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, X2 y2 X xy y2

Using overhead set of tiles What are the polynomials? Copy and solve….

2x2 + 3xy + y2

2x2 + 3xy + y2 X2 X2 xy xy xy y2

The Additive Inverses (negative) These are the negatives of the terms. i.e., -xy - x2 -xy -xy -y2 -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 x2 + x + 1 x 1

2x2 - 2x + 3 X2 X2 1 1 1 x x

2x2 + 2x + 3 (x2 + x + 2) X2 X2 1 1 1 x x

2x2 + 2x + 3 (x2 + x + 2) X2 X2 1 1 1 x x

(x + 1) (x + 2) X 1 X 2

(x + 1) (x + 2) X 1 X 2 X2 x x 1 x 1

Try (x – 3) (x + 1)