LINEAR EQUATIONS






Ennis, Beatrix U.                  Senn Academy High School
645 Westmoreland Drive             1-312-989-3565
Vernon Hills, IL 60061
1-708-816-0921

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.