Teaching Algebra with Manipulatives

Using Overhead Manipulatives
Demonstration 2
Multiplying a Binomial by a Monomial
• Clear the mat. Tell students you want to find 2x(x 3).
• Ask students how to model the length 2x. 2x tiles
• Use an x tile to mark off a width of 2x units.
• Use an x tile and a 1 tile to mark off a length of x 3 as
shown at the right.
x
x
x
1 1 1
• Using the marks as guides, draw a large rectangle and
cover it with 2 yellow x 2 tiles and 6 red x tiles. Point out that
yellow tiles represent the areas with positive dimensions and
red tiles represent areas with 1 negative and 1 positive
dimension. Ask students to explain this use of the tiles. The
product of two positive numbers is positive; the product of
a positive and a negative number is negative.
Ask what color tile would be used if both dimensions were
negative and why. Yellow; the product of two negative
numbers is positive.
• Ask students what the dimensions of the rectangle are. 2x by (x 3)
Have them state the area of the rectangle as an algebraic expression.
2x(x 3)
• Ask students to add the values represented by the tiles to find the area
of the rectangle modeled. 2x 2 6x
• Write 2x(x 3) 2x 2 6x below the model.
x
x
x
x 2
x 2
1 1 1
x x x
x x x
Extension
Given the Area, Model and Find the Length and Width
Have students make possible rectangles for each area. Then have them
find the length and width.
a. 2x 2 4 x 2, 2x b. 3x 6 x 2, 3
Algebra 1—Chapter 8
© Glencoe/McGraw-Hill 143 Teaching Algebra with Manipulatives