Teaching Algebra with Manipulatives

Chapter 8 Teaching Notes and Overview
Mini-Project
Multiplying Binomials
(p. 141 of this booklet)
Use With Lesson 8-5.
Materials
product mat transparency*
algebra tiles*
transparency pen*
two blank transparencies
* available in Overhead Manipulative Resources
Objective Model and find the product of two
binomials.
Materials
algebra tiles*
* available in Overhead Manipulative Resources
This Mini-Project has students draw a rectangle
where the width is one binomial and the length
is the other binomial. Write the area of each
rectangle inside it. Then add the areas of the
individual rectangles, combining those that are
like terms. In groups, ask students to read,
study and discuss the illustrated example.
After the groups have had time to do the latter,
call on them to explain each step. Ask them
questions to check for understanding. Point out
that the binomials x 1 and 3x 2 are the
length and width of the rectangle. Then add the
areas of the individual rectangles and combine
those that are like terms. Be sure students
know that a tile (1)-by-(1) or (1)(1)
represents 1. Have students use this same
procedure to complete the exercises
Answers
1. x 2 x 6 2. 2x 2 x 1
3. 4x 2 4x 3 4. x 2 9
5. x 2 8x 16 6. x 2 4x 4
Using Overhead
Manipulatives
Multiplying a Polynomial
by a Monomial
(pp. 142–143 of this booklet)
Use With Lesson 8-6.
Objective Model the product of a binomial and
a monomial.
This demonstration has two activities and an
extension.
• Demonstration 1 deals with multiplying a
polynomial by a monomial, that is, x(x 1).
Algebra tiles are used in conjunction with
the area of a rectangle to model the process.
Students should recognize the product as the
Distributive Property, namely, x(x 1)
(x)(x) (x)(1).
• Demonstration 2 deals again with multiplying
a polynomial by a monomial, that is, 2x(x 3).
Algebra tiles are used in conjunction with
the area of a rectangle to model the process.
Review the sign of the product of two integers:
()() (), ()() (),
()() (), ()() ().
This is another illustration of the Distributive
Property.
• The Extension challenges students to use
algebra tiles to show a given area, and then
find the length and width.
Answers
Answers appear on the teacher demonstration
instructions on pages 142–143.
Algebra Activity
Recording Sheet
Multiplying Polynomials
(p. 144 of this booklet)
Use With Lesson 8-7 as a preview activity.
This corresponds to the activity on pages
450–451 in the Student Edition.
Objective Model and find the product of two
binomials.
Materials
algebra tiles*
product mat transparency*
* available in Overhead Manipulative Resources
Algebra 1—Chapter 8
© Glencoe/McGraw-Hill 131 Teaching Algebra with Manipulatives