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NYS COMMON CORE MATHEMATICS CURRICULUM 7•3 Student Examples and Exercises 1 G7-Module 3: Topic A Lesson 1: Generating Equivalent Expressions Example 1 a.) Rewrite and by combining like terms. Write the original expressions and expand each term using addition. What are the new expressions equivalents? b.) Find the sum of and . Example 4 f. Alexander says that is equivalent to because of any order, any grouping. Is he correct? Why or why not?
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  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    1

    G7-Module 3: Topic A Lesson 1: Generating Equivalent Expressions

    Example 1

    a.) Rewrite and by combining like terms.

    Write the original expressions and expand each term using addition. What are the new expressions equivalents?

    b.) Find the sum of and .

    Example 4

    f. Alexander says that is equivalent to because of any order, any grouping. Is he correct? Why

    or why not?

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    2

    Lesson 3: Writing Products as Sums and Sums as Products

    Example 1 Space for Drawings

    a.) Draw a tape diagram representing the sum

    using squares for units.

    b.) Redraw the diagram without squares, as two rectangles

    each with a height of 1 unit.

    c.) Draw a rectangular array for .

    Write the product as a sum: ________________________________

    d.) Draw a tape diagram representing the sum

    using square units.

    e.) Redraw the diagram without squares, as two rectangles

    each with a height of 1 unit.

    f.) Draw a rectangular array representing

    Write the product as a sum: __________________________________

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    3

    Example 6:

    A number of square tiles are needed to border a square fountain with side length feet. Express the total

    number of tiles needed in terms of three different ways.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    4

    Lesson 4: Writing Products as Sums and Sums as Products

    Example 2

    and are positive integers. , , and stand for the number of unit squares in a rectangular array.

    Lesson 6: Collecting Rational Number Like Terms

    Example 4:

    Model how to write the expression in standard form using rules of rational numbers.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    5

    G7-Module 3: Topic B Lesson 7: Understanding Equations

    Example 1

    The ages of three sisters are consecutive integers. The sum of their ages is . Find their ages.

    a.) Use a tape diagram to find the situation.

    b.) If represents the age of the youngest sister, write an equation that can be used to find the age of the

    youngest sister and the other sisters ages.

    c.) Determine if your answer from part (a) is a solution to the equation you wrote in part (b).

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    6

    Lesson 8: Using the If-Then Moves in Solving Equations

    Example 1

    Julia, Keller, and Isreal are volunteer firefighters. On Saturday the volunteer fire department held its annual coin drop

    fundraiser at a street light. After one hour, Keller had collected more than Julia and Isreal had collected less

    than Keller. Altogether the three firefighters collected . How much did each person collect?

    Find the solution using an arithmetic approach. Identify which key If-Then Moves are used.

    The amount of money Julia collected is . Write an expression in terms of to represent the amount of money Keller

    collected in dollars.

    Using the expressions for Julia and Keller, write an expression to represent the amount of money that Isreal collected in

    dollars.

    Using the expressions above, write an equation in terms of that can be used to find the amount each person collected.

    Solve the equation written above to determine the number of money each person collected and describe the If-Then

    moves.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    7

    Example 1 (continued)

    In terms of Julia Collected Isreal Collected Keller Collected

    Julias Amount

    Isreals Amount

    Kellers Amount

    Lesson 9: Using the If-Then Moves in Solving Equations

    Example 2

    Shelby is seven times as old as Bonnie. If in 5 years, the sum of Bonnie and Shelbys ages is 98, find Bonnies present age.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    8

    Lesson 10: Angle Problems and Solving Equations

    Example 4

    Two lines intersect in the following figure. The ratio of the measurements of

    the obtuse angle to the acute angle in any adjacent angle pair is 2:1.

    In a complete sentence, describe the angle relationships in the diagram.

    Label the diagram with expressions that describe this relationship. Write an equation to that models the angle

    relationship and solve for . Find the measurements of the acute and obtuse angles.

    Lesson 11: Angle Problems and Solving Equations

    Exercise 2

    In a complete sentence, describe the angle relationships in the diagram.

    Write an equation for the angle relationship shown in the figure and solve

    for x and y. Confirm your answers by measuring with a protractor.

    x2x

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    9

    Lesson 12: Properties of Inequalities

    Station 1

    Die 1 Inequality Die 2 Operation New Inequality Inequality Symbol Preserved or Reversed?

    Add

    Preserved

    Add

    Subtract

    Subtract

    Add

    Examine the results. Make a statement about what you notice and justify it with evidence.

    Station 2

    Die

    1 Inequality

    Die

    2 Operation New Inequality Inequality Symbol Preserved or Reversed?

    Multiply

    by -1

    Reversed

    Multiply

    by -1

    Multiply

    by -1

    Multiply

    by -1

    Multiply

    by -1

    Examine the results. Make a statement about what you notice and justify it with evidence.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    10

    Station 3

    Die 1 Inequality Die 2 Operation New Inequality Inequality Symbol Preserved or Reversed?

    Multiply

    by

    ( ) ( )

    Preserved

    Multiply

    by

    Divide by

    Divide by

    Multiply

    by

    Examine the results. Make a statement about what you notice and justify it with evidence.

    Station 4

    Die 1 Inequality Die 2 Operation New Inequality Graph

    Multiply

    by

    Multiply

    by

    Divide by

    Divide by

    Multiply

    by

    Examine the results. Make a statement about what you notice and justify it with evidence.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    11

    Lesson 13: Inequalities

    Opening Exercise

    Tarik is trying to save $265.49 to buy a new tablet. Right now he has $40 and can save $38 a week from his allowance.

    Write and evaluate an expression to represent the amount of money saved after:

    2 weeks

    3 weeks

    4 weeks

    5 weeks

    6 weeks

    7 weeks

    8 weeks

    When will Tarik have enough money to buy the tablet?

    Write an inequality that will generalize the problem.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    12

    Lesson 14: Solving Inequalities

    Example 1

    A youth summer camp has budgeted for the campers to attend the carnival. The cost for each camper is

    which includes general admission to the carnival, unlimited rides, and meals. The youth summer camp must also pay

    for the chaperones to attend the carnival and for transportation to and from the carnival. What is the

    greatest amount of campers that can attend the carnival if the camp must stay within their budgeted amount?

    Lesson 15: Graphing Solutions to Inequalities

    Example 1

    A local car dealership is trying to sell all of the cars that are on the lot. Currently it has cars on the lot and the

    general manager estimates that they will sell cars per week. How long will it take for the number of cars on the lot to

    be less than ?

    Write an inequality that can be used to find the number of weeks.

    Solve and graph the inequality.

    Interpret the solution in the context of the problem.

    Verify the solution.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    13

    G7-Module 3: Mid-Module Assessment

    MMA Problem #6

    6. Jenny invited Gianna to go watch a movie with her family. The movie theater charges one rate for 3D admission and a different rate for Regular Admission. Jenny and Gianna decided to watch the newest movie in 3D. Jennys mother, father, and grandfather accompany Jennys little brother to the Regular Admission movie. a. Write an expression for the total cost of the tickets. Define the variables.

    b. The cost of the 3D ticket was double the cost of the regular admission. Write an equation to represent the relationship between the two types of tickets.

    c. The family purchased refreshments and spent a total of . If the total amount of money spent on tickets and refreshments was use an equation to find the cost of one regular admission ticket.

  • NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

    14

    G7-Module 3: Topic C Lesson 16: The Most Famous Ratio of All

    Opening Exercise:

  • NYS COMMON CORE MATHEMATI