Unit 3

Multiplying and Dividing Fractions

Unit Goals

Unit Narrative

In this unit, students find the product of two fractions, divide a whole number by a unit fraction, and divide a unit fraction by a whole number.

Previously, students made sense of multiplication of a whole number and a fraction in terms of the side lengths and area of a rectangle. In this unit, students make sense of multiplication of two fractions the same way. Students interpret area diagrams with two unit fractions for their side lengths, a unit fraction and a non-unit fraction, and then two non-unit fractions.

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Family Materials

Section A

Section Goals

Section Narrative

In this section, students reason about multiplication of two fractions. They begin by considering situations that involve finding a fraction of a fraction. Students represent the situations by drawing diagrams that make sense to them.

For example, “A pan of macaroni and cheese is full. Kiran eats of the macaroni and cheese. How much of the whole pan did Kiran...

Section A

1

Let’s solve problems about unit fractions.

2

Let’s write expressions to represent multiplication of unit fractions.

3

Let’s solve equations.

Section B

Section Goals

Section Narrative

In IM Grade 3, students learned that division can be understood in terms of equal-size groups and can be interpreted in two ways. For example, can mean finding the size of each group if 8 is put into 4 equal groups, or finding how many groups of 4 are in 8.

In this section, students extend this idea to divide...

Section B

1

Let’s think about the size of quotients.

2

Let’s divide a unit fraction by a whole number.

3

Let’s use diagrams to represent division of a unit fraction by a whole number.

4

Let’s divide a whole number by a unit fraction.

Section C

Section Goals

Section Narrative

In this section, students solve problems involving multiplication and division of fractions. As they reason about situations and interpret tape diagrams, students see that the same situation or diagram can be expressed with multiplication or division.

For example, if gallon of lemonade is shared equally by 5 friends, each friend gets gallon of lemonade. This also means that each friend...

Section C

1

Let’s solve problems involving multiplying and dividing fractions.

2

Let’s represent problems with multiplication and division equations.

3

Let’s multiply and divide with fractions.

4

Let’s learn about how fractions relate to recipes.

4

Let’s solve problems about multiplying a unit fraction and a non-unit fraction.

5

Let’s multiply a unit fraction and a non-unit fraction.

6

Let’s multiply two non-unit fractions using diagrams and expressions.

7

Let’s use what we’ve learned to multiply any two fractions.

8

Let’s use what we’ve learned to multiply mixed numbers.

9

Let’s solve problems about flags.

5

Let's solve problems by dividing a whole number by a unit fraction.

6

Let’s write situations and solve problems involving division of whole numbers and unit fractions.

7

Let’s apply what we know about division to make sure our answers make sense.

Section A

Section Goals

Section Narrative

In this section, students reason about multiplication of two fractions. They begin by considering situations that involve finding a fraction of a fraction. Students represent the situations by drawing diagrams that make sense to them.

For example, “A pan of macaroni and cheese is full. Kiran eats of the macaroni and cheese. How much of the whole pan did Kiran...

Section B

Section Goals

Section Narrative

In IM Grade 3, students learned that division can be understood in terms of equal-size groups and can be interpreted in two ways. For example, can mean finding the size of each group if 8 is put into 4 equal groups, or finding how many groups of 4 are in 8.

In this section, students extend this idea to divide...

Section C

Section Goals

Section Narrative

In this section, students solve problems involving multiplication and division of fractions. As they reason about situations and interpret tape diagrams, students see that the same situation or diagram can be expressed with multiplication or division.

For example, if gallon of lemonade is shared equally by 5 friends, each friend gets gallon of lemonade. This also means that each friend...

1