Unit 4: Dividing Fractions

Students develop understanding of division of fractions by fractions, generalizing a process for finding quotients and applying it to problems about geometric figures with fractional measurements.

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Unit

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Concept

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Practice

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Set 1

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Set 2

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Advanced

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What this unit covers

A Making Sense of Division · 3 lessons

Goals

• Create a diagram and a multiplication or division equation to represent the relationship in situations involving equal-size groups, and coordinate these representations.
• Interpret a division expression in two ways: as an answer to a “How many groups?” question or to a “How many in each group?” question.

Lessons

1. Size of Divisor and Size of Quotient
2. Meanings of Division
3. Interpreting Division Situations (Optional)

B Meanings of Fraction Division · 6 lessons

Goals

• Create a diagram, a multiplication equation, and a division equation to represent a problem that involves a fractional divisor and that asks “How many groups?” or “How much in one group?”
• Solve problems involving division of fractions by using diagrams, writing equations, or reasoning about the relationship between multiplication and division. Explain the solution methods.

Lessons

1. How Many Groups? (Part 1) (Optional)
2. How Many Groups? (Part 2)
3. Using Diagrams to Find the Number of Groups
4. What Fraction of a Group?
5. How Much in Each Group? (Part 1)
6. How Much in Each Group? (Part 2) (Optional)

C Algorithm for Fraction Division · 2 lessons

Goals

• Generalize a process for dividing a number by a fraction as multiplying by its reciprocal.

Lessons

1. Dividing by Unit and Non-Unit Fractions
2. Using an Algorithm to Divide Fractions

D Fractions in Lengths, Areas, and Volumes · 4 lessons

Goals

• Determine the volume of a rectangular prism by packing it with unit cubes with appropriate unit-fraction edge lengths and by multiplying the edge lengths.
• Solve problems about length comparison, the side lengths and area of a rectangle, and the edge lengths and volume of a rectangular prism using fraction division.

Lessons

1. Fractional Lengths
2. Rectangles with Fractional Side Lengths
3. Fractional Lengths in Triangles and Prisms
4. Volume of Prisms

E Let’s Put It to Work · 2 lessons

Lessons

1. Solving Problems Involving Fractions (Optional)
2. Fitting Boxes into Boxes