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Multiplication and division

Multiplication and division. Math 123. How would you solve the following problems?. One kind of cheese costs $2.19 a pound. How much will a package weighing 3 pounds cost? One kind of cheese costs $2.19 a pound. How much will a package weighing 0.73 pounds cost?

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Multiplication and division

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  1. Multiplication and division Math 123

  2. How would you solve the following problems? • One kind of cheese costs $2.19 a pound. How much will a package weighing 3 pounds cost? • One kind of cheese costs $2.19 a pound. How much will a package weighing 0.73 pounds cost? Did you solve them differently?

  3. Many people struggle with the second problem, and may divide instead of multiplying.

  4. How would you model the following problems? • 6 x ½ cookies • ½ x 6 cookies Did you use the same strategy in both?

  5. 6 x ½, ½ x 6 • “Six times one half” suggests that we can add ½ six times: ½ + ½ + ½ + ½+ ½+ ½ = 3. This is the repeated addition model for multiplication. • “One half times six” suggests “one half of six,” so we can divide six in half, and get 3. This is the operator model of multiplication.

  6. Repeated addition • Megan has 5 bags of cookies. There are 5 cookies in each bag. How many cookies does she have? • A baby elephant gains 4 pounds every day. How many pounds will the baby elephant gain in 8 days? • How much would 5 pieces of gum cost if each piece costs 4 cents? • Young students often think of multiplication as repeated addition, but this does not always work; in fact this model breaks down once fractions and decimals are introduced. For example, how could you find 1.2 x 3.4?

  7. Array (area) model • A farmer plants a rectangular vegetable garden that measures 6 meters along one side and 8 meters along an adjacent side. How many square meters of garden does the farmer plant? • A baker has a pan of fudge that measures 8 inches on one side and 9 inches on another side. If the fudge is cut into square pieces 1 inch on a side, how many pieces of fudge can the pan hold?

  8. Cartesian product • 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?

  9. Note that the previous problem did not mention addition at all, nor could it be solved using addition.

  10. Contexts for multiplication • Repeated addition • Rectangular array • Operator • Cartesian product

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

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