Math Investigations

Help with Opening PDF Files

Chapter 9

Part 1: For the problem in the Teacher's Edition, page 208

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

You may need to review Venn diagrams with the students. Ask the following questions to help the students get started:

  • How many circles will you need for this Venn diagram? (2)
  • What will the circles be labeled? (Rural and Urban)
  • Where would you put “Dog”? Why? (In the intersection of the two circles because “dog” is one of the most common pets in both urban and rural areas)
Venn diagram

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on drawing conclusions and making predictions.


  • graph paper

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.

If you do not want your students to do their own survey, give them the following assignment.

  • Look at the data that was collected by a group of students for their class of 30 students.
    • Survey question: Does your family own a dog?
    • Method of sampling: They used a random sample. They put all of the names of the students in a hat. They drew the names out of the hat and asked the question to every fifth student.
    • Survey Results:
    • Yes: 4
    • No: 2
  • Did they use a good method of sampling? Why or why not?
  • Show a graph of their results.
  • Draw a conclusion about the whole class.

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

Doing the Investigation

Help the students get started by brainstorming some ideas for a survey question.

If it is appropriate for the data a group collected, you could also ask the group to find one or more measures of central tendency.

Have each group give a report on their results. Discuss the method of sampling and the conclusions drawn.


Answers will vary.

Answers for the survey and data we provided:
  • The method of sampling was good because it was random. There were enough responses to be representative of the whole class.
  • bar graph titled Survey Results: Does Your Family Own a Dog?
  • The conclusion will vary. Sample conclusion: In our class, there are more kids with families who have a dog than kids with families who do not have a dog.

Student Report

The Student Report gives students an opportunity to show how they collected and analyzed some data.

Extending the Investigation

Students could give their survey to the whole class or the whole school to find out how close their conclusion was to the actual results.

Houghton Mifflin Math Grade 6