Math Investigations

Help with Opening PDF Files

Chapter 22

Part 1: For the problem in the Teacher's Edition, page 578

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

When students are finished, have them share their drawings with one another. You might want to have them design gardens for other groupings of flowers: for example, 10 red roses, 20 white roses, and 25 pink roses, all planted five in a row.


Students should have two rows of one color of 8 X's to show the daisies, 4 rows of a different color of 8 X's to show the marigolds, and 3 rows of a third color of 8 X's to show the zinnias. They should have a key to show this.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 5 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 the students in groups of two to four to work on the investigation.

Doing the Investigation

Have the students share their answers and how they figured out the answer to each question. Bring out in the discussion the different ways of treating a remainder, according to the kind of question that is asked.


  • Question 1:
    You will need 6 cars.
    If you divide 27 by 5 you get an answer of 5 with a remainder of 2. You need a sixth car for those two people.
  • Question 2:
    You get to take home 2 tomatoes.
    If you divide 50 by 4, you get 12 with a remainder of 2. The remainder tells you how many tomatoes you get to take home.
  • Question 3:
    You will end up with 14 full boxes of lettuce.
    If you divide 87 by 6 you get 14 with a remainder of 3. The quotient without the remainder tells you how many full boxes you will have.

Student Report

The letter back to Maria Martinez gives students an opportunity to answer her questions and explain how they got each answer.

Extending the Investigation

Have the students write problems that involve division with remainders and interpreting those remainders. Have them exchange problems and solve each other's problems.

Houghton Mifflin Math Grade 3