Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 7-3)
Elimination Using Addition and Subtraction
Objective Solve systems of equations by the elimination method using
addition and subtraction.
Materials
• algebra tiles*
• equation mat transparency*
* available in Overhead Manipulative Resources
Demonstration
Elimination Using Addition and Subtraction
• Place 2 positive x-tiles and 1 negative
y-tile on the left side of the equation mat
transparency and 4 positive 1-tiles on the
right side. Ask students what equation is
represented on the mat. 2x y 4
• Below the representation for 2x y 4
on the mat, place 1 positive x-tile and
1 positive y-tile on the left side of the
equation mat and 10 negative 1-tiles on
the right side. Have students state what
equation is represented below 2x y 4.
x y 10
x
x
x
y
y
1 1 1 1
1 1 1 1
1
1 1 1 1 1
• Remind students that, in solving
equations, the goal is to get the 1 positive
x-tile or 1 positive y-tile by themselves
on one side.
• Review the use of zero pairs in adding
and subtracting integers. Tell students
that a zero pair of y-tiles are formed
when a positive y-tile is paired with a
negative y-tile. On the right side of the
mat there are 5 zero pairs. Remove all
zero pairs.
x
x
x
y
y
1 1 1
1 1 1
1
1
1
1
1
1
1
1
• Arrange the remaining tiles on the
right side into 3 equal groups so they
correspond to the 3 x-tiles. Ask students
how many tiles correspond to each x-tile.
2 negative 1-tiles
• Have students substitute 2 for x in
2x y 4 and in x y 10 and solve
for y. Ask students, “What is the solution
to the system of equations 2x y 4
and x y 10?’’ 2, 8
x
x
x
1
1
1
1
1
1
© Glencoe/McGraw-Hill 126 Teaching Algebra with Manipulatives