Math Investigations

Help with Opening PDF Files

Chapter 4

Part 1: For the activity in the Teacher's Edition, page 88

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

The following example will show you how to work with your students to create a circle graph.

circle graph divided into 12 sections. 5 sections to represent hours spent playing baseball. 3 sections for swimming. 4 sections for running.

How I Exercise Each Week

Running: 5 hours
Playing Baseball: 4 hours
Swimming: 3 hours

This person spends 12 hours exercising each week. The students can divide a circle into twelfths by dividing it into fourths and then dividing each fourth into three equal parts. They color 5/12 of the circle to show the number of hours spent running. They color 4/12 a different color to show the number of hours spent playing baseball. They color 3/12 of the circle to show the number of hours spent swimming. The graph shows that running takes up most of the person's time.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 1 on equivalent fractions.

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

If students need help getting started on this, help them see that they can write each firefighter's exercise program in terms of what fraction of the 12 hours they spend on each type of exercise.

For example, Firefighter Joe spends 6/12 or 1/2 of the 12 hours swimming, 3/12 or 1/4 of the 12 hours running, and 3/12 or 1/4 of the 12 hours working with weights. It should be easy to look at the graphs to see what fraction of time is spent on each activity and to find the graph that matches Joe's exercise program.


Firefighter Joe: Circle Graph A
Firefighter Jaime: Circle Graph C
Firefighter Linda: Circle Graph B
Firefighter Tanya: Circle Graph D

Student Report

The student report gives students an opportunity to communicate about mathematics by reporting on what they have done and how they did it.

Extending the Investigation

Have students create a circle graph for the amount of time a friend spends doing different types of exercise.

Houghton Mifflin Math Grade 6