Meanings of Division
In this lesson, students revisit the relationship between multiplication and division that they learned in prior grades. Specifically, students recall that we can think of multiplication as expressing the number of equal-size groups, and that we can find a product if we know thenumber of groups and thesize of each group. They interpret division as a way of finding a missing factor, which can either be the number of groups, or the size of one group. They do so in the context of concrete situations and by using diagrams and equations to support their reasoning.
As they represent division situations with diagrams and equations and interpret division equations in context, students reason quantitatively and abstractly (MP2).
- Identify or generate a multiplication equation that represents the same relationship as a division expression, and explain (orally) the reasoning.
- Interpret and create tape diagrams that represent situations involving equal-sized groups.
- Recognize there are two different ways to interpret a division expression, i.e., asking “how many groups?” or “how many in each group?”
Let’s explore ways to think about division.
- I can explain how multiplication and division are related.
- I can explain two ways of interpreting a division expression such as $27 \div 3$.
- When given a division equation, I can write a multiplication equation that represents the same situation.
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