Teaching Algebra with Manipulatives

Chapter 3 Teaching Notes and Overview
There is one demonstration that deals with
modeling percent of change and an extension
that involves modeling and solving percent of
change problems. Dot paper is used for the
demonstration and the extension. The extension
focuses on a common problem that is sometimes
misunderstood. Students are asked to decide
whether a discount of 20% on a discount of 20%
of the original price is the same as a discount of
40% on the original price. The modeling with
the dot paper assists the students in making
their decision.
Answers
Answers appear on the teacher demonstration
instructions on pages 77–78.
Mini-Project
The Music Business
(p. 79 of this booklet)
Objectives Solve mixture problems using
diagrams and charts to organize information.
Materials
classroom set of Algebra Activity worksheets
transparency master of Algebra Activity
Cut the transparency on the dashed lines and
color Figures 1, 2, and 3 if you wish. Display the
transparency on the overhead transparency and
examine the mixture problem.
Let Figure 1 represent 9 pounds of $6.40/lb
coffee and Figure 2 represent n pounds of
$7.28/lb coffee. Place Figures 1 and 2 on the
diagram as shown in the chart below.
Then place Figure 3 on the diagram to show
that the mixture contains (9 n) pounds of
coffee selling for $6.95/lb.
Use With Lesson 3-7.
Objective Use percent to determine total cost.
Ask students to read and study the information
and the example. Let groups of two students
work on this activity. Talk about the many
expenses involved in producing tapes and
CDs and getting them to the consumer. Ask
questions about the example to check for
student understanding. Some students may be
interested in researching this topic more in
depth. Have them report their findings to the
class.
Answers
1. $11.12
2. $7.19
3. $538.65; $2289.26; $763.09
Algebra Activity
Mixture Problems
(pp. 80–81 of this booklet)
9 lb
$6.40/lb
Complete the chart. Discuss how to select
necessary information and set up a mixture
problem. Practice some similar problems using
the transparency.
In groups, have students complete the
worksheet.
Answers
n lb
$7.28/lb
1. See students’ chart; (3.10)(15)
(1.95)x (2.70)(15 x); 8 lb of peanuts.
2. See students’ chart; (0.10)x
(0.05)(4x) 7.20; 96 nickels, 54 dimes.
3. See students’ chart; 4x (2)(260 x)
700; 90 @ $4, 170 @ $2.
4. See students’ chart; (2.50)x (1.50)2x
396; 72 adult tickets, 144 student tickets.
9
n
$6.59/lb
Algebra 1—Chapter 3
Use With Lesson 3-8.
© Glencoe/McGraw-Hill 55 Teaching Algebra with Manipulatives