1. Everything about Integers

2. Interesting Integers!
We can represent integers using red and yellow counters.
Red tiles will represent negative integers, and yellow tiles will represent positive integers.
Negative integer
Positive integer

3. Definition
Positive number – a number greater than zero. 1 2 3 4 5 6

4. Definition
Negative number – a number less than zero. -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

5. Definition
Opposite Numbers – numbers that are the same distance from zero in the opposite direction -6 -5 -4 -3 -2 -1 1 2 3 4 5 6

6. Definition
Integers – Integers are all the whole numbers their opposites and zero. 7
opposite -7

7. Example: The opposite of 6 is -6
What are Opposites?
Two integers the same distance from the origin, but on different sides of zero
Every positive integer has a negative integer an equal distance from the origin
Example: The opposite of 6 is -6
The opposite of -2 is 2

8. Interesting Integers!
If there are the same number of red tiles as yellow tiles, what number is represented?
zero pair
It represents 0.

9. Definition The absolute value of 9 or of –9 is 9.
Absolute Value – The size of a number with or without the negative sign.
The absolute value of
9 or of –9 is 9.

10. What is Absolute Value?
Distance a number is from zero on a number line (always a positive number)
Indicated by two vertical lines | |
Every number has an absolute value
Opposites have the same absolute values since they are the same distance from zero
Example: |-8| = 8 and |8| = 8
|50| = 50 and |-50| = 50

11. Examples
7 = 7
10 = 10
-100 =
100
5 - 8 =
-3= 3

12. |7| – |-2| = ? -9 -5 5 9

13. |-4 – (-3)| = ? -1 1 7
Purple

14. Negative Numbers Are Used to Measure Temperature

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

16. 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 $5,000.
When counting all their money they add
in -$5.000 to show they still owe the bank.

17. Hint
If you don’t see a negative or positive sign in front of a number it is positive. 9 +

18. ADDITION AND SUBTRACTION
Interesting Integers!
ADDITION AND SUBTRACTION

19. ADDING INTEGERS We can model integer addition with tiles.
Represent -2 with the fewest number of tiles
Represent +5 with the fewest number of tiles.

20. ADDING INTEGERS
What number is represented by combining the 2 groups of tiles?
Write the number sentence that is illustrated.
= +3 +3

21. = -5 + ADDING INTEGERS Use your red and yellow tiles to find each sum.
= ?
ANSWER
= -5 +
= -5

22. + - 4 = +1 = + ADDING INTEGERS -6 + +2 = ? -3 + +4 = ? -6 + +2 = -4
ANSWER
= ? + =
- 4
= -4
= ?
ANSWER = +1 +
= +1

23. Solve the Problems -3 + -5 = 4 + 7 = (+3) + (+4) = -6 + -7 = 5 + 9 == -8 11 7
-13 14
-18

24. Solve These Problems 3 + -5 = -4 + 7 = (+3) + (-4) = -6 + 7 = 5 + -9 == -2 3 -1 1 -4

25. Adding Integers
Number line
T-Method

26. - 3 + 2 = -1 Adding Integers using the number line
Negative three means
move 3 places to the left
Positive two means
move 2 places to the right 1 2 -3 -2 -1
The answer is: -1

27. 8 - 3 = 5 Adding Integers using the number line Positive eight means= 5
Positive eight means
move 8 places to the right
Negative three means
move 3 places to the left 1 2 3 4 5 6 7 8 5 3 6 2 7 1 8
The answer is: 5

28. Adding Integers
T- Method
T-Method

29. Use your red and yellow tiles to find each sum.
2 + 5 = ? - + 2 + = 5 7
T-Method

30. Use your red and yellow tiles to find each sum.
-2 + (-5) = ? - + 2 + = 5 7
T-Method

31. Use your red and yellow tiles to find each sum.
2 + (-5) = ? + - 5 2 2 + = 3
T-Method

32. Use your red and yellow tiles to find each sum.
= ? - + 2 2 5 + = 3
T-Method

33. Subtracting Integers and
T- Method
T-Method

34. SUBTRACTING INTEGERS +3 +3
We often think of subtraction as a “take away” operation.
Which diagram could be used to compute
= ? +3 +3

35. SUBTRACTING INTEGERS
This diagram also represents +3, and we can take away +5.
When we take 5 yellow tiles away, we have 2 red tiles left.
We can’t take away 5 yellow tiles from this diagram. There is not enough tiles to take away!!

36. SUBTRACTING INTEGERS -2 - -4 = ?
Use your red and yellow tiles to model each subtraction problem.
= ?
ANSWER

37. -2 - -4 = +2 SUBTRACTING INTEGERS Now you can take away 4 red tiles.
2 yellow tiles are left, so the answer is…
This representation of -2 doesn’t have enough tiles to take away -4.
Now if you add 2 more reds tiles and 2 more yellow tiles (adding zero) you would have a total of 4 red tiles and the tiles still represent -2.
= +2

38. SUBTRACTING INTEGERS
Work this problem.
= ?
ANSWER

39. +3 - -5 = +8 SUBTRACTING INTEGERS
Add enough red and yellow pairs so you can take away 5 red tiles.
Take away 5 red tiles, you have 8 yellow tiles left.
= +8

40. SUBTRACTING INTEGERS
Work this problem.
= ?
ANSWER

41. -3 - +2 = -5 SUBTRACTING INTEGERS
Add two pairs of red and yellow tiles so you can take away 2 yellow tiles.
Take away 2 yellow tiles, you have 5 red tiles left.
= -5

42. -3 – ( -5) = 4 - 7 = (+3) - (+4) = -6 – (-7) = 5 - 9 = -9 – (-9) =
SUBTRACTING INTEGERS
-3 – ( -5) =
4 - 7 =
(+3) - (+4) =
-6 – (-7) =
5 - 9 =
-9 – (-9) = 2 -3 -1 1 -4

43. 3 – (-5) = -4 - 7 = (+3) - (-4) = -6 - 7 = 5 – (-9)= -9 - 9 =
SUBTRACTING INTEGERS
3 – (-5) = =
(+3) - (-4) = =
5 – (-9)= = 8
-11 7 13 14
-18

44. Keep in mind that subtract means add the opposite.
In order to subtract two integers, you would need to re-write the problem as an addition problem.
Keep in mind that subtract means add the opposite. - - 2 2
(-5) -5 = = + 5
T-Method

45. -8 – ( -2) = 5 - 4 = (+7) - (+2) = -8 – (-7) = 8 - 5 = -10 – (-2) =
SUBTRACTING INTEGERS
-8 – ( -2) =
5 - 4 =
(+7) - (+2) =
-8 – (-7) =
8 - 5 =
-10 – (-2) = 6 1 5 -1 3 -8