lesson 3 introduction add and subtract positive and...

Introduction

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Use What You Know

Lesson 3 Add and Subtract Positive and Negative Integers

Lesson 3Add and Subtract Positive and Negative Integers

In previous lessons, you learned about positive and negative numbers. In this lesson, you will learn how to add and subtract positive and negative numbers. Take a look at this problem.

Amy, Ray, Kim, and Jamal are on a trivia team. They gain points for correct answers and lose points for incorrect answers. During the contest, Amy gains 3 points, Ray loses 4 points, Kim loses 2 points, and Jamal gains 5 points. How many points does the team have at the end of the contest?

Use the math you already know to solve the problem.

a. Which team members can use a positive number to represent their point total?

b. Which team members can use a negative number to represent their point total?

c. Write a positive or negative number to represent the number of points earned by each team member.

Amy’s points: Kim’s points:

Ray’s points: Jamal’s points:

d. What is the number of points Amy and Jamal gain altogether? Would you represent this amount as a positive or negative number? Why?

e. What is the number of points Ray and Kim lose altogether? Would you represent this amount as a positive or negative number? Why?

f. Explain how you could find the total number of points the team has altogether.

7.NS.A.1d

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Find Out More


In the problem on the previous page, positive numbers represent gains, and negative numbers represent losses. You can use a number line to add positive and negative numbers. Move right to add a positive number, and move left to add a negative number.

Amy has 3 points, so start at 3 on the number line.

Ray lost 4 points. 3 2 4 means 3 1 (24). From 3, move left 4 to add 24 points. The result is 21.

Kim lost 2 points. 21 2 2 means 21 1 (22). From 21, move left 2 to add 22 points. The result is 23.

Jamal gained 5 points. To show 23 1 5, start at 23 and move right 5 to add 5. The result is 2.

At the end of the contest, the team has 2 points.

When you add two negative numbers, the sum is always a negative number.

When you add a positive number and a negative number, the sign of the sum will be the sign of the number with the greater absolute value.

3 1 (24) 5 21

| 24 | is greater than | 3 |, so the sign of the answer will be the sign of 24.

23 1 5 5 2

| 5 | is greater than | 23 |, so the sign of the answer will be the sign of 5.

Reflect1 Describe how to add 28 and 14 on a number line that runs from 210 to 10.

543210–1–2–3–4–5

End+5

543210–1–2–3–4–5

–2

543210–1–2–3–4–5

Start–4

Modeled and Guided Instruction

Learn About


Lesson 3


Addition Methods for Integers

Read the problem below. Then explore different ways to understand how to add positive and negative numbers.

Ali wants to make bracelets to sell at a craft fair. She borrows money from her sister to buy beads and cord. Ali spends $8.00 on supplies. At the craft fair, Ali makes $17.00 selling her bracelets. How much money does Ali have after she pays back her sister?

Model It You can use a bar model to understand the problem.

The model shows how much money Ali has after she pays her sister the $8 she borrowed.

8

17

?

Model It You can use a number line to help understand the problem.

109876543210–1

Start at –8

Move right 8 units to get to 0.

Move right 9 more units to add a total of 17.

–2–3–4–5–6–7–8–9–10

Model It You can use an equation to help understand the problem.

Amount of money Ali has before the fair 1

Amount of money Ali earns at the fair 5

Amount of money Ali has after the fair

©Curriculum Associates, LLC Copying is not permitted. 17Lesson 3 Add and Subtract Positive and Negative Integers

Connect It Now you will solve the problem from the previous page using equations.

2 Use the bar model on the previous page to write an expression using subtraction to

represent the amount of money Ali has after the fair.

Write the expression using addition.

3 How are the expressions you wrote in problem 2 related?

4 What does 28 represent on the number line on the previous page? Why is the number

negative?

5 Use the number line on the previous page to write an expression to represent the

amount of money Ali has after the fair.

6 Simplify the expressions you wrote in problem 2 and problem 5 to find the amount of money Ali has left after she pays her sister. Do you get the same answer? Explain.

7 Describe another situation that can be represented by adding a negative number and a

positive number.

Try It Use what you just learned about adding positive and negative numbers to solve these problems. Write and simplify an expression for each problem. Show your work on a separate sheet of paper.

8 In a trivia game, Joshua gets a score of 24 in the first round and 25 in the second round.

What is his total score after the two rounds?

9 A balloon is 23 feet below a tree limb. The balloon floats up 19 feet. What is its position

relative to the tree limb?

Modeled and Guided Instruction

Learn About


Lesson 3


Subtraction Methods for Integers

Read the problem below. Then explore different ways to subtract positive and negative numbers.

Indi, Mark, and Tess each pick a slip of paper with a subtraction expression written on it. The person holding the card with the greatest value wins a prize. Who wins the prize?

Indi

2 2 3

Mark

27 2 (24)

Tess

21 2 (27)

Model It You can rewrite the subtraction problems as addition problems and add them on a number line.

Subtracting a number is the same as adding the opposite of the number.

Indi’s slip: Subtracting 3 is the same as adding 23. Start at 2. Move left 3 units.

109876543210–1–2–3–4–5–6–7–8–9–10

–3

Mark’s slip: Subtracting 24 is the same as adding 4. Start at 27. Move right 4 units.

109876543210–1–2–3–4–5–6–7–8–9–10

+4

Tess’s slip: Subtracting 27 is the same as adding 7. Start at 21. Move right 7 units.

109876543210–1–2–3–4–5–6–7–8–9–10

+7


Connect It Now you will solve the problems on the previous page by writing them as addition problems.

10 What is the same about all of the expressions on the previous page?

11 What do you need to do to write a subtraction problem as an addition problem?

12 Write 2 2 3 as an addition problem. Then simplify the expression.

Write 27 2 (24) as an addition problem. Then simplify the expression.

Write 21 2 (27) as an addition problem. Then simplify the expression.

13 Who has the slip of paper with the greatest value? What is that value?

14 Compare the problems on Mark’s slip and Tess’ slip. When one negative number is subtracted from another negative number, when is the answer positive?

Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

15 Gerry and Jane play a trivia game. Gerry’s score is 217 and Jane’s score is 224. What is

the difference between Gerry’s score and Jane’s score?

16 The table shows the highest and lowest elevations in Louisiana. What is the difference between the elevations?

Elevations in Louisiana

Location Elevation (ft)

Mt. Driskill 535

New Orleans 28

Guided Practice

Practice


Lesson 3


Addition and Subtraction Methods for Integers

Study the example below. Then solve problems 17–19.

Example

Jackie is sitting on a rock 5 feet above the surface of a pond. She drops a stone that falls 8 feet to the bottom of the pond. What is the stone’s final position, relative to the surface of the pond?

Look at how you could show your work using a number line.

5 2 8 5 5 1 (28)

Solution

17 Kelly’s dad compares her running times in a marathon to her times for last year’s race. He records whether she has increased or decreased her time for the first three stages of the race. What is the total increase or decrease in Kelly’s time? Did she improve her time? Explain.

Kelly’s Marathon Times

StageTime Comparison

(in minutes)

First 4

Second 27

Third 23

Solution

5

4

3

2

1

0

–1

–2

–3

–4

Show your work.

Pair/ShareHow else could you solve the problem?

Pair/ShareDescribe other situations you might want to represent with a negative number.

The stone starts 5 feet above the water’s surface and falls 8 feet. A vertical number line helps to picture this situation.

Does a negative number represent an increase or a decrease in Kelly’s time compared to last year?

23 feet, or 3 feet below the surface of the pond


Addition and Subtraction Methods for Integers 18 A helicopter is 19 meters above the top of a canyon wall. It goes down 27 meters, passing into the canyon, and then goes up 5 meters. What is the new position of the helicopter relative to the top of the canyon wall?

Show your work.

Solution

19 At 7:00 am the temperature in Wilton was 268F. By 8:00 am the temperature was 28F. What is the difference in the temperature between 8:00 am and 7:00 am?

A 288F

B 248F

C 48F

D 88F

Siri chose B as the correct answer. How did she get that answer?

Pair/ShareWhat does a negative answer mean in this situation?

Pair/ShareDoes Siri’s answer make sense? Why or why not?

To find the difference between two temperatures, should you add or subtract?

Do you use a positive or a negative number to represent the helicopter going down 27 meters?

Independent Practice

Practice


Lesson 3


Addition and Subtraction Methods for Integers

Solve the problems.

1 A submarine is 50 meters below sea level. It goes up 15 meters, then goes down 40 meters. What is the submarine’s new position relative to sea level?

A 2105 meters

B 275 meters

C 235 meters

D 25 meters

2 The table shows the temperatures and wind-chill temperatures in four towns.

Town Actual Temperature Wind-Chill Temperature

Easton 238F 2138F

Mariton 08F 2158F

Pine Hills 108F 2108F

West Falls 28F 2178F

Which town had the greatest difference between the actual temperature and the wind-chill temperature?

A Easton

B Mariton

C Pine Hills

D West Falls

3 Look at the equations below. Choose True or False for each equation.

a. 27 2 5 1 3 5 1 True False

b. 2(9 1 11) 1 1 5 21 True False

c. 24 2 (26) 2 6 5 24 True False

d. 12 1 (28) 2 1 5 3 True False

e. 2|2 2 7| 1 5 5 0 True False

Self Check


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

4 Which situation could the numeric expression 28 1 10 represent? Select all that apply.

A An atom has a positive charge because it contains 8 electrons that each have a charge of 21 and 10 protons that each have a charge of 11.

B Janice sold 8 goldfish for a total of $10. Therefore, she made a profit of $2.

C At a bus stop, 8 people got off the bus and 10 people got on. This means that the number of passengers increased by 2.

D The temperature dropped 8 degrees and then another 10 degrees. The temperature is now 218 degrees.

5 In golf, each hole has a score called par, which is the number of strokes a good golfer should take to get the ball in the hole. Scores that are under par are represented by a negative number. The table shows the golf scores for team members in a golf tournament. If the team’s total score is 232, what is Curran’s score?

Golfer Score

Rose 29

Garcia 215

Curran ?

Answer

6 Austin is watching a football game. His team loses 9 yards and then gains 5 yards. He doesn’t watch the next play, but afterwards he sees that his team now has a total loss of 1 yard. How many yards did the team gain or lose on the play Austin missed?

Answer

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