ALGEBRA TILES

Variables such as ‘x’ and ‘y’ are used to represent an unknown number Algebra tiles are the generally accepted manipulative to help students understand the concepts of variables and “POLYNOMIALS”

POLYNOMIALS: a series of terms with a number of different variables in it.

i.e., x2 + 2x + 3 or 3x – 2xy + 4y

ALGEBRA TILES

Let the blue square represent X2

x

y

x and the yellow square = y2 y

Therefore,

y

X2y2

xy y2

X

Using overhead set of tiles

What are the polynomials?

Copy and solve….

2x2 + 3xy + y2

2x2 + 3xy + y2

X2X2

xyxyxy

y2

The Additive Inverses (negative)

These are the negatives of the terms. i.e.,

- x2

-xy

-y2

-xy

-xy

-y2

-2x2 + x2 + xy -2xy

- x2

X2

- x2

xy

-xy

-xy

-2x2 + x2 + xy -2xy

- x2

X2

- x2

xy

-xy

-xy

-1x2 -1xy (or -x2 –xy)

- x2 -xy

Change of representation

x2 + x + 1

X2 x 1

2x2 - 2x + 3

X2 X2x x 111

2x2 + 2x + 3

- (x2 + x + 2)

X2 X2x x 111

2x2 + 2x + 3

- (x2 + x + 2)

X2 X2x x 111

(x + 1) (x + 2)

X 1

X

2

(x + 1) (x + 2)

X 1

X

2

X2

x

x

x

1

1

Try

• (x – 3) (x + 1)