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Gifts from Grandma, Variation 3

Alignments to Content Standards: 6.NS.B.3

Task

  1. Juanita spent \$24.50 on each of her 6 grandchildren at the fair. How much money did Juanita spend?
  2. Nita bought some games for her grandchildren for \$42.50 each. If she spent a total of \$340, how many games did Nita buy?
  3. Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of \$227.50, how much did each grandchild get?

IM Commentary

The purpose of this task is to show three problems that are set in the same kind of context, but the first is a straightforward multiplication problem while the other two are the corresponding "How many groups?" and "How many in each group?" division problems. It is important for students to see each of these types of problems. Computational fluency is best put to use when students solve problems set in appropriate contexts.

This task is structurally identical to “3.OA Gifts from Grandma, Variation 1” except that it requires students to work with decimals instead of just whole numbers. A version of this task is being developed to illustrate 5.NBT.7 that shows the intermediate phase student should go through when learning to divide decimals before they are required to be proficient with the standard algorithm.

Solution

  1. Juanita spent 6 groups of \$24.50, which is $6 \times 24.5 = 147$ dollars all together.
  2. Since the number of games represents the number of groups, but we don’t know how many games were purchased, this is a “How many groups?” division problem. We can represent it as $$? \times 42.5 = 340$$ or $$340 \div 42.5 = ?$$ So Nita must have purchased 8 games.
  3. Here we know how many grandchildren there are (so we know the number of groups), but we don’t know how much money each one gets (the number of dollars in each group). So this is a “How many in each group?” division problem. We can represent it as $$7 \times ? = 227.5$$ or $$227.5 \div 7 = ?$$ So Helen must have spent \$32.50 on each grandchild.