Math Investigations

Help with Opening PDF Files

Chapter 10

Part 1: For the problem in the Teacher's Edition, page 254

Help students get started with this Problem Worksheet (PDF file) with the following questions.

  • Suppose two skaters are skating at the same speed. Who burns more calories, the lighter skater or the heavier skater (the heavier skater)
  • If a person weighs less than 120 pounds and is skating at a speed of 10 miles per hour, would they burn more than 7 2/5 calories per minute or less than 7 2/5 calories per minute? (less than 7 2/5 calories per minute)
  • If a person weighs between 120 and 150 pounds and is skating at a speed of 11 miles per hour, what could you say about the calories they burn per minute? (They would burn up between 10 1/2 and 11 9/10 calories per minute.)

Discuss whether each of the three statements is true or false. Ask students to explain their thinking.


  • A 90-pound person skating at 10 mi/h would burn less than 7 2/5 calories per minute. (true)
  • A 180-pound person skating at 8 mi/h would burn more than 5 3/5 calories per minute. (true)
  • A 130-pound person skating at 12 mi/h would burn more than 11 9/10 calories per minute. (false)

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 4 on adding mixed numbers with unlike denominators.


  • small round stickers
  • tape
  • bottle caps or counters
  • rulers

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 four students to work on the investigation. It is very important for this game that each team have the same number of players. If not, the teams with fewer players have an advantage over the teams with more players.

If you do not want to have your students play this game, describe the game to the students and give them the following data from two teams. Ask them to find the score for each team and find the winner.

Team A
Name of Student Distance from Dot to Bottle Cap
Carol 1 3/4 inches
Juan 1/2 inch
LaToya 2 1/4 inch
Jim 2 inches

Team B
Name of Student Distance from Dot to Bottle Cap
Kasib 1 inch
Mio 1 1/2 inches
Tom 3/4 inch
Sue 1 1/4 inch

Doing the Investigation

As you observe students playing the game, observe carefully how they are making their measurements. Give them some help if they need it so that their measurements are accurate.

When all the teams have a score, write the scores on the board. The winner is the team with the lowest score.

Answers for the Data Sheet

  • Team A Score: 6 1/2 inches
  • Team B Score: 4 1/2 inches
  • Team B is the winner.

Student Report

The student report gives students an opportunity to show the measurement recorded for each student and the sum of the individual scores.

Extending the Investigation

Have the students find the difference between their team score and the score of the winning team.

Houghton Mifflin Math Grade 5