1. Integers with Manipulatives

2. Numberlines – Integers (+, -)
Adding –Forward direction (direction you are facing) =
1 + 2 = = 1 2 3 4 -1 -2 -3 -4 1 3 -2

3. Numberlines – Integers (+, -)
Subtracting – change direction
2 - 3 = = = = 1 2 3 4 -1 -2 -3 -4 -1 + -3 +1 -
+ 1

4. Integer Chips / Tiles
Negative -
Positive +

5. The collections shown here are “zero pairs”.
Zero pairs have a value of zero.

6. What is the value?
Has a value of +5.
Has a value of +5.
Has a value of +5.
Has a value of +5.
Build a different collection that has a value of +5.

7. ADDING INTEGERS with Tiles

8. Build your initial collection, add your other collection, then find the value of the collection.
5 + (+3)
= +8

9. Build your initial collection, add your other collection, then find the value of the collection.
zero pairs
5 + (-3)
= 2

10. SUBTRACTING INTEGERS with Tiles

11. Subtracting - take away
Example 1: 9 – 3
= 6
Build your initial collection, then take away the other collection (if you need to add a collection of zero pairs in order to take away then add them), then find the value of the collection
take away

12. Subtracting - take away
Example 2: –8 – (–2)
= –6
take away
Build your initial collection, then take away the other collection (if you need to add a collection of zero pairs in order to take away then add them), then find the value of the collection

13. Subtracting - take away method
Example 3: –8 – (+2)
= –10
Build your initial collection, then take away the other collection (if you need to add a collection of zero pairs in order to take away then add them), then find the value of the collection
take away

14. Adding, Subtracting Integers= = = = = = -3 -1 2

15. Model
MULTIPLYING
INTEGERS

16. 3 × 4
3 groups of 4 +
3 × 4 = 12

17. 3 × (–2)
3 groups of –2 +
3 × (–2) = –6

18. take away 2 groups of positive 3
If multiplying by a positive  add groups, what does it mean to multiply by a negative?
Subtract groups!
Example: –2 × 3
take away 2 groups of positive 3
So you need a collection to subtract from, so build a collection of zero pairs

19. = –6 –2 × 3 Take away 2 groups of 3 Example:
Have to build a collection of zero pairs
= –6

20. Example 2
(–4) × (–2)
= 8

21. Write as a Multiplication Statement
(+3) + (+3) + (+3) + (+3)
4 x +3
4 x (-3)
(-3) + (-3) + (-3) + (-3)
3 x (+3)
Two groups of -2
remove

22. Classwork
Page #5, 6, , 13, 16, 18, 20