Math Investigations

Help with Opening PDF Files

Chapter 4

Part 1: For the problem in the Teacher's Edition, page 84

Provide students with the Problem Worksheet (PDF file).

Ask the following questions to help students with this activity:

  • To get the greatest number of pages, what number of stamps to a page do you want to try first? (4 stamps to a page)
  • Why can't the answer for the greatest number of pages be 25 pages with 4 stamps? (Because there are only 24 pages in the album.)
  • To get the least number of pages, what number of stamps to a page do you want to try first? (6 stamps to a page)

Possible Answers:

  • Greatest number of pages: 20 pages with 4 stamps and 4 pages with 5 stamps
  • Least number of pages: 16 pages with 6 stamps and 1 page with 4 stamps
  • 20 pages with 5 stamps
  • 12 pages with 5 stamps and 10 pages with 4 stamps
  • 10 pages with 6 stamps and 10 pages with 4 stamps

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 7 on problem solving.

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.

You may want to do the equation for one club to help students get started on this activity. Ask the following questions to guide the students through writing and using an equation for the Marble Club.

  • There will be three things in the equation. What are they? (the average price of a marble, the total sales, and the number of marbles sold)
  • How could we write an equation in words? (the number of marbles sold = the total sales ÷ the average price of a marble)
  • How could we put what we know in this equation? (use n for the number of marbles sold, then n = 48 ÷ 3)
  • About how many marbles were sold? (16)
  • Why is the number 16 an estimate of the number of marbles sold? (Because we used the average price of a marble. The actual number of marbles sold could be a little more or a little less than 16.)

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

Doing the Investigation

Most students will find it easier to write word equations rather than equations with variables. However, allow students to use variables if they are able to.

Data Sheet

Marble Collectors Club
Average price of a marble: $3
Total sales to use in equation: $48

Stamp Collectors Club
Average price of a stamp: $7
Total sales to use in equation: $161

Doll Collectors Club
Average price of a doll: $23
Total sales to use in equation: $322

Answers for Data Sheet

Marble Collectors Club
Average price of a marble: $3
Total sales to use in equation: $48

Equation: the number of marbles sold = the total sales ÷ the average price of a marble
number of marbles sold = 48 ÷ 3
number of marbles sold = 16

Stamp Collectors Club
Average price of a stamp: $7
Total sales to use in equation: $161

Equation: the number of stamps sold = the total sales ÷ the average price of a stamp
number of stamps sold = 161 ÷ 7
number of stamps sold = 23

Doll Collectors Club
Average price of a doll: $23
Total sales to use in equation: $322

Equation: the number of dolls sold = the total sales ÷ the average price of a doll
number of dolls sold = 322 ÷ 23
number of dolls sold = 14

Student Report

The letter back to Ken Washington gives students an opportunity to show the equations they have created and how to use them.

Extending the Investigation

Create more problems of this kind to give the students.


Houghton Mifflin Math Grade 5