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}

Book overview

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Chapter 3: Multiplying and Dividing Fractions

  1. Lesson 1Current

    Lesson 1: Represent Unit Fraction Multiplication

  2. Lesson 2

    Lesson 2: Multiply Unit Fractions

  3. Lesson 3

    Lesson 3: Multiply Unit and Non-unit Fractions

  4. Lesson 4

    Lesson 4: Generalize Fraction Multiplication

  5. Lesson 5

    Lesson 5: Apply Fraction Multiplication

  6. Lesson 6

    Lesson 6: My Own Flag (Optional)

  7. Lesson 7

    Lesson 7: Concepts of Division (Optional)

  8. Lesson 8

    Lesson 8: Divide Unit Fractions by Whole Numbers

  9. Lesson 9

    Lesson 9: Divide Whole Numbers by Unit Fractions

  10. Lesson 10

    Lesson 10: Fraction Division Situations

  11. Lesson 11

    Lesson 11: Reason About Quotients

  12. Lesson 12

    Lesson 12: Represent Multiplication and Division Situations

  13. Lesson 13

    Lesson 13: Fraction Games

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}

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 3: Multiplying and Dividing Fractions

  1. Lesson 1Current

    Lesson 1: Represent Unit Fraction Multiplication

  2. Lesson 2

    Lesson 2: Multiply Unit Fractions

  3. Lesson 3

    Lesson 3: Multiply Unit and Non-unit Fractions

  4. Lesson 4

    Lesson 4: Generalize Fraction Multiplication

  5. Lesson 5

    Lesson 5: Apply Fraction Multiplication

  6. Lesson 6

    Lesson 6: My Own Flag (Optional)

  7. Lesson 7

    Lesson 7: Concepts of Division (Optional)

  8. Lesson 8

    Lesson 8: Divide Unit Fractions by Whole Numbers

  9. Lesson 9

    Lesson 9: Divide Whole Numbers by Unit Fractions

  10. Lesson 10

    Lesson 10: Fraction Division Situations

  11. Lesson 11

    Lesson 11: Reason About Quotients

  12. Lesson 12

    Lesson 12: Represent Multiplication and Division Situations

  13. Lesson 13

    Lesson 13: Fraction Games