Skills and Strategies Lesson 7 CCSS Add and Subtract ...images.pcmac.org/.../Documents/TB_L7.pdfLesson 7 ©Curriculum Associates, LLC Copying is not permitted. 56 L7: Add and Subtract

©Curriculum Associates, LLC Copying is not permitted.L7: Add and Subtract Rational Numbers54

Add and Subtract Rational NumbersLesson 7 Part 1: Introduction

In Lessons 1–3, you learned about adding and subtracting integers. Take a look at this problem.

In science class, Ron recorded 2 3 ·· 10 8C as the starting temperature of a saltwater

solution. To complete his experiment, he needs the temperature of the solution to

increase by 4 ··

10

8C. What will Ron record as the ending temperature of the solution?

Explore It

Use the math you already know to solve the problem.

Reread the problem By how much will the temperature of the saltwater solution

increase? 8C

Write an expression to show how to calculate the final temperature of the solution

Explain how you would add 23 1 4

Look at the number line below If you start at 23 tenths of a unit left of zero and then move right 4 tenths of a unit, where do you end up?

–1 0 1510– 5

10

What is 2 3

·· 10 1 4 ·· 10 ?

What is the ending temperature for the solution? 8C

Explain how adding 2 3

·· 10 1 4 ·· 10 is like adding 23 1 4

Develop Skills and Strategies

CCSS7.NS.A.1a

7.NS.A.1b

7.NS.A.1c

7.NS.A.1d

©Curriculum Associates, LLC Copying is not permitted.55L7: Add and Subtract Rational Numbers

Lesson 7Part 1: Introduction

Find Out More

The idea behind adding positive and negative fractions and decimals is the same as the idea behind adding integers

You can use number lines to show addition of fractions or decimals

2 3

·· 10 1 4 ·· 10 5 23 1 4 ······ 10 5 1 ·· 10

–1 0 1

–3

10

410

510– 5

10

+

So, 20 3 1 0 4 5 0 1

–1 0–0.5 0.5 1

–0.3

+0.4

Subtracting positive and negative fractions and decimals is also similar to subtracting integers

How can you solve 3 ·· 8 2 5 ·· 8 ?

First rewrite the subtraction problem as an addition problem using the additive inverse

3 ·· 8 2 5 ·· 8 5 3 ·· 8 1 1 2 5

·· 8 2

You can use a number line to show the problem

3

·· 8 1 1 2 5

·· 8 2 5 3 1 (25) ······· 8 5 2 2

·· 8

–1 0 148

48–

58–

38+

Reflect

1 How is adding positive and negative fractions similar to adding integers? How is it different?

Lesson 7

©Curriculum Associates, LLC Copying is not permitted.

L7: Add and Subtract Rational Numbers56

Part 2: Modeled Instruction

Read the problem below. Then explore different ways to understand adding negative fractions.

A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases

by 7 ··

8 cup. On Day 2, the volume of water in the bowl decreases by 3

··

4 cup. What

number represents the total change in the volume of water in the bowl after two days?

Picture It

You can use a number line to help add negative fractions.

The following number line shows the decrease in the volume of water on Day 1 and Day 2

–2 –1 048

48–1 –

34– 7

8–

Model It

You can use equations to help add negative fractions.

Amount of water missing 1 Change in volume 5 Overall change in at start of Day 1 on Day 1 volume at end of Day 1

0 1 1 2 7

·· 8 2 5 ?

Overall change in volume 1 Change in volume 5 Overall change in at end of Day 1 on Day 2 volume at end of Day 2

2 7

·· 8 1 1 2 3

·· 4 2 5 ?

Lesson 7


Part 2: Guided Instruction

Connect It

Now you will solve the problem from the previous page.

2 Think about the expression 2 7

·· 8 1 1 2 3

·· 4 2 What do you need to do before you can add the fractions?

3 Solve 2 7

·· 8 1 1 2 3

·· 4 2 5

4 What quantity represents the total change in the volume of water in the birdbath after two days? Write your answer as a mixed number

5 Look at the problem on the previous page What does a negative answer mean?

6 How is adding two negative fractions like adding two positive fractions, and how is it different?

7 How is adding two negative fractions similar to adding two negative integers?

Try It

Use what you just learned to solve these problems. Show your work.

8 22 1 ·· 2 2 2 1 ·· 2 5

9 Susan’s cat loses 1 1 ·· 4 pounds Then it loses another 1 ·· 8 pound What is the total change in

the cat’s weight?

Lesson 7



Read the problem below. Then explore different ways to understand adding or subtracting any rational numbers.

Julia is playing a computer game. To enter a new quest she has to pay a “tax” of 2.5 points, but she expects to earn 7.5 points. For each quest, how many points can she gain overall?

Picture It

You can use a number line to help add or subtract rational numbers.

The following number line shows the loss of 2 5 points and the gain of 7 5 points

25 24 23 22 21 0 1 2 3 4 5

pay 2.5 points

earn 7.5 points

Model It

You can use an equation to help add or subtract rational numbers.

22 5 1 7 5 5 ?

Represent the points Julia loses as a negative number, and represent the points she gains as a positive number

Part 3: Modeled Instruction

Lesson 7


Connect It

Now you will solve the problem from the previous page.

10 Think about a loss of 2 5 and a gain of 7 5 Explain how you know whether Julia’s overall result will be a gain or a loss, and whether the result should be represented as positive or negative

11 How can you determine the difference between the gain and the loss?

12 How does knowing the difference between the gain and the loss tell you the overall result?

13 What is 22 5 1 7 5? What is 22 1 ·· 2 1 7 1 ·· 2 ?

14 Explain how you can find the sum when you are adding a positive and a negative decimal or fraction Include how to know whether the sum is positive or negative

15 Explain how to add the additive inverse to find the value of an expression such

as 24 1 ·· 4 2 1 22 1 ·· 4 2

Try It

Use what you just learned to solve these problems. Show your work.

16 What is 24 1 ·· 2 1 7 1 ·· 2 ?

17 What is 2 5 1 (23 5)?

Part 3: Guided Instruction

Student Model

Part 4: Guided Practice Lesson 7



Study the model below. Then solve problems 18–20.

Solve the equation. Simplify your answer.

2 ··

3 2 11

··

12 5 h

Look at how you could show your work using equations.

2 ·· 3 2 11 ··· 12 5 2 ·· 3 1 1 2 11

··· 12 2

5 8 ··· 12 1 1 2 11

··· 12 2

5 8 1 (211) ········ 12 5 2 3

··· 12 5 2 1

·· 4

Solution:

18 At midnight, the temperature in Alto is 23 88C The wind chill makes the temperature feel 5 68C colder than the actual temperature What is the wind-chill temperature?

Show your work.

Solution:

2 3

··· 12 , or 2 1

·· 4 How could you use a number line to check your answer?

Pair/Share

The student rewrote the subtraction as addition, found a common denominator, then added the numerators.

How did you and your partner choose which operation to use?

Pair/Share

Will your answer be positive or negative? How do you know?

Part 4: Guided Practice Lesson 7


19 Solve

2 3

·· 4 2 4 ·· 3 5 h

Show your work.

Solution:

20 Which number makes the following statement TRUE?

20 5 2 h 5 a positive number

A 1 0

B 0 5

C 20 5

D 21 0

Martin chose A as the correct answer How did he get that answer?

How do you know the answer is negative?

Pair/Share

How can you rewrite this problem as addition?

What is another number that makes the statement true?

Pair/Share

Test each choice until you find the one that makes the statement true.

Lesson 7



Solve the problems.

1 On Monday, the value of a stock decreased by 1 } 2 point. On Tuesday, the value increased

by 3 } 4 point. On Wednesday, the value decreased by 3 }

8 point. What number represents the

change in stock value after the three days?

A 7 } 8 point

B 2 } 8 point

C 2 1 } 8 point

D 2 13 }} 8 points

2 Which expression represents a negative number?

10 ab –1

A a 1 b

B a 2 b

C a

D 2b

3 Identify the number that makes each statement true. You may select one or both numbers for each statement.

A 23.7 1 h 5 a positive number. 24.9 3.8

B h 2 1 1 } 3 5 a negative number. 4 }

3 25

C h 1 8 5 0 28 8

D 24.52 1 h 5 a negative number. 25.48 3.86

Part 5: Common Core Practice

Lesson 7


4 Which expression is equivalent to 5 } 8 2 3 }

4 1 8 2 1 }

3 2 1 1? Select Yes or No for each expression.

A 2 33 }} 8

Yes No

B 2 35 }} 8

Yes No

C 26 7 } 8 Yes No

D 24 1 } 8 Yes No

5 Jamal stands on a dock 1.5 meters above the surface of the water. A trout swims 4.8 meters below Jamal. What is the depth of the trout compared to the surface of the water?

Show your work.

Answer

6 Solve the problem.

Part A

Find a number that makes this statement true.

22.5 1 h 5 a positive number

Give an example of a number that makes the statement true?

Answer

Part B

Write an equation showing that your answer makes the statement true.

Answer

Part C

Draw a number line and use arrows to show your equation.

Answer

Go back and see what you can check off on the Self Check on page 1.Self Check

Part 5: Common Core Practice