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Multiplication and division

Multiplication and division. Math 123. Contexts for multiplication. Repeated addition Rectangular array Cartesian product

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Multiplication and division

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  1. Multiplication and division Math 123

  2. Contexts for multiplication • Repeated addition • Rectangular array • Cartesian product The first two make sense both with the set model, and the number line model. In case of the rectangular array, we can no longer think of it in terms of the number line, because multiplication corresponds to area, so we need two dimensions.

  3. Cartesian product approach • This approach is easy to recognize. A typical problem is this: when packing for your trip, you packed three shirts, two pairs of pants, and two jackets. If you want to wear a different outfit every day, how long will you stay on your trip? This is just like the problems we did earlier.

  4. Properties of multiplication • Closure • Commutative • Associative • Identity How does this relate to addition? How are addition and multiplication related?

  5. Distributive property • Use blocks or a picture to explain to a student why 35 x 67 is not equal to 30 x 60 + 5 x 7. This is related to the standard algorithm for multiplication. I will also give you a related handout to work on.

  6. Defining division • Missing factor approach: a/b = c if and only if a = bc.

  7. Different ways to look at division • Divide 12 by 4 using blocks. Compare strategies. Come up with a word problem that goes with your strategies. • There are two different ways to approach division: • Repeated subtraction/measurement • Partitioning

  8. Properties of division • Which properties does division share with multiplication? • How is division related to subtraction?

  9. Properties of division • Like subtraction, division doesn’t have the closure, associative, commutative, or identity property. It is true that any number divided by 1 stays the same, but it is not true that 1÷ a = a.

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