Math Investigations

Help with Opening PDF Files

Chapter 17

Part 1: For the problem in the Teacher's Edition, page 460

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

Use the following questions to guide the students in this problem:

  • What is the area of each room? (The area of Nydia's room is 20 square units. The area of Pedro's room is 19 square units.)
  • Whose room is larger? (Nydia's room)
  • Whose room do you think will have the greater perimeter? (Answers will vary. Accept whatever predictions the students make.)
  • What is the perimeter of each room? (The perimeter of Nydia's room is 18 units and the perimeter of Pedro's room is 20 units.)
  • Does the larger room have the greater perimeter? (No. The perimeter of Nydia's room is 18 units and the perimeter of Pedro's room is 20 units.)

Discuss the results of this problem with the students. Ask them if they were surprised that the larger room did not have the greater perimeter.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 4 on finding area.

Materials

  • graph paper

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.

Point out that for two rectangles to look different they would have to have a different length and/or width.

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

Doing the Investigation

Some students may need to experiment with lots of different rectangles before they find rectangles that match the requirements. Give them the time they need for this experimentation, as it is good practice with both problem solving and visual thinking.

Answers:

Answers will vary.

Student Report

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

Extending the Investigation

Give the students a perimeter, such as 20 units, and ask them to find as many different rectangles as they can with that perimeter. Then give them an area, such as 24, and ask them to find as many different rectangles as they can with that area.


Houghton Mifflin Math Grade 3