Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 8-6)
Multiplying a Polynomial by a Monomial
Objective Model the product of a binomial and a monomial.
Materials
• product mat transparency*
• algebra tiles*
• transparency pen*
• two blank transparencies
* available in Overhead Manipulative Resources
Demonstration 1
Multiplying a Binomial by a Monomial
• Point out that algebra tiles used in previous activities are based on the
fact that the area of a rectangle is the product of its width and length.
Tell students they will use algebra tiles to build larger rectangles. The
length and width of the large rectangle will each represent a polynomial
and the area of the large rectangle will each represent their product.
• Tell students you want to find x(x 1).
• Ask students how to model the length x. Use the length of
an x tile.
• Display the product mat transparency. Use an x tile to mark
off a width of x units.
x
• Ask students how to model x 1. an x tile and a x tile
Use an x tile and a 1 tile to mark off a length of x 1 units.
x 1
x
• Using the marks as guides, draw a large rectangle and cover
it with algebra tiles.
x
1
x
x 2
x
• Ask students what the dimensions of the rectangle are.
x-by-x 1 Ask them to state the area of the rectangle as
an algebraic expression. x(x 1)
• Ask students to add the values represented by the tiles to
find the area of the rectangle modeled. x 2 x
• Write x(x 1) x 2 x below the model.
© Glencoe/McGraw-Hill 142 Teaching Algebra with Manipulatives