Unit 4, Lesson 10
Dividing by Unit and Non-Unit Fractions
Grade 6
Preparation
Lesson Narrative
In this lesson, students begin by using tape diagrams to recall and visualize two ideas from grade 5:
- Dividing by a whole number
has the same outcome as multiplying by the unit fraction . - Dividing by a unit fraction
has the same outcome as multiplying by the whole number .
They apply the second idea to find the value of other expressions of the form
Next, students use the same diagrams to analyze the effects of dividing by non-unit fractions. Through repetition, they notice a pattern in the steps of their reasoning (MP8) and structure in the visual representation of these steps (MP7).
Students see that division of a number by a non-unit fraction can be thought of as having two steps:
- Finding how many unit fractions there are (dividing the number by the unit fraction).
- Putting the unit fractions into groups the size of the non-unit fraction to see how many groups there are (dividing the result by the numerator of the non-unit fraction).
For instance, to divide by
- Interpret and critique explanations (in spoken and written language, as well as in other representations) of how to divide by a fraction.
- Use a tape diagram to represent dividing by a non-unit fraction
and explain (orally) why this produces the same result as multiplying the number by and dividing by .
Required Preparation
None
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