Previously, students looked at division situations in which the number of groups (or the fraction of a group) was unknown. They interpreted division expressions as a way to find out that number (or fraction) of groups. In this lesson, students encounter situations where the number of groups is known but the size of each group is not. They interpret division expressions as a way to answer “how much in a group?” questions.
Students use the same tools—multiplication and division equations and tape diagrams—and the same structure of equal-sized groups to reason about “how much in a group?” questions (MP7). They also continue to relate their reasoning in quantitative contexts to their reasoning on abstract representations (MP2). Students find both whole-number and non-whole-number quotients, recognizing that, like the number of groups, the amount in one group can also be a whole number or a fraction.
- Compare and contrast (orally) strategies for solving problems about “how many groups?” and “how much in 1 group?”
- Create a tape diagram to represent and solve a problem asking “How much in 1 group?” where the dividend, divisor, and quotient may be fractions, and explain (orally) the solution method.
- Write multiplication and division equations to represent a problem asking “How much in 1 group?”
Let’s look at division problems that help us find the size of one group.
- I can tell when a question is asking for the amount in one group.
- I can use diagrams and multiplication and division equations to represent and answer “how much in each group?” questions.
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