ALGEBRA TILESALGEBRA TILES

INTRODUCTIONINTRODUCTION Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions.Algebra tiles can be used to model algebraic expressions and operations with algebraic expressions. Here are three types of ‘tiles’:Here are three types of ‘tiles’:

1. Large square with x as its length and width.1. Large square with x as its length and width.

2. Rectangle with x and 1 as its length and its width2. Rectangle with x and 1 as its length and its width

3. Small square with 1 as its length and width.3. Small square with 1 as its length and width.

x

xx

11

1

INTRODUCTIONINTRODUCTION

Each tile represents an area.Each tile represents an area.x

x Area of large square = x (x) = x2

x Area of rectangle = 1 (x) = x

Area of small square = 1 (1) = 1

1

11

INTRODUCTIONINTRODUCTION Does an x-tile need to be any particular length? Does an x-tile need to be any particular length? Does its length matter?Does its length matter? x-tile does not have to be a particular length because it represents a x-tile does not have to be a particular length because it represents a

variable. Its length does not matter.variable. Its length does not matter.

NOTE

ALGEBRAIC EXPRESSIONSALGEBRAIC EXPRESSIONS

To model 2xTo model 2x22, you need 2 large , you need 2 large squaressquares

x2x2

AGEBRAIC EXPRESSIONSAGEBRAIC EXPRESSIONS

To model xTo model x22 + 3x, you need 1 large square and + 3x, you need 1 large square and 3 rectangles3 rectangles

x2 x x x

ALGEBRAIC EXPRESSIONSALGEBRAIC EXPRESSIONS

►How would you model 2xHow would you model 2x22 + x + 4? + x + 4?

ANSWER

x2 xx2

1 1 1 1

ALGEBRAIC EXPRESSIONSALGEBRAIC EXPRESSIONS

►What algebraic expression is modeled What algebraic expression is modeled below?below?

ANSWER

2x + 3

ALGEBRAIC OPERATIONSALGEBRAIC OPERATIONS

►We can use algebra tiles to model We can use algebra tiles to model adding, subtracting, multiplying, and adding, subtracting, multiplying, and dividing algebraic expressionsdividing algebraic expressions

ALGEBRAIC ADDITIONALGEBRAIC ADDITION►To use algebra tiles to model 3 + (2x + To use algebra tiles to model 3 + (2x +

4) represent each addend with tiles.4) represent each addend with tiles.

3 + 2x + 4

1 1 1

x x1 1 1 1

= 2x + 7

x x1 1 1 1

1 1 1

+ =

Combine the tiles

► Find the sum:Find the sum:► 2x + (5x + 4)2x + (5x + 4)

ALGEBRAIC ADDITIONALGEBRAIC ADDITION

ANSWER

x x + x x x x x1 1 1 1 =

x x

x x x x x

1 1 1 1

2x + (5x + 4) = 7x + 4

ALGEBRAIC ADDITIONALGEBRAIC ADDITION

►Find the sum:Find the sum:►(x + 3) + (2x + 4)(x + 3) + (2x + 4)

ANSWER

x1 1 1 + x x

1 1 1 1 =x x x

1 1 1 1

1 1 1

(x + 3) + (2x + 4) = 3x + 7

► Find the sum:Find the sum:► (x(x22 + 3) + (2x + 3) + (2x22 + x + 2) + x + 2)

ALGEBRAIC ADDITIONALGEBRAIC ADDITION

ANSWER

x2

1 1 1+

x2

x2 x1 1

=

x2

x2

x2

x1 11 1 1

(x2 + 3) + (2x2 + x +2) = 3x2 + x + 5

► To use algebra tiles to model subtraction, represent each To use algebra tiles to model subtraction, represent each expression with tiles. Put the second expression under the first.expression with tiles. Put the second expression under the first.

► (5x + 4) – (2x + 3)(5x + 4) – (2x + 3)

ALGEBRAIC SUBTRACTIONALGEBRAIC SUBTRACTION

x x x x x1 1 1 1

x x1 1 1

5x + 4

2x + 3

Now remove the tiles which

match in each expression.

The answer is the expression

that is left.

(5x + 4) – (2x + 3)= 3x +1(5x + 4) – (2x + 3)= 3x +1

►Use algebra tiles to find the difference.Use algebra tiles to find the difference.►(8x + 5) – (6x + 1)(8x + 5) – (6x + 1)

ALGEBRAIC SUBTRACTIONALGEBRAIC SUBTRACTION

ANSWER

x x x x x x x x 111 1 1

- x x x x x x1

8x + 5

6x + 1

(8x + 5) – (6x + 1) = 2x + 4

►Find the difference.Find the difference.►(6x + 1) – (3x)(6x + 1) – (3x)

ALGEBRAIC SUBTRACTIONALGEBRAIC SUBTRACTION

x x x x1

- x x x

6x + 1

3x

(6x + 1) – (3x) = 3x +1

xx

ANSWER

►Find the difference.Find the difference.►(5x + 6) – (5x)(5x + 6) – (5x)

ALGEBRAIC SUBTRACTIONALGEBRAIC SUBTRACTION

x x x x1

- x x x

5x + 6

5x

(5x + 6) – (5x) = 6

x

ANSWER

1 1 1 1 1

x x

►Use algebra tiles to find the difference.Use algebra tiles to find the difference.►(3x(3x22 + 4x + 5) – (x + 4x + 5) – (x22 + 3x + 4) + 3x + 4)

ALGEBRAIC SUBTRACTIONALGEBRAIC SUBTRACTION

ANSWER

x x x x 111 1 1

- x x x1

3x3x22 + 4x + 5 + 4x + 5

xx22 + 3x + 4 + 3x + 4

(3x(3x22 + 4x + 5) – (x + 4x + 5) – (x22 + 3x + 4) + 3x + 4) = 2x2 + x + 1

x2 x2 x2

x2

1 1 1

Let’s Practice!