1. ADDING & SUBTRACTING INTEGERS NS 1.2 and AF 1.3

2. Integers
Whole numbers and their opposites are integers such as 6 and -6.
Zero is also a whole number. -6 6
Opposites

3. Negative Numbers Are Used to Measure Temperature

4. Negative Numbers Are Used to Measure Under Sea Level30 20 10
-10
-20
-30
-40
-50

5. Negative Numbers Are Used to Show Debt
Let’s say your parents bought a car but had to get a loan from the bank for $15,000.When counting all their money they add in
-$ to show they still owe the bank.

6. INTRODUCTION TO INTEGERS
We can represent integers using red and yellow counters.
Red counters will represent negative integers, and yellow counters will represent positive integers.
Negative integer
Positive integer

7. INTRODUCTION TO INTEGERS
The diagrams below show 2 ways to represent -3.
Represent -3 in 2 more ways. -3 -3

8. INTRODUCTION TO INTEGERS
Each of the following groups of counters represent -3.
You may represent -3 by using 3 red tiles and any number of groups of +1 and -1 tiles

9. INTRODUCTION TO INTEGERS
Tell which integer each group of tiles represents. 1 -2 2

10. INTRODUCTION TO INTEGERS
Tell which integer each group of tiles represents. -1 -4 +4

11. INTRODUCTION TO INTEGERS
Tell which integer each group of tiles represents. +5 -4 -3

12. INTRODUCTION TO INTEGERS
If there are the same number of red tiles as yellow tiles, what number is represented?
It represents 0.

13. Adding and Subtracting Integers=
-3+4=1

14. Adding and Subtracting Integers
6 – 10 =
6 – 10 = -4

15. Adding and Subtracting Integers=
= -13

16. Adding and Subtracting Integers=
= 5

17. Adding and Subtracting Integers
Three Meanings of the Minus Sign
Subtract
Example: 8 – 5 is read “subtract 5 from 8”
Negative
Example: 8 – 5 can be read “8 and negative 5”
The Opposite Of
Example 8 – (-5) can be read “8 and the opposite of (-5)” or 8 + 5

18. Adding and Subtracting Integers
-3 – (-4) =
Reads -3 “and the opposite of” -4
What is the opposite of -4?

19. Adding and Subtracting Integers
-3 – (-4) =
Reads 3 “and the opposite of” -4
-3 – (-4) = 1

20. Adding and Subtracting Integers
5 – (-9) =
What is the opposite of -9?
Reads 5 “and the opposite of” -9

21. Adding and Subtracting Integers
5 – (-9) =
What is the opposite of -9?
Reads 5 “and the opposite of” -9
5 – (-9) = 14

22. Addition with a number line
Add using a number line.
Add -4 + (-2)
Add 5 + (-7) +4 -2
Using the laminated number lines, students can follow along with their finger, or use dry-erase markers to track each problem.
When students use a number line to add integers, they will develop a general understanding that the sum, for example: 12 + (-7), is the number found when moving a total of 7 units from 12 to the left, since 7 is negative.
When adding a positive number, we move to the right. When adding a negative number we move to the left. -7 22

23. Practice with the number line
-2 + (-2)
3 + (-3)
-4 + (-6)
-8 + (-1)
10 + (-4)
-9 + 4
Have students practice using the number line to add integers.
When adding, we move right for positive and left for negative.
You can add more problems for students to practice with. 23

24. Subtraction on a number line
-3 – 2
-6 – (-2)
3 – (-6) -2
-(-2)
Using the laminated number lines, students can follow along with their finger, or use dry-erase markers to track each problem.
Students will see that subtraction is the same thing as adding the opposite.
-(-6) 24

25. Practice with the number line
5 – 9
3 – 10
-5 – 4
-7 – 9
5 – (-6)
-8 – (-8)
Have students practice using the number line to subtract integers.
You can add more problems for students to practice with. 25

26. On your own -4 + 4 = -6 – 15 = -6 + 13 = -21 2 + -13 = -4 – (-4) = 7
-9 – (-9) =
-21 7
-11