LESSON Lesson 3 OVERVIEW Add and Subtract … 14 ©Curriculum Associates, LLC Copying is not permitted Lesson 3 Add and Subtract Positive and Negative Integers Lesson 3 Add and Subtract

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LESSON OVERVIEW

Lesson 3 Add and Subtract Positive and Negative Integers


DomainThe Number System (NS)

ClusterApply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

Standard7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.d. Apply properties of operations as

strategies to add and subtract rational numbers.

Additional Standard7.NS.1c (See page B1 for full text.)

Standards for Mathematical Practice (SMP) 2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics. Learning Progression

in Grade 7 students built on these understandings to operate with rational numbers.

In this lesson students develop their skills in adding and subtracting integers using number lines and equations.

Later in Grade 7 students will use the same methods to add and subtract negative rational numbers (fractions and decimals).

In Grade 6 students became � uent with operations with positive numbers. They understood negative numbers as numbers less than 0 and placed them on a number line. They understood opposites both as pairs of numbers the same distance from 0 in opposite directions on the number line and as pairs of numbers whose sum is 0. Earlier

Lesson Objectives Prerequisite Skills

• Add and subtract integers.

• Represent addition and subtraction of integers on horizontal and/or vertical number lines.

• Apply properties of operations to add and subtract integers.

• Know how to add and subtract whole numbers.

• Know how to graph whole numbers on a number line.

• Recognize that the di� erence between two positive numbers on a number line represents the distance between the numbers.

Lesson Vocabulary

There is no new vocabulary.

MS CCRS Focus

Lesson Pacing Guide

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Whole Class Instruction

Lesson 3


Small Group Differentiation

Teacher-Toolbox.comDay 145–60 minutes

Toolbox: Interactive TutorialAddition and Subtraction of Positive and Negative Integers

Practice and Problem SolvingAssign pages 19–20.

Introduction

• Use What You Know 20 min• Find Out More 15 min• Re� ect 10 min

Day 245–60 minutes

Modeled and Guided Instruction

Learn About Addition Methods for Integers• Model It/Model It/Model It 15 min• Connect It 20 min• Try It 10 min




Learn About Subtraction Methods for Integers• Model It 15 min• Connect It 20 min• Try It 10 min



Guided Practice

Practice Addition and Subtraction Methods for Integers• Example 5 min• Problems 17–19 15 min• Pair/Share 15 min• Solutions 10 min



Independent Practice

Practice Addition and Subtraction Methods for Integers• Problems 1–6 25 min• Quick Check and Remediation 10 min• Hands-On or Challenge Activity 10 min

Toolbox: Lesson QuizLesson 3 Quiz

ReteachReady Prerequisite Lessons 45–90 min

Grade 6• Lesson 12 Understand Positive and

Negative Numbers

Grade 7• Lesson 1 Understand Addition of Positive

and Negative Integers• Lesson 2 Understand Subtraction of

Positive and Negative Integers

Teacher-led Activities Tools for Instruction 15–20 min

Grade 7 (Lesson 3)• Add Positive and Negative

Rational Numbers• Subtract Positive and Negative

Rational Numbers

Personalized Learning

i-Ready.com

Independenti-Ready Lessons 15–20 min

Grade 7 (Lesson 3)• Addition and Subtraction of Positive and

Negative Integers

Introduction

14 ©Curriculum Associates, LLC Copying is not permitted



Students explore the use of positive and negative numbers in daily life. They also use number lines as models for addition and subtraction of positive and negative integers.

• Work through Use What You Know as a class.

• Tell students that this page models addition of positive and negative integers.

• Have students read the problem at the top of the page.

SMP TIP Reason Abstractly and Quantitatively Students use integers to represent a real-world context, and they understand the meaning of the numbers as they relate to the context. During the lesson, continue to ask students what the integers represent and, in particular, what 0 represents in the problem context. (SMP 2)

Mathematical Discourse 1

• Point out that Amy and Jamal have positive points because the problem says they gain points.

• Point out that Ray and Kim have negative points because the problem says they lose points.

• Ask student pairs or groups to explain their answers to part f.

Mathematical Discourse 2 and 3

At A Glance

Step By Step

Mathematical Discourse

1 How did you decide who has negative points?Listen for comments that demonstrate an understanding that the scores of players who lose points are represented as negative numbers.

2 How did you decide how many points Kim and Ray have together?Students may refer to counting, combining, or adding. Some students may think about the problem as subtracting and then subtracting more.

3 How was that di� erent from � nding the number of points for Amy and Jamal? How was it the same?Listen for responses that indicate that for both groups you are combining the points but one group has positive points and the other negative points.

Visual ModelModel subtraction on a horizontal number line.

Materials: number line

• Include a visual model (horizontal or vertical number lines, integer chips, real-world models) whenever possible.

• Ask students to think of subtracting integers as adding the opposite.

• Use a number line to subtract 27 2 (22).

• Ask students to start at 27.

• Add the opposite of 22. The opposite of 22 is 12.

• Because 2 is positive, move in the positive direction (right) 2 spaces. The answer is 25.

• Have students try several other subtraction problems using a number line.

Introduction

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Use What You Know


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.1d

Sample answer: I could add the positive and negative numbers together.

3

24 5

22

Amy, Jamal

Ray, Kim

8; positive; gaining points is represented by a positive number.

26; negative; losing points is represented by a negative number.

14

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Lesson 3


©Curriculum Associates, LLC Copying is not permitted. 15

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

Start at 28. Draw an arrow 14 units to the right until you get to 6; 28 1 14 5 6

15

• Read Find Out More as a class.

• Use a horizontal number line to demonstrate the problem.

Visual Model

• Ask students to describe another situation that involves positive or negative numbers.

Real-World Connection

• Discuss Re� ect. Guide students to think about how they would use a number line to add 28 and 14.

Hands-On Activity

Assign Practice and Problem Solving pages 19–20 after students have completed this section.

Step By Step

Mathematics PRACTICE AND PROBLEM SOLVING

Hands-On ActivityWalk on a number line to reinforce integer addition.

Materials: painter’s tape

• Use painter’s tape to create a large number line on the � oor in the front of your classroom.

• Give students integer addition problems and ask them to model them by physically walking on the number line.

Real-World Connection

Explain that we often use positive and negative numbers in our daily lives. Gains are represented by positive numbers, and losses are represented by negative numbers. Ask students to think of examples of gains and losses in the real world.

Examples: the stock market, balancing a checkbook, buying and selling goods, temperatures, and so on


16 ©Curriculum Associates, LLC Copying is not permittedLesson 3 Add and Subtract Positive and Negative Integers

Lesson 3 Add and Subtract Positive and Negative Integers 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

16

16 Lesson 3 Add and Subtract Positive and Negative Integers

Students use a bar model, a number line, and an equation to model a real-world problem. Then they revisit the problem and solve it using equations.

• Read the problem at the top of the page as a class.

Model It• Point out that the � rst Model It

demonstrates the problem using a bar model. Explain that Ali had a total of $17.00. One part is the amount she owes her sister, $8.00, and the rest is the amount she can keep for herself.

• Ask students how much Ali can keep. Ask how they reached their answer.

Model It• Indicate that the second Model It uses a

number line to add the amount Ali has before the fair (2$8) to the amount Ali makes at the fair ($17).

• Use the number line to show how much money Ali has after she pays her sister what she borrowed. [Start at 28 and move 17 to the right.]

Mathematical Discourse 1

Model It• Ask students how the third Model It

represents the situation. [with words]

• Ask students how the number line model compares to the equation.

SMP TIP Model with Mathematics Students need many opportunities to connect and explain the connections between di� erent representations. Guide students to understand that the bar model, number line, and equation all model the same problem situation. (SMP 4)


At A Glance

Step By Step


1 How would you explain using a number line to add integers in your own words? Listen for responses that demonstrate an understanding that you start at the � rst number and then move left if the second number is negative or right if the second number is positive.

2 How is adding positive and negative integers di� erent from adding only positive integers?Responses should indicate that you move left to represent negative numbers instead of always moving right.

3 Can you think of another way to explain how to add integers?Students may mention using integer chips or explain rules in their own words.

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

Lesson 3

©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 � nd 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 � rst 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 � oats up 19 feet. What is its position

relative to the tree limb?

17 2 8

17 1 (28)

You can think of subtraction as adding the opposite number. The opposite of 8 is

28, so 17 2 8 5 17 1 (28).

28 represents the amount of money Ali has before the fair. The number

is negative because she owes her sister $8.

28 1 17

9; 9; Yes, both expressions are equal to 9.

Possible answer: The temperature starts at 25 degrees and

increases 12 degrees.

24 1 (25) 5 29

223 1 19 5 24 feet

17

Connect It• Discuss each Connect It problem as a class

using the discussion points outlined below.

• You may choose to have students work in pairs or small groups to encourage sharing ideas.

Visual Model

• Ask students to complete the Try It problems. Ask them to show their work.

Try It8 Solution

29; Students may draw a number line to illustrate 24 1 (25).

9 Solution24 feet; Students may draw a number line to illustrate 223 1 19.

Error Alert Students who wrote 4 used the opposite sign. Students sometimes have di� culty determining the sign of a sum, especially when there is one positive and one negative addend. Students may also forget to include the negative sign in front of the number.

SMP TIP Critique Reasoning Ask a group to share their thinking or solutions to the Try It problems. Ask other students to restate the explanations and have the � rst student con� rm or correct the restatement. Listeners may ask clarifying questions (for example, “I think you said. . . . Is that right?”).

Discussions in which students listen to and ask questions of one another gives them practice in critiquing the reasoning of others (SMP 3).


Step By Step


Visual ModelUse integer chips to model operations.

Materials: red and yellow integer chips

• Red chips represent negative integers. Yellow chips represent positive integers.

• Model the problem 28 1 17 with integer chips.

• Show students that one red chip together with one yellow chip have a sum of 0 and can be called a “zero pair.”

• Start with 8 red chips to model 28.

• Add 17 yellow chips to the space.

• Pair up as many “zero pairs” as possible.

• Remind students that a number and its opposite have a sum of 0 (additive inverse).

• Remove the zero pairs. The 9 yellow chips that remain model the sum of the integers.

• Model several additional problems.





1 How would you explain subtracting integers in your own words?Students might explain how to use the number line or to add the opposite.

2 Is there another way you can explain it?Students might explain how to use integer chips or rules.

Hands-On ActivitySubtract using integer chips.

Materials: red and yellow integer chips

• Review integer addition with students using integer chips.

• Model the problem 22 1 4. Start with 2 red (negative) chips and add 4 yellow (positive) chips. Pair up 2 of the yellow chips with the 2 red chips to create “zero pairs” and remove

them. There are 2 yellow chips remaining. The sum is 12.

• Now model 22 2 4. Start with 2 red chips. Tell students to remove 4 yellow chips (positive 4). There are no yellow chips to take away. Remind students that zero pairs have a value of 0, so adding them does not change the value. Add zero pairs to the space until there are 4 yellow chips. Take away the 4 yellow chips. There are 6 red chips remaining. The di� erence is 26.

• Alternatively, you could expand on the students’ knowledge of adding the opposite. Ask students to start with 2 red chips and then add the opposite of 4 yellow chips (4 red chips). The answer will be 6 red chips (26).

Students use a number line to model integer subtraction. They use words to describe how to use the number line. Afterwards, students revisit the problem and develop general rules for integers.

Model It• Read the problem at the top of the page as

a class.

• Guide students to understand how the number lines model subtraction problems.

Hands-On Activity


At A Glance

Step By Step


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

18


Lesson 3


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 di� erence between Gerry’s score and Jane’s score?

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

Elevations in Louisiana

Location Elevation (ft)

Mt. Driskill 535

New Orleans 28

They all involve subtraction and have at least one negative number.

Add the opposite of the number being subtracted to the first number.

2 1 (23) 5 21

21 1 7 5 6

27 1 4 5 23

Tess; 6

When two negative numbers are subtracted, the result will be positive if the

number being subtracted has a greater absolute value than the number from

which it is being subtracted.

7

543 feet

English Language Learners

ELL students bene� t from working in small groups with their peers. Small group activities allow them to practice their speaking skills in a less-threatening atmosphere than talking in front of the whole class. They are able to increase their understanding of a topic by hearing and discussing the viewpoints of the teacher and other students.

Connect It• Discuss each Connect It problem as a class

using the discussion points outlined below.

• Ask students to explain how subtracting a number is the same as adding its opposite.

• Ask a volunteer to describe his or her answer to problem 14.

• Ask students to complete the Try It problems and discuss their answers.

English Language Learners

Try It15 Solution

7; Students may rewrite the problem as an addition problem: 217 1 24.

Error Alert Students who wrote 241 added 217 1 (224).

16 Solution543 feet; Students may rewrite the problem as 535 1 8.


Step By Step

Mathematics PRACTICE AND PROBLEM SOLVING19

Guided Practice

Teacher Notes


Lesson 3 Add and Subtract Positive and Negative Integers 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 � rst 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

Stage Time 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?How else could you How else could you

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

Describe other Describe other

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

26; A negative number means Kelly’s time this year

decreased from last year, so she improved her time.

4 1 (27) 1 (23)

23 1 (23) 5 26

20

Students use models, number lines, or equations to solve word problems involving addition and subtraction of integers.

• Ask students to solve the problems individually.

• Pair/Share When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group.

Example 23 feet, or 3 feet below the surface of the pond; Students could solve the problem using a vertical number line to model 5 – 8.

17 Solution26; A negative number means Kelly’s time decreased, which means that her time improved. Students could solve the problem by rewriting it as an addition problem: 4 1 (27) 1 (23).DOK 1

At A Glance

Step By Step

Solutions

Teacher Notes


Lesson 3


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 di� erence 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?

What does a negative What does a negative

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

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?

The helicopter is 23 m from the top of the canyon wall.

Sample student work:

Siri added 2 1 (26) to get 24. She should have found 2 2 (26) to

find the difference between 2 and 26.

19 m

+5 m

–8 m

–3 m–27 m

wall

21

18 Solution23 meters; Students could solve the problem by rewriting it as an addition problem: 19 1 (227) 1 5. DOK 1

19 SolutionD; Siri added 2 1 (26). She should have found 2 2 (26).Explain to students why the other two answer choices are not correct:A is not correct because 2 was subtracted from 26.C is not correct because 2 was subtracted from 6. DOK 3


Solutions




Quick Check and Remediation


• Ask students to � nd 212 2 (23). [29]

• For students who are struggling, use the chart to guide remediation.

• After providing remediation, check students’ understanding. Ask students to explain their thinking while � nding the di� erence of 3 2 (25). [8]

• If a student is still having di� culty, use Ready Instruction, Grade 6, Lessons 12 and 13.


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 di� erence 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

3

3

3

3

3

22

Students add and subtract integers to solve word problems that might appear on a mathematics test.

1 SolutionB; Start with 250, then add 15 and subtract 40.DOK 2

2 SolutionC; For each town, subtract to � nd the di� erence between the actual temperature and the wind-chill temperature. DOK 1

3 Solutiona. False; b. False; c. True; d. True; e. True DOK 1

At A Glance

Solutions

If the error is . . . Students may . . . To remediate . . .

215 have added 23

Have students sketch a number line and label 0 and 212. Remind them that when subtracting integers, they should add the opposite. The opposite of 23 is 13. Have them use the number line to add 212 and 3.

115have added the opposite of 212 and 23

Write the problem 212 2 (23) and ask students to read the problem aloud so they focus on the signs. Remind them that when subtracting integers, they should add the opposite of the second number: 212 1 3. Have them use the number line to add 212 and 3.

19 have missed the signs and subtracted 12 2 3.

Remind students to read the problem carefully to make sure they are using the correct signs.


Lesson 3

Quick Check and Remediation

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 gold� sh for a total of $10. Therefore, she made a pro� t of $2.

C At a bus stop, 8 people got o� 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

Curran had a score of 28.

29 1 5 5 2424 1 ? 5 2124 1 3 5 21

The team gained 3 yards on the play Austin missed.

29 1 (215) 5 224224 1 ? 5 232224 1 (28) 5 232

23

Hands-On Activity Use a number line to subtract integers.

Materials: large classroom number lines

• Ask students to model an integer subtraction problem on a number line.

• Given the problem 9 2 (22), students should start by standing on positive 9. They should illustrate adding the opposite of 22 by moving 2 spaces to the right. The result is 111.

• Repeat with additional problems as time allows.

Challenge Activity Find numbers with a given difference.

Tell students that the di� erence between two numbers is 27. Challenge students to write a subtraction problem with a di� erence of 27. Ask them to write an addition problem with a sum of 27.

4 SolutionA; 8 electrons that each have a charge of 21 represents 28, and 10 protons that each have a charge of 11 represents 110. C; 8 people getting o� the bus represents 28, and 10 people getting on the bus represents 110. DOK 2

5 SolutionCurran had a score of 28. See possible student work above. DOK 2

6 Solution The team gained 3 yards on the play Austin missed. See possible student work above.DOK 2

Solutions

23b ©Curriculum Associates, LLC Copying is not permitted

Teacher-Toolbox.com

LESSON QUIZ



Overview

Assign the Lesson 3 Quiz and have students work independently to complete it.

Use the results of the quiz to assess students’ understanding of the content of the lesson and to identify areas for reteaching. See the Lesson Pacing Guide at the beginning of the lesson for suggested instructional resources.

2©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 7 Lesson 3 Add and Subtract Positive and

Negative Integers

Name ___________________________________________________________ Date ____________________

Lesson 3 Quiz continued

3 Let a represent a positive number and let b represent a negative number.

Tell whether each statement is True or False.

a. The difference ( a 2 b ) could be negative. u True u False

b. The difference ( b 2 a ) cannot be positive. u True u False

c. The sum ( a 1 b ) could be positive. u True u False

d. The sum ( b 1 a ) must be negative. u True u False

4 Write the letter for each expression in the box under the correct category in the table.

A 9 1 (23) 1 (22)

B 212 1 1 1 11

C 23 1 8 1 (24)

D 24 1 9 1 (210)

E 3 1 (22) 1 (24)

F 2 1 (24) 1 2

Negative Sum Zero Sum Positive Sum

5 Mei wrote the subtraction expression shown. She will rewrite it as an addition expression to � nd its value.

2 8 2 ( 2 4) 2 9

Part A

Write a number in each blank to show an equivalent addition expression.

1 1

Part B

What is the value of Mei’s expression?

Show your work.

Answer:

1©Curriculum Associates, LLC

Copying permitted for classroom use.Grade 7 Lesson 3 Add and Subtract Positive and

Negative Integers

Name ___________________________________________________________ Date ____________________

Lesson 3 QuizReady® Mathematics

Solve the problems.

1 The di� erence between two numbers is 2 3. Which of the expressions could represent the subtraction problem?

Choose all that apply.

A 24 2 1

B 8 2 11

C 2 2 (21)

D 21 2 2

E 25 2 (22)

2 In golf, scores that are under the expected score are represented by negative numbers. Calvin played three games of golf during a tournament. His score for each game is shown in the table.

Part A

Which statement is true about Calvin’s score during the tournament?

A Calvin’s score changed from Game 1 to Game 2 by 2 2.

B Calvin’s score changed from Game 1 to Game 3 by 2 1.

C Calvin’s score changed from Game 2 to Game 3 by 2 1.

D Calvin’s score changed from Game 1 to Game 3 by 2 3.

Part B

What was Calvin’s total score for the three games?

Show your work.

Answer:

Game Score1 12 233 22

Tested Skills

Assesses 7.NS.1d

Problems on this assessment form require students to be able to apply properties of operations as strategies to add and subtract rational numbers. Students will also need to be familiar with adding and subtracting whole numbers.

23c©Curriculum Associates, LLC Copying is not permitted Lesson 3 Add and Subtract Positive and Negative Integers

Lesson 3

Common Misconceptions and Errors

Errors may result if students:

• overlook negative signs when � nding the di� erence between integers.

• add instead of subtracting, or vice versa.

• misinterpret parentheses around negative integers as multiplication.

Grade 7 Lesson 3 Add and Subtract Positive and Negative Integers ©Curriculum Associates, LLC

Lesson 3 Quiz Answer Key

Ready® Mathematics

1. B , D , E DOK 1

2. Part A: D DOK 2

Part B: 2 4 DOK 1

3. a. False b. True c. True d. False DOK 3

4. Negative Sum Zero Sum Positive SumD, E B, F A, C

DOK 2

5. Part A: Possible answer: 2 8, 4, 2 9 DOK 2

Part B: 2 13 DOK 2

Documents

LESSON Lesson 3 OVERVIEW Add and Subtract … 14 ©Curriculum Associates, LLC Copying is not permitted Lesson 3 Add and Subtract Positive and Negative Integers Lesson 3 Add and Subtract