Teaching Algebra with Manipulatives

Chapter
6
Solving Linear Inequalities
Teaching Notes and Overview
Using Overhead
Manipulatives
Solving Inequalities Using Addition
and Subtraction
(pp. 111–113 of this booklet)
Use With Lesson 6-1.
Objective Model and solve inequalities using
addition and subtraction.
Materials
inequality mat transparency*
overhead counters*
equation mat transparency*
number line transparency*
transparency pen*
two blank transparencies prepared
as described for the activity
* available in Overhead Manipulative Resources
There are two demonstrations and one
extension.
• Demonstration 1 involves using the Addition
and Subtraction Properties for Inequality
found in the Student Edition. It is important
that students know how to use these
properties. Displaying the properties using
transparencies, as well as referencing them in
the text, are beneficial to the visual learners
in the class. After using the inequality mat to
develop the solution to 4 x 2, write the
solution set on the transparency. Make sure
students understand how to read the solution
set and what it means.
Ask students several questions about the set
to check their understanding. For example,
“Is 6, a member of the set? Explain.” No,
the member must be greater than 6. Some
students may find it helpful to see another
similar type of inequality developed and
solved with the mat transparency. Use the
same process for finding the solution set of
2x 3 3x 7.
• Demonstration 2 deals with translating a
sentence containing an inequality phrase
into mathematical symbols. Then the mat
transparency is used to solve it. Once again,
using a transparency to display the inequality
chart, as well as pointing them out in the
text, are needed to assist the visual learners.
• The Extension involves graphing the three
solution sets developed in the two
demonstrations.
Answers
Answers appear on the teacher demonstration
instructions on pages 111–113.
Mini-Project
Multiplying Inequalities by 1
(p. 114 of this booklet)
Use With Lesson 6-1.
Objective Multiplying inequalities by 1.
This project requires students to work with a
partner. They are asked to read and understand
the three examples, and then do exercises that
check on their understanding. It is essential
that students know that when an inequality is
multiplied by 1, the sense of the inequality
must change.
Answers
1. x 2 2. x 5
3. x 6 4. x 7
5. x 4 6. x 8
7. x 10 8. x 0
9. ;
10. The direction of the inequality symbol must
be reversed.
Algebra Activity
Recording Sheet
Solving Inequalities
(p. 115 of this booklet)
Use With Lesson 6-2 as a preview activity.
This corresponds to the activity on page 324 in
the Student Edition.
Objective Solving inequalities.
© Glencoe/McGraw-Hill 108 Teaching Algebra with Manipulatives