Transcript

NYS COMMON CORE MATHEMATICS CURRICULUM 73 Student Examples and Exercises

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

Opening Exercise:

NYS COMMON CORE MATHEMATI

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