, weights, capacities, times, and temperatures using appropriate units.
Topic 11 - Geometry Obj. 157 - Measure, draw, & name angles
NYC M2.h - Chooses appropriate units of measure and converts with ease between like units, e.g., inches and miles, within a customary or metric system. (Conversions between customary and metric are not required.)
Topic 12 - Measurement Obj. 177 - Convert customary units
Obj. 178 - Convert metric unitsObj. 179 - Convert complex units
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M2.i - Reasons proportionally in situations with similar figures.
Topic 11 - Geometry Obj. 175 - Similar triangles & proportions
NYC M2.j - Reasons proportionally with measurements to interpret maps and to make smaller and larger scale drawings.
Topic 12 - Measurement Obj. 182 - Scale drawings
NYC M2.k - Models situations geometrically to formulate and solve problems.
Topic 11 - Geometry Obj. 176 - WP: Similar triangles & proportions
NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Discovers, describes, and generalizes patterns, including linear, exponential, and simple quadratic relationships, i.e., those of the form f(n)=n^2 or f(n)=cn^2, for constant c, including A = (pi)r^2, and represents them with variables and expressions.
Topic 2 - Number Theory Obj. 23 - Write expression describing a pattern
Topic 4 - Variables, Expressions, and Functions
Obj. 53 - Function tables
NYC M3.b - Represents relationships with tables, graphs in the coordinate plane, and verbal or symbolic rules.
Topic 4 - Variables, Expressions, and Functions
Obj. 44 - Word phrases to algebraic expressions
Obj. 56 - Multiple representations of linear equations
Topic 5 - Linear Equations Obj. 74 - Graph lines from standard formObj. 77 - Determine graph from equation or situation
Topic 6 - Linear Inequalities Obj. 92 - Graph linear inequalities (coordinate plane)
NYC M3.c - Analyzes tables, graphs, and rules to determine functional relationships.
Topic 4 - Variables, Expressions, and Functions
Obj. 54 - Determine if a relation is a function
NYC M3.d - Finds solutions for unknown quantities in linear equations and in simple equations and inequalities.
Topic 5 - Linear Equations Obj. 58 - Verify solutions to equations
Obj. 59 - Solve 1-step eqns, add & subtract (integers)Obj. 60 - Solve 1-step eqns, add & subt (decimal & fraction)
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
Obj. 63 - Solve 1-step eqns, multiply & divide by reciprocalObj. 64 - Solve 1-step eqns, multiply & divide (decimals)Obj. 66 - Solve 2-step eqns (integers)
Obj. 67 - Solve 2-step eqns (decimal & fraction)Obj. 82 - Verify solutions to linear equations
Topic 6 - Linear Inequalities Obj. 85 - Solve 1-step inequalitiesNYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student produces evidence that demonstrates understanding of statistics and probability concepts; that is, the student:NYC M4.a - Collects data, organizes data, and displays data with tables, charts, and graphs that are appropriate, i.e., consistent with the nature of the data.
Topic 9 - Statistics and Graphs Obj. 136 - Histograms
NYC M4.b - Analyzes data with respect to characteristics of frequency and distribution, including mode and range.
Topic 9 - Statistics and Graphs Obj. 139 - Box-and-whisker plots
NYC M4.c - Analyzes appropriately central tendencies of data by considering mean and median.
Topic 9 - Statistics and Graphs Obj. 130 - Means, medians, modes, & ranges for data sets
NYC M4.d - Makes conclusions and recommendations based on data analysis.
Topic 9 - Statistics and Graphs Obj. 141 - Analyze conclusions from data, graphs
NYC M4.e - Critiques the conclusions and recommendations of others’ statistics.NYC M4.f - Considers the effects of missing or incorrect information.
Topic 9 - Statistics and Graphs Obj. 140 - Misleading graphs
NYC M4.g - Formulates hypotheses to answer a question and uses data to test hypotheses.
Topic 9 - Statistics and Graphs Obj. 142 - Use data to test hypotheses
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M4.h - Represents and determines probability as a fraction of a set of equally likely outcomes; recognizes equally likely outcomes, and constructs sample spaces (including those described by numerical combinations and permutations).
Topic 10 - Probability Obj. 150 - Probability of single events
NYC M4.i - Makes predictions based on experimental or theoretical probabilities.NYC M4.j - Predicts the result of a series of trials once the probability for one trial is known.
Topic 10 - Probability Obj. 155 - Experimental and sample-based probability
NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion. - FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: formulates and solves a variety of meaningful problems.NYC M5.a.ii - The student participates in the formulation of problems; that is, given the basic statement of a problem situation, the student: extracts pertinent information from situations and figures out what additional information is needed. - IMPLEMENTATION
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: uses and invents a variety of approaches and understands and evaluates those of others.NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: invokes problem solving strategies, such as illustrating with sense-making sketches to clarify situations or organizing information in a table.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: determines, where helpful, how to break a problem into simpler parts.NYC M5.b.iv - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: solves for unknown or undecided quantities using algebra, graphing, sound reasoning, and other strategies.
Topic 3 - Rational Number Operations
Obj. 41 - WP: Multiply & divide rational #s
Topic 5 - Linear Equations Obj. 68 - WP: Solve multi-step equations
Topic 6 - Linear Inequalities Obj. 89 - WP: InequalitiesTopic 8 - Ratio, Proportion, and Percent
Obj. 114 - WP: Proportions
Obj. 121 - WP: Percents and taxes
Obj. 125 - WP: PercentObj. 126 - WP: Discount or markup
Obj. 127 - WP: Percent changeObj. 128 - WP: Simple interestObj. 129 - WP: Commission, Interest, Gratuities
Topic 10 - Probability Obj. 148 - WP: Permutations
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
Obj. 149 - WP: CombinationsTopic 11 - Geometry Obj. 161 - WP: Angles formed by
transversalObj. 176 - WP: Similar triangles & proportions
Topic 13 - Perimeter, Area, and Volume
Obj. 194 - WP: Area
Obj. 200 - WP: VolumeTopic 14 - Right Triangles Obj. 203 - WP: Pythagorean
TheoremTopic 16 - Problem Solving Obj. 223 - Use similar problem or
partial steps to solve probObj. 224 - Work backward to solve a problemObj. 225 - Use guess & check, drawing, patterns, simpler probObj. 226 - Solve problems with given constraints
NYC M5.b.v - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: integrates concepts and techniques from different areas of mathematics.
NYC M5.b.vi - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: works effectively in teams when the nature of the task or the allotted time makes this an appropriate strategy.
- CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: verifies and interprets results with respect to the original problem situation.
Accelerated Math Grades 5 - 8
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Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: generalizes solutions and strategies to new problem situations.
- MATHEMATICAL REASONINGNYC M5.d - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student:NYC M5.d.i - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: formulates conjectures and argues why they must be or seem true.NYC M5.d.ii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes sensible, reasonable estimates.
Topic 3 - Rational Number Operations
Obj. 42 - WP: Estimate rational #s
Topic 8 - Ratio, Proportion, and Percent
Obj. 123 - WP: Estimate the percent of a quantity
NYC M5.d.iii - The student demonstrates mathematical reasoning by generalizing patterns, making conjectures and explaining why they seem true, and by making sensible, justifiable statements; that is, the student: makes justified, logical statements.
NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task (perhaps referring to notes, or books, perhaps working to reconstruct a method); that is, the student:
NYC M6.a - Computes accurately with arithmetic operations on rational numbers.
Topic 1 - Integers Obj. 5 - Add integers
Obj. 7 - Subtract integersObj. 10 - WP: Add & subtract integersObj. 11 - Multiply integersObj. 12 - Divide integersObj. 13 - WP: Multiply & divide integers
Topic 3 - Rational Number Operations
Obj. 30 - Add decimals
Obj. 31 - Add fractions & mixed #sObj. 32 - Subtract decimalsObj. 33 - Subtract fractions & mixed #sObj. 34 - Multiply decimalsObj. 35 - Multiply fractions & mixed #sObj. 36 - Divide decimalsObj. 37 - Divide fractions & mixed #s
Obj. 38 - Operations w/fractions & mixed-numbers, pos/negObj. 41 - WP: Multiply & divide rational #sObj. 43 - WP: Add & subtract rational #s
Topic 4 - Variables, Expressions, and Functions
Obj. 48 - Evaluate expressions
Topic 7 - Roots and Exponents Obj. 95 - Raise integers to powerObj. 96 - Evaluate expressions with exponents
NYC M6.b - Knows and uses the correct order of operations for arithmetic computations.
Topic 1 - Integers Obj. 14 - Order of operations with integers
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M6.c - Estimates numerically and spatially.
Topic 3 - Rational Number Operations
Obj. 40 - Estimate rational #s
Obj. 42 - WP: Estimate rational #sTopic 8 - Ratio, Proportion, and Percent
Obj. 123 - WP: Estimate the percent of a quantity
NYC M6.d - Measures length, area, volume, weight, time, and temperature accurately.NYC M6.e - Refers to geometric shapes and terms correctly.
Topic 11 - Geometry Obj. 162 - Identify polygons & quadrilateralsObj. 163 - SolidsObj. 173 - Classify angles & triangles
NYC M6.f - Uses equations, formulas, and simple algebraic notation appropriately.
Topic 2 - Number Theory Obj. 23 - Write expression describing a pattern
Topic 4 - Variables, Expressions, and Functions
Obj. 44 - Word phrases to algebraic expressions
Topic 6 - Linear Inequalities Obj. 84 - Translate with inequalities
NYC M6.g - Reads and organizes data on charts and graphs, including scatter plots, bar, line, and circle graphs, and Venn diagrams; calculates mean and median.
Topic 9 - Statistics and Graphs Obj. 130 - Means, medians, modes, & ranges for data sets
Obj. 134 - Bar graphsObj. 136 - HistogramsObj. 137 - Circle graphsObj. 138 - Stem-and-leaf plots
NYC M6.h - Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions.
NYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M7.a - Uses mathematical language and representations with appropriate accuracy, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs, and diagrams.NYC M7.b - Organizes work, explains facets of a solution orally and in writing, labels drawings, and uses other techniques to make meaning clear to the audience.NYC M7.c - Uses mathematical language to make complex situations easier to understand.NYC M7.d - Exhibits developing reasoning abilities by justifying statements and defending work.NYC M7.e - Shows understanding of concepts by explaining ideas not only to teachers and assessors but to fellow students or younger children.
NYC M7.f - Comprehends mathematics from reading assignments and from other sources.
NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of middle school, conducts investigations or projects drawn from three of the kinds. A single investigation or project may draw on more than one kind.NYC M8.a - Data study based on civic, economic, or social issues, in which the student:NYC M8.a.i - Data study based on civic, economic, or social issues, in which the student: selects an issue to investigate.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M8.a.ii - Data study based on civic, economic, or social issues, in which the student: makes a hypothesis on an expected finding, if appropriate.NYC M8.a.iii - Data study based on civic, economic, or social issues, in which the student: gathers data.
NYC M8.a.iv - Data study based on civic, economic, or social issues, in which the student: analyzes the data using concepts from Standard 4, e.g., considering mean and median, and the frequency and distribution of the data.
Topic 9 - Statistics and Graphs Obj. 130 - Means, medians, modes, & ranges for data sets
Obj. 133 - Frequency distributions & line plots
NYC M8.a.v - Data study based on civic, economic, or social issues, in which the student: shows how the study’s results compare with the hypothesis.NYC M8.a.vi - Data study based on civic, economic, or social issues, in which the student: uses pertinent statistics to summarize.NYC M8.a.vii - Data study based on civic, economic, or social issues, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.b - Mathematical model of physical phenomena, often used in science studies, in which the student:
NYC M8.b.i - Mathematical model of physical phenomena, often used in science studies, in which the student: carries out a study of a physical system using a mathematical representation of the structure.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M8.b.ii - Mathematical model of physical phenomena, often used in science studies, in which the student: uses understanding from Standard 3, particularly with respect to the determination of the function governing behavior in the model.
NYC M8.b.iii - Mathematical model of physical phenomena, often used in science studies, in which the student: generalizes about the structure with a rule, i.e., a function, that clearly applies to the phenomenon and goes beyond statistical analysis of a pattern of numbers generated by the situation.
NYC M8.b.iv - Mathematical model of physical phenomena, often used in science studies, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: generates a plan to build something of value, not necessarily monetary value.NYC M8.c.ii - Design of a physical structure, in which the student: uses mathematics from Standard 2 to make the design realistic or appropriate, e.g., areas and volumes in general and of specific geometric shapes.NYC M8.c.iii - Design of a physical structure, in which the student: summarizes the important features of the structure.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M8.c.iv - Design of a physical structure, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.NYC M8.d - Management and planning, in which the student:NYC M8.d.i - Management and planning, in which the student: determines the needs of the event to be managed or planned, e.g., cost, supply, scheduling.NYC M8.d.ii - Management and planning, in which the student: notes any constraints that will affect the plan.NYC M8.d.iii - Management and planning, in which the student: determines a plan.NYC M8.d.iv - Management and planning, in which the student: uses concepts from any of Standards 1 to 4, depending on the nature of the project.NYC M8.d.v - Management and planning, in which the student: considers the possibility of a more efficient solution.NYC M8.d.vi - Management and planning, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the plan.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: extends or "plays with," as with mathematical puzzles, some mathematical feature, e.g., properties and patterns in numbers.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 5-8, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Grade 8
NYC M8.e.ii - Pure mathematics investigation, in which the student: uses concepts from any of Standards 1 to 4, e.g., an investigation of Pascal’s triangle would have roots in Standard 1 but could tie in concepts from geometry, algebra, and probability; investigations of derivations of geometric formulas would be rooted in Standard 2 but could require algebra.
NYC M8.e.iii - Pure mathematics investigation, in which the student: determines and expresses generalizations from patterns.
Topic 2 - Number Theory Obj. 23 - Write expression describing a pattern
NYC M8.e.iv - Pure mathematics investigation, in which the student: makes conjectures on apparent properties and argues, short of formal proof, why they seem true.NYC M8.e.v - Pure mathematics investigation, in which the student: prepares a presentation or report that includes the question investigated, a detailed description of how the project was carried out, and an explanation of the findings.
Accelerated Math Grades 5 - 8
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Uses addition, subtraction, multiplication, division, exponentiation, and root-extraction in forming and working with numerical and algebraic expressions.
Topic 3 - Exponents Obj. 41 - Evaluate expressions, positive exponents
Topic 6 - Polynomial Operations Obj. 92 - Add polynomials
Obj. 93 - Subtract polynomialsObj. 94 - Add/subtract 3 polynomials
Obj. 96 - Multiply monomials by polynomialsObj. 97 - Multiply 2 binomials, (x + a)(x + b)Obj. 98 - Multiply 2 binomials, (ax + b)(cx + d)Obj. 99 - Multiply 2 binomials, (ax + by)(cx + dy)Obj. 100 - Square a binomialObj. 102 - Multiply binomials by trinomialsObj. 103 - Cube binomials, (x + a)Obj. 104 - Expand binomialsObj. 105 - Simplify rational expr containing polynomialObj. 106 - Multiply, divide monomials w/ common base (variables, integers exponents)Obj. 107 - Divide polynomials by monomialsObj. 108 - Divide polynomials by binomialsObj. 109 - Divide polynomials by quadratics
Topic 8 - Relations and Functions
Obj. 132 - Add, sub, mult, & div functions
Topic 12 - Rational Expressions and Equations
Obj. 177 - Rational expr, rewrite with given denominatorObj. 179 - Multiply rational expressions
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 180 - Divide rational expressions
Obj. 181 - Multiply & divide 3 rational expressionsObj. 182 - Add rational expressions (like denominators)Obj. 183 - Add rational expressions
Obj. 184 - Subtract rational expressions (like denominators)Obj. 185 - Subtract rational expressionsObj. 187 - Solve equations containing rational expressionsObj. 189 - Algebraic proportions (linear, quadratic solns)
NYC M1.b - Understands and uses operations such as opposite, reciprocal, raising to a power, taking a root, and taking a logarithm.
Topic 2 - Introduction to Algebra Obj. 30 - Additive inverses of rational #s
Obj. 31 - Reciprocals of rational #sTopic 9 - Quadratic Equations Obj. 135 - Solve quadratic eqns,
square root ruleNYC M1.c - Has facility with the mechanics of operations as well as understanding of their typical meaning and uses in applications.
Topic 1 - Integers and Rational Numbers
Obj. 10 - Distributive property
Obj. 11 - Order of operationsObj. 12 - Order of operations with grouping
Topic 2 - Introduction to Algebra Obj. 29 - Absolute values of real #s
Topic 3 - Exponents Obj. 40 - Write repeated mult as powerObj. 44 - Simplify expressions using properties of exponentsObj. 50 - Division & power properties of exponentsObj. 51 - WP: Evaluate exponential expressions
NYC M1.d - Understands and uses number systems: natural, integer, rational, and real.
Topic 2 - Introduction to Algebra Obj. 28 - Order real #s
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M1.e - Represents numbers in decimal or fraction form and in scientific notation, and graphs numbers on the number line and number pairs in the coordinate plane.
Topic 1 - Integers and Rational Numbers
Obj. 1 - Graph integers on number lines
Obj. 2 - Interpret scientific calculator displays
Topic 5 - Graph and Write Linear Equations
Obj. 66 - Graph ordered pairs
NYC M1.f - Compares numbers using order relations, differences, ratios, proportions, percents, and proportional change.
Topic 2 - Introduction to Algebra Obj. 28 - Order real #s
Topic 14 - Ratio and Proportion Obj. 201 - Ratios as fractions, lowest termsObj. 202 - Equivalent ratiosObj. 205 - Ratios as proportions
NYC M1.g - Carries out proportional reasoning in cases involving part-whole relationships and in cases involving expansions and contractions.
Topic 14 - Ratio and Proportion Obj. 201 - Ratios as fractions, lowest terms
Obj. 202 - Equivalent ratiosObj. 203 - Unit ratesObj. 205 - Ratios as proportionsObj. 206 - Word statements to proportionsObj. 207 - Solve proportionsObj. 208 - WP: Solve proportionsObj. 209 - Solve direct & indirect variation problems
NYC M1.h - Understands dimensionless numbers, such as proportions, percents, and multiplicative factors, as well as numbers with specific units of measure, such as numbers with length, time, and rate units.
Topic 14 - Ratio and Proportion Obj. 201 - Ratios as fractions, lowest terms
Obj. 203 - Unit ratesObj. 205 - Ratios as proportions
Topic 15 - Data and Statistics Obj. 232 - Percentile rankNYC M1.i - Carries out counting procedures such as those involving sets (unions and intersections) and arrangements (permutations and combinations).
Topic 1 - Integers and Rational Numbers
Obj. 24 - Complement of a given subset
Obj. 25 - Union and intersection of sets
Accelerated Math Grades 9 - 10
091207Page 159 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Topic 15 - Data and Statistics Obj. 234 - Determine number of outcomes/eventsObj. 235 - Permutations
NYC M1.j - Uses concepts such as prime, relatively prime, factor, divisor, multiple, and divisibility in solving problems involving integers.
Topic 1 - Integers and Rational Numbers
Obj. 7 - WP: Multiply integers
NYC M1.k - Uses a scientific calculator effectively and efficiently in carrying out complex calculations.
Topic 1 - Integers and Rational Numbers
Obj. 2 - Interpret scientific calculator displays
NYC M1.l - Recognizes and represents basic number patterns, such as patterns involving multiples, squares, or cubes.
Topic 8 - Relations and Functions
Obj. 133 - Patterns and their equations
NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:NYC M2.a - Models situations geometrically to formulate and solve problems.
Topic 5 - Graph and Write Linear Equations
Obj. 73 - Plot points to write or graph eqns
Topic 8 - Relations and Functions
Obj. 134 - Identify function type from graph
Topic 9 - Quadratic Equations Obj. 142 - Graph to find quadratic roots
Topic 11 - Inequalities and Absolute Value
Obj. 168 - Solve & graph inequalities
Obj. 169 - Solve & graph compound inequalities
NYC M2.b - Works with two- and three-dimensional figures and their properties, including polygons and circles, cubes and pyramids, and cylinders, cones, and spheres.
Topic 9 - Quadratic Equations Obj. 146 - WP: Pythagorean problems
Topic 16 - Measurement Obj. 240 - Find angle measure in right triangle, given sidesObj. 241 - Find side of right triangle, given 1 angle/1 side
NYC M2.c - Uses congruence and similarity in describing relationships between figures.
Accelerated Math Grades 9 - 10
091207Page 160 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M2.d - Visualizes objects, paths, and regions in space, including intersections and cross sections of three dimensional figures, and describes these using geometric language.NYC M2.e - Knows, uses, and derives formulas for perimeter, circumference, area, surface area, and volume of many types of figures.
Topic 9 - Quadratic Equations Obj. 148 - WP: Area & perimeter
NYC M2.f - Uses the Pythagorean Theorem in many types of situations, and works through more than one proof of this theorem.
Topic 9 - Quadratic Equations Obj. 146 - WP: Pythagorean problems
NYC M2.g - Works with similar triangles, and extends the ideas to include simple uses of the three basic trigonometric functions.NYC M2.h - Analyzes figures in terms of their symmetries using, for example, concepts of reflection, rotation, and translation.NYC M2.i - Compares slope (rise over run) and angle of elevation as measures of steepness.
Topic 5 - Graph and Write Linear Equations
Obj. 68 - Find slopes from 2 points
Obj. 69 - Find slopes from a graphNYC M2.j - Investigates geometric patterns, including sequences of growing shapes.
Topic 8 - Relations and Functions
Obj. 133 - Patterns and their equations
NYC M2.k - Works with geometric measures of length, area, volume, and angle; and non-geometric measures such as weight and time.
Topic 16 - Measurement Obj. 236 - Enlargement: Surface area and volume
Obj. 237 - Conversion within meas systemsObj. 238 - Relative error in square, cubic unitsObj. 239 - Find sin/cos/tan ratiosObj. 240 - Find angle measure in right triangle, given sidesObj. 241 - Find side of right triangle, given 1 angle/1 side
NYC M2.l - Uses quotient measures, such as speed and density, that give "per unit" amounts; and uses product measures, such as person-hours.
Topic 14 - Ratio and Proportion Obj. 203 - Unit rates
Accelerated Math Grades 9 - 10
091207Page 161 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M2.m - Understands the structure of standard measurement systems, both SI and customary, including unit conversions and dimensional analysis.
Topic 16 - Measurement Obj. 237 - Conversion within meas systems
NYC M2.n - Solves problems involving scale, such as in maps and diagrams.NYC M2.o - Represents geometric curves and graphs of functions in standard coordinate systems.NYC M2.p - Analyzes geometric figures and proves simple things about them using deductive methods.
NYC M2.q - Explores geometry using computer programs such as CAD software, Sketchpad programs, or LOGO.NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Models given situations with formulas and functions, and interprets given formulas and functions in terms of situations.
Topic 9 - Quadratic Equations Obj. 141 - Graph quadratic equations
Obj. 146 - WP: Pythagorean problemsObj. 147 - WP: Number problemsObj. 148 - WP: Area & perimeter
Topic 10 - Systems of Equations Obj. 156 - WP: Solve systems, number problemsObj. 157 - WP: Solve systems, motion problemsObj. 158 - WP: Solve systems, age problemsObj. 159 - WP: Solve systems, investment problemsObj. 160 - WP: Solve systems, mixture problems
Topic 11 - Inequalities and Absolute Value
Obj. 164 - WP: Solve 1-var inequalitiesObj. 166 - WP: Identify absolute value inequalities
Accelerated Math Grades 9 - 10
091207Page 162 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 175 - WP: Solve 2-var ineq using linear programming
Topic 12 - Rational Expressions and Equations
Obj. 188 - WP: Rational expressions
Topic 13 - Radical Expressions and Equations
Obj. 199 - WP: Solve radical equations
Topic 14 - Ratio and Proportion Obj. 204 - WP: Calculate ratesNYC M3.b - Describes, generalizes, and uses basic types of functions: linear, exponential, power, rational, square and square root, and cube and cube root.
Topic 8 - Relations and Functions
Obj. 123 - Domain & range, relations & functions
Obj. 125 - Determine if functions are one-to-oneObj. 130 - Find specified values of functionsObj. 134 - Identify function type from graph
Topic 11 - Inequalities and Absolute Value
Obj. 174 - Max or min functions with constraints
NYC M3.c - Utilizes the concepts of slope, evaluation, and inverse in working with functions.
Topic 5 - Graph and Write Linear Equations
Obj. 70 - Find slopes from equations
Obj. 74 - Write eqns in standard/slope-intercept formObj. 75 - Write eqns given slope & y-intObj. 82 - Graph lines, slope-intercept form
Topic 8 - Relations and Functions
Obj. 129 - Find inverses of relations
NYC M3.d - Works with rates of many kinds, expressed numerically, symbolically, and graphically.
Topic 5 - Graph and Write Linear Equations
Obj. 71 - Slope as rate of change btw indep./dep. variables
Topic 14 - Ratio and Proportion Obj. 203 - Unit ratesObj. 204 - WP: Calculate ratesObj. 209 - Solve direct & indirect variation problems
NYC M3.e - Represents constant rates as the slope of a straight line graph, and interprets slope as the amount of one quantity (y) per unit amount of another (x).
Topic 5 - Graph and Write Linear Equations
Obj. 68 - Find slopes from 2 points
Obj. 71 - Slope as rate of change btw indep./dep. variables
Accelerated Math Grades 9 - 10
091207Page 163 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M3.f - Understands and uses linear functions as a mathematical representation of proportional relationships.
Topic 4 - Solving Linear Equations
Obj. 64 - WP: Mixture problems
NYC M3.g - Uses arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively.
Topic 8 - Relations and Functions
Obj. 133 - Patterns and their equations
NYC M3.h - Defines, uses, and manipulates expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities.
Topic 2 - Introduction to Algebra Obj. 35 - Algebraic expressions vs. algebraic equations
Topic 3 - Exponents Obj. 41 - Evaluate expressions, positive exponentsObj. 44 - Simplify expressions using properties of exponentsObj. 47 - Divide expressions with positive exponents
Topic 12 - Rational Expressions and Equations
Obj. 186 - Simplify complex fractions
Topic 13 - Radical Expressions and Equations
Obj. 190 - Radical expressions, simplifyObj. 193 - Radical expressions, multiply then simplifyObj. 194 - Radical expressions, multiply 2 binomialsObj. 195 - Radical expressions, divide
NYC M3.i - Represents functional relationships in formulas, tables, and graphs, and translates between pairs of these.
Topic 5 - Graph and Write Linear Equations
Obj. 87 - Graph absolute value equations
Topic 8 - Relations and Functions
Obj. 133 - Patterns and their equations
Topic 9 - Quadratic Equations Obj. 141 - Graph quadratic equations
NYC M3.j - Solves equations symbolically, graphically, and numerically, especially linear, quadratic, and exponential equations; and knows how to use the quadratic formula for solving quadratic equations.
Topic 3 - Exponents Obj. 51 - WP: Evaluate exponential expressions
Topic 4 - Solving Linear Equations
Obj. 57 - Solve 1-step eqns, add & subtract
Accelerated Math Grades 9 - 10
091207Page 164 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 58 - Solve 1-step eqns, multiply & divideObj. 59 - Solve multi-step equations
Obj. 60 - Solve eqns, combine like termsObj. 61 - Solve eqns, combine like terms with parenthesesObj. 62 - Solve eqns, multiply by LCD
Obj. 63 - Solve formulas for specified variables
Topic 5 - Graph and Write Linear Equations
Obj. 86 - Solve absolute value equations
Topic 9 - Quadratic Equations Obj. 135 - Solve quadratic eqns, square root ruleObj. 136 - Solve quadratic equations (integer)Obj. 137 - Solve quadratic equations (rational)Obj. 139 - Solve quadratic eqns, complete the squareObj. 140 - Solve quadratic eqns, quadratic formula
Topic 12 - Rational Expressions and Equations
Obj. 187 - Solve equations containing rational expressions
Topic 13 - Radical Expressions and Equations
Obj. 198 - Solve equations containing radicalsObj. 200 - Solve equations containing multiple radicals
Topic 14 - Ratio and Proportion Obj. 207 - Solve proportionsNYC M3.k - Makes predictions by interpolating or extrapolating from given data or a given graph.
Topic 15 - Data and Statistics Obj. 223 - Use line of best fit to make predictions
NYC M3.l - Understands the basic algebraic structure of number systems.
Topic 1 - Integers and Rational Numbers
Obj. 1 - Graph integers on number lines
Obj. 3 - Add integersObj. 4 - Subtract integersObj. 6 - Multiply integersObj. 8 - Divide integersObj. 13 - Raise integers to powersObj. 14 - Add rational #s (fraction)Obj. 15 - Subtract rational #s (decimal)Obj. 17 - Multiply rational #s (decimal)Obj. 18 - Divide rational #s (fraction)
Accelerated Math Grades 9 - 10
091207Page 165 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Topic 2 - Introduction to Algebra Obj. 28 - Order real #s
Obj. 29 - Absolute values of real #s
Obj. 30 - Additive inverses of rational #sObj. 31 - Reciprocals of rational #sObj. 36 - Combine like termsObj. 37 - Combine like terms with parentheses
Topic 3 - Exponents Obj. 52 - Standard notation to scientific notationObj. 53 - Scientific notation to standard notationObj. 54 - Scientific notation, multiply & divide
Topic 12 - Rational Expressions and Equations
Obj. 176 - Rational expressions, domains
Topic 13 - Radical Expressions and Equations
Obj. 190 - Radical expressions, simplify
NYC M3.m - Uses equations to represent curves such as lines, circles, and parabolas.
Topic 5 - Graph and Write Linear Equations
Obj. 75 - Write eqns given slope & y-int
Obj. 76 - Write eqns given point & slopeObj. 77 - Write eqns given 2 pointsObj. 79 - Write eqns parallel or perp to a lineObj. 81 - Describe graphs of equations
NYC M3.n - Uses technology such as graphics calculators to represent and analyze functions and their graphs.
NYC M3.o - Uses functions to analyze patterns and represent their structure.
Topic 8 - Relations and Functions
Obj. 133 - Patterns and their equations
Obj. 134 - Identify function type from graph
NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student demonstrates understanding of statistics and probability concepts; that is, the student:
Accelerated Math Grades 9 - 10
091207Page 166 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M4.a - Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distributions, circle graphs, line plots, histograms, and summary statistics.
Topic 15 - Data and Statistics Obj. 210 - Qualitative vs. quantitative data
Obj. 211 - Univariate vs. bivariate dataObj. 212 - Determine if sample population is biasedObj. 214 - Stem-and-leaf plotsObj. 216 - Box-and-whisker plotsObj. 217 - Cumulative frequency histogramsObj. 222 - Scatter plotsObj. 224 - Construct line of best fit; determine eqnObj. 227 - Evaluate data and conclusionsObj. 228 - Means of data setsObj. 229 - Medians of data setsObj. 230 - Modes of data setsObj. 232 - Percentile rank
NYC M4.b - Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients.
Topic 15 - Data and Statistics Obj. 222 - Scatter plots
Obj. 224 - Construct line of best fit; determine eqnObj. 225 - Pos. & neg. correlations and causal relationships
NYC M4.c - Uses sampling techniques to draw inferences about large populations.
Topic 15 - Data and Statistics Obj. 212 - Determine if sample population is biased
Obj. 226 - Determine if sample question is biased
NYC M4.d - Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty.NYC M4.e - Formulates hypotheses to answer a question and uses data to test hypotheses.
Topic 15 - Data and Statistics Obj. 227 - Evaluate data and conclusions
Accelerated Math Grades 9 - 10
091207Page 167 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M4.f - Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents.
Topic 15 - Data and Statistics Obj. 215 - Interpret elements of box-and-whisker plots
Obj. 223 - Use line of best fit to make predictionsObj. 225 - Pos. & neg. correlations and causal relationshipsObj. 227 - Evaluate data and conclusionsObj. 232 - Percentile rank
NYC M4.g - Explores questions of experimental design, use of control groups, and reliability.
Topic 15 - Data and Statistics Obj. 212 - Determine if sample population is biased
Obj. 226 - Determine if sample question is biased
NYC M4.h - Creates and uses models of probabilistic situations and understands the role of assumptions in this process.
Topic 15 - Data and Statistics Obj. 234 - Determine number of outcomes/events
NYC M4.i - Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance.
Topic 15 - Data and Statistics Obj. 213 - Probability of single events
Obj. 218 - Conditional probabilityObj. 219 - Empirical probabilityObj. 220 - Probability of independent/dependent eventsObj. 221 - Probability of compound eventsObj. 234 - Determine number of outcomes/eventsObj. 235 - Permutations
NYC M4.j - Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities.
Topic 15 - Data and Statistics Obj. 234 - Determine number of outcomes/events
Obj. 235 - PermutationsNYC M4.k - Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely.NYC M4.l - Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event.
Topic 15 - Data and Statistics Obj. 218 - Conditional probability
Accelerated Math Grades 9 - 10
091207Page 168 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M4.m - Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event.
Topic 15 - Data and Statistics Obj. 219 - Empirical probability
NYC M4.n - Designs simulations including Monte Carlo simulations to estimate probabilities.NYC M4.o - Works with the normal distribution in some of its basic applications.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion. - FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: fills out the formulation of a definite problem that is to be solved.
Topic 5 - Graph and Write Linear Equations
Obj. 85 - WP: Linear equations
Topic 6 - Polynomial Operations Obj. 95 - WP: Add & subtract polynomialsObj. 101 - WP: Multiply binomials
Topic 8 - Relations and Functions
Obj. 128 - Verbal sentences and eqns/inequalities
Topic 10 - Systems of Equations Obj. 155 - Write systems of equations
Topic 11 - Inequalities and Absolute Value
Obj. 166 - WP: Identify absolute value inequalities
Accelerated Math Grades 9 - 10
091207Page 169 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M5.a.ii - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: extracts pertinent information from the situation as a basis for working on the problem.
Topic 3 - Exponents Obj. 40 - Write repeated mult as power
Topic 5 - Graph and Write Linear Equations
Obj. 85 - WP: Linear equations
Topic 6 - Polynomial Operations Obj. 95 - WP: Add & subtract polynomialsObj. 101 - WP: Multiply binomials
Topic 8 - Relations and Functions
Obj. 128 - Verbal sentences and eqns/inequalities
Topic 11 - Inequalities and Absolute Value
Obj. 166 - WP: Identify absolute value inequalities
NYC M5.a.iii - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: asks and answers a series of appropriate questions in pursuit of a solution and does so with minimal "scaffolding" in the form of detailed guiding questions. - IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: chooses and employs effective problem solving strategies in dealing with non-routine and multi-step problems.
Topic 4 - Solving Linear Equations
Obj. 64 - WP: Mixture problems
Obj. 65 - WP: Motion problemsTopic 9 - Quadratic Equations Obj. 146 - WP: Pythagorean
problemsObj. 147 - WP: Number problemsObj. 148 - WP: Area & perimeter
Topic 12 - Rational Expressions and Equations
Obj. 188 - WP: Rational expressions
Topic 14 - Ratio and Proportion Obj. 204 - WP: Calculate rates
Accelerated Math Grades 9 - 10
091207Page 170 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: selects appropriate mathematical concepts and techniques from different areas of mathematics and applies them to the solution of the problem.
Topic 6 - Polynomial Operations Obj. 101 - WP: Multiply binomials
Topic 8 - Relations and Functions
Obj. 133 - Patterns and their equations
Topic 9 - Quadratic Equations Obj. 146 - WP: Pythagorean problemsObj. 148 - WP: Area & perimeter
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: applies mathematical concepts to new situations within mathematics and uses mathematics to model real world situations involving basic applications of mathematics in the physical and biological sciences, the social sciences, and business.
Topic 1 - Integers and Rational Numbers
Obj. 5 - WP: Add & subtract integers
Obj. 16 - WP: Add & subtract rational #s (fraction)Obj. 19 - WP: Multiply or divide rational #s (fraction)
Topic 3 - Exponents Obj. 55 - WP: Scientific notationTopic 4 - Solving Linear Equations
Obj. 64 - WP: Mixture problems
Obj. 65 - WP: Motion problemsTopic 5 - Graph and Write Linear Equations
Obj. 85 - WP: Linear equations
Topic 10 - Systems of Equations Obj. 159 - WP: Solve systems, investment problems
Topic 14 - Ratio and Proportion Obj. 204 - WP: Calculate ratesObj. 208 - WP: Solve proportions
- CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:
Accelerated Math Grades 9 - 10
091207Page 171 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: concludes a solution process with a useful summary of results.
NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: evaluates the degree to which the results obtained represent a good response to the initial problem.NYC M5.c.iii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: formulates generalizations of the results obtained.
NYC M5.c.iv - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: carries out extensions of the given problem to related problems.
- MATHEMATICAL REASONINGNYC M5.d - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student:
Accelerated Math Grades 9 - 10
091207Page 172 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M5.d.i - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student: employs forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counterexamples and indirect proof.
Topic 1 - Integers and Rational Numbers
Obj. 22 - Venn diagrams and logic
Topic 2 - Introduction to Algebra Obj. 38 - Evaluate written arguments for validity
NYC M5.d.ii - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student: differentiates clearly between giving examples that support a conjecture and giving proof of the conjecture.
Topic 2 - Introduction to Algebra Obj. 39 - Missing steps in algebraic proofs
NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Grades 9 - 10
091207Page 173 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, or books, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate.
Topic 1 - Integers and Rational Numbers
Obj. 3 - Add integers
Obj. 4 - Subtract integersObj. 6 - Multiply integersObj. 8 - Divide integersObj. 9 - Write products as quotients & vice versaObj. 10 - Distributive propertyObj. 11 - Order of operationsObj. 12 - Order of operations with groupingObj. 13 - Raise integers to powersObj. 14 - Add rational #s (fraction)Obj. 15 - Subtract rational #s (decimal)Obj. 17 - Multiply rational #s (decimal)Obj. 18 - Divide rational #s (fraction)
Topic 2 - Introduction to Algebra Obj. 29 - Absolute values of real #s
Topic 3 - Exponents Obj. 41 - Evaluate expressions, positive exponentsObj. 42 - Evaluate expressions, negative/zero exponentsObj. 43 - Evaluate expressions, fractional exponentsObj. 54 - Scientific notation, multiply & divide
Accelerated Math Grades 9 - 10
091207Page 174 of 230
Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M6.b - Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy.NYC M6.c - Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology.
Topic 8 - Relations and Functions
Obj. 123 - Domain & range, relations & functions
Obj. 124 - Determine if relations are functionsObj. 125 - Determine if functions are one-to-oneObj. 126 - Identify constant, linear, & quad polynomialsObj. 130 - Find specified values of functionsObj. 132 - Add, sub, mult, & div functionsObj. 134 - Identify function type from graph
Topic 12 - Rational Expressions and Equations
Obj. 187 - Solve equations containing rational expressions
Topic 13 - Radical Expressions and Equations
Obj. 200 - Solve equations containing multiple radicals
NYC M6.d - Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems.
Topic 9 - Quadratic Equations Obj. 148 - WP: Area & perimeter
NYC M6.e - Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution.
Topic 5 - Graph and Write Linear Equations
Obj. 73 - Plot points to write or graph eqns
Topic 9 - Quadratic Equations Obj. 144 - Find vertex/axis of symm of parabola, given graph
NYC M6.f - Uses the number line and Cartesian coordinates in the plane and in space.
Topic 1 - Integers and Rational Numbers
Obj. 1 - Graph integers on number lines
Topic 5 - Graph and Write Linear Equations
Obj. 66 - Graph ordered pairs
Obj. 69 - Find slopes from a graphObj. 73 - Plot points to write or graph eqnsObj. 81 - Describe graphs of equations
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 82 - Graph lines, slope-intercept formObj. 83 - Graph lines, standard form
Obj. 84 - Graph lines, horizontal & verticalObj. 87 - Graph absolute value equations
Topic 8 - Relations and Functions
Obj. 134 - Identify function type from graph
Topic 9 - Quadratic Equations Obj. 141 - Graph quadratic equations
Obj. 142 - Graph to find quadratic rootsObj. 144 - Find vertex/axis of symm of parabola, given graph
Topic 10 - Systems of Equations Obj. 149 - Graph systems, real solutionsObj. 150 - Graph systems, no solutions
Topic 11 - Inequalities and Absolute Value
Obj. 167 - Graph 1-var inequalities
Obj. 168 - Solve & graph inequalities
Obj. 169 - Solve & graph compound inequalitiesObj. 170 - Graph absolute value inequalitiesObj. 171 - Graph 2-var inequalities
NYC M6.g - Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms.
Topic 5 - Graph and Write Linear Equations
Obj. 69 - Find slopes from a graph
Obj. 73 - Plot points to write or graph eqnsObj. 81 - Describe graphs of equationsObj. 82 - Graph lines, slope-intercept formObj. 83 - Graph lines, standard form
Obj. 84 - Graph lines, horizontal & verticalObj. 87 - Graph absolute value equations
Topic 8 - Relations and Functions
Obj. 134 - Identify function type from graph
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Topic 9 - Quadratic Equations Obj. 141 - Graph quadratic equations
Obj. 142 - Graph to find quadratic rootsObj. 144 - Find vertex/axis of symm of parabola, given graph
Topic 11 - Inequalities and Absolute Value
Obj. 167 - Graph 1-var inequalities
Obj. 168 - Solve & graph inequalities
Obj. 169 - Solve & graph compound inequalitiesObj. 170 - Graph absolute value inequalitiesObj. 171 - Graph 2-var inequalities
Topic 15 - Data and Statistics Obj. 214 - Stem-and-leaf plotsObj. 216 - Box-and-whisker plotsObj. 217 - Cumulative frequency histogramsObj. 222 - Scatter plotsObj. 223 - Use line of best fit to make predictionsObj. 224 - Construct line of best fit; determine eqn
NYC M6.h - Sets up and solves equations symbolically (when possible) and graphically.
Topic 4 - Solving Linear Equations
Obj. 57 - Solve 1-step eqns, add & subtract
Obj. 58 - Solve 1-step eqns, multiply & divideObj. 59 - Solve multi-step equations
Obj. 60 - Solve eqns, combine like termsObj. 61 - Solve eqns, combine like terms with parenthesesObj. 62 - Solve eqns, multiply by LCD
Obj. 63 - Solve formulas for specified variablesObj. 64 - WP: Mixture problemsObj. 65 - WP: Motion problems
Topic 5 - Graph and Write Linear Equations
Obj. 85 - WP: Linear equations
Obj. 86 - Solve absolute value equations
Topic 9 - Quadratic Equations Obj. 135 - Solve quadratic eqns, square root ruleObj. 136 - Solve quadratic equations (integer)
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 137 - Solve quadratic equations (rational)Obj. 139 - Solve quadratic eqns, complete the squareObj. 140 - Solve quadratic eqns, quadratic formulaObj. 146 - WP: Pythagorean problemsObj. 147 - WP: Number problemsObj. 148 - WP: Area & perimeter
Topic 12 - Rational Expressions and Equations
Obj. 187 - Solve equations containing rational expressions
Topic 13 - Radical Expressions and Equations
Obj. 198 - Solve equations containing radicalsObj. 199 - WP: Solve radical equationsObj. 200 - Solve equations containing multiple radicals
Topic 14 - Ratio and Proportion Obj. 207 - Solve proportionsObj. 208 - WP: Solve proportionsObj. 209 - Solve direct & indirect variation problems
NYC M6.i - Knows how to use algorithms in mathematics, such as the Euclidean Algorithm.NYC M6.j - Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem.NYC M6.k - Writes a simple computer program to carry out a computation or simulation to be repeated many times.NYC M6.l - Uses tools such as rulers, tapes, compasses, and protractors in solving problems.NYC M6.m - Knows standard methods to solve basic problems and uses these methods in approaching more complex problems.
NYC M7 - MATHEMATICAL COMMUNICATION
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Is familiar with basic mathematical terminology, standard notation and use of symbols, common conventions for graphing, and general features of effective mathematical communication styles.
Topic 1 - Integers and Rational Numbers
Obj. 2 - Interpret scientific calculator displays
Obj. 23 - Set builder and interval notation
Topic 3 - Exponents Obj. 40 - Write repeated mult as powerObj. 52 - Standard notation to scientific notationObj. 53 - Scientific notation to standard notationObj. 54 - Scientific notation, multiply & divide
Topic 5 - Graph and Write Linear Equations
Obj. 66 - Graph ordered pairs
Obj. 67 - Identify quadrants & axes of pointsObj. 68 - Find slopes from 2 pointsObj. 69 - Find slopes from a graphObj. 72 - Find lines' interceptsObj. 73 - Plot points to write or graph eqnsObj. 74 - Write eqns in standard/slope-intercept form
NYC M7.b - Uses mathematical representations with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
Topic 1 - Integers and Rational Numbers
Obj. 1 - Graph integers on number lines
Topic 5 - Graph and Write Linear Equations
Obj. 66 - Graph ordered pairs
Obj. 67 - Identify quadrants & axes of pointsObj. 68 - Find slopes from 2 points
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 69 - Find slopes from a graphObj. 70 - Find slopes from equations
Obj. 71 - Slope as rate of change btw indep./dep. variablesObj. 72 - Find lines' interceptsObj. 73 - Plot points to write or graph eqnsObj. 74 - Write eqns in standard/slope-intercept formObj. 75 - Write eqns given slope & y-intObj. 76 - Write eqns given point & slopeObj. 77 - Write eqns given 2 pointsObj. 78 - Determine parallel lines, given equationsObj. 79 - Write eqns parallel or perp to a lineObj. 80 - Equations parallel to x- or y-axisObj. 82 - Graph lines, slope-intercept formObj. 83 - Graph lines, standard form
Obj. 84 - Graph lines, horizontal & verticalObj. 85 - WP: Linear equationsObj. 86 - Solve absolute value equationsObj. 87 - Graph absolute value equations
Topic 8 - Relations and Functions
Obj. 128 - Verbal sentences and eqns/inequalitiesObj. 133 - Patterns and their equationsObj. 134 - Identify function type from graph
Topic 9 - Quadratic Equations Obj. 141 - Graph quadratic equations
Topic 11 - Inequalities and Absolute Value
Obj. 167 - Graph 1-var inequalities
Obj. 170 - Graph absolute value inequalitiesObj. 171 - Graph 2-var inequalities
Topic 15 - Data and Statistics Obj. 214 - Stem-and-leaf plotsObj. 215 - Interpret elements of box-and-whisker plotsObj. 216 - Box-and-whisker plots
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
Obj. 217 - Cumulative frequency histogramsObj. 222 - Scatter plotsObj. 223 - Use line of best fit to make predictions
NYC M7.c - Organizes work and presents mathematical procedures and results clearly, systematically, succinctly, and correctly.NYC M7.d - Communicates logical arguments clearly, showing why a result makes sense and why the reasoning is valid.
Topic 5 - Graph and Write Linear Equations
Obj. 77 - Write eqns given 2 points
NYC M7.e - Presents mathematical ideas effectively both orally and in writing.
Topic 1 - Integers and Rational Numbers
Obj. 23 - Set builder and interval notation
Topic 5 - Graph and Write Linear Equations
Obj. 73 - Plot points to write or graph eqnsObj. 74 - Write eqns in standard/slope-intercept formObj. 75 - Write eqns given slope & y-intObj. 76 - Write eqns given point & slopeObj. 79 - Write eqns parallel or perp to a line
Topic 8 - Relations and Functions
Obj. 127 - Write verbal expressions
Obj. 128 - Verbal sentences and eqns/inequalities
NYC M7.f - Explains mathematical concepts clearly enough to be of assistance to those who may be having difficulty with them.NYC M7.g - Writes narrative accounts of the history and process of work on a mathematical problem or extended project.NYC M7.h - Writes succinct accounts of the mathematical results obtained in a mathematical problem or extended project, with diagrams, graphs, tables, and formulas integrated into the text.NYC M7.i - Keeps narrative accounts of process separate from succinct accounts of results, and realizes that doing so can enhance the effectiveness of each.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M7.j - Reads mathematics texts and other writing about mathematics with understanding.NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of high school, conducts investigations or projects drawn from at least three of the kinds. A single investigation or project may draw on more than one kind.
NYC M8.a - Data study, in which the student:NYC M8.a.i - Data study, in which the student: carries out a study of data relevant to current civic, economic, scientific, health, or social issues.
NYC M8.a.ii - Data study, in which the student: uses methods of statistical inference to generalize from the data.NYC M8.a.iii - Data study, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.b - Mathematical model of a physical system or phenomenon, in which the student:NYC M8.b.i - Mathematical model of a physical system or phenomenon, in which the student: carries out a study of a physical system or phenomenon by constructing a mathematical model based on functions to make generalizations about the structure of the system.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M8.b.ii - Mathematical model of a physical system or phenomenon, in which the student: uses structural analysis (a direct analysis of the structure of the system) rather than numerical or statistical analysis (an analysis of data about the system).
NYC M8.b.iii - Mathematical model of a physical system or phenomenon, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: creates a design for a physical structure.NYC M8.c.ii - Design of a physical structure, in which the student: uses general mathematical ideas and techniques to discuss specifications for building the structure.
NYC M8.c.iii - Design of a physical structure, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.d - Management and planning analysis, in which the student:NYC M8.d.i - Management and planning analysis, in which the student: carries out a study of a business or public policy situation involving issues such as optimization, cost-benefit projections, and risks.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M8.d.ii - Management and planning analysis, in which the student: uses decision rules and strategies both to analyze options and balance trade-offs; and brings in mathematical ideas that serve to generalize the analysis across different conditions.NYC M8.d.iii - Management and planning analysis, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: carries out a mathematical investigation of a phenomenon or concept in pure mathematics.NYC M8.e.ii - Pure mathematics investigation, in which the student: uses methods of mathematical reasoning and justification to make generalizations about the phenomenon.NYC M8.e.iii - Pure mathematics investigation, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.f - History of a mathematical idea, in which the student:
NYC M8.f.i - History of a mathematical idea, in which the student: carries out a historical study tracing the development of a mathematical concept and the people who contributed to it.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra1
NYC M8.f.ii - History of a mathematical idea, in which the student: includes a discussion of the actual mathematical content and its place in the curriculum of the present day.NYC M8.f.iii - History of a mathematical idea, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Uses addition, subtraction, multiplication, division, exponentiation, and root-extraction in forming and working with numerical and algebraic expressions.
NYC M1.b - Understands and uses operations such as opposite, reciprocal, raising to a power, taking a root, and taking a logarithm.
NYC M1.c - Has facility with the mechanics of operations as well as understanding of their typical meaning and uses in applications.NYC M1.d - Understands and uses number systems: natural, integer, rational, and real.NYC M1.e - Represents numbers in decimal or fraction form and in scientific notation, and graphs numbers on the number line and number pairs in the coordinate plane.
Topic 2 - Introduction to the Coordinate Plane
Obj. 16 - Ordered pairs
NYC M1.f - Compares numbers using order relations, differences, ratios, proportions, percents, and proportional change.NYC M1.g - Carries out proportional reasoning in cases involving part-whole relationships and in cases involving expansions and contractions.
Topic 9 - Similarity Obj. 115 - Solve proportions
NYC M1.h - Understands dimensionless numbers, such as proportions, percents, and multiplicative factors, as well as numbers with specific units of measure, such as numbers with length, time, and rate units.
Topic 3 - Transformational Geometry
Obj. 41 - Dilations
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M1.i - Carries out counting procedures such as those involving sets (unions and intersections) and arrangements (permutations and combinations).NYC M1.j - Uses concepts such as prime, relatively prime, factor, divisor, multiple, and divisibility in solving problems involving integers.NYC M1.k - Uses a scientific calculator effectively and efficiently in carrying out complex calculations.
NYC M1.l - Recognizes and represents basic number patterns, such as patterns involving multiples, squares, or cubes.
Topic 4 - Reasoning and Proofs Obj. 45 - Visual patterns
Obj. 46 - Numerical patternsNYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:NYC M2.a - Models situations geometrically to formulate and solve problems.NYC M2.b - Works with two- and three-dimensional figures and their properties, including polygons and circles, cubes and pyramids, and cylinders, cones, and spheres.
Topic 6 - Triangles Obj. 70 - Interior & exterior angles of triangles
Obj. 73 - Angle measures in isosceles trianglesObj. 76 - Use segment joining midpoints of 2 sides of triangleObj. 77 - Use centroid for indirect measure
Topic 7 - Right Triangles and Trigonometry
Obj. 88 - 30-60-90 triangles
Obj. 89 - 45-45-90 trianglesObj. 90 - Apply special right triangles
Obj. 91 - WP: Special right triangles
Topic 8 - Polygons Obj. 103 - Polygon propertiesObj. 104 - Sum of interior angles of polygons
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Obj. 105 - Interior or exterior angles of polygonsObj. 106 - WP: PolygonsObj. 110 - Use properties of trapezoids to solve problems
Topic 10 - Circles Obj. 126 - Parts of circlesObj. 132 - Perpendicular line to tangent at point of tangencyObj. 137 - Two intersecting chords of a circle
NYC M2.c - Uses congruence and similarity in describing relationships between figures.
Topic 6 - Triangles Obj. 79 - Rule that proves triangle congruence
Topic 9 - Similarity Obj. 117 - Similar polygon characteristics
NYC M2.d - Visualizes objects, paths, and regions in space, including intersections and cross sections of three dimensional figures, and describes these using geometric language.
Topic 10 - Circles Obj. 149 - Solve compound loci problems using coordinates
Obj. 150 - WP: LociNYC M2.e - Knows, uses, and derives formulas for perimeter, circumference, area, surface area, and volume of many types of figures.
Topic 10 - Circles Obj. 140 - Circumference
Topic 11 - Area Obj. 153 - Area & perimeter of rectangles & squaresObj. 154 - Area of parallelogramsObj. 155 - Area of trianglesObj. 156 - Area of trapezoidsObj. 157 - Area of rhombuses & kites
Obj. 158 - Area of circlesObj. 159 - Area of sector or segment
Obj. 161 - Area of regular polygonsObj. 162 - Area of composite shapes
Obj. 163 - Perimeter of composite shapes
Topic 12 - Surface Area and Volume
Obj. 169 - Surface area of rectangular prismsObj. 170 - Surface area of non-rectangular prismsObj. 171 - Volume of rectangular prisms & cubes
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Obj. 172 - Volume of non-rectangular prismsObj. 173 - Surface area of rectangular pyramidsObj. 175 - Volume of pyramidsObj. 176 - Surface area of cylinders
Obj. 177 - Surface area of conesObj. 178 - Volume of cylindersObj. 179 - Volume of conesObj. 180 - Volume or surface area of spheresObj. 181 - Volume of composite solidsObj. 182 - Surface area of composite solidsObj. 184 - Solve area, surface area, volume problems
NYC M2.f - Uses the Pythagorean Theorem in many types of situations, and works through more than one proof of this theorem.
Topic 7 - Right Triangles and Trigonometry
Obj. 82 - Pythagorean Theorem to solve sides
Obj. 83 - Pythagorean Theorem to determine right triangleObj. 84 - Pythagorean triplesObj. 87 - WP: Pythagorean Theorem
NYC M2.g - Works with similar triangles, and extends the ideas to include simple uses of the three basic trigonometric functions.
Topic 7 - Right Triangles and Trigonometry
Obj. 92 - Sine & cosine ratios
Obj. 93 - Tangent ratioObj. 94 - Trig to solve sides in triangleObj. 96 - WP: Trigonometry
Topic 9 - Similarity Obj. 118 - Proofs: Similar trianglesObj. 120 - Similar triangles & proportionsObj. 121 - WP: Similar triangles & proportions
NYC M2.h - Analyzes figures in terms of their symmetries using, for example, concepts of reflection, rotation, and translation.
Topic 3 - Transformational Geometry
Obj. 29 - Translations
Obj. 30 - ReflectionsObj. 31 - Glide reflectionsObj. 32 - RotationsObj. 39 - Lines of symmetry
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M2.i - Compares slope (rise over run) and angle of elevation as measures of steepness.
Topic 2 - Introduction to the Coordinate Plane
Obj. 18 - Slope of a line
NYC M2.j - Investigates geometric patterns, including sequences of growing shapes.
Topic 4 - Reasoning and Proofs Obj. 45 - Visual patterns
NYC M2.k - Works with geometric measures of length, area, volume, and angle; and non-geometric measures such as weight and time.
Topic 1 - The Basics of Geometry
Obj. 9 - Angle definitions, notation, & properties
Obj. 10 - Classify angles as acute, right, or obtuseObj. 11 - Estimate & draw angles
NYC M2.l - Uses quotient measures, such as speed and density, that give "per unit" amounts; and uses product measures, such as person-hours.
NYC M2.m - Understands the structure of standard measurement systems, both SI and customary, including unit conversions and dimensional analysis.NYC M2.n - Solves problems involving scale, such as in maps and diagrams.
Topic 3 - Transformational Geometry
Obj. 42 - Scale drawings
NYC M2.o - Represents geometric curves and graphs of functions in standard coordinate systems.
Topic 2 - Introduction to the Coordinate Plane
Obj. 19 - Graph line on coordinate plane
Topic 10 - Circles Obj. 143 - Equations of circlesNYC M2.p - Analyzes geometric figures and proves simple things about them using deductive methods.
Topic 4 - Reasoning and Proofs Obj. 57 - Proofs: Angle & segment addition
Obj. 58 - Proofs: AnglesTopic 5 - Parallel Lines and Line Relationships
Obj. 63 - Proofs: Parallel lines
Topic 6 - Triangles Obj. 80 - Proofs: TrianglesObj. 81 - Proofs: Direct & indirect
Topic 7 - Right Triangles and Trigonometry
Obj. 100 - Proofs: Right triangle congruenceObj. 101 - Proofs: Flow & paragraph
Topic 8 - Polygons Obj. 109 - Proofs: QuadrilateralsObj. 113 - Proofs: Coordinate geometryObj. 114 - Proofs: Coordinate with quadrilaterals
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Topic 9 - Similarity Obj. 118 - Proofs: Similar trianglesNYC M2.q - Explores geometry using computer programs such as CAD software, Sketchpad programs, or LOGO.NYC M3 - FUNCTION AND ALGEBRA CONCEPTSNYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Models given situations with formulas and functions, and interprets given formulas and functions in terms of situations.
NYC M3.b - Describes, generalizes, and uses basic types of functions: linear, exponential, power, rational, square and square root, and cube and cube root.NYC M3.c - Utilizes the concepts of slope, evaluation, and inverse in working with functions.
Topic 2 - Introduction to the Coordinate Plane
Obj. 18 - Slope of a line
NYC M3.d - Works with rates of many kinds, expressed numerically, symbolically, and graphically.
NYC M3.e - Represents constant rates as the slope of a straight line graph, and interprets slope as the amount of one quantity (y) per unit amount of another (x).
Topic 2 - Introduction to the Coordinate Plane
Obj. 18 - Slope of a line
NYC M3.f - Understands and uses linear functions as a mathematical representation of proportional relationships.NYC M3.g - Uses arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M3.h - Defines, uses, and manipulates expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities.
Topic 2 - Introduction to the Coordinate Plane
Obj. 25 - Solve system of equations
Topic 10 - Circles Obj. 143 - Equations of circlesObj. 146 - WP: Equations of circles
NYC M3.i - Represents functional relationships in formulas, tables, and graphs, and translates between pairs of these.NYC M3.j - Solves equations symbolically, graphically, and numerically, especially linear, quadratic, and exponential equations; and knows how to use the quadratic formula for solving quadratic equations.NYC M3.k - Makes predictions by interpolating or extrapolating from given data or a given graph.NYC M3.l - Understands the basic algebraic structure of number systems.NYC M3.m - Uses equations to represent curves such as lines, circles, and parabolas.
Topic 2 - Introduction to the Coordinate Plane
Obj. 22 - Write equation of a line
Obj. 23 - Write eqn of line given point & parallel/perp line eqnObj. 24 - Write eqn of perp bisector, given segment endpts
Topic 10 - Circles Obj. 143 - Equations of circlesObj. 144 - Find eqn of circle, given graphObj. 146 - WP: Equations of circles
NYC M3.n - Uses technology such as graphics calculators to represent and analyze functions and their graphs.
NYC M3.o - Uses functions to analyze patterns and represent their structure.NYC M4 - STATISTICS AND PROBABILITY CONCEPTS
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M4-1 - The student demonstrates understanding of statistics and probability concepts; that is, the student:NYC M4.a - Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distributions, circle graphs, line plots, histograms, and summary statistics.
NYC M4.b - Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients.NYC M4.c - Uses sampling techniques to draw inferences about large populations.NYC M4.d - Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty.NYC M4.e - Formulates hypotheses to answer a question and uses data to test hypotheses.NYC M4.f - Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents.
NYC M4.g - Explores questions of experimental design, use of control groups, and reliability.NYC M4.h - Creates and uses models of probabilistic situations and understands the role of assumptions in this process.NYC M4.i - Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance.NYC M4.j - Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M4.k - Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely.NYC M4.l - Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event.
Topic 11 - Area Obj. 164 - Geometric probability using area
NYC M4.m - Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event.NYC M4.n - Designs simulations including Monte Carlo simulations to estimate probabilities.NYC M4.o - Works with the normal distribution in some of its basic applications.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion. - FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: fills out the formulation of a definite problem that is to be solved.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M5.a.ii - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: extracts pertinent information from the situation as a basis for working on the problem.NYC M5.a.iii - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: asks and answers a series of appropriate questions in pursuit of a solution and does so with minimal "scaffolding" in the form of detailed guiding questions. - IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: chooses and employs effective problem solving strategies in dealing with non-routine and multi-step problems.
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: selects appropriate mathematical concepts and techniques from different areas of mathematics and applies them to the solution of the problem.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: applies mathematical concepts to new situations within mathematics and uses mathematics to model real world situations involving basic applications of mathematics in the physical and biological sciences, the social sciences, and business.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
- CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: concludes a solution process with a useful summary of results.
NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: evaluates the degree to which the results obtained represent a good response to the initial problem.NYC M5.c.iii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: formulates generalizations of the results obtained.
NYC M5.c.iv - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: carries out extensions of the given problem to related problems.
- MATHEMATICAL REASONING
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M5.d - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student:
NYC M5.d.i - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student: employs forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counterexamples and indirect proof.
Topic 4 - Reasoning and Proofs Obj. 47 - Apply inductive reasoning in conjectures
Obj. 48 - Conditionals & logical statementsObj. 49 - Determine the negation of a statementObj. 50 - Converses, inverses, & contrapositivesObj. 51 - CounterexamplesObj. 52 - Biconditional statements & definitionsObj. 53 - Conjunctions & disjunctions
Obj. 54 - Symbolic notation of logical statements
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Obj. 55 - Form conclusions by applying laws of logicObj. 56 - Proofs: Algebra & properties of equalityObj. 57 - Proofs: Angle & segment additionObj. 58 - Proofs: Angles
Topic 5 - Parallel Lines and Line Relationships
Obj. 63 - Proofs: Parallel lines
Topic 6 - Triangles Obj. 80 - Proofs: TrianglesObj. 81 - Proofs: Direct & indirect
Topic 7 - Right Triangles and Trigonometry
Obj. 100 - Proofs: Right triangle congruenceObj. 101 - Proofs: Flow & paragraph
Topic 8 - Polygons Obj. 113 - Proofs: Coordinate geometryObj. 114 - Proofs: Coordinate with quadrilaterals
Topic 9 - Similarity Obj. 118 - Proofs: Similar trianglesNYC M5.d.ii - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student: differentiates clearly between giving examples that support a conjecture and giving proof of the conjecture.
NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, or books, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate.NYC M6.b - Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy.NYC M6.c - Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology.
Topic 2 - Introduction to the Coordinate Plane
Obj. 17 - Midpoints in the coordinate plane
Obj. 18 - Slope of a lineTopic 7 - Right Triangles and Trigonometry
Obj. 82 - Pythagorean Theorem to solve sidesObj. 86 - Distance formulaObj. 97 - Law of Sines & Cosines
Topic 10 - Circles Obj. 140 - CircumferenceObj. 141 - Arc length
Topic 12 - Surface Area and Volume
Obj. 169 - Surface area of rectangular prismsObj. 170 - Surface area of non-rectangular prismsObj. 171 - Volume of rectangular prisms & cubesObj. 172 - Volume of non-rectangular prismsObj. 173 - Surface area of rectangular pyramidsObj. 175 - Volume of pyramidsObj. 176 - Surface area of cylinders
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Obj. 177 - Surface area of conesObj. 178 - Volume of cylindersObj. 179 - Volume of conesObj. 180 - Volume or surface area of spheres
NYC M6.d - Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems.
Topic 1 - The Basics of Geometry
Obj. 1 - Collinear & coplanar points
Obj. 3 - Points, lines, planes, & space
Obj. 9 - Angle definitions, notation, & propertiesObj. 10 - Classify angles as acute, right, or obtuse
Topic 6 - Triangles Obj. 67 - Name parts of trianglesObj. 68 - Classify triangles as scalene, isos, or equilObj. 69 - Classify triangles as acute, obtuse, or right
Topic 8 - Polygons Obj. 102 - Identify polygons by # of sides
NYC M6.e - Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution.
Topic 3 - Transformational Geometry
Obj. 42 - Scale drawings
NYC M6.f - Uses the number line and Cartesian coordinates in the plane and in space.
Topic 1 - The Basics of Geometry
Obj. 5 - Find distances & midpoints on number lines
Topic 2 - Introduction to the Coordinate Plane
Obj. 17 - Midpoints in the coordinate planeObj. 18 - Slope of a lineObj. 19 - Graph line on coordinate planeObj. 21 - Betweenness & collinearity
Obj. 26 - Graph to solve system w/one linear, one quadratic eqnObj. 28 - Area with Coordinates
Topic 3 - Transformational Geometry
Obj. 36 - Find coordinates under transformations
NYC M6.g - Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M6.h - Sets up and solves equations symbolically (when possible) and graphically.
Topic 2 - Introduction to the Coordinate Plane
Obj. 25 - Solve system of equations
NYC M6.i - Knows how to use algorithms in mathematics, such as the Euclidean Algorithm.NYC M6.j - Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem.NYC M6.k - Writes a simple computer program to carry out a computation or simulation to be repeated many times.NYC M6.l - Uses tools such as rulers, tapes, compasses, and protractors in solving problems.
Topic 5 - Parallel Lines and Line Relationships
Obj. 65 - Constructions: Angles & triangles
Obj. 66 - Constructions: Bisectors, lines, equi. triangle
Topic 8 - Polygons Obj. 111 - Constructions: Quadrilaterals
Topic 10 - Circles Obj. 147 - Constructions: Circles, arcs, tangents, & chords
NYC M6.m - Knows standard methods to solve basic problems and uses these methods in approaching more complex problems.
NYC M7 - MATHEMATICAL COMMUNICATIONNYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Is familiar with basic mathematical terminology, standard notation and use of symbols, common conventions for graphing, and general features of effective mathematical communication styles.
Topic 1 - The Basics of Geometry
Obj. 1 - Collinear & coplanar points
Obj. 3 - Points, lines, planes, & space
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
Obj. 9 - Angle definitions, notation, & propertiesObj. 10 - Classify angles as acute, right, or obtuse
Topic 6 - Triangles Obj. 67 - Name parts of trianglesObj. 68 - Classify triangles as scalene, isos, or equilObj. 69 - Classify triangles as acute, obtuse, or right
Topic 8 - Polygons Obj. 102 - Identify polygons by # of sides
NYC M7.b - Uses mathematical representations with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
NYC M7.c - Organizes work and presents mathematical procedures and results clearly, systematically, succinctly, and correctly.NYC M7.d - Communicates logical arguments clearly, showing why a result makes sense and why the reasoning is valid.NYC M7.e - Presents mathematical ideas effectively both orally and in writing.NYC M7.f - Explains mathematical concepts clearly enough to be of assistance to those who may be having difficulty with them.NYC M7.g - Writes narrative accounts of the history and process of work on a mathematical problem or extended project.NYC M7.h - Writes succinct accounts of the mathematical results obtained in a mathematical problem or extended project, with diagrams, graphs, tables, and formulas integrated into the text.NYC M7.i - Keeps narrative accounts of process separate from succinct accounts of results, and realizes that doing so can enhance the effectiveness of each.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M7.j - Reads mathematics texts and other writing about mathematics with understanding.NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of high school, conducts investigations or projects drawn from at least three of the kinds. A single investigation or project may draw on more than one kind.
NYC M8.a - Data study, in which the student:NYC M8.a.i - Data study, in which the student: carries out a study of data relevant to current civic, economic, scientific, health, or social issues.
NYC M8.a.ii - Data study, in which the student: uses methods of statistical inference to generalize from the data.NYC M8.a.iii - Data study, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.b - Mathematical model of a physical system or phenomenon, in which the student:NYC M8.b.i - Mathematical model of a physical system or phenomenon, in which the student: carries out a study of a physical system or phenomenon by constructing a mathematical model based on functions to make generalizations about the structure of the system.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M8.b.ii - Mathematical model of a physical system or phenomenon, in which the student: uses structural analysis (a direct analysis of the structure of the system) rather than numerical or statistical analysis (an analysis of data about the system).
NYC M8.b.iii - Mathematical model of a physical system or phenomenon, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: creates a design for a physical structure.NYC M8.c.ii - Design of a physical structure, in which the student: uses general mathematical ideas and techniques to discuss specifications for building the structure.
NYC M8.c.iii - Design of a physical structure, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.d - Management and planning analysis, in which the student:NYC M8.d.i - Management and planning analysis, in which the student: carries out a study of a business or public policy situation involving issues such as optimization, cost-benefit projections, and risks.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M8.d.ii - Management and planning analysis, in which the student: uses decision rules and strategies both to analyze options and balance trade-offs; and brings in mathematical ideas that serve to generalize the analysis across different conditions.NYC M8.d.iii - Management and planning analysis, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: carries out a mathematical investigation of a phenomenon or concept in pure mathematics.NYC M8.e.ii - Pure mathematics investigation, in which the student: uses methods of mathematical reasoning and justification to make generalizations about the phenomenon.NYC M8.e.iii - Pure mathematics investigation, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.f - History of a mathematical idea, in which the student:
NYC M8.f.i - History of a mathematical idea, in which the student: carries out a historical study tracing the development of a mathematical concept and the people who contributed to it.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Geometry
NYC M8.f.ii - History of a mathematical idea, in which the student: includes a discussion of the actual mathematical content and its place in the curriculum of the present day.NYC M8.f.iii - History of a mathematical idea, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective DescriptionNYC M1 - ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTSNYC M1-1 - The student produces evidence that demonstrates understanding of number and operation concepts; that is, the student:NYC M1.a - Uses addition, subtraction, multiplication, division, exponentiation, and root-extraction in forming and working with numerical and algebraic expressions.
Topic 1 - The Real Numbers Obj. 6 - Operations with rational #s
Obj. 7 - Order of operationsObj. 8 - Evaluate expressions for given values
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 72 - Square roots
Obj. 73 - Write square roots as exponential expressionsObj. 74 - Write expression w/fraction exp as a radicalObj. 75 - Simplify expressions w/fractional exponentsObj. 76 - Simplify nth rootsObj. 78 - Simplify expressions w/rational exponentsObj. 79 - Evaluate exponential expressionsObj. 80 - Rewrite expr using only positive exponentsObj. 81 - Add & subtract radical expressionsObj. 82 - Rationalize denominators
Topic 8 - Polynomials Obj. 119 - Evaluate polynomials for given valuesObj. 120 - Add polynomialsObj. 121 - Subtract polynomialsObj. 122 - Add & subtract polynomialsObj. 123 - Square a binomial, ax + by
Obj. 124 - Multiply 2 binomialsObj. 125 - Multiply monomials by polynomialsObj. 126 - Multiply binomials by trinomialsObj. 127 - Square trinomials
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Obj. 128 - Simplify polynomial expressions using multiplicationObj. 129 - Divide polynomials by monomialsObj. 130 - Divide polynomialsObj. 131 - Long division, factor higher term polynomials
Topic 10 - Rational Expressions and Equations
Obj. 155 - Simplify rational expressionsObj. 156 - Simplify rational expressions by factoringObj. 158 - Multiply & simplify rational expressionsObj. 159 - Divide & simplify rational expressionsObj. 160 - Add rational expressions
Obj. 161 - Subtract rational expressionsObj. 162 - Add & subtract rational expressionsObj. 164 - Simplify complex rational expressions
NYC M1.b - Understands and uses operations such as opposite, reciprocal, raising to a power, taking a root, and taking a logarithm.
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 72 - Square roots
Obj. 76 - Simplify nth rootsObj. 77 - WP: Roots
Topic 9 - Exponents and Logarithms
Obj. 141 - Find logs by converting to exponential formObj. 142 - Find natural logs of numbers
NYC M1.c - Has facility with the mechanics of operations as well as understanding of their typical meaning and uses in applications.NYC M1.d - Understands and uses number systems: natural, integer, rational, and real.
Topic 1 - The Real Numbers Obj. 1 - Determine if #s are irrational
Obj. 2 - Classify Real #sObj. 3 - Properties of real #s
NYC M1.e - Represents numbers in decimal or fraction form and in scientific notation, and graphs numbers on the number line and number pairs in the coordinate plane.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M1.f - Compares numbers using order relations, differences, ratios, proportions, percents, and proportional change.
Topic 1 - The Real Numbers Obj. 5 - Order rational #s
NYC M1.g - Carries out proportional reasoning in cases involving part-whole relationships and in cases involving expansions and contractions.NYC M1.h - Understands dimensionless numbers, such as proportions, percents, and multiplicative factors, as well as numbers with specific units of measure, such as numbers with length, time, and rate units.NYC M1.i - Carries out counting procedures such as those involving sets (unions and intersections) and arrangements (permutations and combinations).
Topic 13 - Probability Obj. 206 - Fundamental Counting Principle
Obj. 209 - Combinations & permutations
NYC M1.j - Uses concepts such as prime, relatively prime, factor, divisor, multiple, and divisibility in solving problems involving integers.NYC M1.k - Uses a scientific calculator effectively and efficiently in carrying out complex calculations.
NYC M1.l - Recognizes and represents basic number patterns, such as patterns involving multiples, squares, or cubes.NYC M2 - GEOMETRY AND MEASUREMENT CONCEPTSNYC M2-1 - The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:NYC M2.a - Models situations geometrically to formulate and solve problems.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M2.b - Works with two- and three-dimensional figures and their properties, including polygons and circles, cubes and pyramids, and cylinders, cones, and spheres.NYC M2.c - Uses congruence and similarity in describing relationships between figures.NYC M2.d - Visualizes objects, paths, and regions in space, including intersections and cross sections of three dimensional figures, and describes these using geometric language.NYC M2.e - Knows, uses, and derives formulas for perimeter, circumference, area, surface area, and volume of many types of figures.
Topic 15 - Trigonometry Obj. 263 - Areas of parallelograms and triangles
NYC M2.f - Uses the Pythagorean Theorem in many types of situations, and works through more than one proof of this theorem.
Topic 7 - Quadratic Obj. 110 - WP: Pythagorean Theorem
NYC M2.g - Works with similar triangles, and extends the ideas to include simple uses of the three basic trigonometric functions.
Topic 15 - Trigonometry Obj. 260 - Find a side given side & angle
Obj. 261 - Find unknown sides of right triangles
NYC M2.h - Analyzes figures in terms of their symmetries using, for example, concepts of reflection, rotation, and translation.NYC M2.i - Compares slope (rise over run) and angle of elevation as measures of steepness.NYC M2.j - Investigates geometric patterns, including sequences of growing shapes.NYC M2.k - Works with geometric measures of length, area, volume, and angle; and non-geometric measures such as weight and time.
Topic 15 - Trigonometry Obj. 237 - Degrees to radians
Obj. 238 - Radians to degreesObj. 239 - Manipulate degrees, minutes, & seconds
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M2.l - Uses quotient measures, such as speed and density, that give "per unit" amounts; and uses product measures, such as person-hours.
NYC M2.m - Understands the structure of standard measurement systems, both SI and customary, including unit conversions and dimensional analysis.NYC M2.n - Solves problems involving scale, such as in maps and diagrams.NYC M2.o - Represents geometric curves and graphs of functions in standard coordinate systems.
Topic 3 - Relations, Functions, and Graphs
Obj. 35 - Graph linear equations, ax + by = c
Obj. 36 - Graph linear equations, y = ax + bObj. 46 - Sketch the graph of a functionObj. 47 - Graph/write eqn that is result of transformation
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 85 - Graph square roots
Obj. 86 - Graph nth rootsTopic 7 - Quadratic Obj. 106 - Graph quadratic functions
Topic 9 - Exponents and Logarithms
Obj. 146 - Graph log functions
Obj. 152 - Graph exponential functions
Topic 10 - Rational Expressions and Equations
Obj. 157 - Graph rational functions & equations
Topic 15 - Trigonometry Obj. 248 - Graph sine & cosine functionsObj. 249 - Graph trig functions
NYC M2.p - Analyzes geometric figures and proves simple things about them using deductive methods.
NYC M2.q - Explores geometry using computer programs such as CAD software, Sketchpad programs, or LOGO.NYC M3 - FUNCTION AND ALGEBRA CONCEPTS
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M3-1 - The student produces evidence that demonstrates understanding of function and algebra concepts; that is, the student:
NYC M3.a - Models given situations with formulas and functions, and interprets given formulas and functions in terms of situations.
Topic 3 - Relations, Functions, and Graphs
Obj. 38 - WP: Function problems
Obj. 41 - WP: Linear equationsTopic 7 - Quadratic Obj. 107 - WP: Graph quadratic
functionsNYC M3.b - Describes, generalizes, and uses basic types of functions: linear, exponential, power, rational, square and square root, and cube and cube root.
Topic 3 - Relations, Functions, and Graphs
Obj. 26 - Use function notation
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 77 - WP: Roots
Topic 9 - Exponents and Logarithms
Obj. 150 - WP: Growth & decay problemsObj. 151 - WP: Earthquake problems
NYC M3.c - Utilizes the concepts of slope, evaluation, and inverse in working with functions.
Topic 3 - Relations, Functions, and Graphs
Obj. 34 - Find inverses of functions
NYC M3.d - Works with rates of many kinds, expressed numerically, symbolically, and graphically.
NYC M3.e - Represents constant rates as the slope of a straight line graph, and interprets slope as the amount of one quantity (y) per unit amount of another (x).NYC M3.f - Understands and uses linear functions as a mathematical representation of proportional relationships.NYC M3.g - Uses arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively.
Topic 12 - Sequences and Series Obj. 190 - Common differences of arithmetic sequences
Obj. 191 - Find terms of arith seq (1st term & common diff)
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Obj. 192 - Find specified term of arithmetic sequenceObj. 193 - Find terms of arith seq (formula for nth term)Obj. 194 - WP: Arithmetic sequences
Obj. 195 - Find sums of arithmetic seriesObj. 196 - Find terms of geo seqObj. 197 - Find ratios of geo seq given 3 termsObj. 198 - Find specified term of geo seq given first 3 termsObj. 199 - Find general terms of geo seq given first 4 termsObj. 200 - WP: Geometric sequencesObj. 201 - Find sums of finite geometric seriesObj. 202 - Find sums of infinite geometric series
NYC M3.h - Defines, uses, and manipulates expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities.
Topic 2 - Linear Equations and Inequalities
Obj. 11 - Solve linear equations
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 84 - Solve formulas for specified variables
Topic 7 - Quadratic Obj. 98 - Factor quadratics, real roots
Obj. 100 - Factor quadratics, roots with radicalsObj. 105 - Solve quad eqns containing rational expr
NYC M3.i - Represents functional relationships in formulas, tables, and graphs, and translates between pairs of these.
Topic 3 - Relations, Functions, and Graphs
Obj. 35 - Graph linear equations, ax + by = c
Obj. 36 - Graph linear equations, y = ax + bObj. 46 - Sketch the graph of a function
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 85 - Graph square roots
Obj. 86 - Graph nth rootsTopic 7 - Quadratic Obj. 106 - Graph quadratic functions
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Topic 8 - Polynomials Obj. 137 - Graph polynomial functions
Topic 9 - Exponents and Logarithms
Obj. 146 - Graph log functions
Obj. 152 - Graph exponential functions
Topic 10 - Rational Expressions and Equations
Obj. 157 - Graph rational functions & equations
Topic 14 - Statistics Obj. 224 - Write function for regression model, given data
NYC M3.j - Solves equations symbolically, graphically, and numerically, especially linear, quadratic, and exponential equations; and knows how to use the quadratic formula for solving quadratic equations.
Topic 2 - Linear Equations and Inequalities
Obj. 11 - Solve linear equations
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 83 - Solve equations containing radicals
Topic 7 - Quadratic Obj. 95 - Solve quad eqns, square root rule (real roots)Obj. 96 - Solve quad eqns, square root rule (complex roots)Obj. 101 - Quadratic formula, 2 real rootsObj. 114 - Solve cubic equations
Topic 9 - Exponents and Logarithms
Obj. 145 - Solve log equations
Obj. 147 - Solve exponential equationsObj. 148 - Solve equations involving natural logs
Topic 10 - Rational Expressions and Equations
Obj. 165 - Solve equations containing rational expressions
NYC M3.k - Makes predictions by interpolating or extrapolating from given data or a given graph.
Topic 7 - Quadratic Obj. 107 - WP: Graph quadratic functions
NYC M3.l - Understands the basic algebraic structure of number systems.
Topic 1 - The Real Numbers Obj. 3 - Properties of real #s
Obj. 4 - Reflex, symm, trans, & subst properties
NYC M3.m - Uses equations to represent curves such as lines, circles, and parabolas.
Topic 3 - Relations, Functions, and Graphs
Obj. 39 - Write equation from slope & point, ax + by = c
Obj. 45 - Write equation of circle given graph
Topic 7 - Quadratic Obj. 104 - Write quad eqns given solutions
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Topic 11 - Conics and Second-Degree Equations
Obj. 170 - Circles, write eqns given centers & radiiObj. 171 - Circles, write eqns using given factsObj. 175 - Ellipses, write eqns using given factsObj. 176 - Graph hyperbolas (standard equation)Obj. 177 - Graph hyperbolas (general equation)Obj. 180 - Parabolas, find vertex from equationObj. 184 - Identify eqns of conics
NYC M3.n - Uses technology such as graphics calculators to represent and analyze functions and their graphs.
NYC M3.o - Uses functions to analyze patterns and represent their structure.NYC M4 - STATISTICS AND PROBABILITY CONCEPTSNYC M4-1 - The student demonstrates understanding of statistics and probability concepts; that is, the student:NYC M4.a - Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distributions, circle graphs, line plots, histograms, and summary statistics.
Topic 14 - Statistics Obj. 230 - Group frequency distributions
NYC M4.b - Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients.
Topic 14 - Statistics Obj. 223 - Name type of regression model, given scatterplot
NYC M4.c - Uses sampling techniques to draw inferences about large populations.NYC M4.d - Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M4.e - Formulates hypotheses to answer a question and uses data to test hypotheses.NYC M4.f - Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents.
NYC M4.g - Explores questions of experimental design, use of control groups, and reliability.NYC M4.h - Creates and uses models of probabilistic situations and understands the role of assumptions in this process.NYC M4.i - Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance.NYC M4.j - Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities.
Topic 13 - Probability Obj. 215 - Probability of independent events
Obj. 216 - Conditional probabilityObj. 217 - Probability of dependent events
NYC M4.k - Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely.NYC M4.l - Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event.NYC M4.m - Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event.
Topic 13 - Probability Obj. 219 - WP: Calculate empirical probability
NYC M4.n - Designs simulations including Monte Carlo simulations to estimate probabilities.NYC M4.o - Works with the normal distribution in some of its basic applications.NYC M5 - PROBLEM SOLVING AND MATHEMATICAL REASONING
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M5-1 - The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution process--formulation, implementation, and conclusion. - FORMULATIONNYC M5.a - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student:
NYC M5.a.i - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: fills out the formulation of a definite problem that is to be solved.
NYC M5.a.ii - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: extracts pertinent information from the situation as a basis for working on the problem.NYC M5.a.iii - The student participates in the formulation of problems; that is, given the statement of a problem situation, the student: asks and answers a series of appropriate questions in pursuit of a solution and does so with minimal "scaffolding" in the form of detailed guiding questions. - IMPLEMENTATIONNYC M5.b - The student makes the basic choices involved in planning and carrying out a solution; that is, the student:
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M5.b.i - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: chooses and employs effective problem solving strategies in dealing with non-routine and multi-step problems.
NYC M5.b.ii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: selects appropriate mathematical concepts and techniques from different areas of mathematics and applies them to the solution of the problem.
NYC M5.b.iii - The student makes the basic choices involved in planning and carrying out a solution; that is, the student: applies mathematical concepts to new situations within mathematics and uses mathematics to model real world situations involving basic applications of mathematics in the physical and biological sciences, the social sciences, and business. - CONCLUSIONNYC M5.c - The student provides closure to the solution process through summary statements and general conclusions; that is, the student:NYC M5.c.i - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: concludes a solution process with a useful summary of results.
NYC M5.c.ii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: evaluates the degree to which the results obtained represent a good response to the initial problem.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M5.c.iii - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: formulates generalizations of the results obtained.
NYC M5.c.iv - The student provides closure to the solution process through summary statements and general conclusions; that is, the student: carries out extensions of the given problem to related problems.
- MATHEMATICAL REASONINGNYC M5.d - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student:
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M5.d.i - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student: employs forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counterexamples and indirect proof.
Topic 16 - Problem solving and reasoning
Obj. 266 - Proof by induction
Obj. 267 - Indirect proofNYC M5.d.ii - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general; that is, the student: differentiates clearly between giving examples that support a conjecture and giving proof of the conjecture.
NYC M6 - MATHEMATICAL SKILLS AND TOOLS
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M6-1 - The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, or books, perhaps working to reconstruct a method; that is, the student:
NYC M6.a - Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate.
Topic 1 - The Real Numbers Obj. 6 - Operations with rational #s
Obj. 7 - Order of operationsObj. 8 - Evaluate expressions for given valuesObj. 9 - WP: Evaluate expressions
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 72 - Square roots
Obj. 75 - Simplify expressions w/fractional exponentsObj. 76 - Simplify nth rootsObj. 78 - Simplify expressions w/rational exponentsObj. 79 - Evaluate exponential expressionsObj. 80 - Rewrite expr using only positive exponentsObj. 81 - Add & subtract radical expressions
Topic 8 - Polynomials Obj. 119 - Evaluate polynomials for given valuesObj. 120 - Add polynomialsObj. 121 - Subtract polynomialsObj. 122 - Add & subtract polynomialsObj. 123 - Square a binomial, ax + by
Obj. 124 - Multiply 2 binomialsObj. 125 - Multiply monomials by polynomialsObj. 126 - Multiply binomials by trinomialsObj. 127 - Square trinomials
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Obj. 128 - Simplify polynomial expressions using multiplicationObj. 129 - Divide polynomials by monomialsObj. 130 - Divide polynomialsObj. 131 - Long division, factor higher term polynomialsObj. 132 - Factor trinomials, ax(x + b)(x - c)Obj. 133 - Factor difference of squaresObj. 134 - Factor sum or difference of 2 cubesObj. 135 - Factor polynomials into binomials & trinomialsObj. 136 - Factor 4-term expressions by grouping
Topic 10 - Rational Expressions and Equations
Obj. 155 - Simplify rational expressionsObj. 156 - Simplify rational expressions by factoringObj. 158 - Multiply & simplify rational expressionsObj. 159 - Divide & simplify rational expressionsObj. 160 - Add rational expressions
Obj. 161 - Subtract rational expressionsObj. 162 - Add & subtract rational expressionsObj. 164 - Simplify complex rational expressions
NYC M6.b - Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy.NYC M6.c - Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology.
Topic 9 - Exponents and Logarithms
Obj. 141 - Find logs by converting to exponential form
Obj. 142 - Find natural logs of numbersObj. 145 - Solve log equationsObj. 146 - Graph log functions
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Obj. 147 - Solve exponential equationsObj. 148 - Solve equations involving natural logs
Topic 10 - Rational Expressions and Equations
Obj. 153 - Rational expressions, domains
NYC M6.d - Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems.
NYC M6.e - Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution.NYC M6.f - Uses the number line and Cartesian coordinates in the plane and in space.
Topic 3 - Relations, Functions, and Graphs
Obj. 40 - Find slopes from 2 points
Obj. 45 - Write equation of circle given graph
Topic 11 - Conics and Second-Degree Equations
Obj. 167 - Find distances between 2 pointsObj. 170 - Circles, write eqns given centers & radiiObj. 171 - Circles, write eqns using given facts
NYC M6.g - Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms.
Topic 2 - Linear Equations and Inequalities
Obj. 19 - Graph inequalities (number line)
Obj. 20 - Graph inequalities, 1-variable (coordinate plane)Obj. 21 - Graph linear inequalities in 2-variablesObj. 22 - Graph absolute value inequalities (number line)Obj. 23 - Graph absolute value ineq (coordinate plane)Obj. 24 - Solve & graph compound inequalities
Topic 3 - Relations, Functions, and Graphs
Obj. 35 - Graph linear equations, ax + by = cObj. 36 - Graph linear equations, y = ax + bObj. 47 - Graph/write eqn that is result of transformation
Topic 6 - Roots, Radicals, and Complex Numbers
Obj. 85 - Graph square roots
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Obj. 86 - Graph nth rootsTopic 7 - Quadratic Obj. 106 - Graph quadratic functions
Obj. 107 - WP: Graph quadratic functionsObj. 116 - Graph quadratic inequalities
Topic 8 - Polynomials Obj. 137 - Graph polynomial functions
Topic 9 - Exponents and Logarithms
Obj. 146 - Graph log functions
Obj. 152 - Graph exponential functions
Topic 10 - Rational Expressions and Equations
Obj. 157 - Graph rational functions & equations
Topic 11 - Conics and Second-Degree Equations
Obj. 168 - Graph circles
Obj. 173 - Graph ellipsesObj. 176 - Graph hyperbolas (standard equation)Obj. 177 - Graph hyperbolas (general equation)Obj. 179 - Hyperbolas, graph inequalitiesObj. 181 - Graph parabolas (y = x^2)
Obj. 182 - Graph parabolas (x = y^2)
NYC M6.h - Sets up and solves equations symbolically (when possible) and graphically.
Topic 1 - The Real Numbers Obj. 9 - WP: Evaluate expressions
Topic 2 - Linear Equations and Inequalities
Obj. 12 - WP: Solve linear equations
Obj. 18 - WP: Solve linear inequalitiesObj. 25 - WP: Absolute value & inequalities
Topic 3 - Relations, Functions, and Graphs
Obj. 38 - WP: Function problems
Obj. 41 - WP: Linear equationsTopic 4 - Systems of Equations and Inequalities
Obj. 55 - WP: Solve systems, number problemsObj. 56 - WP: Solve systems, motion & distance problemsObj. 57 - WP: Solve systems, age problemsObj. 58 - WP: Solve systems, coin problems
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
Obj. 59 - WP: Solve systems, mixture & investment problems
Topic 7 - Quadratic Obj. 107 - WP: Graph quadratic functionsObj. 109 - WP: Variation problemsObj. 110 - WP: Pythagorean TheoremObj. 111 - WP: Number problems using quad eqnsObj. 112 - WP: Area & perimeterObj. 113 - WP: Other problems using quad eqns
Topic 8 - Polynomials Obj. 138 - WP: PolynomialsTopic 9 - Exponents and Logarithms
Obj. 149 - WP: Interest problems
Obj. 150 - WP: Growth & decay problemsObj. 151 - WP: Earthquake problems
Topic 10 - Rational Expressions and Equations
Obj. 163 - WP: Rational expressions
Topic 11 - Conics and Second-Degree Equations
Obj. 172 - WP: Circles
Obj. 183 - WP: Production & profit problems
NYC M6.i - Knows how to use algorithms in mathematics, such as the Euclidean Algorithm.NYC M6.j - Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem.NYC M6.k - Writes a simple computer program to carry out a computation or simulation to be repeated many times.NYC M6.l - Uses tools such as rulers, tapes, compasses, and protractors in solving problems.NYC M6.m - Knows standard methods to solve basic problems and uses these methods in approaching more complex problems.
NYC M7 - MATHEMATICAL COMMUNICATION
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M7-1 - The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is, the student:NYC M7.a - Is familiar with basic mathematical terminology, standard notation and use of symbols, common conventions for graphing, and general features of effective mathematical communication styles.
NYC M7.b - Uses mathematical representations with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams.
NYC M7.c - Organizes work and presents mathematical procedures and results clearly, systematically, succinctly, and correctly.NYC M7.d - Communicates logical arguments clearly, showing why a result makes sense and why the reasoning is valid.NYC M7.e - Presents mathematical ideas effectively both orally and in writing.NYC M7.f - Explains mathematical concepts clearly enough to be of assistance to those who may be having difficulty with them.NYC M7.g - Writes narrative accounts of the history and process of work on a mathematical problem or extended project.NYC M7.h - Writes succinct accounts of the mathematical results obtained in a mathematical problem or extended project, with diagrams, graphs, tables, and formulas integrated into the text.
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M7.i - Keeps narrative accounts of process separate from succinct accounts of results, and realizes that doing so can enhance the effectiveness of each.NYC M7.j - Reads mathematics texts and other writing about mathematics with understanding.NYC M8 - PUTTING MATHEMATICS TO WORKNYC M8-1 - The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of high school, conducts investigations or projects drawn from at least three of the kinds. A single investigation or project may draw on more than one kind.
NYC M8.a - Data study, in which the student:NYC M8.a.i - Data study, in which the student: carries out a study of data relevant to current civic, economic, scientific, health, or social issues.
NYC M8.a.ii - Data study, in which the student: uses methods of statistical inference to generalize from the data.NYC M8.a.iii - Data study, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.b - Mathematical model of a physical system or phenomenon, in which the student:
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M8.b.i - Mathematical model of a physical system or phenomenon, in which the student: carries out a study of a physical system or phenomenon by constructing a mathematical model based on functions to make generalizations about the structure of the system.
NYC M8.b.ii - Mathematical model of a physical system or phenomenon, in which the student: uses structural analysis (a direct analysis of the structure of the system) rather than numerical or statistical analysis (an analysis of data about the system).
NYC M8.b.iii - Mathematical model of a physical system or phenomenon, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
NYC M8.c - Design of a physical structure, in which the student:NYC M8.c.i - Design of a physical structure, in which the student: creates a design for a physical structure.NYC M8.c.ii - Design of a physical structure, in which the student: uses general mathematical ideas and techniques to discuss specifications for building the structure.
NYC M8.c.iii - Design of a physical structure, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.d - Management and planning analysis, in which the student:
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M8.d.i - Management and planning analysis, in which the student: carries out a study of a business or public policy situation involving issues such as optimization, cost-benefit projections, and risks.
NYC M8.d.ii - Management and planning analysis, in which the student: uses decision rules and strategies both to analyze options and balance trade-offs; and brings in mathematical ideas that serve to generalize the analysis across different conditions.NYC M8.d.iii - Management and planning analysis, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.e - Pure mathematics investigation, in which the student:NYC M8.e.i - Pure mathematics investigation, in which the student: carries out a mathematical investigation of a phenomenon or concept in pure mathematics.NYC M8.e.ii - Pure mathematics investigation, in which the student: uses methods of mathematical reasoning and justification to make generalizations about the phenomenon.NYC M8.e.iii - Pure mathematics investigation, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.NYC M8.f - History of a mathematical idea, in which the student:
Accelerated Math Grades 9 - 10
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Agency Tag Set NameNew York City, Math, Adopted 1998, Revised 2001, Grade 9-10, New Standards Performance Standards--Mathematics, produced by City of New York Department of Education
Standard Topic Description Objective Description
Standards List with Aligned Product SkillsProduct NameAM NY Custom Algebra2
NYC M8.f.i - History of a mathematical idea, in which the student: carries out a historical study tracing the development of a mathematical concept and the people who contributed to it.NYC M8.f.ii - History of a mathematical idea, in which the student: includes a discussion of the actual mathematical content and its place in the curriculum of the present day.NYC M8.f.iii - History of a mathematical idea, in which the student: prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
Accelerated Math Grades 9 - 10
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