Unit 3, Lesson 7
Finding an Algorithm for Dividing Fractions
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students reason with tape diagrams to develop a general algorithm for dividing a fraction by a fraction. Through repetition, they notice a pattern in the steps of their reasoning (MP8) and structure in the visual representation of these steps (MP7).
First, students see that division of a whole 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).
Then students calculate quotients of two fractions using the steps they observed previously when dividing a whole number by a fraction—multiply the number by the denominator of the fraction and divide by the numerator. They compare the results to quotients found by reasoning with a tape diagram and verify that the two methods produce the same quotient. They sum up the steps as an algorithm: To divide a number by , we multiply by .
- Generalize a process for dividing a number $n$ by a fraction $\frac{a}{b}$, and justify (orally) why it can expressed as $n \boldcdot \frac{b}{a}$.
- Interpret and critique explanations (in spoken and written language, as well as in other representations) of how to divide by a fraction.
Let’s look for patterns when we divide by a fraction.
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.