# Lesson 13

Perimeter and Area of Rectangles

### Lesson Purpose

The purpose of this lesson is for students to examine rectangles with given perimeter or area, plotting their length and width on the coordinate grid.

### Lesson Narrative

The purpose of this lesson is to plot the lengths and widths of different rectangles with a given perimeter or with a given area. In a previous course, students found rectangles with the same area and different perimeter and rectangles with the same perimeter and different area. Graphing the possible lengths and widths helps to visualize and quantify these relationships. Specifically, when the perimeter is given, the relationship between the length and width is that each unit taken away from the length is added to the width. When the area is given, the relationship is more complicated and the graphs of the two situations reveal this. As students calculate side lengths they also have opportunities to perform arithmetic with fractions and decimals.

• Representation
• MLR8

### Learning Goals

Teacher Facing

• Use the coordinate grid to understand the length and width of rectangles with fixed area.
• Use the coordinate grid to understand the length and width of rectangles with fixed perimeter.

### Student Facing

• Let’s explore the perimeter and area of rectangles on the coordinate grid.

Building Towards

### 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 you finish up this unit, reflect on the norms and routines that have supported each student in learning math. How have you seen each student grow as a young mathematician throughout this work? How have you seen yourself grow as a teacher?

### Suggested Centers

• Can You Draw It? (1–5), Stage 7: Grade 5 Shapes (Addressing)
• Picture Books (K–5), Stage 3: Find Shapes (Addressing)

### Print Formatted Materials

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