1. *Make sure all tiles are positive side up (negative [red] side down)*
Algebra Tiles
*Make sure all tiles are positive side up (negative [red] side down)* 1 1 x x
x2 Tile
Area = 1 5 y y 1 x
Unit Tile
Area = x
Area = x2 1
x Tile
5 Piece
Area = 5 1 y
Area = y
Area = y2
y2 Tile
xy Tile x
y Tile y
Area = xy

2. Algebra Tiles: Perimeter
*Make sure all tiles are positive side up (negative [red] side down)*
Algebra Tiles: Perimeter 1 y 1 1 x 1 1 1 1 x x x x
P = 4 5 5 y y y y 1 x
P =
2x + 2
P = 4x 1
P = 12 y 1 y
P =
2y + 2
P =
y + y + y + y
= 4y x x y
P =
2x +2y

3. algebra 1 2-3: Jumbled Piles
chapter two
2-3: Jumbled Piles
What is the best description for this collection of tiles?
Algebra 1: Chapter 2 Notes

4. algebra 1 2-4: Jumbled Piles
chapter two
2-4: Jumbled Piles
What is the best description for this collection of tiles?
Algebra 1: Chapter 2 Notes

5. Answers to 2-4

6. algebra 1 2-13: Find perimeter / area chapter two x2 y2 xy y x x y x 1
Algebra 1: Chapter 2 Notes

7. Answers to 2-13

8. Commutative Properties
Are two the expressions equivalent?
Commutative Property of Addition: When adding two or more numbers together, order is not important
Commutative Property of Multiplication: When multiplying two or more numbers together, order is not important
Are there Commutative Properties for Subtraction and Division?

9. A symbol which represents an unknown.
Variable
A symbol which represents an unknown.
Examples: m x z y

10. Combining like Terms
Terms: Variable expressions separated by a plus or minus sign. Like terms: Terms with the same variable(s) raised to the same power. Combine Like Terms: Add the numbers the liked terms are being multiplied by.
Ex: Simplify the expression below:
6x2 + 4x x2 + 3x + 6
The x2 Tile
The x Tile x2 x 5 x2 x 6
8x2 + 7x + 11
Unit Tiles
6+2
4+3
5+6

11. Substitution and Evaluation
Substitution: Replace each variable with its indicated value.
Evaluation: Simplify the expression with proper order of operations.
Example: Evaluate the expression below if x = 3 and y = -2. P E MD AS

12. Square Notation Evaluate the following:
The opposite of 5 squared
Evaluate the following if x = -3:
Square -3
The opposite of -3 squared

13. Legal Mat Move: Flipping+ –
To move a tile between the positive and opposite regions, it must be placed on the opposite side.
Algebra

14. Rules for Showing Work with Mats+ –
In order to receive credit for a tile and mat problem…
Copy at least the original mat and tiles
Circle zeros, use arrows to show flipping, etc.
It must be organized and clear. Draw a second table if necessary.
Do NOT make a Picasso!

15. L.M.M. – Removing Zeros in Same Region+ –
To remove two tiles in the same region, the tiles must be of opposite signs (one positive and the other negative).
Algebra

16. L.M.M. – Removing Zeros in Different Regions+ –
To remove two tiles in different regions, the tiles must be the same sign (both positive or both negative).
Algebra

17. Legal Mat Move – Balancing+ – + –
Adding (or subtracting) like tiles to (or from) the same region of both sides of the mat is allowed.
Algebra ?

18. 2-65: Recording Your Work Right Side is Greater + – + – ? Left Right
Explntn
Original
Flip
Remove 0’s
Balance ?
Right Side is Greater

19. 2-75a: Solving for x x = 3 + – + – = Explntn Original Flip Remove 0’s
CLT =
Balance
Balance
Divide
x = 3

20. 2-75: Solving for x When is 0 equal to 0? Infinite Solutions + – + – =
Explntn
Original
Flip
Remove 0’s
CLT =
Balance
TRUE
When is 0 equal to 0?
Infinite Solutions

21. 2-82 a: Solving for x x = 3 + – + – = Explntn Original Flip Remove 0’s
CLT =
Balance
Balance
Divide
x = 3

22. 2-83 : Solving for y When is 2 equal to -2? No solution + – + – =
Explntn
Original
Flip
Remove 0’s
Balance =
FALSE
When is 2 equal to -2?
No solution

23. Solving for x and Checking the Answer+ – + –
Explntn
Original
Balance
Divide =
The left side must equal the right side.
Check:

24. Using a Table to solve a Proportion Question
Toby uses seven tubes of toothpaste every ten months. How many tubes would he use in 5 years?
5 years = 5x12 = 60 months
Months
Tubes 10 7 x6 x6 60 42 ?
42 Tubes

25. Using a Table to solve a Proportion Question
Toby uses seven tubes of toothpaste every ten months. How long would it take him to use 100 tubes?
Months
Tubes 10 7
x14.286
x14.286
142.86 ?
100
Months

26. Using a Diagram to solve a Proportion Question
One more way to organize your work for 2-99
÷ 1.8 15
x 1.8
7.83 = 0x 6 y
= 27 20
14.1
10.8 36
x 1.8