Math Investigations

Help with Opening PDF Files

Chapter 20

Part 1: For the problem in the Teacher's Edition, page 526

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

Use the following questions to guide the students as they solve the problem.

  • How many players are in the elimination tournament? (8)
  • How many games would be played in the first round? (4)
  • How many games would be played in the second round? (2)
  • How many games would be played in the third round? (1)
  • Does there need to be a fourth round? Why? (No. There does not need to be a fourth round because only one player has not been eliminated and that player is the winner.)
  • How many rounds would be played in all? (3)
  • How many games would be played in all? (7)


3 rounds: In the first round, each player plays one other player and 4 go on. In the second round, 4 players each play and 2 go on. In the third round, 2 players play each other and there is one winner; 7 games

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 2 on probability concepts.

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

Give help to those students who are having a hard time finding a strategy for creating the spinner. You might suggest that since there are six sections in the spinner, they work with fractions that have a denominator that is a multiple of six, such as 12, 18, or 24. Suggest that they use trial and error to find six fractional parts that will add up to 1 and meet all the requirements.

When students are finished, have them discuss the strategies they used to create the spinner and meet all the requirements. This is a good example of a problem with more than one answer, so have different groups show their results.

Answers for Data Sheet

Possible answer:

Circle graph divided into twenty-four sections, numbered as follows: ten sections with ones, three sections with twos, two sections with threes, two sections with fours, six sections with fives, and one section with six.

Student Report

The letter back to Sam Hart gives students an opportunity to show what they have done.

Houghton Mifflin Math Grade 5