K-12 Teaching and Learning From the UNC School of Education

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Learning outcomes

Students will calculate the area and perimeter of a random shape on a grid.

Teacher planning

Time required for lesson

4 days


pencil and paper

Technology resources

Either a computer lab or one classroom computer. Internet access and a color monitor are required.


Day 1

  1. Ask students to recall information about polygons. You might ask students to consider how they might trace the perimeter of a polygon that is drawn on the board, or you may begin the day by running the perimeter of the school!
  2. Let the students know what it is they will be doing and learning today. Say something like this:
    Today, Class, we will be talking more about the perimeter of polygons. We will learn exactly what this term means, and we will learn how to calculate the perimeter of random shapes.

    We are going to use the computers to learn about perimeter, but please do not turn your computers on or go to this page until I ask you to. I want to show you a little about the Perimeter Explorer applet first. Click on the Help tab for directions.

    (I always emphasize RIM in peRIMeter. I say that we are measuring the outside RIM of our shape.)
  3. Do the Perimeter Explorer Activity.

Day 2

Explain the term “area” and give examples of how to calculate the area of random shapes using Area Explorer. Click on the Help tab for directions.

Day 3

Use Shape Explorer to practice both area and perimeter. Click on the Help tab for directions.

Day 4

Assess student understanding of area and perimeter skills by observing and recording students’ use of the applets from Days 1–3. See Assessment section.


Given ten random shapes on a grid, the students will be able to calculate the area and perimeter.

Rubric for scoring:

  • 9–10 correct: 5 points
  • 7–8 correct: 3 points
  • 6 correct: 1 point
  • less than 6 correct: 0 points

You may wish to observe students calculate area and perimeter individually or in small groups, while other students practice. Students may also record their own results.

Supplemental information


Another option for independent practice is to have the students work in pairs (carefully chosen so that both students are of the same ability group). Have them race to find the correct area and perimeter using the Shape Explorer applet. Who ever wins gets a point. At the end of the allotted time for the game give the winning member of each pair a reward of some type.

This plan borrows heavily, with permission, from Shodor.org. You may want to explore their website for more classroom ideas.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 3

        • Measurement & Data
          • 3.MD.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
          • 3.MD.7Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find...
          • 3.MD.8Solve 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...
        • Grade 4

          • 4.MD.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with...

North Carolina curriculum alignment

Mathematics (2004)

Grade 4

  • Goal 2: Measurement - The learner will understand and use perimeter and area.
    • Objective 2.01: Develop strategies to determine the area of rectangles and the perimeter of plane figures.
    • Objective 2.02: Solve problems involving perimeter of plane figures and areas of rectangles.