Session 4, Part C:
Colored-Chip Models

In This Part: Addition | Subtraction | Multiplication | Division

In this section, multiplication is defined as "putting in" to a circle, or "taking out" from a circle. Remember, in Part A we described 3 • 4 as three groups of four. Three could be thought of as the operator -- it tells us what to do with the second number. In this section, we need to know the sign of the operator. If the sign is positive, you put things into the circle. If the sign is negative, you take things out of the circle. In this case, you must put in zeros until you have enough to follow instructions.

 • To find the product of +2 • (+3), start with an empty circle: Since the 2 is positive, +2 • (+3) means that you should "put in" "two" sets of "three black chips": Record what is left; i.e., six positives (+6): +2 • (+3) = +6 • To find the product of +2 • (-3), start with an empty circle. Since the 2 is positive, +2 • (-3) means that you should "put in" "two" sets of "three red chips": Record what is left; i.e., six negatives (-6): +2 • (-3) = -6 • To find the product of -2 • (+3), start with an empty circle. Since the 2 is negative, -2 • (+3) means that you should "take out" "two" sets of "three black chips": But there are no black chips. So put in zeros (pairs of positive and negative chips) until there are enough black chips for you to take out two sets of three. Then take them out: Record what is left; i.e., six negatives (-6): -2 • (+3) = -6 • To find the product of -2 • (-3), start with an empty circle. Since the 2 is negative, -2 • (-3) means that you should "take out" "two" sets of "three red chips." But there are no red chips. So put in zeros (pairs of positive and negative chips) until there are enough red chips for you to take out two sets of three. Then take them out: Record what is left; i.e., six positives (+6): -2 • (-3) = +6 Draw or make a diagram to show the colored-chip model for each of the following:

Problem C5

-3 • (-3)

 Problem C6 +3 • (-3)

 Session 4: Index | Notes | Solutions | Video