1. Integers Whole Numbers = { 0,1,2,3,….}
Natural Numbers or Positive Integers = {1,2,3,4,…}
Negative Integers = { -1,-2,-3,-4,….}
Integers ={ …-3,-2,-1,0,1,2,3,…}
Zero is neither positive nor negative.

2. Additive Inverse
For every integer n the negative of n is called the additive inverse of n.
N + -N = 0
Negative of a Negative
-(-N) = N
Think of - as “the opposite of”

3. Integer Representation
Colored counters
Black = +
Red = -
Game keeping score.
Mail Time Representation
Number Line Representaion

4. Absolute Value
The Absolute Value of a number is the distance on the number line away from 0.
5 and -5 are both 5 units away from 0.
| 5 | = 5
|-5| = 5

5. Homework
Pg 291 #1,2,457,8,29

6. Ordering Integers
The larger integer is the integer further to the right on the number line.
In the case of a thermometer, the higher number (more degrees, more heat)

7. Addition of Integers
Represent sum of integers using colored counter diagrams.
Mail Time Stories ( pg 297)
Number Line

8. Subtraction of Integers
Using colored Counters.
7- 4
BBBBBBB
RRRRRRRR

9. Subtraction of Integers
Using colored Counters.
7 – (-3)
Since we have to take away -3 (3 red counters), we have to represent 7 using 3 red counters.
BBBBBBB BBB
RRR

10. Subtraction of Integers
Using colored Counters.
8 – 9
Since we have to take away 9 ( black counters), we have to represent 8 using 9 black counters.
BBBBBBBB B R

11. Draw Diagrams for each of the following:
7 – 4
8 - -5
7 – 10
-7 - 3

12. Subtraction of Integers
Subtracting an integer is the same as adding its opposite.
A – B =
A + (-B)

13. Rewrite each of the following as adding the opposite
8 – 6
8 – -6
-6 – 5
8 – 12
– 6 –

14. Homework
Pg 310 # 1,2,34,5,11 43

15. Multiplication of Integers
4 x 3 = =12
4 x (-3) = = -12
Doesn’t work for -4 x -3

16. Pattern of Products 4 x 3 = 4 x 2 = 4 x 1 = 4 x 0 = 4 x -1 = 4x -2 =
Positive times a Negative = Negative

17. 3 x -3 =
2 x -3 =
1 x -3 =
0 x -3 =
-1 x -3 =
-2 x -3 =
-3 x -3 =
Negative times a Negative = Negative

18. Rules for Multiplication of Integers
MULTIPLY THE NUMBERS:
Positive x Positive = Positive
Positive X Negative = Negative
Negative x Positive = Negative
Negative X Negative = Positive

19. Mail Time Stories
Pg 317

20. Division of Integers 12 / 4 = 3 since 3 x 4 = 12

21. Rules for Dividing Integers
Divide THE NUMBERS:
Positive ÷ Positive = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative
Negative ÷ Negative = Positive

22. Homework
Pg 320 # 1 all, 2all, 10