# Lesson 13

Area and Properties of Operations

### Lesson Purpose

The purpose of this lesson is for students to analyze area diagrams and use the properties of operations to represent the area of rectangles.

### Lesson Narrative

In previous lessons, students applied what they know about multiplication of whole numbers and fractions to decompose a rectangle to find its area. In this lesson, students use the properties of operations to represent the area of rectangles with expressions. As students go through the activities, they will apply concepts they have seen and used in earlier grades, units, and lessons, such as:

• the distributive property
• the relationship between fractions and division
• the relationship between multiplication and division
• the relationship between addition and subtraction

Students use diagrams and expressions to investigate the distributive property, with both addition and subtraction. The diagrams provide a way to visualize how the different expressions represent the area of a given figure. This generalizes work that students have done in earlier grades with whole numbers. Understanding how the distributive property can be represented with diagrams helps students understand the structure of expressions representing products (MP7) and generalizes what they learned in an earlier grade using whole numbers (MP8).

• Action and Expression
• MLR8

### Learning Goals

Teacher Facing

• Represent the decomposition of a rectangle with diagrams and expressions.

### Student Facing

• Let’s write expressions to represent the area of rectangles.

### Required Materials

Materials to Copy

• Card Sort: Diagrams and Expressions

### Required Preparation

Activity 1:

• Create a set of cards from the blackline master for each group of 2.

### 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 use different expressions to represent and find the area of rectangles?

### Suggested Centers

• How Close? (1–5), Stage 7: Multiply Fractions and Whole Numbers to 5 (Addressing)
• Rectangle Rumble (3–5), Stage 3: Factors 1–10 (Supporting)

### Print Formatted Materials

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