Learn on PengiIllustrative Mathematics, Grade 5Chapter 3: Multiplying and Dividing Fractions

Lesson 1: Represent Unit Fraction Multiplication

In this Grade 5 lesson from Illustrative Mathematics Chapter 3, students learn to interpret and represent a unit fraction of a unit fraction using diagrams, building toward the concept of multiplying two fractions. Using a real-world context like a pan of macaroni and cheese, students draw and explain area diagrams and tape diagrams to find fractional quantities such as one-fifth of one-half. This lesson aligns with standard 5.NF.B.4.a and prepares students to connect visual representations to multiplication expressions in later lessons.

Section 1

Introduction: A Fraction of a Fraction

Property

Finding a fraction of another fraction means you are taking a part of an existing part. For example, taking one-half of a one-half piece results in a one-fourth piece of the original whole.

12 of 12=14\frac{1}{2} \text{ of } \frac{1}{2} = \frac{1}{4}

Section 2

Procedure: Modeling a Unit Fraction of a Unit Fraction

Property

To find a unit fraction of another unit fraction, you can model the first fraction with an area model, then take a fractional part of that shaded area. This shows how one small piece relates to the whole.

1b of 1d=1b×d\frac{1}{b} \text{ of } \frac{1}{d} = \frac{1}{b \times d}

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Introduction: A Fraction of a Fraction

Property

Finding a fraction of another fraction means you are taking a part of an existing part. For example, taking one-half of a one-half piece results in a one-fourth piece of the original whole.

12 of 12=14\frac{1}{2} \text{ of } \frac{1}{2} = \frac{1}{4}

Section 2

Procedure: Modeling a Unit Fraction of a Unit Fraction

Property

To find a unit fraction of another unit fraction, you can model the first fraction with an area model, then take a fractional part of that shaded area. This shows how one small piece relates to the whole.

1b of 1d=1b×d\frac{1}{b} \text{ of } \frac{1}{d} = \frac{1}{b \times d}