Algebra Tiles AlgeTile Uses Algebra tiles can be

Algebra Tiles

Alge-Tile Uses Algebra tiles can be used for (among other things): ØIdentifying ‘like’ and ‘unlike’ terms ØAdding and Subtracting Integers ØSimplifying Expressions ØMultiplying in algebra ØFactorising trinomials ØDoing linear equations

Alge-Tiles Remember that RED = minus (-) & Any other colour = plus (+)

Variables 1 x 2 x -1 -x 2 -x

Unit length 1 x x 2 (x)(x)= x 2 x x (x)(1)= x 1 1 (1)(1)= 1

Addition of Integers Ex. 1, -3, 15, -10 • Addition = “combining”. • Must form and remove all zero pairs. (+3) + (-1) = (+4) + (-4) =

Zero Pairs • Zero pairs = added oposites of each other. • When put together, they cancel each other out to equal zero. • Like (-1) + (+1) = 0

Subtracting Integers • • Subtraction =“take-away. ” Or think of it as “adding the opposite. ” (+3) – (-5) (-4) – (+1)

Monomials • Has one term: – A number (integer) – Or variable x 2 or 1 1 1 or x 2 or -x -x

Polynomials • a sum of different terms. x 2 x 2 + -x -x + 1 1 1

Modeling Polynomials ¢Algebra tiles can be used to model expressions. ¢Aid in the simplification of expressions. ¢Add, subtract, multiply, divide, or factor polynomials.

Modeling Polynomials • Let the blue square represent x 2, the green rectangle xy, and the yellow square y 2. The red square (flip-side of blue) represents –x 2, the red rectangle (flip-side of green) –xy, and the small red square (flip-side of yellow) –y 2. • As with integers, the red shapes and their corresponding flip-sides form a zero pair.

Modeling Polynomials ¢Represent each of the following with algebra tiles, draw a pictorial diagram of the process, then write the symbolic expression. 2 x 2 4 xy 3 y 2

Modeling Polynomials 2 x 2 4 xy 3 y 2

Modeling Polynomials 3 x 2 + 5 y 2 -2 xy -3 x 2 – 4 xy • Textbooks do not always use x and y. Use other variables in the same format. Model these expressions. -a 2 + 2 ab 5 p 2 – 3 pq + q 2

More Polynomials • Would not present previous material and this information on the same day. • Let the blue square represent x 2 and the large red square (flip-side) be –x 2. • Let the green rectangle represent x and the red rectangle (flip-side) represent –x. • Let yellow square represent 1 and the small red square (flip-side) represent – 1.

More Polynomials ¢Represent each of the given expressions with algebra tiles. ¢Draw a pictorial diagram of the process. ¢Write the symbolic expression. x+4

Example Represent the following trinomials using alge-tiles: 1. 2 x 2+3 x+5 2. x 2 -2 x-3