Teaching Algebra with Manipulatives

Using Overhead Manipulatives
Demonstration 1
Solving Equations by Using Subtraction (Continued)
• Clear the mat. Place a cup and 5 negative counters on the left side and
13 positive counters on the right side. Ask students to state an equation
for the model. x 5 13 or x (5) 13 Ask them what they could
remove, or subtract, from each side to isolate the cup. Remove 5
negative counters from each side. Ask what you would do to be able to
remove 5 negative counters from the right side. Add 5 zero pairs to the
right side. Add the zero pairs, remove the counters, and ask students to
state the solution. 18
• Clear the mat. Write n 6 11 at the base of the mat. Ask students
how to model the equation and how to solve it. Place a cup and 6
negative counters on the left and 11 negative counters on the right.
Remove 6 negative counters from each side. The solution is 5.
Demonstration 2
Solving Equations by Using Subtraction
• Write 7 b 2 at the base of the mat. Write a negative sign on one of
the cups. Place that cup along with 7 positive counters on the left side of
the equation mat transparency. Place 2 negative counters on the right
side.
• Ask students what you should remove from each side to isolate the cup,
and how to accomplish the removal. Remove 7 positive counters from
each side; first you must add 7 zero pairs to the right side. Complete
those steps and ask students what equation remains. b 9
• Remind students that the variable in a solution must have a coefficient
of positive 1. Show students these two ways to complete the solution.
1) Add a positive cup and 9 positive counters to each side. Remove the
zero pairs. The resulting equation is 9 b or b 9.
2) Recall that b means the opposite of b. If b 9, then b must be
the opposite of 9 or 9.
© Glencoe/McGraw-Hill 64 Teaching Algebra with Manipulatives