Math Investigations

Help with Opening PDF Files

Chapter 4

Part 1: For the problem in the Teacher's Edition, page 82

Provide students with the Problem Worksheet (PDF file)

Some students might need counters to help them solve the problem.

Possible Answer:
1 row of 18
2 rows of 9
3 rows of 6
6 rows of 3
9 rows of 2
18 rows of 1

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 5 on multiplication and division facts to ten.

Introducing the Investigation

Introduce the investigation by reading aloud the letter at the top of the first page of the Description of Investigation and Student Report (PDF file), having one of your students read the letter aloud, or having the students read the letter individually.

To help students get started, you might want to do one example where there are enough dancers and one example where there would not be enough dancers.

Example 1: 7 rows with 4 dancers in each row
How would you figure out how many dancers are needed? (Multiply 7 by 4.) What is 7 times 4? (28) Would there be enough dancers? (Yes.)
Example 2: 9 rows with 5 dancers in each row
How would you figure out how many dancers are needed? (Multiply 9 by 5.) What is 9 times 5? (45) Would there be enough dancers? (No.) How could you find out how many more dancers are needed? (Subtract 35 from 45.) How many more dancers would be needed? (10)

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

Doing the Investigation

Be sure students are telling how many dancers would be used or how many more dancers would be needed.

Answers: 7 rows with 5 dancers in each row
(This will work. You would use 35 dancers.)
8 rows with 5 dancers in each row
(This will not work. You would need 5 more dancers.)
4 rows with 8 dancers in each row
(This will work. You would use 32 dancers.)
6 rows with 6 dancers in each row
(This will not work. You would need 1 more dancer.)
9 rows with 4 dancers in each row
(This will not work. You would need 1 more dancer.)
10 rows with 3 dancers in each row
(This will work. You would use 30 dancers.)

Student Report

The letter back to Sharon Stein gives students an opportunity to show what they have done.

Extending the Investigation

Have students make up their own problems like this to solve and trade.


Houghton Mifflin Math Grade 4