week 1 of the first quarter - atlanta public schools · web view2.2.7 m7n1c, d practice adding and...

Atlanta Public Schools Teaching Plans Seventh Grade Quarter: 2 Week: 1

Instructional Unit Plan

Unit III Georgia Performance Standards

M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.

Unit 3 Framework Enduring Understandings

Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Absolute value is useful in ordering and graphing positive and negative numbers.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Positive and negative numbers are often used to solve problems in everyday life.

Unit 3 Framework Essential Questions

When are negative numbers used and why are they important?

Why is it useful for me to know the absolute value of a number?

Unit III Assessments

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35.

VocabularyAbsolute valueIntegersNatural numbersNegative numbersOpposite numbersPositive numbersSignWhole numbers

Literacy GPSELA7R2 The student understands and acquires new vocabulary and uses it correctly in reading and writing.

ELA7RC3 The student acquires new vocabulary in each content area and uses it correctly.

ELA7RC4 The student establishes a context for information acquired by reading across subject areas

- 1 –Draft for Content June 25


Georgia Performance Standards

M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Absolute value is useful in ordering and graphing positive and negative numbers.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Positive and negative numbers are often used to solve problems in everyday life.


When are negative numbers used and why are they important?

Why is it useful for me to know the absolute value of a number?

. VocabularyAbsolute valueIntegersNatural numbersNegative numbersOpposite numbersPositive numbersSignWhole numbers





Warm-Up / Quick PracticeWrite prime factorizations for numbers

Use the distributive property to simplify numerical expressions

Skill Mastery: Solve equations

Problem Solving Solve routine problems and a non-routine problem using the Make an Organized List Strategy

Focus LessonsRef# State/District

StandardsObjectives Resources Materials

2.1.1 M7N1a, b, d Solve problems involving time zones

MIC: Operations, “What Time Is It There?,” Problems 1 and 2, pp 1 - 2; “World Time Zones,” Problems 3 and 4, pp. 3 - 4

Student Activity Sheet 1, MIC T. E. p. 75ScissorsTape

2.1.2 M7N1a, b, d Use positive and negative numbers to solve problems involving time change between different time zones

MIC: Operations, “Positive and Negative,” Problems 5 - 10, pp. 5 – 6 and “Additional Practice, Section A, p. 52

Student Activity Sheet 1, MIC T. E. p. 75MIC, pp. 5 - 6, and 52

2.1.3 M7N1a, b, c, d Use positive and negative numbers to describe elevation relative to the sea levelModel combination of integers on a vertical number line in a real-world context using concept of absolute value

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Helicopters and Submarines,” pp. 10 - 12 of 35.

Copies of tasks

2.1.4 M7N1b, c, d Compare and order positive and negative numbers on a number line

Use a vertical number line for elevation to add and subtract integers

MIC: Operations, “Ordering the Numbers,” Problems 1 - 9, pp. 12 – 15

MIC, pp. 12 – 15

2.1.5 See Differentiated Instruction


Variety of Instructional Tasks

Weekly Focus: Solve problems involving integers and absolute value using Holt Mathematics Course 2, pp. 76 – 78.

Maintenance: Solve problems involving the multiplication of fractions and mixed numbers with “Model Fraction Multiplication (and Division) and problems 54-58 from Holt Mathematics Course 2, pp. 194 and 199.

Maintenance: Solve two-step equations from Holt Mathematics Course 2, “Solving Two-Step Equations,” pp. 678- 680.

Exploration: Order numbers on a number line using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Using the Number Line,” pp. 12 - 14 of 35.Explore graphs using graphing calculators.

Intervention: Include in reteaching representing the relationship between two variables in forms of a table, graph, and an equation using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Helicopters and Submarines,” pp. 10 - 12 of 35..

Homework

Weekly Focus: Identify integers on a number line; compare and order integers

Maintenance: Evaluate expressions

Skill: Solve equations

Reflection with Closure/JournalDescribe how to compare the following types of numbers when it comes to which is larger: two positive numbers (2) two negative numbers(a) a positive and a negative numberDoes it matter whether a number line is drawn vertically or horizontally when solving a problem? Explain your answer.Create a real-life situation where absolute value can be applied.

JournalTell which number is greater and why -4,500 or =10,000.Name the greatest negative integer and the least nonnegative integer. Then compare their absolute values of these integers.

Evidence of Learning (Assessments)

Weekly Focus: Teacher-selected assessment items including MIC: Operations Section A

Skill Mastery: Solve equations. (1) 2m = 24 (2) 416 = 4c (3) 3s + 8 = 26 (4) 92 – 16t = 12Performance Tasks:

Culminating Activities:



M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.


Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Positive and negative numbers are often used to solve problems in everyday life.


What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?

Vocabulary

IntegersNegative numbersOpposite numbersPositive numbersSign

Literacy GPS





Warm-Up / Quick PracticeMental Math: Multiply two digit factors working left to right (for example for 23 x 45, think 20 x 40 = 800, then 3 x 10 = 120 for 920, then 5 x 20 = 100 for 1020, and finally 3 x 5 = 15 for a final product of 1035)Compare and order integersPerform the given transformationSM: Multiply and divide decimals

Problem Solving Solve routine problems and a non-routine problem using the Make a Table Strategy Refer to Holt Mathematics Course 2, Problem Solving Handbook.



2.2.6 M7N1c, d Model the relationship between adding and subtracting integers

MIC: Operations, “Ronnie the Robot,” Problems 10 - 15, pp. 16 – 19; Activity, p. 18

MIC, pp. 12 – 15Colored tape or rope or long stringCards with positive and negative Numbers

2.2.7 M7N1c, d Practice adding and subtracting integers with a number line and arithmetic trees

MIC: Operations, “Adding and Subtracting,” Problems 1 - 7, pp. 22 – 25

MIC, pp. 22 – 25Student Activity Sheet 2, p. 76

2.2.8 M7N1c, d Continue to practice adding and subtracting with integers using the Integer Game and using arithmetic trees

MIC: Operations, “Adding and Subtracting,” Problems 8 - 11, pp. 26, 27, and 55Additional Practice, Section C, Problem 3

MIC, pp. 22 – 25Student Activity Sheet 2, p. 76MIC T. E., p. 55T

2.2.9 M7N1a, c, d Add and subtract integers using two-colored counters

Holt Mathematics Course 2, “Model Integer Addition,” pp. 80- 85 and “Model Integer Subtraction,” pp. 86-91.

Two color counters



Weekly Focus: Model subtraction of integers with “Hands On Lab” from Holt Mathematics Course 2, pp. 86-87.

Maintenance: Order numbers on a number line using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Using the Number Line,” pp. 12 - 14 of 35. Choose additional sets of rational numbers for students to order on a number line.

Maintenance: Model and solve problems involving the division of fractions and mixed numbers with “Model Fraction (Multiplication and Division) and Industrial Arts Link from Holt Mathematics Course 2, pp. 194 and 203.

Exploration: Explore misleading graphs using Holt Mathematics Course 2, “Misleading Graphs,” pp. 422 - 425.

Intervention: Plot coordinate points using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Connect the Dots,” pp. 7 - 9 of 35. Include the reteaching of comparing and ordering negative and positive integers.

Homework

Weekly Focus: Add and subtract integers

Maintenance: Compare and order integers

Skill: Multiply and divide decimals

Reflection with ClosureDraw pictures to model the addition problem -3 + 5 = ___ using three different strategies. Which strategy do you prefer and why?When adding two integers, how can one determine if the sum will be positive, negative, or zero?How are zero pairs used in the modeling of addition and subtraction of integers?

JournalCompare the method used to add integers with like signs and the method used to add integers with different signs.Tell whether you can reverse the order of integers when you are subtracting and still get the same answer. Why or why not.



Weekly Focus: Teacher-selected assessment items including MIC: Operations Section B and C

Skill Mastery: Multiply and divide decimals (1) 200 x 0.004 = (2) 4.3 x 2.8 = (3) 380 x 0.125 (4) 0.01 ÷ 100 = (5) 85 ÷ 0.5 = (6) 4.416 ÷ 19.2 =

Performance Tasks:

Culminating Activity:



M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Positive and negative numbers are often used to solve problems in everyday life.


When are negative numbers used and why are they important?What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?

Vocabulary

IntegersNegative numbersOpposite numbersPositive numbersSign

Literacy GPS




Warm-Up / Quick PracticeMental Math: Add fractions when one addend contains the common denominator (for example, for ½ + 3/8 = , think ½ = 4/8 and 4/8 + 3/8 = 7/8)Use two-colored counters to model addition and subtraction of integersWrite decimals in wordsSM: Add and subtract fractions and mixed numbers

Problem Solving Select and apply the appropriate operations to solve single and multi-step word problems involving mixed numbers or decimals



2.3.11 M7N1c, d Find the mean of a data set that contains negative and positive numbers.

MIC: Operations, “Temperatures and Altitudes,” Problems 12 - 18, pp. 28 - 30

MIC, pp. 28 – 30

2.3.12 M7N1c, d Solve problems involving elevation and temperature changes

MIC: Operations, “Higher and Higher,” Problems 19 - 26, pp. 30 - 33

MIC, pp. 30 – 33

2.3.13 M7N1c, d Multiply with positive and negative numbers

MIC: Operations, “Calculations Using Differences,” Problems 1 - 7, pp. 36 - 39

MIC, pp. 30 – 33

2.3.14 M7N1c, d Explore a pattern to support the rules for multiplying integers and complete arithmetic trees for integers

MIC: Operations, “Multiplication with Positive and Negative Numbers,” Problems 8 - 13, pp. 36 - 41

MIC, pp. 36 – 41Student Activity Sheet 3, p. 77




Weekly Focus: Model integer multiplication and division using Holt Mathematics Course 2, “Model Integer Multiplication and Division, Hands-On Lab,” pp. 92 – 93.

Maintenance: Order numbers on a number line using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Using the Number Line,” pp. 12 - 14 of 35. Choose additional sets of rational numbers for students to order on a number line.

Maintenance: Adding and Multiplying rational numbers using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Sums and Products,” pp. 14 - 19 of 35.

Exploration: Explore misleading graphs using Holt Mathematics Course 2, “Misleading Graphs,” pp. 424 - 425.

Intervention: Include the reteaching of adding and subtracting integers using various strategies using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Always, Sometimes, Never,” pp. 20 - 22 of 35..

Homework

Weekly Focus: Multiply integers

Maintenance: Model the addition and subtraction of integers

Skill: Add and subtract fractions and mixed numbers

Reflection with Closure

Write a strategy for multiplying two integers. Be sure to include all possible combinations—positive integers, negative integers, and zero. Verify your strategy with examples. Design a table to show rules for multiplying integers. Be sure to include all possible combinations of positive integers, negative integers, and zero.Is it possible to have a data set with a negative mean? If possible give an example of the data set and determine its mean.

JournalList at least four different multiplication examples that have 24 as their product. Use both negative and positive integers.Explain how the signs of two integers affect their product and their quotient


Weekly Focus: Teacher-selected assessment items including MIC: Operations Sections C and D items

Skill Mastery: Add and subtract fractions and mixed numbers.(1) 3 ¼ + 7 5/8 = (2) 34 4/5 + 72 1/3 = (3) 56 ½ - 38 ¾ = (4) 67 2/3 - 56 ¾ = (5) 101 2/5 + 128 ¾ + 175 2/3 =Performance Tasks:




M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.M7A1a Translate verbal phrases to algebraic expressions.M7A1b Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.M7A1c Add and subtract linear expressions.M7A2a Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.M7A2b Use the addition and multiplication properties of equality to solve one- and two-step equations.


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Absolute value is useful in ordering and graphing positive and negative numbers.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Properties of real numbers hold for all rational numbers.Positive and negative numbers are often used to solve problems in everyday life.


When are negative numbers used and why are they important?Why is it useful for me to know the absolute value of a number?What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?What properties and conversions do I need to understand in order to simplify and evaluate algebraic expressions?

VocabularyAbsolute valueAssociative propertyCommutative propertyDistributive propertyIntegersNatural numbersNegative numbersOpposite numbersPositive numbersRational numbersSignWhole numbers






Warm-Up / Quick PracticeMental Math: Add fractions when one addend contains the common denominator.Add and subtract integersFind the mean, mode, median, and range of a data setSM: Compare and order integers

Problem Solving Solve non-routine problems involving the Work Backwards or Look for a Pattern strategy Refer to Holt Mathematics Course 2, Problem Solving Handbook.



2.4.16 M7N1c, d Divide integers Holt Mathematics Course 2, “Multiplying and Dividing Integers,” pp. 94-96.

Two-color counters

2.4.17 M7N1c, dM7A1a, cM7A2a

Demonstrate an understanding of even and odd numbers using algebraic expressionsUse knowledge of consecutive integers to solve problems

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Working with Integers,” pp. 25 - 31 of 35.

Copies of tasks

2.4.18 M7N1a, b, c, dM7A1a, b, cM7A2a b

Compare and order rational numbersAdd, subtract, multiply, and divide integersCreate and solve problems involving rational numbersDemonstrate an understand of properties of real numbers

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35. Class presentations of assignment on the following Monday.

PostersAccess to supplies—markers, rulers, crayons, textbooks, etc.


Create and solve problems involving rational numbers

Demonstrate an understand ofproperties of real numbers

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35. Continue to work on culminating activity.

PostersAccess to supplies—markers, rulers, crayons, textbooks, etc.



Weekly Focus: Evaluate expressions using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Working with Integers,” pp. 25 - 31of 35.

Maintenance: Extend patterns with “Find a Pattern in Sequences” Problems 8 – 15 and “Combine Science Link” from Holt Mathematics Course 2, pp. 232-234.

Maintenance: Interpret graphs using Holt Mathematics Course 2, “Interpreting Graphs,” pp. 232 – 234.

Exploration: Use logical reasoning to create puzzles with “Reaching All Learners” from Holt Mathematics Course 2, pp. 53 and 57.

Intervention: Include the reteaching of addition and subtraction of integers without modeling.

Homework

Weekly Focus: Solve problems involving rational numbers

Maintenance: Write equations to describe real-life situations

Skill: Compare and order integers

Reflection with ClosureCreate a set of rules for comparing negative and positive numbers.When subtracting two negative numbers, do you always get a negative number? Why or why not? Give examples to justify your answer.

JournalExplain how to find the quotient of two integers.How is division of integers related to multiplication of integers? Draw a model to justify your answer.



Weekly Focus: Teacher-selected assessment items

Skill Mastery: Compare and order integers(1) Arrange the integers in order from least to greatest. -1 0 5 -5 -2 1 -10 7Compare using <, >, or =. (2) -10 -5 (3) 2 -7 (4) -110

10 (5) 52 5 (6) -34 -14

Performance Tasks:




M7A1a Translate verbal phrases to algebraic expressions.M7A2a Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.M7A2b Use the addition and multiplication properties of equality to solve one- and two-step equations.M7N1a Find the absolute value of a number and understand it as a distance from zero on a number line.M7N1b Compare and order rational numbers, including repreating decimals.M7N1c Add, subtract, multiply, and divide positive and negative numbers.M7N1d Solve problems using rational numbers.M7A3a Plot points on a coordinate plane.M7A3b Represent, describe, and analyze relations from tables, graphs, and formulas.M7A3c Describe how change in one variable affects the other variable.


Negative numbers are used to represent quantities that are less than zero such as temperature, scores in games or sports, and loss of income in business.Absolute value is useful in ordering and graphing positive and negative numbers.Computation with positive and negative numbers is often necessary to determine relationships between quantities.Models, diagrams, manipulatives and patterns are useful in developing and remembering algorithms for computing with positive and negative numbers.Properties of real numbers hold for all rational numbers.Positive and negative numbers are often used to solve problems in everyday life.


When are negative numbers used and why are they important?Why is it useful for me to know the absolute value of a number?What strategies are most useful in helping me develop algorithms for adding, subtracting, multiplying and dividing positive and negative numbers?What properties and conversions do I need to understand in order to simplify and evaluate algebraic expressions?

VocabularyAbsolute valueAssociative propertyCommutative propertyDistributive propertyIntegersRational numbers




Warm-Up / Quick PracticeMental Math: Subtract fractions when one addend contains the common denominator (for example, with 2/3 – 1/6 =, think 2/3 = 4/6 and 4/6 – 1/6 = 3/6 or ½)Compare and order integersSketch a graph of a narrativeSM: Divide fractions and mixed numbers

Problem Solving Select and apply the appropriate operations to solve single and multi-step word problems involving positive and negative integers




Compare and order rational numbersAdd, subtract, multiply, and divide integersDemonstrate an understanding of properties of real numbers

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35. Class presentations

Culminating Activity Posters


Compare and order rational numbersAdd, subtract, multiply, and divide integersCreate and solve problems involving rational numbers

GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35. Final touches to culminating activity. Students are to make appropriate changes to culminating activity as suggested during presentations.

Culminating Activity PostersAccess to supplies—markers, rulers, crayons, textbooks, etc.

2.5.23 M7A3a, b, c Plot and label points on a coordinate system

Predict what will happen to a figure when the coordinates are changed

MIC: Operations, “Changing Shapes,” Problems 5 - 13, pp. 46 - 48

MIC, pp. 46 – 48Copies o f Student Activity Sheet 4, p. 78Rulers

2.5.24 M7A3a, b, c Reflect on the effect of a negative number on the shape of a figure in the coordinate planeInvestigate the effect of multiplication on the coordinates of given figures

MIC: Operations, “Changing Shapes,” Problems 14 - 19, pp. 46 - 48

MIC, pp. 46 – 48Copies o f Student Activity Sheet 4, p. 78Rulers




Weekly Focus: Solve equations involving integers with “Model Integer Equations” from Holt Mathematics Course 2, pp. 98-99.

Maintenance: Extend patterns with “Find a Pattern in Sequences” Problem 8 – 15 and “Computer Science Link” from Holt Mathematics Course 2, pp. 244-245.

Maintenance: Interpret graphs using Holt Mathematics Course 2, “Interpreting Graphs,” pp. 232 – 234.

Exploration: Use logical reasoning to create equality puzzles with “Reaching All Learners” from Holt Mathematics Course 2, pp 53 and 57.

Intervention: Include the reteaching of adding, subtracting, multiplying, and dividing integers.

Homework

Weekly Focus: Add, subtract, multiply, and divide integers

Maintenance: Determine central tendencies of data

Skill: Divide fractions and mixed numbers

Reflection with ClosureWhy is there not a Commutative Property of Subtraction? Explain with examples.Illustrate how the Commutative Property of Addition holds for all rational numbers.Illustrate how the Associative Property of Addition holds for all rational numbers.

JournalExplain whether point (4, 5) is the same as point (5, 4).Suppose the equator represents the x-axis on a map of the Earth and the prime meridian which passes through England represents the y-axis. Starting at the origin, which of these directions, east, south, north, and west are positive? And which are negative?


Weekly Focus: Teacher-selected assessment items including MIC: Operations Section E items

Skill Mastery: Divide fractions and mixed numbers. (1) 3/4 ÷ 1/2 = (2) 4/9 ÷ 2 = (3) 2/3 ÷ 2 1/2 = (4) 5 ÷ 1 1/3 = (5) 1 1/4 ÷ 3 1/2 = Performance Tasks:

Culminating Activity: GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Culminating Activity: A Poster,” pp. 31 - 35 of 35.


Instructional Unit Plan

Unit IV Georgia Performance Standards

M7G2a Demonstrate understanding of translations, dilations, rotations, refelctionbs, and relate symmetry to appropriate transformations.M7G2b Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.


Reflections, translations, and rotations are actions that produce congruent geometric objects.


How can the coordinate plane help me understand properties of reflections, translations, and rotations?What is the relationship between reflections, translations, and rotations?

Unit IV AssessmentGPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Instructing Constructing,” pp. 61 - 62 of 62

VocabularyTransformationReflectionTranslationRotationReflection lineSymmetryReflection Symmetry

Literacy GPS

ELA7R2 The student understands and acquires new vocabulary and uses it correctly in reading and writing.






M7G2a Demonstrate understanding of translations, dilations, rotations, refelctionbs, and relate symmetry to appropriate transformations.M7G2b Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.





VocabularyTransformationReflectionTranslationRotationReflection lineSymmetryReflection Symmetry

Literacy GPS





Warm-Up / Quick PracticeMental Math: Subtract fractions when one addend contains the common denominatorFind the range, mean, median, and mode of a set of dataWrite equivalent fractions and decimalsSM: Convert metric units of length, capacity, and mass

Problem Solving Solve non-routine problems involving the Logical Reasoning or Draw a Model strategyRefer to Holt Mathematics Course 2, Problem Solving Handbook



2.6.26 M7G2a Investigate translations, rotations, and reflections in a simple drawing

Investigate reflections and rotations by folding paper and making cutouts

MIC: Triangles and Beyond, “Stamps and Stencils,” Problems 1 - 5, pp. 35 - 38

“Stencil Transformed Activity” may be carried over to next day.

MIC, pp. 35 – 38Copies of monkeysScissors / Plain paper /Tracing paperCongruent triangles Overhead projector

2.6.27 M7G2a Identify lines of symmetry in a drawingSolve problems involving lines of symmetry

MIC: Triangles and Beyond, “Line Symmetry,” Problems 6 - 9, pp. 39 - 41

MIC, pp. 39 – 41Tracing paperGraph paperHand-held mirrors

2.6.28 M7G2a, b Develop the understanding that reflections preserve the properties of figuresDraw reflections of figuresName the coordinates of both the original and reflected image

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Mirrored Mappings,” pp. 8 - 12 of 62

Copies of tasksGraph or grid paper

2.6.29 M7G2a Explore reflection symmetry informallyUse tracing paper to analyze designs to determine symmetryDesign shapes that have specified symmetries

Holt Mathematics Course 2, “Symmetry,” pp. 494- 498.

Optional: Magazine pictures or real objects that show symmetry




Weekly Focus: Review terminology and basic skills relating to lines with “Building Blocks of Geometry” from Holt Mathematics Course 2, p. 444.

Maintenance: Multiply and add integers using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Sums and Products,” pp. 14 - 19 of 35.

Maintenance: Estimate solutions to fraction computations with “Estimate with Fractions” from Holt Mathematics Course 2, pp. 182-183.

Exploration: Explore solving for variables in terms of other variables with “Extension Solving for a Variable” from Holt Mathematics Course 2, pp. 710-711.

Intervention: Introduce Reflections using GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Introduction to Reflections,” pp. 7 - 8 of 35. Include the reteaching of simplifying expressions with negative and positive rational numbers.

Homework

Weekly Focus: Solve problems involving lines of symmetry

Maintenance: Display and interpret data

Skill: Convert metric units of length, capacity, and mass


How can you determine whether a figure has reflection symmetry?Create a list of five words that are symmetrical.Do all circles represent translations, reflections, and rotations? Give an example and explain if not.

JournalDescribe a classroom situation that illustrates translation.Explain how a figure skater might perform a translation and a rotation at the same time.Determine whether an equilateral triangle has rotational symmetry. If so, tell how many times it shows rotational symmetry within one full rotation.


Weekly Focus: Teacher-selected assessment items including MIC: Triangles and Beyond Section E items.

Skill Mastery: Convert metric units of length, capacity, and mass. Write the equivalence. (1) 3,850 m = _____ km (2) 0.08 L = _____ mL (3) 84.2 kg = _____ g (4) 0.9 cm = _____ mm (5) 4.5 g = _____ mg (6) 6,700mL = _____ L

Performance Tasks:




M7G1a Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment, copying an angle, bisecting a segment, bisecting an angle, constructing perpendicular lines, including the perpendicular bisector of a line segment, and constructing a line parallel to a given line through a point not on the line.

M7G1b Recognize that many constructions are based on the creation of congruent triangles.M7G2a Demonstrate understanding of translations, dilations, rotations, refelctionbs, and relate symmetry to appropriate transformations.





VocabularyReflectionReflection lineBisectorParallel linePerpendicular lineCongruentPointLineLine segment or segmentEndpointsIntersectionRay AngleParallelogram

Literacy GPS






Warm-Up / Quick PracticeMental Math: Subtract fractions from whole numbers (for example, for 3 – 1/4, think 1 – ¼ = ¾ so this answer is 2 ¾)Identify the performed transformationFind the mean of a set of data including rational numbersSM: Compare and order rational numbers

Problem Solving Select and apply the appropriate operations to solve single and multi-step word problems involving percents and ratios



2.7.31 M7G1aM7G2a

Construct a line segment

Copy an angle

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “A Second Challenge: Can you copy any line segment?,” p. 14 of 62 and “A New Challenge: Can you copy an angle?,” pp. 34 – 35 of 62

Copies of tasksCompassStraightedges

2.7.32 M7G1aM7G2a

Bisect a line segment

Construct a reflection over a line

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Battle of the Triangles,” pp. 21 - 23 of 62 and “A True Challenge: Constructing a Reflection,” pp. 23 – 27 of 62

Copies of tasksCompassStraightedges

2.7.33 M7G1a, bM7G2a

Construct parallel lines

Solve problems involving parallel lines and angles formed by lines that intersect parallel lines

Construct a set of parallelograms and describe their similarities and difference

MIC Triangles and Beyond, “Constructing Parallel Lines,” Problems 1- 7, pp. 42 – 46

Lesson may continue to next day.

MIC, pp. 42 – 46StraightedgesTriangle template or one cutout from strong cardboardTransparency sheetsScissors

2.7.34 M7G1a Construct parallel lines with a compass and straightedge

Construct a perpendicular line

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Constructing Parallel Lines,” pp. 36 - 43 of 62

Copies of taskCompassStraightedge



Weekly Focus: GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Constructing Translations,” pp. 44 - 48 of 62.

Maintenance: Multiply and add integers using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Sums and Products,” pp. 14 - 19 of 35.

Maintenance: Estimate solutions to fraction computations with “Estimate with Fractions” from Holt Mathematics Course 2, pp. 182-183.

Exploration: Explore solving for variables in terms of other variables with “Extension Solving for a Variable” from Holt Mathematics Course 2, pp. 710-711.

Intervention: Introduce Translations using GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Introduction to Translations,” pp. 31 - 32 of 35. Include the reteaching of reflecting an image across a coordinate plane.

Homework

Weekly Focus: Solve problems involving parallel lines and angles formed by lines that intersect parallel lines

Maintenance: Reflect an image across a line

Skill: Compare and order rational numbers


Describe the steps you take to reflect an image over a line. Draw pictures to illustrate your steps.Compare constructing a perpendicular line to a line to constructing a line parallel to a line. How is it alike? How is it different?

JournalAsk students to explain which type of lines—parallel, perpendicular, or skew they find most interesting and why.Ask students to draw a design and describe transformations that they see.



Weekly Focus: Teacher-selected assessment items including MIC: Triangles and Beyond Section F items

Skill Mastery:Compare and order rational numbers. List in order from least to greatest.(1) 4.2 4 1/3 4.022 4 2/5 4.3 (2) 5 3 ½ 6.6 4 3/5 ¾ (3) 2.5 ¾ 1 1/6 9/8

2.

Performance Tasks:





M7G1b Recognize that many constructions are based on the creation of congruent triangles.M7G2a Demonstrate understanding of translations, dilations, rotations, refelctionbs, and relate symmetry to appropriate transformations.M7G2b Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.M7A3a Plot points on a coordinate plane.M7A3b Represent, describe, and analyze relations from tables, graphs, and formulas.


Coordinate geometry can be a useful tool for understanding geometric shapes and transformations.Reflections, translations, and rotations are actions that produce congruent geometric objects.Many geometric constructions are based upon congruent triangles.


How can the coordinate plane help me understand properties of reflections, translations, and rotations?What is the relationship between reflections, translations, and rotations?Why is the definition of a circle a foundation for geometric constructions?In what ways can I use congruent triangles to justify many geometric constructions?

Vocabulary

TransformationReflection Reflection lineTranslation RotationBisector Parallel linePerpendicular lineCongruent PointLine PlaneLine segment or segmentEndpoints IntersectionRay AngleCorresponding sidesCorresponding anglesAngle of Rotation

Literacy GPS





Warm-Up / Quick PracticeMental Math: Subtract fractions from whole numbers Evaluate an expression with rational numbersInterpret data from a tableSM: Add and subtract integers

Problem Solving Solve non-routine problems involving the Guess and Check or Work Backwards strategyRefer to Holt Mathematics Course 2, Problem Solving Handbook



2.8.36 M7G1a, b Review bisect of a line

Bisect an angle

Construct a regular octagon

Holt Mathematics Course 2, “Hands-On Lab 8-3: Construct Bisectors and Congruent Angles,” pp. 456 – 457 andGPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “A Final Challenge: Constructing a Regular Octagon,” pp. 28 - 30 of 62

Text, pp. 456 – 457StraightedgesCompasses

2.8.37 M7G2a, bM7A3a

Model transformations on a coordinate plane

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Coordinating Rotations,” pp. 50 - 52 of 62

Grid paperOptional: Tracing paper or wax paper

2.8.38 M7G2a, bM7A3a, b

Develop appropriate language to describe rigid motionsPerform three rigid transformations: reflections, translations, and rotations

Holt Mathematics Course 2, “Translations, Reflections, and Rotations,” pp. 488-491.

Grid paper

2.8.39 M7G2a, bM7A3a, b

Write rules for rotations MIC Triangles and Beyond, “Transformations,” pp. 37 – 38




Weekly Focus: Perform translations on a coordinate plane using GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Coordinating Translations,” pp. 32 - 34 of 62.

Maintenance: Demonstrate an understanding of math properties using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Always, Sometimes, Never,” pp. 20 - 22 of 35.

Maintenance: Add, subtract, multiply, and divide integers with “Solving Equations Containing Integers” from Holt Mathematics Course 2, p. 102-103.

Exploration: Extend algebraic reasoning skills with “Flapjacks” from Holt Mathematics Course 2, p. 712.

Intervention: Introduce Translations using GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Introduction to Reflections,” pp. 31 -32 of 35.Include the reteaching of constructing congruent line segments and parallel lines.

Homework

Weekly Focus: Perform three rigid transformations: reflections, translations, and rotations

Maintenance: Construct a line segment; bisect a line segment; construct parallel lines; and draw a perpendicular line through a line.

Skill: Add and subtract integers

Reflection with ClosureWhat is meant by a bisector? Draw three examples of bisectors and describe what you have drawn.Are all similar triangles congruent? Explain.Are all congruent triangles similar? Explain.Can two figures on a coordinate plane with unlike coordinates be congruent? Explain and give an example if possible.

JournalHave students draw examples of congruent figures and explain why they are congruent.Ask students to think of five real-world places where they see different triangles and to describe these in their journal.


Weekly Focus: Teacher-selected assessment items from Holt Mathematics Course 2 Chapter 8.

Skill Mastery: Add and subtract integers (1) -78 + -37 = (2) 765 + -129 = (3) -708 + 329 = (4) 681 – 932 = (5) -32 – (-23) =

Performance Tasks:





M7G1b Recognize that many constructions are based on the creation of congruent triangles.M7G2a Demonstrate understanding of translations, dilations, rotations, refelctionbs, and relate symmetry to appropriate transformations.M7G2b Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.


Coordinate geometry can be a useful tool for understanding geometric shapes and transformations.Reflections, translations, and rotations are actions that produce congruent geometric objects.Many geometric constructions are based upon congruent triangles.


How can the coordinate plane help me understand properties of reflections, translations, and rotations?What is the relationship between reflections, translations, and rotations?Why is the definition of a circle a foundation for geometric constructions?In what ways can I use congruent triangles to justify many geometric constructions?

Unit IV AssessmentGPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Instructing Constructing,” pp. 61 - 62 of 62

Vocabulary

TransformationReflection Reflection lineTranslation RotationBisector Parallel linePerpendicular lineCongruent PointLine PlaneLine segment or segmentEndpoints IntersectionRay AngleCorresponding sidesCorresponding anglesAngle of Rotation

Literacy GPS






Warm-Up / Quick PracticeMental Math: Subtract mixed numbers from whole numbers, starting with the whole number amounts (for example, for 5 – 35/6 =, think 5 – 3 = 2, and 2 – 5/6 = 1 1/6)Translate a figure on a coordinate planeSolve one- and two-step equationsSM: Multiply and divide integers

Problem Solving Select and apply the appropriate operations to solve single and multi-step word problems involving measurement units.



2.9.41 M7G1a, bM7G2a, b

Relate mathematics to other content areasDemonstrate an understanding of basic constructions and transformations

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Analyzing Quilts,” pp. 60 - 62 of 62This activity is part of a four-day assignment

ComputersAccess to supplies

2.9.42 M7G1a, bM7G2a, b

Demonstrate an understanding of basic constructions and transformations

GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Instructing Constructing,” pp. 61 - 62 of 62Students’ presentations will begin on third day of this assignment.

ComputersAccess to supplies

2.9.43 M7G1a, bM7G2a, b


GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Instructing Constructing,” pp. 61 - 62 of 62

Access to supplies

2.9.44 M7G1a, bM7G2a, b


GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Instructing Constructing,” pp. 61 - 62 of 62Students may begin presentations.

Access to supplies



Weekly Focus: Analyze real world situations involving transformations with “Social Studies Link” from Holt Mathematics Course 2, p. 492.

Maintenance: Demonstrate an understanding of math properties using GPS Framework, Grade 7, Unit 3, Rational Reasoning, “Always, Sometimes, Never,” pp. 20 - 22 of 35.

Maintenance: Add, subtract, multiply, and divide integers with “Solving Equations Containing Integers” from Holt Mathematics Course 2, pp. 102 – 103.

Exploration: Extend algebraic reasoning skills with “Flapjacks” from Holt Mathematics Course 2, p. 712.

Intervention: Introduce Rotations using GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Introduction to Rotations,” pp. 48 - 49 of 35. Include the reteaching of bisecting an angle.

Homework

Weekly Focus: Demonstrate an understanding of basic constructions and transformations

Maintenance: Identify and perform transformations

Skill: Multiply and divide integers

Reflection with ClosureWhat does it mean for shapes to be congruent? How can you determine whether or not shapes are congruent?Create a design that has reflectional symmetry, rotational symmetry, and an image that is translated.

JournalHave students to invent their own typefaces using a variety of polygons. Ask students to create capital and lowercase letters and the numerals from 0 to 9.Ask students to describe what is meant by symmetry and why they think it is so pleasing to the eye.



Weekly Focus: Teacher-selected assessment items

Skill Mastery: Multiply and divide integers. (1) -42 x 53 = (2) -35 x 123 = (3) -132 x -56 = (4) -144 ÷ -12 = (5) 692 ÷ -4 =

Performance Tasks:

Culminating Activity: GPS Framework, Grade 7, Unit 4, Flip, Slide, and Turn, “Culminating Activity: ‘Instructing Constructing,” pp. 61 - 62 of 62

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