Multi-Digit and Fraction Computation

Lesson 3

Objective

Divide a whole number by a fraction using visual models.

Common Core Standards

Core Standards

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  • 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

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  • 5.NF.B.7

Criteria for Success

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  • Understand division of a whole number by a fraction as asking the question “How many fractional pieces are in the whole?”
  • Use division to solve problems in which a whole number is given as a fractional part of an unknown amount.
  • Draw and interpret a visual model to represent a whole amount being divided by a fraction.
  • Write a division problem to represent a context. 
  • Interpret a remaining piece in a visual model in context of the size of the divisor. 

Tips for Teachers

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  • There are four Anchor Problems; however, the first problem is a review of fifth-grade skills and may be used as a preview to the lesson rather than as part of the lesson, depending on the needs of your students. 
  • Similarly to Lesson 2, the focus of this lesson is on using visual models to solve problems. Students should not be using the “invert and multiply” rule as an algorithm yet in order to continue to build conceptual understanding. This concept will be introduced in Lesson 4 and reinforced throughout the lessons to follow

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Anchor Problems

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Problem 1

A package contains $$4$$ cups of oatmeal. There is $${\frac {1}{3}}$$ cup of oatmeal in each serving.
How many servings of oatmeal are there in the package? Explain. Draw a picture to illustrate your solution.

Guiding Questions

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References

Illustrative Mathematics How Many Servings of Oatmeal?

How Many Servings of Oatmeal?, accessed on Sept. 28, 2017, 12:25 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 2

George bought $$4$$ submarine sandwiches for a birthday party. If each person will eat $${\frac{2}{3}}$$ of a sandwich, how many people can George feed?

Write a division problem and use a visual model to solve.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 2Exercise 2

Grade 6 Mathematics > Module 2 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 3

One thermos of hot chocolate uses $${\frac{2}{3}}$$ cup of cocoa powder. How many thermoses can Nelli make with $$3$$ cups of cocoa powder?

  1. Solve the problem by drawing a picture.
  2. Explain how you can see the answer to the problem in your picture.
  3. Which of the following multiplication or division equations represents this situation? Explain your reasoning.

$$3 \times {\frac{2}{3}}= ? $$                 $$3\div {\frac{2}{3}} =?$$                 $${\frac{2}{3}} \div 3 =?$$

Guiding Questions

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References

Illustrative Mathematics Making Hot Cocoa, Variation 1

Making Hot Cocoa, Variation 1, accessed on Sept. 28, 2017, 12:31 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 The Match Foundation, Inc.

Problem 4

Molly has $$9$$ cups of flour. If this is $${\frac{2}{3}}$$ of the amount that she needs to make bread, how many cups does she need?

Draw a diagram to show your solution

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 2Example 2

Grade 6 Mathematics > Module 2 > Topic A > Lesson 2 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem Set

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

  • Include problems where students are given visual models and asked to write an equation or division problem that represents the model.

Target Task

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A jar has 5 tablespoons of honey in it. One serving of honey is $${\frac{3}{4}}$$ of a tablespoon. How many servings of honey are in the jar? 

Draw a diagram to solve the problem and explain how your diagram shows the solution.

Mastery Response

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