In the previous lesson, students began to develop a general algorithm for dividing a fraction by a fraction. They complete that process in this lesson. Students calculate quotients using the steps they observed previously (i.e., to divide by \(\frac ab\), we can multiply by \(b\) and divide by \(a\)), and compare them to quotients found by reasoning with a tape diagram. Through repeated reasoning, they notice that the two methods produce the same quotient and that the steps can be summed up as an algorithm: to divide by \(\frac ab\), we multiply by \(\frac ba\) (MP8). As students use the algorithm to divide different numbers (whole numbers and fractions), they begin to see its flexibility and efficiency.
Lesson overview
 11.1 Warmup: Multiplying Fractions (5 minutes)

11.2 Activity: Dividing a Fraction by a Fraction (15 minutes)
 There is a digital applet in this activity.

11.3 Activity: Using an Algorithm to Divide Fractions (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 11.4 Cooldown: Watering A Fraction of House Plants (5 minutes)
Learning goals:
 Coordinate (orally) different strategies for dividing by a fraction.
 Find the quotient of two fractions, and explain (orally, in writing, and using other representations) the solution method.
 Generalize a process for dividing a number by a fraction, and justify (orally) why this can be abstracted as \(n\cdot \frac{b}{a}\).
Learning goals (student facing):
 Let’s divide fractions using the rule we learned.
Learning targets (student facing):
 I can describe and apply a rule to divide numbers by any fraction.
Glossary:
 Access the complete Grade 6 glossary.
Standards:

This lesson builds on the standard: CCSS.5.NF.B.4MO.5.NF.B.7aMO.5.NF.B.7bMO.5.NF.B.7cMS.5.NF.4
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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