Math Investigations

Help with Opening PDF Files

Chapter 18

Part 1: For the problem in the Teacher's Edition, page 450

Provide students with the Problem Worksheet (PDF file).

Have your students look at the blueprint on page 450 of the student book. Ask your students how they could draw a blueprint to be an accurate representation of their classroom. If one of the students does not offer a solution, suggest that they make 1 foot equivalent to 1 inch or 1 centimeter.

Answers will vary.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 7 on using formulas.

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

Doing the Investigation

The students will most likely have different strategies for solving this problem. Some will use the formula for the volume of a rectangular prism. Using the formula, they can see that the depth of either box must be 3 inches or the box will be too high. Once they have assigned 3 inches to the depth of the box, they can plug numbers into the formula to get the height for each box.

Other students will use a trial and error method, trying different combinations of numbers until they find the combination that works.

Allow the students to use whatever strategy works for them. When the students have finished, have them share their strategies with each other.


Cereal Box A

  • Name of cereal: Answers will vary.
  • Width: 8 inches
  • Depth: 3 inches
  • Height: 12 inches
  • Volume: 288 cubic inches

Cereal Box B

  • Name of cereal: Answers will vary.
  • Width: 7 inches
  • Depth: 3 inches
  • Height: 10 inches
  • Volume: 210 cubic inches

Student Report

The student report gives the students an opportunity to show what they have done and to tell how they solved the problem, thus communicating about mathematics.

Extending the Investigation

Have the students construct the cereal boxes and create a design for each box.

Houghton Mifflin Math Grade 4