1. ALGEBRA TILES

2. INTRODUCTION
Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions.
Here are three types of ‘tiles’:
1. Large square with x as its length and width.
2. Rectangle with x and 1 as its length and its width
3. Small square with 1 as its length and width. x 1 1 x x 1

3. INTRODUCTION Each tile represents an area.x
Area of large square = x (x) = x2 x 1 x
Area of rectangle = 1 (x) = x 1 1
Area of small square = 1 (1) = 1

4. INTRODUCTION Does an x-tile need to be any particular length?
Does its length matter?
x-tile does not have to be a particular length because it represents a variable. Its length does not matter.
NOTE

5. ALGEBRAIC EXPRESSIONS
To model 2x2, you need 2 large squares x2 x2

6. AGEBRAIC EXPRESSIONS
To model x2 + 3x, you need 1 large square and 3 rectangles x2 x x x

7. ALGEBRAIC EXPRESSIONS
How would you model 2x2 + x + 4?
ANSWER x2 x2 x 1 1 1 1

8. ALGEBRAIC EXPRESSIONS
What algebraic expression is modeled below?
ANSWER
2x + 3

9. ALGEBRAIC OPERATIONS
We can use algebra tiles to model adding, subtracting, multiplying, and dividing algebraic expressions

10. ALGEBRAIC ADDITION 3 + 2x + 4 2x + 7 = = +
To use algebra tiles to model 3 + (2x + 4) represent each addend with tiles. 3 +
2x + 4
2x + 7 = x x x x = + 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Combine the tiles

11. ALGEBRAIC ADDITION + = 2x + (5x + 4) = 7x + 4 Find the sum:
ANSWER x x x x x x x + x x x x x = 1 1 1 1 x x 1 1 1 1
2x + (5x + 4) = 7x + 4

12. ALGEBRAIC ADDITION + = (x + 3) + (2x + 4) = 3x + 7 Find the sum:
ANSWER x x x x x x + = 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(x + 3) + (2x + 4) = 3x + 7

13. ALGEBRAIC ADDITION + = (x2 + 3) + (2x2 + x +2) = 3x2 + x + 5
Find the sum:
(x2 + 3) + (2x2 + x + 2)
ANSWER x2 x2 + x2 x2 = x2 x 1 1 1 x 1 1 1 1 1 x2 1 1
(x2 + 3) + (2x2 + x +2) = 3x2 + x + 5

14. ALGEBRAIC SUBTRACTION
To use algebra tiles to model subtraction, represent each expression with tiles. Put the second expression under the first.
(5x + 4) – (2x + 3)
Now remove the tiles which match in each expression.
5x + 4 x x x x x
The answer is the expression that is left. 1 1 1 1 x x
2x + 3 1 1 1
(5x + 4) – (2x + 3)= 3x +1

15. ALGEBRAIC SUBTRACTION
Use algebra tiles to find the difference.
(8x + 5) – (6x + 1)
ANSWER
8x + 5 x x x x x x x x 1 1 1 1 1
6x + 1 - x x x x x x 1
(8x + 5) – (6x + 1) = 2x + 4

16. ALGEBRAIC SUBTRACTION
Find the difference.
(6x + 1) – (3x)
ANSWER
6x + 1 x x x x x x 1 - x 3x x x
(6x + 1) – (3x) = 3x +1

17. ALGEBRAIC SUBTRACTION
Find the difference.
(5x + 6) – (5x)
ANSWER
5x + 6 x x x x x 1 1 1 1 1 1 - 5x x x x x x
(5x + 6) – (5x) = 6

18. ALGEBRAIC SUBTRACTION
Use algebra tiles to find the difference.
(3x2 + 4x + 5) – (x2 + 3x + 4)
3x2 + 4x + 5
ANSWER x2 x2 x2 x x x x 1 1 1 1 1
x2 + 3x + 4 - x2 x x x 1 1 1 1
(3x2 + 4x + 5) – (x2 + 3x + 4) = 2x2 + x + 1

19. Let’s Practice!