Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 9-2)
Factoring Using the Distributive Property
Objective Factor polynomials using algebra tiles.
Materials
• polynomial models transparency*
• algebra tiles*
• transparency pen*
• blank transparencies
• red and yellow acetate, if available
* available in Overhead Manipulative Resources
Algebra 1—Chapter 9
Demonstration 1
Factoring 2x 6 and 2x 2 3x
• Remind students that when you multiplied polynomials,
you first constructed a rectangle using the factors as the
width and length. You then covered the rectangle with
algebra tiles to determine the product. Tell students they
can reverse the process to find the factors of a polynomial.
• Display the polynomial models transparency and review the
values of the algebra tiles.
• Write 2x 6 on a blank transparency. Ask students how to
model this binomial using the tiles. 2 x tiles and 6 1 tiles
Model 2x 6 on top of the transparency.
• Tell students that if you can form a rectangle with these tiles,
then you can find its width and length, and you will know the
factors of the binomial. Ask students to form a rectangle using
these tiles.
• Ask them to state the width and length of the rectangle.
2, x 3 Write the width and length next to the appropriate
sides of the rectangle. Have them state the factors of 2x 6.
2, x 3 Write the factors on the transparency.
• Ask students how to factor 2x 2 3x. Build a rectangle with an
area of 2x 2 3x. Place the tiles on the screen.
• Have students suggest ways to arrange the tiles into a
rectangle. Try each suggestion until they arrive at the
rectangle shown at the right.
• Ask students to state the width and length of the rectangle.
x, 2x 3 Have them state the factors of 2x 2 3x. x, 2x 3
Write 2x 2 3x x(2x 3) on the transparency.
x x
1 1 1 1 1 1
x 1 1 1
x 1 1 1
x 3
x 1 1 1
2
x 1 1 1
2x 6 2(x 3)
2x 3
x x 2 x 2
x x x
(continued on the next page)
© Glencoe/McGraw-Hill 157 Teaching Algebra with Manipulatives