Math Investigations

Help with Opening PDF Files

Chapter 17

Part 1: For the problem in the Teacher's Edition, page 444

Provide students with the Problem Worksheet (PDF file).

Before the students start on this problem, discuss with them what would have to be true about the size of an individual small container so that the large container could be filled with smaller containers with no space left over. Bring out in the discussion that when each dimension of the larger container is divided by one of the dimensions of the smaller container, there should be no remainder. Also, all three dimensions of the smaller container would have to be used as a divisor.

Possible answer: 32 containers that are 2 feet wide × 5 feet long × 4 1/4 feet high

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on volume.

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

Remind the students that if the box or crate they designed is measured in inches, they will have to convert the measurements to feet or convert the dimensions of the large container to inches.

Some students most likely will decide to find the volume of the large container and then divide by the volume of the small box or crate that they have designed. If students do this, use it as an opportunity to discuss with the class why this won't work. Bring out in the discussion that the box or crate with the object in it cannot be cut up in order to fit more into the space. So in many cases, there will be space left over.

Answers for Data Sheet

Answers will vary.

Suppose the size of the box the students design is 3 feet × 5 feet × 4 feet. Three boxes 3 feet wide can fit across the 8-foot width of the large container. Four boxes 5 feet long can fit across the 20-foot length of the container. Two boxes 4 feet high can fit across the 8 1/2-foot height of the container. Twenty-four boxes can fit into the container.

Student Report

The student report gives the students an opportunity to show how they calculate the number of crates or boxes that would fit into the larger shipping container.

Extending the Investigation

Have the students calculate how much space is left over in the shipping container when it is full of the smaller crates or boxes they designed.

Houghton Mifflin Math Grade 5