Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 3-5)
Solving Equations with the Variables on Both Sides
Objective Model and solve equations with a variable on each side.
Materials
• overhead counters*
• equation mat transparency*
• transparency pen*
• two-dimensional cups*
• blank transparency * available in Overhead Manipulative Resources
Demonstration 1
Solving Equations with the Variables on Both Sides
• Place the blank transparency under the mat
transparency so you can write equations below the mat.
• Mark several cups with a negative sign. Write the
equation 2x 2 x 8 below the mat. Ask students
how to model each side of the equation. Place 2 cups and
2 positive counters on the left. Place a “negative” cup
and 8 positive counters on the right. Place the
cups and counters on the mat.
• Remind students that you can solve equations by pairing and removing
items from each side. Explain that for this equation you will remove
both cups and counters.
• Add a zero pair of cups to the left side of the equation. Pair and remove
a negative cup from each side.
2x 2 x 8
Algebra 1—Chapter 3
• Pair and remove 2 positive counters from each side. Ask students to
state the resulting equation. 3x 6
• Arrange the counters on the right side into 3 equal groups corresponding
to the 3 cups. Ask students what the value of x is for this equation. 2
• Check the solution by replacing the cups in the original equation with 2
positive counters. Remind students that x is the opposite of x, so you
will replace x with the opposite of 2 positive counters, or 2 negative
counters.
© Glencoe/McGraw-Hill 73 Teaching Algebra with Manipulatives