Multi-Digit and Fraction Computation

Lesson 2

Objective

Divide a fraction by a whole number using visual models and related multiplication problems.

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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  1. Draw and interpret a visual model to represent a fractional amount being divided by a whole number.
  2. Write a division problem to represent a context. 
  3. Understand that dividing an amount by a whole number, $$n$$, is the same as taking $$\frac{1}{n}$$th of the amount or multiplying by $$\frac{1}{n}$$. (For example, dividing by $$3$$ is the same as multiplying by $$\frac{1}{3}$$.)

Tips for Teachers

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  • Students may need to be reminded of Criteria for Success #3. This can be done using visual models, dividing a whole unit by a certain number, $$n$$, and then observing that each piece represents $$\frac{1}{n}$$ th of the whole unit. 
  • The focus of this lesson is on using visual models to solve fraction-divided-by-whole-number 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.
  • Note that standard 6.NS.1 is a culminating standard; it is the last standard in the progression of standards that extends on the operations to include fractions.

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Anchor Problems

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Problem 1

Leonard made $${\frac{1}{4}}$$ of a gallon of lemonade and poured all of it into $$3$$ glasses, divided equally. How much lemonade is in each glass? Write a division problem and draw a visual model.

Guiding Questions

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Problem 2

$${\frac{3}{4}}$$ quart of soup is split equally between two people. How much soup does each person get?
Write a division problem and draw a visual model.

 

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 1Example 1

Grade 6 Mathematics > Module 2 > Topic A > Lesson 1 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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Target Task

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You follow a recipe to make a dipping sauce for chicken. The recipe makes $${\frac{2}{3}}$$ cup of sauce and serves $$4$$ people. How many cups of sauce are in each serving? 

  1. Draw a visual model to represent the situation and solution.
  2. Write a division and multiplication problem to represent the situation. Show that your solution from your calculations is the same as from your model. 

Mastery Response

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