**LINEAR EQUATIONS**

Ennis, Beatrix U. Senn Academy High School

1-312-989-3565

**OBJECTIVES**
1. Students will emulate the steps in solving linear equations by means of a
manipulative.
2. Students will be able to transfer the operations performed on the manipulatives
in equation form.
**EQUIPMENT AND MATERIALS NEEDED**
Overhead Projector/Marker
Twenty-five Black Squares (Overhead Set)
Twenty-five Clear Squares (Overhead Set)
Ten Black Circles (Overhead Set)
Ten Clear Circles (Overhead Set)
Thirty cubes and ten dixie cups of same color (Classroom Set)
Thirty cubes and ten dixie cups of a different color (Classroom Set)
Classroom set of "Work Area Sheets"
One balance scale
**RECOMMENDED STRATEGY**
Using the overhead, present a short set of notes with a definition and interpretation
of an equation. Ask the students to distinguish between given examples of an
expression and an equation. Using the overhead black and clear squares (which
represent unit integers) and black and clear circles (which represent unit variables)
create an equation. Present the two rules: 1) In order to remove a clear square
(negative integer) you must add a black square (positive integer). Stress that the
colors are opposite. 2) The same number of color squares must be added to **both **
**sides**. Stress balance. For example the equation x + 6 = -2 with manipulatives would

be solved in the following manner. A black circle and six black squares would

represent x + 6 and two clear square would represent -2. Step 1) Add six clear

squares to the left side (stress opposite). 2) Add six clear squares to the right

side (stress balance). 3) Write an equation of steps one and two. (x + 6 - 6 = -2 -

6) 4) Eliminate the squares on left side. 5) Combine the squares on the right side.

6) Write an equation of the results of steps four and five. 7) Results: One black

circle equals ten clear squares, or x = -10. Present several examples on the overhead.

Ask the students what would happen if they did not add the opposite to **both** sides.

Use the balance scale to demonstrate the results. Then give the students their own

set of manipulatives and have them solve equations.

Return to Mathematics Index