Math Investigations

Help with Opening PDF Files

Chapter 20

Part 1: For the problem in the Teacher's Edition, page 538

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

To help students get started, ask a volunteer to give you one example of an actual price that is possible for the hammer. For example, a student might suggest $8.32. Ask:

  • Does $8.32 round to $8.00? (yes)
  • Is the sum of the digits in $8.32 13? (yes)

You might also show an example that doesn't work, such as $8.51. $8.51 rounds to $9.00 rather than $8.00, and the sum of the digits is not 13.


  • $7.51,
  • $7.60,
  • $8.05,
  • $8.14,
  • $8.23,
  • $8.32,
  • $8.41

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 8 on adding and subtracting decimals.

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.

Have students look at pages 556–558 in their student book to see pictures of castle playhouses.

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

Doing the Investigation

Have students discuss how they got each answer. Many students will keep adding the cost for one item until they get to the target number of items. Some students may find an interesting way to use information in the table. For example, to get the cost of 7 small packages of nails they could add the cost of 3 small packages and 4 small packages. Some students may find a way to use patterns. For example, the cost of 1 hook is $0.10, 2 hooks is $0.20, etc., so the cost of 9 hooks must be $0.90.


Material Cost
7 packages of small nails $3.50
9 hooks $0.90
5 yards of cloth $3.00
6 boards $7.50

Student Report

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

Houghton Mifflin Math Grade 3