Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 3-3)
Solving Equations by Using Multiplication and Division
Objective Use models to solve equations involving multiplication and division
Materials
• equation models transparency*
• equation mat transparency*
• overhead counters*
• two-dimensional cups*
• transparency pen*
• blank transparency * available in Overhead Manipulative Resources
Demonstration 1
Solving Equations by Using Division
• Remind students that a cup represents an unknown
value. Ask them how you can represent 3x. 3 cups Place
3 cups on the left side of the mat and 15 negative
counters on the right side. Ask students to state the
equation you have modeled. 3x 15 Write the equation
at the base of the mat.
• Say, “To solve this equation, we need to find how many
counters are in one cup. To do this, we will match each
cup with an equal number of counters.” Arrange the
counters in three equal groups to correspond to the 3
cups. Ask students what the value of x is in the equation.
5 Then ask them what “operation” you performed on
each side of the mat. divided each side by 3
• Clear the mat. Mark two cups with negative signs. Use the
cups and 4 negative counters to model the equation 2x 4.
Ask students what equation is modeled. Write the equation
at the base of the mat.
• Arrange the counters into 2 equal groups to correspond to the 2 cups.
Ask students what equation is represented by each group. x 2
Point out that x means the opposite of x. Remind students that the
Multiplication Property of Equality states that you can multiply each
side of an equation by the same number without changing the result.
Replace each negative cup with a positive cup. Ask students to verify
that you have just multiplied the left side by 1. Ask them to tell you
what to do to the right side to show multiplying by 1. Replace the
negative counters with positive counters. Ask them to state the
solution of the equation. 2 Point out that you solved this equation by
dividing each side by the opposite of 2, or 2.
© Glencoe/McGraw-Hill 66 Teaching Algebra with Manipulatives