Math Background

Lesson: Finding Perimeter and Area
Developing the Concept

In the previous lesson, students explored perimeter by counting the number of units around a figure. In this lesson, students will progress to finding perimeter by using addition. Students will also broaden their understanding of area by counting whole square units and half square units.

Materials: one piece of square grid paper for each student

Preparation: Draw a 2-by-2 square grid on the chalkboard.

Prerequisite Skills and Background: Students should understand the concepts of perimeter and area and know how to find perimeter and area by counting units and square units.

  • Ask:How many sides does a rectangle have? Are the sides of rectangles always the same length?
    Students should know that a rectangle has four sides and that pairs of opposite sides may have different lengths.
  • Point to the short line segments that make up the squares on the grid at the board.
  • Say:Each short line segment on the grid stands for one unit. Draw a rectangle on your paper that has two sides 2 units long and two sides 5 units long.
  • When students finish, have them label the length of each side.
  • Ask:What is the distance around a figure called? (perimeter) How could you find the perimeter of the rectangle?
    Some students may say to count the units along the sides of the rectangle. Lead them to discover that they could also add the lengths of the sides.
  • Ask:What number sentence describes the perimeter of the rectangle?
    Have a volunteer write the number sentence on the board: 2 + 5 + 2 + 5 = 14.
  • Ask:Why are there four addends in the number sentence?
    Students should realize that there are four addends because a rectangle has four sides.
  • Ask:What is the perimeter of the rectangle? (14 units)
    Encourage students to include “units” in their answer.
  • Say:Draw a polygon that has five or more sides. The sides can be any length you want. Make sure you draw the sides directly on the line segments that represent units on your grid paper.
    Observe students to make sure that the sides of the polygons they draw are on, not between, the line segments on their grid paper.
  • When student finish, have them label the length of each side of their polygons.
  • Ask:Who drew a polygon that has five sides? What is the name of a polygon that has five sides? (pentagon) How many addends will be in a number sentence that describes the perimeter of a pentagon? (5)
    Repeat these questions for polygons with six or more sides.
  • Have students find the perimeter of the polygons they drew. Ask volunteers to share their drawings and number sentences with the class.
  • Ask:How many sides does a square have? How would you describe the lengths of the sides of a square?
    Students should know that a square has four sides and that all sides are the same length.
  • Say:Draw a square that has sides 4 units long. Then shade all the square units that cover the square.
  • Ask:What is the number of square units that cover a figure called? (area) What is the area of the square? (16 square units)
    Encourage students to include “square units” in their answer.
  • Say:Draw a line from the top left corner to the bottom right corner of the square.
  • Ask:What two polygons are formed?
    Students should recognize the polygons as right triangles.
  • Say:Shade one of the right triangles.
    Make sure that students shade the entire triangle.
  • Ask:Are any of the square units shaded just halfway? (yes)
  • Say:They are half square units.
  • Ask:How many half square units did you shade? (4) How many whole square units do 4 half square units equal? (2)
    If students are unsure of how to answer this question, show them that 2 half square units equal 1 whole square unit, so 4 half square units equal 2 whole square units.
  • Ask:How many whole square units did you shade? (6) What is the area of the triangle? (8 square units)

Wrap-Up and Assessment Hints
These hands-on activities will help your students differentiate between perimeter and area. You can assess their understanding by having them draw different polygons on square grid paper and find the perimeter and area of the polygons. They should be able to explain to you the process they are following to find each measure.


Houghton Mifflin Math Grade 3