Math Investigations

Help with Opening PDF Files

Chapter 8

Part 1: For the problem in the Teacher's Edition, page 204

Provide students with the Problem Worksheet (PDF file)

Divide the students into groups of three, four, five, and six. Have each group decide what it will collect. When the students have finished dividing the items equally, find out which groups had items left over. The groups of three students and the groups of six students should have items left over, while the groups of four students and groups of five students will not have items left over. Ask all the groups of three to get together, all the groups of four to get together, etc. Ask them to compare notes and see if they got the same results.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 3 on interpreting remainders.

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

If students need help figuring this out, refer them to Lesson 3 on interpreting remainders on pages 210-212.


Problem 1:
There are 49 of us going to a stamp collector's conference. Four people can go in each car. How many cars do we need to take?

49 ÷ 4 = 12 R1

I have to increase 12 R1 to 13. We will need 13 cars so we have enough cars to accommodate the one remaining student.

Problem 2:
Saul has 68 stamps in his stamp album. He puts six stamps on a page. How many full pages of stamps does he have?

68 ÷ 6 = 11 R2

I have to drop the remainder because there are only 11 full pages.

Problem 3:
At the end of the conference, I am going to give a present to each of the three people who helped me organize the conference. I have 68 stamps. I am going to divide them equally among the three people. How many stamps will I have left over that I can keep?

68 ÷ 3 = 22 R2

For this problem, the remainder is the answer. I will have two stamps left that I can keep after I give my three helpers an equal number of stamps.

Student Report

The letter back to Carla Santos gives students an opportunity to show and explain what they have done.

Extending the Investigation

Have the students write word problems where the solution involves a division problem that has a remainder. Have them write the answers to the problems they wrote. They can exchange problems so they can solve the problems that other students wrote.

Houghton Mifflin Math Grade 4