Teaching Algebra with Manipulatives

Using Overhead Manipulatives
• Ask them to state the width of the rectangle. a b Have students state
the length of the rectangle. a b
• Ask students to state an expression for the area of the rectangle.
(a b)(a b) Point out that the area of the L-shaped figure is a 2 b 2 ,
so the expressions have the same value. Write a 2 b 2 (a b)(a b)
below the rectangle.
• Have students describe the factors of the difference of two squares.
One factor is the sum of the square roots of the terms; the other
is the difference of the square roots of the terms.
Extension
Factoring the Difference of Squares Using Algebra Tiles
• Tell students that you can use algebra tiles to factor the
differences of squares. Place a positive x 2 tile and a negative
y 2 tile on top of a blank tranparency as shown. Point out that
these tiles represent the difference of squares, x 2 y 2 .
x 2 y 2
• Ask students what would be needed to form a square from the
tiles. 2 xy tiles Remind students that you can add a zero pair
of tiles without affecting the value of what is shown. Place a
zero pair of xy tiles on the screen to complete the square.
• Label the sides of the square as shown. Ask students to
state the factors of x 2 y 2 . x y, x y Write x 2 y 2
(x y)(x y) below the square. Ask students if this
matches the description they gave at the end of the previous
demonstration. yes
x y
x 2
x y
xy
xy y 2
© Glencoe/McGraw-Hill 166 Teaching Algebra with Manipulatives