Teaching Algebra with Manipulatives

Chapter 8 Teaching Notes and Overview
As a preview to Lesson 8-7, have students
form groups of two or three to complete this
recording sheet using algebra tiles. There are
three activities used as examples. Discuss each
activity, and then have the students use the
algebra tiles to model it along with you. The
three activities are to use tiles to find:
(x 2)(x 5); (x 1)(x 4); and (x 3)(2x 1).
In their groups, have students complete
Exercises 1–3. Then go over their answers. Let
them do Exercises 4–11 on their own. As soon
as the groups are finished, discuss the answers.
Answers
See Teacher Wraparound Edition pp. 450–451.
Using Overhead
Manipulatives
Multiplying Polynomials
(pp. 145–146 of this booklet)
Use With Lesson 8-7.
Objective Model and find the product of two
binomials.
Materials
algebra tiles*
product mat transparency*
transparency pen*
blank transparency
* available in Overhead Manipulative Resources
This demonstration contains two activities and
an extension.
• Demonstration 1 involves finding the product
of two binomials, namely, (x 1)(x 4) using
algebra tiles.
• Demonstration 2 involves finding the product
of two binomials, namely, (x 2)(2x 3)
using algebra tiles.
• The Extension deals with comparing the use
of algebra tiles to find a product with the
FOIL method.
Answers
Answers appear on the teacher demonstration
instructions on pages 145–146.
Algebra Activity
Multiplying Polynomials
(pp. 147–148 of this booklet)
Use With Lesson 8-7.
Objective Multiply polynomials by using the
Distributive Property.
Materials
classroom set of Algebra Activity worksheets
transparency master of Algebra Activity
Before class, cut the figures on the transparency
that are below the dashed line and color them if
you wish. You may want to make similar sets of
squares and rectangles for students from heavy
paper.
Discuss how to find the area of figures A–D on
the transparency. Students need to know that
the area of a rectangle is the product of its
length and width.
A Area (6)(6)
B Area (6)(4) (6)(2)
C Area (6)(6) (6)(2)
D Area (3)(4) (3)(2) (3)(4) (3)(2)
Be sure students understand that this is an
application of the Distributive Property.
Have students complete Exercises 1–3 on the
worksheet.
Assign area values to the models: x-by-x x 2 ,
1-by-x x and 1-by-1 1. Place the models
over matching spaces of figures E–H on the
transparency. Discuss finding the products by
adding the areas.
E Area x(x 1) x 2 x
F Area x(x 3) x 2 3x
G Area x(x 2) x 2 2x
H Area (x 1)(x 4) x 2 5x 4
In groups, have students use diagrams or
models to complete the worksheet.
As an extension, challenge students to factor
polynomials by creating a rectangle and
working backwards.
© Glencoe/McGraw-Hill 132 Teaching Algebra with Manipulatives