Teaching Algebra with Manipulatives

Using Overhead Manipulatives
Demonstration 3
Finding the Product of a Sum and a Difference
• Place 1 yellow x 2 tile, 1 yellow x tile, 1 red x tile, and 1 red 1 tile on a
blank transparency to form a square.
• Ask students, “This is a model of the product of what two binomials?”
(x 1) and (x 1)
Ask why the 1 tile is red. The product of 1 and 1 is 1.
• Review the use of zero pairs in adding and subtracting integers. Tell
students that zero pairs of tiles are formed when a positive tile is paired
with a negative tile of the same size and shape. Remove all zero pairs.
• Ask students what kind of tiles remain and how many there are of each.
1 positive x 2 tile and 1 negative 1 tile.
• Ask them to write the simplest form of the product of x 1 and x 1.
x 2 1.
• Have students repeat the procedure to model the products of
(x 2)(x 2), (x 3)(x 3), and (x 4)(x 4). x 2 4; x 2 9; x 2 16
• Tell students to use the patterns found in the above products to derive a
general form for the product of (a b)(a b). (a b)(a b) a 2 b 2
Extension
Modeling and Finding More Products
• Have students make possible rectangles to model and find each product.
a. (2x 2) 2 b. (2x 2) 2 c. (2x 3)(2x 3)
4x 2 8x 4 4x 2 8x 4 4x 2 9
Algebra 1—Chapter 8
© Glencoe/McGraw-Hill 151 Teaching Algebra with Manipulatives