Lesson 6

Multiply Fractions

Lesson Purpose

The purpose of this lesson is for students to calculate areas of rectangles where both side lengths are non-unit fractions.

Lesson Narrative

As in previous lessons, students represent a product of fractions with a diagram. This diagram represents the product \(\frac{3}{6} \times \frac{4}{5}\). The diagram shows \(\frac{3}{6}\) of \(\frac{4}{5}\) of the square so that’s \(\frac{3}{6}  \times \frac{4}{5}\). The number of shaded pieces is \(3 \times 4\), the product of the numerators. The number of pieces in the whole square is \(6 \times 5\), the product of the denominators. So the value of the product can also be written as \(\frac{3 \times 4}{6 \times 5}\). In the first activity, students relate expressions to the area in diagrams like this and then they use this structure to find products of non-unit fractions in the second activity.

  • Action and Expression

Learning Goals

Teacher Facing

  • Represent multiplication of two non-unit fractions with expressions.

Student Facing

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

Required Preparation

CCSS Standards


Lesson Timeline

Warm-up 10 min
Activity 1 15 min
Activity 2 20 min
Lesson Synthesis 10 min
Cool-down 5 min

Teacher Reflection Questions

With which math ideas from today’s lesson did students grapple most? Did this surprise you or was this what you expected?

Suggested Centers

  • Rolling for Fractions (3–5), Stage 4: Multiply Fractions (Addressing)
  • How Close? (1–5), Stage 7: Multiply Fractions and Whole Numbers to 5 (Supporting)

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