Lesson 9: Connecting Perimeter and Area

Getting Started

Questions to Explore

  • How are perimeter and area related?

Skills

  • Apply the area and perimeter formulas for rectangles in real world and mathematical problems
  • Use area to determine perimeter and vice versa

Materials

  • fine point dry-erase markers (kit)
  • laminated grid (kit)
  • whiteboard (kit)

Introduction

Materials: fine point dry-erase markers (kit), laminated grid (kit)
Give your child the laminated grid and dry-erase markers, and ask him to draw three rectangles that have an area of 16 square centimeters. As needed, remind him that a square is a rectangle (though it's a special one). He should draw the following rectangles:
  • 1 cm × 16 cm
  • 2 cm × 8 cm
  • 4 cm × 4 cm
Now, tell him to find the perimeter of each one. He should find the following perimeters:
  • 1 cm × 16 cm = 34 cm
  • 2 cm × 8 cm = 20 cm
  • 4 cm × 4 cm = 16 cm
Ask, "How does the perimeter of the square compare to the other perimeters?" He should note that it's the smallest. Now, ask, "Do you think it's always true that a square has the smallest perimeter when compared with other rectangles with the same area?" Provide time for him to prove whether this is true by creating three or four rectangles, including a square, with an area of 36 and then finding their perimeters. He should find that the square does have the smallest perimeter.

Next, ask your child to create three different rectangles, including a square, that have a perimeter of 16 centimeters. Possible rectangles include:
  • 4 cm × 4 cm
  • 5 cm × 3 cm
  • 6 cm × 2 cm
  • 7 cm × 1 cm
Now, tell him to find the area of each rectangle. He should find the following areas:
  • 4 cm × 4 cm = 16 square cm
  • 5 cm × 3 cm = 15 square cm
  • 6 cm × 2 cm = 12 square cm
  • 7 cm × 1 cm = 7 square cm
Ask him what he notices about the areas of the rectangles. He should note that the square has the greatest area. Invite him to test whether this is always true by creating rectangles having a perimeter of 12 centimeters. He should find that the square will have the greatest area when the perimeters are the same.

Explain that during this lesson, your child will be using what he knows about the relationship between perimeter and area to solve problems.