Math Investigations

Help with Opening PDF Files

Chapter 20

Part 1: For the problem in the Teacher's Edition, page 524

Provide students with a copy of the Activity page (PDF file).

When students have finished designing their gardens and finding the areas and perimeters, have them share their work with each other. Have them compare the gardens using the following questions as a guide:

  • Which garden has the largest (smallest) area?
  • Which garden has the largest (smallest) perimeter?
  • Which garden has the longest walkway?

Answers will vary.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 7 on area of circles.

Introducing the Investigation

Introduce the investigation by reading aloud the assignment at the top of the Description of Investigation and Student Report (PDF file), by having one of your students read aloud the assignment, or by having the students read the assignment individually.

Put students in groups of two to four to work on the investigation.

Doing the Investigation

If students are having trouble getting started on this, help them develop a strategy. If they find the total area of the whole garden and then subtract the areas that are not covered by sod, they will have the area of the garden that will be covered by sod. Multiplying this figure by $1 will give them the cost of the sod.


  • The cost of the sod will be $1,800.50.
  • The area of the entire garden is 2,000 square feet (40 ft x 50 ft).
  • The area of the circular region in the garden is 78.50 square feet (3.14 x 5 ft x 5 ft).
  • The area of the square region in the garden is 49 square feet (7 ft x 7 ft).
  • The area of the rectangular region in the garden is 72 square feet (8 ft x 9 ft).
  • The total area not covered by sod is 199.50 square feet (78.50 + 49 + 72).
  • The area covered by sod is 1,800.50 square feet (2,000 − 199.50).
  • The cost of the sod is $1800.50 (1,800.50 x $1).

Student Report

The student report gives students an opportunity to show what they have done.

Houghton Mifflin Math Grade 6