# 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.

### 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)

### Print Formatted Materials

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