Using Diagrams to Find the Number of Groups
This is the second lesson in a series of three lessons exploring the “how many groups?” interpretation of division in situations involving fractions.
In the preceding lesson and in this one, the number of groups in each given situation is 1 or greater. In the next lesson, students find the number of groups that is less than 1 (“what fraction of a group?”).
Students have used different diagrams to represent multiplication and division. In this lesson, tape diagrams are spotlighted and used more explicitly. They are more abstract and more flexible than other representations students may have chosen for thinking about division problems that involve fractions. Because they use measurement along the length of the tape, tape diagrams are closer to the number line representation of fractions, and ultimately help students visualize division problems on the number line. (Students are not required to do that in this lesson, however.)
Students continue to make the journey from reasoning with concrete quantities to reasoning with abstract representations of fraction
- Explain (orally) how to create a tape diagram to represent and solve a problem asking “How many groups?”
- Justify (orally and using other representations) the answer to a problem asking “How many groups?” in which the divisor is a non-unit fraction and the quotient is a fraction greater than 1.
Let’s draw tape diagrams to think about division with fractions.
- I can use a tape diagram to represent equal-sized groups and find the number of groups.
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