Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 8-8)
Three Special Products
Objective Model the square of a sum, the square of a difference, and the
product of a sum and a difference
Materials
• product mat transparency*
• algebra tiles*
• transparency pen*
• blank transparencies
* available in Overhead Manipulative Resources
Demonstration 1
Finding the Square of a Sum
x
1
• Tell students you want to find (x 1) 2 . Remind them that
(x 1) 2 means (x 1)(x 1) so you want to model a square that
measures x 1 on each side.
• On the product mat transparency, use an x-tile to mark off a
square x 1 units on each side.
x
1
• Using the marks as guides, complete the square by filling it in
with tiles.
• Ask students what the area of the large square is. x 2 2x 1
x 1
• Ask students what (x 1) 2 is. x 2 2x 1
x 1
x 2
x
• Have students model (x 2) 2 .
• Ask students what the area of the large square is. x 2 4x 4
x
1
• Have students model (x 3) 2 .
• Ask students what the area of the large square is. x 2 6x 9
• Have students model (x 4) 2 .
• Ask students what the area of the large square is. x 2 8x 16
• On a blank transparency, list four equations that represent the
the areas of the four large squares:
(x 1) 2 x 2 2x 1
(x 2) 2 x 2 4x 4
(x 3) 2 x 2 6x 9
(x 4) 2 x 2 8x 16
• Ask students if there is a relationship between the terms of the binomial
and the terms of its equivalent trinomial. Yes, the first and last terms of
the trinomial are squares of the respective terms of the binomial, and
the middle term of the trinomial is twice the product of the first and
second terms of the binomial.
• Have students find (x 8) 2 without modeling. x 2 16x 64 Then ask
them to check their result using the FOIL method.
Algebra 1—Chapter 8
© Glencoe/McGraw-Hill 149 Teaching Algebra with Manipulatives