Math Investigations

Help with Opening PDF Files

Chapter 21

Part 1: For problem in Teacher's Edition, page 540

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

Ask the following questions to guide the students in answering the question:

  • How long does a section of soccer last for the over-17 age group? (0.75 hours)
  • How would you show 0.75 as a fraction? (75/100 or 3/4)
  • Would two sections of soccer for this age group last more or less than one hour? (more than one hour)
  • How do you know? (Two 3/4-hour sections would add up to 1 1/2 hours, which is more than one hour.)


  • The game would last more than one hour: 0.75 is 3/4 of an hour, so 2 sections of 0.75 hours would have to be more than 1 hour.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on comparing and ordering decimals.


  • centimeter 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.

Demonstrate how to measure both the hand length and the hand span. Also show how to measure to the nearest centimeter.

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

Doing the Investigation

Observe students as they measure, and give help to any who are having trouble measuring to the nearest tenth of a centimeter.


Answers will vary.

Student Report

The letter back to Sonya Martinez gives students an opportunity to show what they have done.

Extending the Investigation

Work with the class to compile the data for the whole class. Have the students write a letter to Sonya Martinez with a recommendation for the glove and mitten measurements.

Houghton Mifflin Math Grade 4