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
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. After choosing the best design, they should calculate its perimeter and area.
Perimeter and Area Activity Sheet
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
Questions for Students
1. 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.]
2. 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
3. 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
4. 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.]
- 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?
- Identify perimeter and area.
- Apply problem-solving strategies.
NCTM Standards and Expectations
- Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way.
- Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders.
- Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes.
Common Core State Standards – Mathematics
Grade 3, Measurement & Data
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Grade 3, Measurement & Data
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.