Math Investigations

Help with Opening PDF Files

Chapter 10

Part 1: For the activity in the Teacher's Edition, page 258

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

Help students develop a strategy to solve these problems. A strategy such as the following works:

  1. Divide to find what the animal shelter paid for one item.
  2. Subtract what the animal shelter paid for that item from the cost of that item shown in the chart.
  3. Multiply that amount by the number of the items the shelter bought to find the total amount saved on buying the items.

Answer:

Money saved on grooming brushes:
$30 ÷ 10 = $3
$4 - $3 = $1
Total amount of money saved on grooming brushes: $1 × 10 = $10

Money saved on doggy shears:
$18 ÷ 9 = $2
$3 - $2 = $1
Total amount of money saved on doggy shears: $1 × 9 = $9

Total amount of money saved in all: $10 + $9 = $19

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on dividing by 5.

Materials

  • counters

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 counters available for students to use.

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

Doing the Investigation

Discuss the solutions after students have completed the work. Ask questions such as:

  • Why couldn't you put 18 small dog bone treats into seven packages? (There is no way to do that and get the same number of treats in each package.)
  • Why couldn't you put 18 small dog bone treats into nine packages? (You would only get two dog treats in a package and there has to be at least four dog treats in a package.)
Answers:

18 small dog bone treats
Name of treat: Answers will vary.

Number of Packages Number of Treats in Each Package
2 9
3 6

20 large dog bone treats
Name of treat: Answers will vary.

Number of Packages Number of Treats in Each Package
4 5
5 4
2 10

24 small doggie cookies
Name of treat: Answers will vary.

Number of Packages Number of Treats in Each Package
4 6
6 4
3 8

25 large doggie cookies
Name of treat: Answers will vary.

Number of Packages Number of Treats in Each Package
5 5

Student Report

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

Extending the Investigation

Give students other numbers of doggie treats (such as 32 and 45) for them to figure out the packaging possibilities using the same rules.


Houghton Mifflin Math Grade 3