Math Investigations

Help with Opening PDF Files

Chapter 18

Part 1: For the activity in the Teacher's Edition, page 496

Provide students with a copy of the Activity Page (PDF file).

To help your students get started with the investigation, read the activity and then say, Suppose you were going to make your design in a circle or a square. What would be an easy way to divide the circle or the square into eighths? Discuss the ways your students suggest. One easy way to divide a region into eighths is to divide it into fourths first and then divide each fourth in half.

Answers will vary.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on finding equivalent fractions.

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.

Say, Susie Yang is a fabric designer. What do fabric designers do? (They design material that is used for clothing, furniture, etc.)

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

Doing the Investigation

Make sure students understand that they write a statement on the write-on line only if the helper's statement is false.

When students have finished, have them share what they found with each other. Have them tell you how they know a statement is true or false.

Answers:

John's Design
There is a square that is divided into fourths with a vertical line and a horizontal line. Two squares that are not adjacent to each other are colored black. The other two squares are colored white.
My design is exactly one-fourth black. [False]
True statement: My design is exactly one-half black.
Mio's Design
There is a square that is divided into fourths with diagonal lines to make four congruent triangles. Two triangles that are not adjacent to each other are colored black. The other two triangles are colored white.
My design is exactly one-half black. [True]
Write-on line should be blank.
Tan's Design
There is a rectangle that is divided into fourths with a three vertical lines to make four congruent rectangles. Three rectangles in a row are colored black. The other rectangle colored white.
My design is exactly one-half black. [False]
True statement: My design is exactly three-fourths black.
Lupe's Design
There is a rectangle that is divided into sixths with a vertical line down the middle and two horizontal lines across to make six rectangles. In one half of the rectangle the top rectangle and the bottom rectangle are colored black. In the other half of the rectangle, the middle rectangle is colored black. The other three rectangles are colored white.
My design is exactly one-half black. [True]
Write-on line should be blank.

Student Report

The letter back to Susie Yang gives students an opportunity to show what they have done.

Extending the Investigation

Have the students create their own designs and statements to go with the designs. Have students trade designs and say whether the statements are true or false.

Houghton Mifflin Math Grade 3