Math Investigations

Help with Opening PDF Files

Chapter 23

Part 1: For the problem in the Teacher's Edition, page 594

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

You might want to discuss different examples of removing 3 bags and the effect it would have on the likelihood of items being picked. For example, if 3 bags of stuffed animals are removed, a bag of action figures is still the most likely to be picked. A bag of marbles and a bag of stuffed animals have the same likelihood of being picked and they are both less likely to be picked than a set of action figures.

Possible Answer:

It depends on which items are removed. If 3 action figures are removed, then there should be an equal number of action figures and stuffed animals, making the probability that they are picked equally likely.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 3 on making predictions.


  • crayons

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

Doing the Investigation

There are many different possible correct answers for each of the spinner designs. Have the students share the designs for each spinner and have them evaluate whether the requirements for that spinner have been met.

Possible Answers:

Spinner A:
spinner divided into one fourth red, one fourth blue, and one half purple.
Spinner B:
spinner divided into two thirds blue, and one third yellow.
Spinner C:
spinner divided into one fourth yellow, one fourth blue, and one half green.
Spinner D:
spinner divided into 3 equal sections labelled red, orange, and purple.

Student Report

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

Houghton Mifflin Math Grade 4