Develop Skills and Strategies
Lesson 13A
Part 1: Introduction
MS CCRS
6.NS.9a
6.NS.9b
6.NS.9d
Add with Integers
In previous lessons, you learned about positive and negative numbers and how
they appear on the number line. Take a look at this problem.
A football team gets the ball on the 5-yard line. The team gains 4 yards on its
first play, and then loses 4 yards on its second play. Where does the team begin the
next play?
Explore It
Use the math you already know to solve the problem.
Which football play can be represented by a positive number? Which football play can be represented by a negative number? Write the positive or negative number to represent each play.
Gain of 4 yards Loss of 4 yards How far is each number from 0 on a number line? What does this tell you about the
numbers? If the ball moves 4 yards in one direction and then 4 yards in the opposite direction,
where is the final position of the ball? The ball started at the 5-yard line. What is the position of the ball after these two
plays? Explain how you could find the overall change in yards. MS128
L13A: Add with Integers
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Part 1: Introduction
Lesson 13A
Find Out More
In the problem on the previous page, a positive number represents a gain and a negative
number represents a loss. 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.
Start
The football team begins on the 5-yard line,
so start at 5 on the number line.
0
The team gains 4 yards on the first play.
The gain is represented by 14. From 5, move
right 4 units to add 14 yards. The result is 9.
The team loses 4 yards on the next play.
The loss is represented by 24. From 9, move
4 units to the left to add 24. The result is 5.
1
2
3
4
5
6
7
8
9 10
8
9 10
8
9 10
+4
0
1
2
3
4
5
6
End
0
1
2
3
7
–4
4
5
6
7
The football team ended up back where they started, on the 5-yard line. The overall
change in yards was 0 yards.
The numbers 14 and 24 are opposite numbers. The sum of a number and its opposite is 0.
4 1 (24) 5 0
Two numbers that have a sum of zero are also known as additive inverses. So a number
and its opposite are additive inverses.
Reflect
1 What is the additive inverse of 210? Explain how you know.
L13A: Add with Integers
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MS129
Part 2: Modeled Instruction
Lesson 13A
Read the problem below. Then explore ways to add integers.
All matter is made up of tiny particles called atoms.
Atoms consist of even smaller particles that can carry
positive charges or negative charges. For example,
an atom of oxygen has 8 positive charges, called
–
protons, and 8 negative charges, called electrons.
–
–
–
++ +
+ + +
+ +
–
What is the overall charge of an oxygen atom?
–
– –
Picture It
You can compare the positive and negative charges using integer chips.
The yellow side of an integer chip (shown here as light orange) represents +1 and the red
side of an integer chip (shown here as dark orange) represents –1. Use integer chips to
represent 18 and 28.
A zero pair is a combination of one
positive integer chip and one negative
integer chip. A zero pair has a sum of 0.
=0
Model It
You can use a number line to add the positive and negative charges.
Move 8 units
left to add –8.
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
MS130
0
1
2
3
4
5
6
Start at +8.
7
8
9 10
L13A: Add with Integers
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Part 2: Guided Instruction
Lesson 13A
Connect It
Now you will use the models to solve the problem.
2 Look at the integer chips in Picture It. Circle each zero pair. How many zero pairs are
there? What is the overall value?
3 Look at Model It. Where did the arrow end on the number line? 4 Use the number line in Model It to write an addition equation to describe the problem.
Value of positive
charges
1
Value of negative
charges
1
5
Overall Charge of
Oxygen atom
5
5 Would the result be the same if you started at –8 and added 8? Explain using a
number line. 6 How are charges in an atom like additive inverses? 7 How would the overall charge change if an oxygen atom lost two electrons (negative
charges)? Explain using integer chips. Try It
Apply what you just learned about adding opposite integers to solve these
problems. Show your work on a separate sheet of paper.
8 The temperature is 27°F at sunrise and rises 7°F by noon. What is the temperature
at noon? 9 Depositing money into a bank account is a positive entry in a statement. Withdrawing
money is a negative entry. Jenvieve withdraws $20 from her account. Now her
balance is $0. How much money did she have in her account before making the
withdrawal? L13A: Add with Integers
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MS131
Part 3: Modeled Instruction
Lesson 13A
Read the problem below. Then relate adding integers to absolute value.
A whale is located 9 meters below the surface of the water. The whale swims up
through the water and jumps into the air for a total rise of 13 meters.
How high above the water does the whale jump?
Picture It
You can model the problem using a vertical number line.
Consider the surface of the water as the 0-meter
mark.
• Depths below the surface can be considered
negative points on the number line.
• Heights above the surface can be considered
positive points on the number line.
5
4
3
2
1
0
–1
–2
–3
Moves up 13
units
–4
–5
–6
–7
–8
–9
–10
Model It
You can use an equation to solve the problem.
Starting position 1 Rise in position 5 Final position
29
MS132
113 5?
L13A: Add with Integers
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Part 3: Guided Instruction
Lesson 13A
Connect It
Now you will add integers to analyze the whale’s motion described on the
previous page.
10 Look at Picture It. Where did the whale end on the number line after it went up
13 meters? 11 Solve the equation in Model It that describes the whale’s change in position. How high
above the water does the whale rise? 12 How many meters did the whale rise on the negative side of the number line? How many meters did the whale rise on the positive side of the number line? Complete the equation: |4| 1 |29| 5 13 Imagine that the whale swam down 13 meters instead of up. Write and solve an
equation to describe the end position of the whale. Use a number line if needed.
Where does the whale end up? 14 Explain how to predict the sign of the sum when adding: two positive integers, a
positive and a negative integer, or two negative integers. Try It
Use what you just learned about adding integers to solve this problem. Show your
work on a separate sheet of paper.
15 A submarine is 40 meters below sea level. What is its new position relative to sea level
if the submarine rises 25 meters? What is its new position relative to sea level if it
descends 25 meters? Write and solve equations to find the answers. L13A: Add with Integers
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MS133
Part 4: Modeled Instruction
Lesson 13A
Read the problem below. Then analyze ways to add the integers.
You owe your sister $5. Then you earn $12 babysitting. How much money will you
have after paying your sister back?
Picture It
You can use integer chips. Count the chips left over after removing the zero pairs.
–
–
–
–
–
+
+
+
+
+
+
+
+
+
+
+
+
Model It
You can write an equation and use additive inverses to solve it.
25 1 12
The additive inverse of 25 is 5.
25 1 5 1 7
Rewrite the 12 as the sum of 5 and 7.
25 1 5 1 7 5 ?
MS134
L13A: Add with Integers
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Part 4: Guided Instruction
Lesson 13A
Connect It
Now you will solve the problem on the previous page using additive inverses.
16 Look at Picture It. How many integer chips were left after removing the zero pairs?
Were they positive or negative? 17 Rewrite the Model It expression 25 1 5 1 7 by first combining the additive inverses.
Then find the sum. 18 How much money do you have after paying your sister back? 19 How was using additive inverses helpful when adding the integers?
Try It
Use what you just learned about adding integers to solve this problem. Show your
work on a separate sheet of paper.
20 A bird is flying in a canyon 6 m below the top of
the canyon wall. The bird rises 11 meters. What is the
new position of the bird relative to the top of the
canyon wall?
8
7
6
5
4
3
2
1
0
–1
–2
–3
–4
–5
–6
–7
–8
L13A: Add with Integers
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MS135
Part 5: Guided Practice
Lesson 13A
Study the student model below. Then solve problems 21–23.
Student Model
The band member
crosses from the positive
side of the number line
into the negative side.
The total distance
includes the distances
on both sides of 0.
The school band uses a number line on the gym floor to practice
marching. A band member begins at 15 and marches 8 steps left.
On what mark does the band member end?
Look at how you could show your work using an equation and a
number line.
5 1 (28) 5 23
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9 10
Pair/Share
What is another way you
could solve the problem?
How can you use additive
inverses to solve this
problem?
Solution: The band member ends at –3.
21 The lowest point in Mississippi is sea level at the Gulf Coast. A hiker is
at an elevation of 91 meters above sea level. How far must the hiker
descend to reach sea level? Write an addition equation to show the
change in position.
Pair/Share
Describe another
situation that involves
additive inverses.
MS136
Solution: L13A: Add with Integers
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Part 5: Guided Practice
22 The high temperature one day in Gulfport, MS, was 89°F. After
sunset, the temperature dropped 18°F. What was the temperature
after sunset?
Show your work. Include an addition equation.
Lesson 13A
Do you use a positive or a
negative number to
represent the change in
temperature?
Pair/Share
Solution: 23 During a game, hockey teams count each goal scored against them
as 21 point and each goal they score as 11 point. These points are
added together after each game to get a scoring number. Suppose a
team scores two goals in the first period, has one goal scored
against them in the second period, and has two goals scored against
them in the third period. What is the scoring number for this game?
Why is using additive
inverses an easier way to
solve this problem than
using integer chips or a
number line?
You can begin by writing
the integers that
represent the points in
the three periods of the
game.
A 23
B 21
C 11
D 12
Millie chose C as the correct answer. How did she get that answer?
L13A: Add with Integers
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Pair/Share
What are some
strategies for adding
more than two integers?
MS137
Part 6: Independent Practice
Lesson 13A
Solve the problems.
1
2
3
The table shows several bank deposits and withdrawals on an account. Which combinations
result in a balance of $0? Choose Yes or No for each combination.
Deposits
Withdrawals
A
$5, $10
$20
B
$25, $5
$20, $10
C
$8, $15
$20
D
$6, $10
$16
Yes
No
An airplane leaves an airport and flies 80 kilometers east and then 150 kilometers west.
What is the final position of the airplane relative to the airport?
A
70 kilometers east
B
230 kilometers east
C
70 kilometers west
D
230 kilometers west
The diagram shows an atom of carbon. How can you
determine the overall charge on the atom?
–
–
Answer –
+
+ + +
+ +
–
–
–
MS138
L13A: Add with Integers
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Part 6: Independent Practice
4
Lesson 13A
Which equations are correct? Select all that apply.
A
29 1 3 5 26 D15 1 (215) 5 30
B12 1 (28) 5 4 E 213 1 (25) 5 218
C
5
24 1 (25) 5 21
The temperature on Monday at 8:00 AM was 24º F, and the temperature dropped 8º F by
noon. The temperature on Tuesday at 8:00 AM was 3º F and it dropped 14º F by noon. Which
of these days was colder at noon? How much colder?
Show your work.
6
A bird is flying in Death Valley. The bird begins at sea level,
then rises 26 feet, dives down 80 feet, and rises back up 50 feet.
Part A
Write an addition expression to describe the bird’s change in
position.
Answer Part B
Choose one method of adding integers, and use it to find the bird’s
final position relative to sea level. Explain why this method is helpful.
0 sea level
Answer –282 Death
Valley
L13A: Add with Integers
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MS139