Math Investigations

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Chapter 21

Part 1: For the problem in the Teacher's Edition, page 550

Provide students with a copy of the Problem Worksheet (PDF file).

Point out to the students that there is more than one solution to this problem. Before they begin trying to solve the problem, hold a discussion in which students can share their ideas of how they would solve it. One suggestion would be to look for a smaller box, with a dimension that divides evenly into the dimension of the larger box.

Possible answer:

72 containers that are 2 in. thick x 2 in. long x 7 in. high; 28 cubic in.

Answers will vary.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 5 on surface area.

Introducing the Investigation

Introduce the investigation by reading aloud the assignment at the top of the first page 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

There are many steps involved in solving this problem. Students must find the surface area of each building and then multiply that area by the number of that type of building. Finally they must add all the surface areas together to get a total. Make sure that the students follow all the steps. You might want to have them write a plan before starting.


Building A:
surface area = (1 x 3) + (3 x 1) + (1 x 1) = 7 square feet
3 buildings = 3 x 7 = 21 square feet

Building B:
surface area = (5 x 2) + (5 x 1) + (1 x 2) = 17 square feet
1 building = 1 x 17 = 17 square feet

Building C:
surface area = (2 x 4) + (1 x 4) + (1 x 2) = 14 square feet
2 buildings = 14 x 2 = 28 square feet

Total Amount of Material Needed for Construction: 21 + 17 + 28 = 66 square feet.

Student Report

The student report gives students an opportunity to show the solution to the problem and how they solved it.

Extending the Investigation

Have the students create their own model village and calculate the amount of material they need.

Houghton Mifflin Math Grade 6