1. Adding and Subtracting Integers
What rules can you come up with that can sum up adding & subtracting integers?
Remember, rules must apply at all times, and must be clear.
5 + 2 = 7
-5 + (-2) = -7
= 2
8 + (-10) = -2
5 – 3 = 2
-7 – (-4) = -3
5 – (-10) = 15
-10 – 5 = -15

2. Add Integers with the Same Sign

3. Add Integers with the Same Sign
Find –6 + (–3).
Use a number line.
Start at 0.
Move 6 units left to show –6.
From there, move 3 units left to show –3.
Answer: So, –6 + (–3) = –9.

4. Add Integers with the Same Sign
Find –34 + (–21).
–34 + (–21) = –55 Both integers are negative, so the sum is negative.
Answer: –55

5. Add Integers with Different Signs

6. Add Integers with Different Signs
Find 8 + (–7).
Use a number line.
Start at zero.
Move 8 units right.
Then move 7 units left.
Answer: So, 8 + (–7) = 1.

7. Add Integers with Different Signs
Find –5 + 4.
Use a number line.
Start at 0.
Move 5 units left.
Then move 4 units right.
Answer: So, –5 + 4 = -1.

8. Add Integers with Different Signs

9. Find 5 + (–19) + (–5).

10. Subtraction of Integers

11. Subtract Positive Integers
Find 2 – 15.
2 – 15 = 2 + (–15) To subtract 15, add –15.
= –13 Simplify.
Answer: –13

12. Subtract Positive Integers
Find –13 – 8.
–13 – 8 = –13 + (–8) To subtract 8, add –8.
= –21 Simplify.
Answer: –21

13. Subtract Negative Integers
Find 12 – (–6).
12 – (–6) = To subtract –6, add 6.
= 18 Simplify.
Answer: 18

14. Let’s model 12 – (-6) in a different way:
First, use 12 positive counters to model the number 12.
Now we have -6 to take away!
Now ask yourself, do I have 6 negative counters I can take away? No
Let’s use “zero pairs” to create the negatives that we need.
Reminder: a “zero pair” is a positive and negative counter that cancels each other out, leaving you with a sum of zero.
That’s right! (-6) = 18
Which is the same as = 18
What’s left?

15. Subtract Negative Integers
Find –21 – (–8).
–21 – (–8) = – To subtract –8, add 8.
= –13 Simplify.
Answer: –13

16. Evaluate an Expression
ALGEBRA Evaluate g – h if g = –2 and h = –7.
g – h = –2 – (–7) Replace g with –2 and h with –7.
= –2 + 7 To subtract –7, add 7.
= 5 Simplify.
Answer: 5

17. Write an addition expression to describe the situation
Write an addition expression to describe the situation. Then find each sum and explain its meaning.
SKATEBOARDING Hakeem starts at the top of a half pipe 8 feet above street level. He descends 14 feet to the lowest point in his run.

18. Write an addition expression to describe the situation
Write an addition expression to describe the situation. Then find each sum and explain its meaning.
SUBMARINE A submarine dives 106 feet below the water. Then it rises 63 feet.

19. FIND THE ERROR  Alicia and Mitsu are finding -16 - (-19) . Who is correct? Explain your reasoning.

20. SPACE The temperatures on the moon vary from -173ºC to 127ºC
SPACE  The temperatures on the moon vary from -173ºC to 127ºC. Find the difference in temperatures.

21. MONEY  Camilia owes her brother $25, so she gives her brother the $18 she earned dog-sitting for the neighbors. Write an addition sentence to describe this situation. Then find the sum and explain its meaning.