(7) Lesson 3.2 - Add Integers

1. Course 2, Lesson 3-2
Write an integer for each situation.
1. stock market down 56 points
2. a score of 3
3. a bank deposit of $25
Evaluate each expression.
4.
5.
6. What is the value of if k = −6 and m = −2
19
+12 2
k m

2. Course 2, Lesson 3-2
ANSWERS
1. −56
2. 3
3. 25
4. 19
5. 14
6. 4

3. WHAT happens when you add,
subtract, multiply, and divide integers?
The Number System
Course 2, Lesson 3-2

4. Course 2, Lesson 3-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.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.
• 7.NS.1a Describe situations in which opposite quantities combine to
make 0.
• 7.NS.1b Understand p + q as the number located a distance |q| from
p, in the positive or negative direction depending on whether q is
positive or negative. Show that a number and its opposite have a sum
of 0 (are additive inverses). Interpret sums of rational numbers by
describing real-world contexts.
• 7.NS.1d Apply properties of operations as strategies to add and
subtract rational numbers.

5. The Number System
• 7.NS.3 Solve real-world and mathematical problems involving the four
operations with rational numbers.
• 7.EE.3 Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as
appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics
7 Look for and make use of structure.
Course 2, Lesson 3-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.

6. • To add integers with the same sign
• To add integers with different signs
Course 2, Lesson 3-2
The Number System

7. Course 2, Lesson 3-2
The Number System
• opposites
2 and –2
• additive inverse

8. Course 2, Lesson 3-2
The Number System
Words To add integers with the same sign, add their absolute
values. The sum is:
• positive if both integers are positive.
• negative if both integers are negative.
Examples 7 + 4 = 11 −7 + (−4) = −11

9. 1
Need Another Example?
2
3
Step-by-Step Example
1. Find –3 + (–2).
Start at 0. Move 3 units down
to show –3.
From there, move 2 units
down to show –2.
So, –3 + (–2) = –5.

10. Answer
Need Another Example?
Find –6 + (–3).
–9

11. 1
Need Another Example?
Step-by-Step Example
2. Find –26 + (–17).
–26 + (–17) = –43 Both integers are negative, so the sum
is negative.

12. Answer
Need Another Example?
Find –34 + (–21).
–55

13. Course 2, Lesson 3-2
The Number System
Words To add integers with the different signs, subtract their
absolute values. The sum is:
• positive if the positive integer’s absolute value is greater.
• negative if the negative integer’s absolute value is
greater.
Examples 9 + (−4) = 5 −9 + 4 = −5

14. 1
Need Another Example?
2
Step-by-Step Example
3. Find 5 + (–3).
So, 5 + (–3) = 2.

15. Answer
Need Another Example?
Find 8 + (–7).
1

16. 1
Need Another Example?
2
Step-by-Step Example
4. Find –3 + 2.
+2
–3
So, –3 + 2 = –1.

17. Answer
Need Another Example?
Find –5 + 4.
–1

18. 1
Need Another Example?
Step-by-Step Example
5. Find 7 + (–7).
7 + (–7) = 0 Subtract absolute values; 7 – 7 = 0. 7 and (–7) are opposites.
The sum of any number and its opposite is always zero.

19. Answer
Need Another Example?
Find 5 + (–5).
0

20. 1
Need Another Example?
Step-by-Step Example
6. Find –8 + 3.
–8 + 3 = –5 Subtract absolute values; 8 – 3 = 5. Since –8 has
the greater absolute value, the sum is negative.

21. Answer
Need Another Example?
Find –9 + 6.
–3

22. 1
Need Another Example?
2
3
4
Step-by-Step Example
7. Find 2 + (–15) + (–2).
Commutative Property (+)2 + (–15) + (–2) = 2 + (–2) + (–15)
Associative Property (+)= [2 + (–2)] + (–15)
Additive Inverse Property= 0 + (–15)
= –15 Additive Identity Property

23. Answer
Need Another Example?
Find 11 + (–4) + (–11).
–4

24. 1
Need Another Example?
2
3
4
Step-by-Step Example
8. A roller coaster starts at point A. It goes up 20 feet, down
32 feet, and then up 16 feet to point B. Write an addition
sentence to find the height at point B in relation to point A.
Then find the sum and explain its meaning.
20 + (–32) + 16 = 20 + 16 + (–32) Commutative Property (+)
20 + 16 = 36
Subtract absolute values.
= 36 + (–32)
= 4
Point B is 4 feet higher than point A.

25. Answer
Need Another Example?
Max owes his brother $20. He gives his brother
$10 one week and then the next week he gives
$5. Write an addition expression to describe this
situation. Then find the sum and explain its
meaning.
–20 + 10 + 5; –$5; Max still owes his brother $5.

26. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide integers?
Course 2, Lesson 3-2
The Number System

27. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide integers?
Course 2, Lesson 3-2
The Number System
Sample answers:
• The sum of two positive integers is positive.
• The sum of two negative integers is negative.
• To find the sum of two integers with different signs,
subtract their absolute values and use the sign of the
integer with the greater value.

28. Find the sum –3 + (– 5)
and the sum – 3 + 5.
Then write a few sentences
comparing and contrasting
the expressions.
Ratios and Proportional RelationshipsThe Number System
Course 2, Lesson 3-2