Positive-Negative Charge Model For Integers

Williams, Barbara J. N. Thorp School

Objective: To represent operations on integers with positive and negative charges. Materials: Overhead projector, drawing of an empty beaker on an acetate, bingo chips (two colors needed). Procedure: The "positive-negative" model was used to represent addition and subtraction, however, this model can also be extended to represent division and multiplication. To use this model the blue chips represent negative charges. The red chips represent positive charges. The beaker represented on the acetate will be used to combine the charges. We are not concerned with individual charges, but with collection of charges in the beaker. Therefore, an empty jar would have a collective charge of zero. If the jar contains an equal number of blue and red chips, the charge is also zero. Three positive (red) chips and three negative (blue) chips form a 1:1 correspondence and they therefore cancel each other. The collective charge of the beaker is zero. Addition
Ex. 1. +3+(4)=+7
Place three red chips in the beaker, add four red chips. The collective
charge is now a positive seven.
Ex. 2. -5+(2)=-3
Place five blue chips in the beaker then add two red chips. Match a
blue and and red chip 1:1 until two sets of zeroes are matched.
Remove the matched chips from the beaker. There are now three blue
chips remaining in the beaker. The collective charge is now
represented by as negative three. The answer -3 represented by the
three blue chips.
Subtraction Ex. 3. -2-(+7) Place two blue chips in the beaker. We now must create +7. Add zeroes (seven red chips and seven blue chips), to the beaker. The collective charge is -2. Now, remove the seven positive (red) charges. Only blue (negative) chips remain. Your answer is represented by the nine blue chips that remain. Multiplication and division can be similarly represented. A COMPLETE MODEL FOR OPERATIONS ON INTEGERS by Michael Battista
Arithmetic Teacher, May 1983.
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