Lesson 9

Relate Area to Multiplication

Lesson Purpose

The purpose of this lesson is for students to calculate the area of a rectangle whose side lengths are a unit fraction and a whole number in a way that makes sense to them.

Lesson Narrative

Students build on their understanding of multiplication and area from grade 3 as they work with areas with fractional side lengths. Students may count the number of smaller parts within a rectangle and will need to recognize and consider the size of these parts, which is a fraction of a square unit. It is important to be precise in the units used to describe the area and teachers should make sure to refer to “square units” rather than “squares.”

As with the area work in grade 3, the commutative property may come up. The commutative property allows students to find products in a way that makes sense to them. For example a student might find the area of a rectangle with side lengths $$\frac{1}{2}$$ and 4 by thinking of 4 groups of $$\frac{1}{2}$$.

In Unit 6, students have another opportunity to interpret the product of a fraction and a whole number in the context of multiplication as scaling. This section is about area.

• Action and Expression
• MLR8

Learning Goals

Teacher Facing

• Find the area of a rectangle with a unit fraction side length in a way that makes sense to them.

Student Facing

• Let’s explore the area of rectangles with one side length that is a unit fraction.

Required Materials

Materials to Copy

• Grid Paper 5

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

As students shared their ideas today, how did you ensure all students’ voices were heard and valued as an important part of the collective learning?

Suggested Centers

• Target Measurements (2–5), Stage 5: Fractions of Angles (Addressing)
• How Close? (1–5), Stage 6: Multiply to 3,000 (Supporting)