Lesson 13
Area and Properties of Operations
Lesson Purpose
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
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
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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Additional Resources
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