Teaching Algebra with Manipulatives

Chapter
7
Solving Systems of Linear
Equations and Inequalities
Teaching Notes and Overview
Mini-Project
Comparing Options
(p. 124 of this booklet)
Use With Lesson 7-1.
Objective Use given information to compare
options.
This Mini-Project requires students to work in
groups of two. They read information about how
their performance on five 100-point tests and
the number of times they do their homework
in a quarter will affect their grade. The
information provides two options in equation
form. In the exercises, the groups are asked to
graph the equations and choose which option
will give the higher grade for the quarter.
Answers
1. See students’ graphs; second option
2. See students’ graphs; 1 st option,
1
y 1 00 x 4 5 ,2nd 1
option, y 1 50 x 5 6 ;
second option
Algebra Activity
Recording Sheet
Using Substitution
(p. 125 of this booklet)
Use With the activity on page 376 in Lesson
7-2 of the Student Edition.
Objective Using substitution to solve systems
of equations.
Be sure students are comfortable using the
equation mats and the algebra tiles. You may
want to review and model a similar system of
equations on the mat.
Form groups of two or three to do this activity.
Allow sufficient time for students to complete
the exercises under the Model and Analyze
section. Then go over their responses. Tell
each group that you would like to check their
equation mat for Exercise 5. Then they may
begin to write their explanation for solving the
system using algebra tiles.
Answers
See Teacher Wraparound Edition p. 376.
Using Overhead
Manipulatives
Elimination Using Addition and
Subtraction
(p. 126 of this booklet)
Use With Lesson 7-3.
Objective Solve systems of equations by
the elimination method using addition and
subtraction. The demonstration contains one
activity and an extension.
• This demonstration shows students how
to use the method of elimination to solve
systems of equations. Model 2x y 4 on
the equation mat. Review what the tiles
represent. Then model x y 10 on the
same mat. Tell that the goal is to get the
1 positive x-tile or the 1 positive y-tile by
themselves on one side. Review the process
of making zero pairs and arranging tiles on
the right side into 3 equal groups so they
correspond to the 3 x-tiles. Explain the
solution and how to check it.
• The Extension deals with solving a system
of equations containing three variables with
algebra tiles on the equation mat. Students
should be confident about solving a system
of equations containing two variables before
attempting to work the more complex system.
Ask students to check their solution.
Materials
algebra tiles*
equation mat transparency*
* available in Overhead Manipulative Resources
Answers
Answers appear on the teacher demonstration
instructions on page 126.
© Glencoe/McGraw-Hill 122 Teaching Algebra with Manipulatives