Math Investigations

Help with Opening PDF Files

Chapter 19

Part 1: For the problem in the Teacher's Edition, page 488

Students can practice their data collection skills by doing the survey. Or you can provide them with the data sheet found in the Problem Worksheet (PDF file).

Once students have the survey results, you may want to review Venn diagrams. Have six volunteers who are wearing the color red and/or blue come to the front of the class. Show how to construct a Venn diagram with two overlapping circles, one circle for red, one circle for blue, and one circle for red and blue. Have students tell you where to put the name of each of the six students in the diagram.

In addition to asking what fraction of people surveyed said they like both types of juice, you may also want to ask the following questions:

  • What fraction of the people surveyed said they like orange juice only?
  • What fraction of the people surveyed said they like grapefruit juice only?

Answer:

If students do their own survey, answers will vary.

Answer for data we provided:
1/3 of the people surveyed like both orange juice and grapefruit juice.
1/2 of the people surveyed like orange juice only.
1/6 of the people surveyed like grapefruit juice only.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 7 on mixed numbers and improper fractions.

Materials

  • 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 on the board what it means for a horse to be one length behind another horse. Draw a horizontal number line and put an “x” to represent a horse at the end of the line on the right side. Then use a ruler to show one inch to the left or one horse length behind.

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

Doing the Investigation

Students will most likely want to put the winning horse on the right. That means they will be measuring lengths to the left of the endpoint of the line. This may be a little different way of measuring for them. Give help to any students who are having trouble.

Some students may want to put the winning horse on the left. That is fine, as long as they make it clear in the diagram.

Answers:

number line that is a little over 3 inches long.

  • Point that is 1/4 inch to the left of point labeled Black Jet is labeled Satin Dream.
  • Point that is 1/2 inch to the left of point labeled Black Jet is labeled Swiftly.
  • Point that is 21/2 inches to the left of point labeled Black Jet is labeled Last Chance.
  • Point that is 23/4 inches to the left of point labeled Black Jet is labeled Sapphire Surprise.
  • Point that is 3 inches to the left of point labeled Black Jet is labeled Moon Shadow.

Student Report

The student report gives students an opportunity to show what they have done.

Extending the Investigation

Have students find data on actual horse races in the newspaper and record the position of the horses on a number line.


Houghton Mifflin Math Grade 4