# 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

Addressing

### 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

### 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)