Illuminations: Junior Architects

Junior Architects

Finding Perimeter and Area

In this lesson, students develop strategies for finding the perimeter and area for rectangles and triangles using geoboards and graph paper. Students learn to appreciate how measurement is a critical component to planning their clubhouse design.

Learning Objectives
 
Students will:
  • Identify perimeter and area.
  • Apply problem-solving strategies.

Materials
 
Masking Tape
Geoboards
One-Inch Graph Paper
Perimeter and Area Activity Sheet

Instructional Plan
Students will be working with perimeter and area throughout this lesson and, in fact, throughout this unit. Consequently, they will need to have some prior knowledge regarding these concepts. You may need to spend some time teaching or reviewing these concepts prior to using this lesson.

For this lesson, you will want students to begin to develop a sense of size, so that they can determine dimensions for their clubhouse that are realistic and proportional to human size. To develop these spatial concepts, place masking tape on the floor of the classroom in a variety of rectangular shapes with various dimensions to represent different room sizes. Then, pose the question, "How would you compare the different room sizes?" This will prompt students to think about perimeter and area. "What can you fit into a 10 × 10 room?" This question will elicit conversation about the scarcity of space and how students will need to determine what kinds of furniture will be most needed in a small space.

Students will complete the Perimeter and Area activity sheet which explores the measurement of perimeter and area. For the in‑class activity of creating their own floor plan, allow students to work with geoboards or the Geoboard E‑Example available on the NCTM web site. After choosing the best design, they should calculate its perimeter and area.

Perimeter and Area Activity Sheet Perimeter and Area Activity Sheet

Geoboard E-Example Geoboard E-Example

If you allow students to use the Geoboard E-Example, be sure to circulate while they are working to ensure that they remain on‑task. As you walk around, ask students how the design they create on the geoboard relates to their clubhouse design.

To close the lesson, have students explore the many possible sizes and designs for their clubhouse that will change the perimeter and area. Some students might maximize the area in their design, while others might opt for a design that is aesthetically pleasing but smaller.

Questions for Students
 
What is the difference between perimeter and area? How would an architect or construction worker use these different measurements?
[Perimeter is the measure of the distance around an object. Area is the measure of all the space inside an object.]

How did you find the area? How did you find the perimeter of the clubhouse? Compare your method with your classmates.

[To find the perimeter, add the lengths of all sides. To find the area, count the number of squares inside the figure. If the figure is a rectangle, you can simply multiply the length times the width.]

How many different rectangles can you build with an area of 24 square inches? What are the perimeters of the different rectangles?

[If the dimensions are limited to integers, then there are four different rectangles with an area of 24 square units could be built: 1 × 24, 2 × 12, 3 × 8, and 4 × 6. If the dimensions are not restricted to integers, then the number of different rectangles is infinite.]

What happens to the area of a shape as the perimeter increases? What happens as the perimeter decreases? Is there a relationship between perimeter and area?

[There is not a systematic relationship between area and perimeter. For example, notice that a 3 × 8 rectangle has a perimeter of 22 units and an area of 24 square units. For a 5 × 5 rectangle, the perimeter is decreased to 20 units, and the area is increased to 25 square units; for a 3 × 10 rectangle, the perimeter is increased to 26 units and the area is increased to 30 square units. Notice that the area of both of these new rectangles is greater than the area of the original rectangle, yet for one the perimeter is greater and for the other the perimeter is less.

Rectangles could also be found such that the area decreases, regardless of whether the perimeter increases or decreases.]

Assessment Options
 
  1. Give students five minutes to explain in their design logs how the math they learned in this lesson will help them design their clubhouses.
  2. Observe students while they work on the geoboards. Collect the Perimeter and Area activity sheet as a form of assessment.

Extensions
 
  1. Allow students to test their skills with the Shodor Foundations's Shape Explorer applet. This interactive tool randomly generates shapes, and students must determine the area and perimeter. Users can continue to guess until they enter the correct answers.

Teacher Reflection
 
  • Did students have the opportunity to make conjectures about how the perimeter and the area changed with different rectangles?
  • Did students prefer using the geoboards or the graph paper?
  • Did they enjoy using the electronic geoboard or the physical geoboards?
  • What values do you see in using the virtual geoboard?

NCTM Standards and Expectations
 
Measurement 3-5
  1. Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.
  2. Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms.
  3. Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes.
This lesson prepared by Jennifer Suh.
  
1 period   

NCTM Resources

Navigating through Measurement in 3‑5

Web Sites
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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