Curriculum  /  Math  /  6th Grade  /  Unit 3: Multi-Digit and Fraction Computation  /  Lesson 6

Multi-Digit and Fraction Computation

Lesson 6

Math

Unit 3

6th Grade

Lesson 6 of 17

Objective

Solve problems involving division with fractions.

Common Core Standards

Core Standards

  • 6.NS.A.1 — Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Foundational Standards

  • 5.NF.B.6
  • 5.NF.B.7

Criteria for Success

  • Solve fraction division problems using a variety of strategies including visual models and computation.

Tips for Teachers

The Problem Set Guidance includes many great resources for problems. The focus of this lesson is on students internalizing the concepts from the previous lessons and beginning to develop fluency with solving fraction division problems. Ensure students have ample time to solve a variety of problems and to engage in conversation with each other around solutions. It may be valuable to include any unused problems from previous lessons to reinforce the conceptual understanding. Any problems not used from the Problem Set Guidance in this lesson can be used for review at the end of the unit prior to the post-unit assessment.

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Anchor Problems

25-30 minutes

Problem 1

It requires $${\frac {1}{4}}$$ of a credit to play a video game for one minute.

a.   Emma has $${{\frac {7}{8}}}$$ credits. Can she play for more or less than one minute? Explain how you know.

b.   How long can Emma play the video game with her $${{\frac {7}{8}}}$$ credits? How many different ways can you show the solution? 

Guiding Questions

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Student Response

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References

Illustrative Mathematics Video Game Credits

Video Game Credits, accessed on Sept. 28, 2017, 2:04 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

Solve the two problems below using a visual diagram and computation.

Problem 1:

Alisa had $${\frac {1}{2}}$$ liter of juice in a bottle. She drank $${{\frac{3}{8}}}$$ liters of juice. What fraction of the juice in the bottle did Alisa drink?

Problem 2:

Alisa had some juice in a bottle. Then she drank $${{\frac{3}{8}}}$$ liters of juice. If this was $${\frac{3}{4}}$$ of the juice that was originally in the bottle, how much juice was there to start?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Drinking Juice, Variation 2

Drinking Juice, Variation 2, accessed on Sept. 28, 2017, 2:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Illustrative Mathematics Drinking Juice, Variation 3

Drinking Juice, Variation 3, accessed on Sept. 28, 2017, 2:07 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

You are stuck in a big traffic jam on the freeway and you are wondering how long it will take to get to the next exit, which is $${1 \frac {1}{2}}$$ miles away. You are timing your progress and find that you travel $${\frac{2}{3}}$$ of a mile in one hour. If you continue to make progress at this rate, how long will it be until you reach the exit? 

Solve the problem with a diagram and explain your answer. Then find the answer using an equation and show that it is the same as what you got in your diagram.

Student Response

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References

Illustrative Mathematics Traffic Jam

Traffic Jam, accessed on Sept. 14, 2017, 1:31 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Word Problems and Fluency Activities

Next

Add and subtract decimals using the standard algorithm.

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Dividing with Fractions

Topic B: Computing with Decimals

Topic C: Applying the Greatest Common Factor and the Least Common Multiple

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