california standards map for mathematics grade...

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Basic Math Skills © 2003

correlated to

California Standards Map for Mathematics Grade 7

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Publisher: American Guidance Service, Inc. Program Title: Basic Math Skills ©2003 Components: SE: Student Edition; TE: Teacher’s Edition; ACT: Activity in Teacher’s Resource Library (TRL); WB: Workbook Activity in TRL; CC: Community Connections; MJ: Math on the Job Grade Level: Grade Seven Intended Audience: High school and adult learners who are below grade level in comprehension skills or who need

extra help grasping new concepts.

California Standards Map – Grade Seven By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.

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(California Standards Map, Grade 7: AGS Basic Math Skills, Cont.)

PUBLISHER’S CITATIONS* MEETS STANDARD

GRADE STANDARD #

TEXT OF STANDARD INTRODUCED PRACTICED TAUGHT TO MASTERY

Y N

NUMBER SENSE

7 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:

7 1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.

SE 106; TE 106 SE 106-107; TE 106-107; WB 55-58; ACT 44

SE 107; TE 107

7 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

SE 68-69, 72, 75, 79, 99, 101, 103, 106, 108; TE 68-69, 72, 75, 79, 99, 101, 103, 106, 108

SE 68-69, 70-71, 72-73, 74, 75-76, 77-78, 79-80, 81-82, 83-85, 86, 99-100, 101-102, 103-105, 106-107, 108-113; TE 68-69, 70-71, 72-73, 74, 75-76, 77-78, 79-80, 81-82, 83-85, 86, 99-100, 101-102, 103-105, 106-107, 108-113; WB 33-46, 52-61; ACT 28-37, 42-45; MJ 3; CC 3

SE 68-69, 70-71, 72-73, 74, 75, 77, 81, 83, 101, 103, 106, 108, 110, 112; TE 68-69, 70-71, 72-73, 74, 75, 77-78, 79, 81, 83, 101, 103, 106, 108-109

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GRADE STANDARD #


Y N

NUMBER SENSE 1.0, Cont.

7 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms, Cont.:

7 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

SE 115, 143-144; TE 115, 143-144

SE 115, 116-117, 143-147; TE 115, 116-117, 143-147; WB 63, 64, 71; ACT 47, 48, 55

SE 115, 116, 143; TE 115, 116, 143

7 1.4 Differentiate between rational and irrational numbers.

SE 116-117, 245; TE 116, 244

SE 116-117, 245-246, 247-248, 250; TE 116-117, 245-246, 247-248, 250; WB 64, 110-112; ACT 48, 95-97

SE 116-117, 245-246, 247-248, 249-250; TE 116-117, 245-246, 247-248, 249-250

7 1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

SE 114; TE 114 SE 114, 116-117; TE 114, 116-117; WB 62, 64; ACT 46, 48

SE 114, 116-117; TE 114, 116-117

4



GRADE STANDARD #


Y N


7 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms, Cont.:

7 1.6 Calculate the percentage of increases and decreases of a quantity.

SE 158; TE 158 SE 159, 160-161, 162, 163, 164, 165, 166; TE 158-159, 160-161, 162, 163, 164, 165, 166;WB 78-83, ACT 62-67; MJ 6; CC 6

SE 158, 160, 161, 162, 163, 164, 165, 166; TE 158-159, 160-161, 162, 163, 164, 165, 166

7 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

SE 158, 160, 161, 162, 163, 164, 165; TE 158, 160, 161, 162, 163, 164, 165

SE 159, 160-161, 162, 163, 164, 165, 166; TE 158-159, 160-161, 162, 163, 164, 165, 166;WB 78-83, ACT 62-67; MJ 6; CC 6

SE 158, 160, 161, 162, 163, 164, 165, 166; TE 158-159, 160-161, 162, 163, 164, 165, 166

7 2.0 Students use exponents, powers, and roots and use exponents in working with fractions:

7 2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.

SE 106; TE 106 SE 106-107; TE 106-107; WB 55-58; ACT 44

SE 106; TE 106-107

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GRADE STANDARD #


Y N


7 2.0 Students use exponents, powers, and roots and use exponents in working with fractions, Cont.

7 2.2 Add and subtract fractions by using factoring to find common denominators.

SE 38, 77, 81; TE 38, 77, 81

SE 38, 48-49, 51, 52-53, 78, 81-82, 83-85, 86; TE 38, 48-49, 51, 52-53, 77-78, 81-82, 83-85, 86; WB 17, 23, 25, 26, 40, 42-46; ACT 12, 18, 20, 21, 33, 35-37

SE 38, 48-49, 51, 52-53, 77, 81, 83; TE 38, 48-49, 51, 52-53, 77-78, 81-82, 83-85

7 2.3 Multiply, divide, and simplify rational numbers by using exponent rules.

SE 106; TE 106 SE 106-107; TE 106-107; WB 55-58; ACT 44

SE 106; TE 106-107

7 2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.

6



GRADE STANDARD #


Y N

ALGEBRA AND FUNCTIONS

7 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:

7 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).

SE 316; TE 316 SE 316, 329, 338; TE 316, 329, 338; WB 129; ACT 114

SE 316; TE 316

7 1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 52).

SE 31; TE 31 SE 31; TE 31; WB 16; ACT 11

SE 31; TE 31

7 1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.

SE 319-321; TE 319-321

SE 319-321; TE 319-321; WB 131; ACT 116

SE 319-321; TE 319-321

7



GRADE STANDARD #


Y N

ALGEBRA AND FUNCTIONS, Cont.

7 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs, Cont.

7 1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.

SE 308, 310, 312, 324, 325, 326; TE 308, 310, 312, 324, 325, 326

SE 308-309, 310-313, 324, 325, 326-329; TE 308-309, 310-313, 324, 325, 326-329; WB 126, 127, 133-135; ACT 111, 112, 118-120

SE 308-309, 310-313, 324, 325, 326-329; TE 308-309, 310-313, 324, 325, 326-329

7 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

SE 262, 265, 271, 277; TE 262, 265, 271, 277

SE 263-264, 266-270, 271-272, 273, 275-276, 277-279, 281-283, 284; TE 263-264, 266-270, 271-272, 273, 275-276, 277-279, 281-283, 284; WB 115-121; ACT 100-106; MJ 11; CC 11

SE 262-264, 266, 367-268, 270, 271-272, 273, 274, 276, 277, 279, 280, 284; TE 262-264, 265-270, 271-272, 273, 274-276, 277-279, 280-283, 284

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GRADE STANDARD #


Y N


7 2.0 Students interpret and evaluate expressions involving integer powers and simple roots:

7 2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.

SE 30, 106; TE 30, 106 SE 30, 106-107, 346; TE 30, 106-107, 346; WB 15, 55-58; ACT 10, 44

SE 30, 106; TE 30, 106-107

7 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.

SE 330-331; TE 330-331

SE 331-333, 334-335; TE 331-333, 334-335; WB 136-137; ACT 121-122

SE 330-333, 334-335; TE 330-333, 334-335

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GRADE STANDARD #


Y N


7 3.0 Students graph and interpret linear and some nonlinear functions:

7 3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.

7 3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).

SE 201, 235, 249 SE 202-204, 235-236, 249-250; TE 202-204, 235-236, 249-250; WB 94, 108, 112; ACT 79, 93, 97

7 3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of the graph.

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GRADE STANDARD #


Y N


7 3.0 Students graph and interpret linear and some nonlinear functions, Cont.

7 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

7 4.0 Students solve simple linear equations and inequalities over the rational numbers:

7 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

SE 334; TE 334 SE 334-335; TE 334-335; WB 137; ACT 122

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GRADE STANDARD #


Y N


7 4.0 Students solve simple linear equations and inequalities over the rational numbers, Cont.

7 4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

SE 222, 223, 251; TE 222, 223, 251

SE 105, 111, 113, 212, 222, 223-225, 251-252, 253-255, 256; TE 26, 212, 222, 223-225, 251-252, 253-255, 300; WB 102, 103, 113, 114; ACT 87, 88, 98, 99

SE 222, 223-225, 251-252, 253-255, 256; TE 222, 223-225, 251-252, 253-255, 256

MEASUREMENT AND GEOMETRY

7 1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:

7 1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).

SE 192, 193, 195, 196, 201, 205, 206, 209, 210, 218, 219, 220, 237; TE l192, 193, 195, 196, 201, 205, 206, 209, 210, 218, 219, 220, 237

SE 192, 194, 195, 196-197, 202-205, 206-208, 209, 210-211, 218, 219, 220-221, 222, 223-225, 235-236, 237, 238; TE 192, 194, 195, 196-197, 202-205, 206-208, 209, 210-211, 218, 219, 220-221, 222, 223-225, 235-236, 237, 238; WB 89-92, 94-103, 108-109; ACT 74-77, 79-88, 93, 94; MJ 8; CC 8

SE 192-197, 205-211, 218-225, 235-237; TE 192-197, 205-211, 218-225, 235-237

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GRADE STANDARD #


Y N

MEASUREMENT AND GEOMETRY, Cont.

7 1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems, Cont.

7 1.2 Construct and read drawings and models made to scale.

SE 290; TE 290 SE 290-293, 295, 297-298, 299-301, 302; TE 290-293, 295, 297-298, 299-301, 302; WB 122-125; ACT 107-110; MJ 12; CC 12

SE 290-293, 294-295, 296-298, 299-301; TE 290-293, 294-295, 296-298, 299-301

7 1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

SE 148, 153, 158, 160; TE 148, 153, 158, 160

SE 105, 111, 113, 148, 153-155, 159, 160-161, 162, 163, 164, 212; TE 26, 148, 153-155, 159, 160-161, 162, 163, 252; WB 75-76, 78-81; ACT 59-60, 62-65

SE 148, 153-155, 158-159, 160-161, 162, 163; TE 148, 153-155, 158-159, 160-161, 162, 163

13



GRADE STANDARD #


Y N


7 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale.

7 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

SE 198, 201, 226, 229, 235; TE 198, 201, 226, 229, 235

SE 197, 199-200, 202-204, 227-228, 230-231, 232-233, 234, 235-236, 237, 238, 249-250; TE 197, 199-200, 202-204, 227-228, 230-238, 249-250; WB 93, 94, 104-109; ACT 78, 79, 89, 95; MJ 9; CC 9

SE 198-200, 201-204, 226-228, 229-231, 232-233, 234, 235-236, 237; TE 198-200, 201-204, 226-228, 229-231, 2332-233, 234, 235-236, 237

7 2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.

SE 234; TE 234 SE 234; TE 234; WB 107; ACT 92

SE 234; TE 234

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GRADE STANDARD #


Y N


7 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale, Cont.

7 2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.

SE 201, 235; TE 201, 235

SE 202-204, 207-208, 211, 235-236, 237, 238; TE 202-204, 207-208, 211, 235-236, 237, 238; WB 94, 96, 108, 109; ACT 79, 81, 93, 94

SE 201-204, 207-208, 211, 235-236, 237, 238; TE 201-204, 207-208, 211, 235-236, 237, 238

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GRADE STANDARD #


Y N


7 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale, Cont.

7 2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches of =[1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).

SE 195, 196, 206, 210; TE 195, 196, 206, 210

SE 195, 196-197, 206-208, 210-211; TE 195, 196-197, 206-208, 210-211; WB 92, 96, 98; ACT 77, 81, 83

SE 195, 196-197, 206-208, 210-211; TE 195, 196-197, 206-208, 210-211

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GRADE STANDARD #


Y N


7 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:

7 3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, mid-points, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

SE 176-177; TE 176-177

SE 177-179, 186; TE 177-179, 186, 246, 247; WB 86; ACT 70

SE 176-179, 186; TE 176-179, 186

7 3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

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GRADE STANDARD #


Y N


7 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures, Cont.

7 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.

7 3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.

SE 294; TE 294 SE 297-298; TE 297-298; WB 124; ACT 109

SE 296; TE 296

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GRADE STANDARD #


Y N


7 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures, Cont.

7 3.5 Construct two-dimensional patterns for three dimensional models, such as cylinders, prisms, and cones.

SE 184, 235; TE 184, 235

SE 238; TE 185, 238

7 3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).

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GRADE STANDARD #


Y N

STATISTICS, DATA ANALYSIS, AND PROBABILITY

7 1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:

7 1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.

SE 262, 265, 271, 274, 277; TE 262, 265, 271, 274, 277

SE 263-264, 266-270, 271-272, 273, 275-276, 277-279; TE 262-264, 265-270, 271-272, 273, 274-276, 277-279; WB 115-120; ACT 100-105

7 1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).

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GRADE STANDARD #


Y N

STATISTICS, DATA ANALYSIS, AND PROBABILITY, Cont.

7 1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program, Cont.

7 1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.

MATHEMATICAL REASONING

7 1.0 Students make decisions about how to approach problems.

7 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

*1 (see Publisher’s Notes at end of correlation)

*1 *1

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GRADE STANDARD #


Y N

MATHEMATICAL REASONING, Cont.

7 1.0 Students make decisions about how to approach problems, Cont.

7 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.

*1 *1 *1

7 1.3 Determine when and how to break a problem into simpler parts.

*1 *1 *1

7 2.0 Students use strategies, skills, and concepts in finding solutions:

7 2.1 Use estimation to verify the reasonableness of calculated results.

7 2.2 Apply strategies and results from simpler problems to more complex problems.

*2 *2 *2

22



GRADE STANDARD #


Y N


7 2.0 Students use strategies, skills, and concepts in finding solutions, Cont.

7 2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

7 2.4 Make and test conjectures by using both inductive and deductive reasoning.

7 2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

*3 *3 *3

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GRADE STANDARD #


Y N


7 2.0 Students use strategies, skills, and concepts in finding solutions, Cont.

7 2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

*1 *1 *1

7 2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to specified degree of accuracy.

SE 4 SE 4-7, 20, 29, 95-98; TE 4-7, 20, 95-98; WB 4, 50; ACT 2, 40

SE 4-7, 95-98, 112, 117, 144, 145, 147, 158, 160; TE 4-7, 95-98

7 2.8 Make precise calculations and check the validity of the results from the context of the problem.

*1 *1 *1

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GRADE STANDARD #


Y N


7 3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:

7 3.1 Evaluate the reasonableness of the solution in the context of the original situation.

*1 *1 *1

7 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

*4 *4 *4

7 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.

*5 *5 *5

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(California Standards Map, Grade 7: AGS Basic Math Skills, Cont.) PUBLISHER’S NOTES: *1 = See Exercises, Problem Solving, and Application problems throughout. *2 = In each lesson and chapter throughout, students begin with basic problems and then apply mathematical principles to increasingly complex problems. See, for example, Chapter 6: Percent (SE/TE pages 138-169). Students begin by understanding the meaning of percent (page 140), move on to conversion among fractions, decimals, and percents (pages 141-147), understanding a percentage sentence and solving for each part (pages 148-155), extending percents to include proportions (pages 156-157), and applying percent calculations to discounts, tax, interest, commission, and tips (pages 158-165). *3 = Throughout. See the following examples: •Words: See definitions of key words and concepts in blue boxes at the beginning of many lessons. •Numbers: SE pages 62, 63, 75-76, 101-102, 114, 148, 149 •Symbols: SE pages 124-125, 175, 245-248 •Charts/Tables: SE pages 86, 98, 130-131, 132, 134, 161 •Graphs: SE pages 262, 263, 265-267, 271-272, 274-275 •Diagrams/Models: SE pages 52-53, 60, 140, 180-181, 202 *4 = In each lesson throughout, problem solving is demonstrated in green “Example” sections. Students then solve similar problems in Exercise and Problem Solving sections. See, for example, SE pages 70-71, 83-84, 103-105, 143-144, 147, 156, 248, 249, 268-269 *5 = In addition to the methods outlined in 3.2 above, students apply new problem-solving strategies in Application sections following each chapter. See pages 32, 54, 86, 118, 134, 166, 186, 212, 238, 256, 284, 302, 338

california standards map for mathematics grade...

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