1. Modeling Review

2. Zero Pairs
One of the first concepts students need to understand when using Algebra Tiles is “zero pairs”
You can always add and take away “zero pairs” when needed
This concepts is key for all other concepts
You can tie in the Additive Inverse and Identity Properties here

3. Zero Principle
1+ (-1) = 0
2 + (-2) = 0

4. Adding Integers Example 1: 3 + 5 = 8
Model 3
Model 5
Combine the tiles and read the answer

5. Adding Integers Example 2: 2 + (-4) = ?-2
Model 2
Model -4
Combine the tiles and remove any zero pairs
read the answer

6. Subtracting Integers 6-2 = ?4
Remove 2 yellow tiles and read the answer
Model 6

7. Subtracting Integers -5 – (-3) = ?-2
Remove 3 red tiles and read the answer
Model -5

8. Subtracting Integers 4 – (-3) = ?7
Remove 3 red tiles and read the answer
Add 3 zero pairs
Model 4

9. Subtracting Integers -3 – 2 = ?-5
Model -3
Add 2 zero pairs
Remove 2yellow tiles and read the answer

10. Multiplying Integers Based on whole number representation
Use counters to represent a number of groups of a quantity of tiles

11. Prerequisites Students must understand whole number multiplication
That a x b means a groups of b

12. Multiplying Integers 3 x 2 -> 3 groups of 2 yellow tiles
3 x -2 -> 3 groups of -2 red tiles
-3 x 2 -> “the opposite” of 3 groups of 2 yellow tiles
-3 x -2 -> “the opposite” of 3 groups of 2 red tiles
You can also think of “the opposite” as “to remove”. Making this change forces students to put zero pairs on the mat.

13. Multiplying Integers 2 x 5 = ?10
2 groups of 5 yellow tiles

14. Multiplying Integers 2 x -4 = ?-8
2 groups of 4 red tiles

15. Multiplying Integers -2 x 6 = ?
-12
The opposite of
2 groups of 6 yellow
tiles

16. Multiplying Integers -2 x -3 = ?6
The opposite of
2 groups of 3 red tiles

17. Dividing Integers Same concept as multiplication
The dividend tells you how many of what color tiles you have.
The divisor tells you to make those tiles and make groups
If the divisor is negative then you would take the opposite

18. Prerequisites
Students should know how division works with positive whole numbers.
Students should work with multiplication of integers before moving on to division.

19. 3 Dividing Integers 6 ÷ 2 You start with 6 yellow tiles
Split the 6 yellow tiles into two groups
How many, of what tiles are in each row?

20. -4 Dividing Integers -8 ÷ 2 You start with 8 red tiles
Split the 8 red tiles into two groups
How many, of what tiles are in each row?

21. -5 Dividing Integers 10 ÷ -2 You start with 10 yellow tiles
Split the 10 yellow tiles into two groups…
then take the opposite
How many, of what tiles are in each row?

22. 4 Dividing Integers -12 ÷ -3 You start with 12 red tiles
Split the 12 red tiles into three groups…
then take the opposite
How many, of what tiles are in each row?