ALGEBRA TILESExpressions and Equations

OBJECTIVES

Provide a visual model to help students develop conceptual understanding for variables as unknown values.

Build conceptual understanding of solving equations.

Construct meaning for algebraic solutions of equations.

The value of each piece is determined by its area.

A new piece is created by developing

a new dimension, “x”.

for practical reasons, “x” is not a multiple of the dimension

representing “1”.

The value of this piece is

x, because 1 x = x.

ALGEBRAIC EXPRESSIONS

1

x

Use tiles to express the following:

x + 2

3x

2x -1

-4x

EXAMPLES

COMBINING EXPRESSIONS

3x – 2x

x + 4 + x – 3

2x + 3 – x + 1

= x

= 2x + 1

= x + 4

DISTRIBUTION

3(x + 2) - 4

(5x - 6) -(3x - 2)

Tiles make the concepts simple.

3x + 2

2x - 4

MODEL THE EXPRESSION

-2(3x -1) Begin inside the parenthesis.

-6x + 2

3x - 1 There are two sets,

and their signs are opposite of the

originals.

SOLVING EQUATIONSMODEL 2x + 1 = 5

To solve, SUBTRACT 1 tile from each side. NEW EQUATION 2x = 4

Isolate x by DIVIDING into two groups

=

x = 2

2x = 4

x = 2

SOLVING EQUATIONS

2x + 3 = 7

2x = 4 2 2

Subtract 3 from each side of the equationDivide by 2 on each side of the

equation

The operations and the result are exactly the same.

x = 2=-3 -3

SOLVE

x – 4 = 5

x = 9

=

SOLVE2(x - 3) = 10

2x = 16

x = 8

=

2x - 6 = 10

Demonstrate the behavior of numbers so students can form INNATE conceptual understandings.

Reaffirm arithmetic and algebraic concepts using a visual model

Reassure and encourage struggling students, allowing them to develop number sense and confidence with signed numbers

ALGEBRA TILES