Lesson 11

Fractional Side Lengths Greater Than 1

Lesson Purpose

The purpose of this lesson is for students to find the area of a rectangle where one of the side lengths is a fraction greater than 1.

Lesson Narrative

In previous lessons, students multiplied fractions by whole numbers and found the area of rectangles with one fractional side length when the fraction was less than 1. They used visual representations to support their reasoning. For example, students use this picture to explain why \(\frac{2}{3} \times 4 = (2 \times 4) \times \frac{1}{3}\).

Area diagram. Length, 4. Width, 2 thirds.

In this lesson, students apply these strategies to find the area of a rectangle with a fractional side length greater than 1.

Area diagram.

Using an area diagram like this, the same reasoning shows that \(\frac{5}{3} \times 4 = (5 \times 4) \times \frac{1}{3}\).

  • Engagement
  • MLR8

Activity 1: Greater Than One

Learning Goals

Teacher Facing

  • Find the area of a rectangle with one fractional side length greater than 1 in a way that makes sense to them.
  • Represent the area of a rectangle with a multiplication expression.

Student Facing

  • Let’s find the area of more rectangles.

Required Preparation

CCSS Standards

Addressing

Lesson Timeline

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

Teacher Reflection Questions

  • Why is it important for students to be able to write and interpret different expressions to represent and find the area of rectangles with fractional side lengths?

Suggested Centers

  • How Close? (1–5), Stage 7: Multiply Fractions and Whole Numbers to 5 (Addressing)
  • How Close? (1–5), Stage 6: Multiply to 3,000 (Supporting)

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