Teaching Algebra with Manipulatives

Using Overhead Manipulatives
Demonstration 2
Solving Special Equations with the Variables on Both Sides
• Tell students that not all equations have a simple
solution. Model the equation 3x 12 3x 5 on the
mat. Remove 3 cups from each side. Ask students
whether the remaining counters represent a true
statement. no Inform them that this equation does
not have a solution. That is, no value substituted for
the cups in the original equation will produce a true
statement.
• Clear the mat. Write the equation 2(x 3) 1 2x 5
below the mat. Place a cup and 3 positive counters on
the left side. Ask students what the expression 2(x 3)
means and how you can model it. 2 times the quantity
x plus 3; make 2 groups of a cup and 3 counters each.
Add another cup and 3 counters to the left
side. Place a negative counter also on the left side to
show 1. Ask students if the model shows 2(x 3) 1.
yes Model 2x 5 on the right side.
2(x 3) 1 2x 5
• Remove the zero pair from the left side. Regroup the
models so that both sides appear the same. Replace
each cup with 2 negative counters to show that 2
is a solution. Then replace each cup with 3 positive
counters to show that 3 is a solution. Ask students if
any number of counters will result in a true statement.
yes Tell students that the solution of this equation is
all values of x.
© Glencoe/McGraw-Hill 74 Teaching Algebra with Manipulatives