Teaching Algebra with Manipulatives

Demonstration 2
Factoring 4x 2 4x 1
• Have students model 4x 2 4x 1.
Using Overhead Manipulatives
x 2 x 2 x 2 x 2
x x x x
1
Algebra 1—Chapter 9
• Ask students to form a square using
these tiles.
2x 1
• Ask them what the length and width
are. 2x 1, 2x 1
x 2 x 2
x
• Have them state the factors of
4x 2 4x 1. 2x 1, 2x 1 Have
them check the product of the factors
by using the FOIL method.
2x 1
x 2 x 2
x x
x
1
Extension
Analyzing Perfect Square Trinomials
• Ask students what was true about the x 2 -tiles and the 1-tiles in each
demonstration. They formed squares.
• Ask what this means about the first and last term of these trinomials.
They are perfect squares.
• Ask if those terms can ever be negative in a perfect square trinomial,
and why. No, any number squared is always positive. Point out that the
middle term could be either positive or negative.
• Ask whether 2x 2 2x 4 is a perfect square trinomial and why. No, the
first term is not a perfect square.
© Glencoe/McGraw-Hill 169 Teaching Algebra with Manipulatives