Math Investigations

Help with Opening PDF Files

Chapter 15

Part 1: For the activity in the Teacher's Edition, page 388

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

The students can practice their research skills by finding examples of structures that use geometric figures. Or you can bring in some pictures of structures with geometric figures. Some examples you might want to use are the Louvre Pyramid, bridges and tall buildings from around the world, Native American structures, etc.

Have the students show each other what they have found. Ask the students to point out the geometric figures that they see in each picture. Create a bulletin board display for the pictures.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 5 on quadrilaterals and other polygons.


  • crayons

Introducing the Investigation

Take down any maps of the United States that you have in the room before you begin this 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.

Make some drawings on the chalkboard to show students examples of what it means to color the map so that none of the borders of a state have the same color on each side of the border. Show that corners can have the same color on each side of the corner but that edges cannot.

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

Doing the Investigation

When they finish, have the students share what they have found. If you have a colored-in map of the United States that uses just four colors, show it to the students.

Answers for the Data Sheet

The students should be able to do this with four different colors.

Student Report

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

Extending the Investigation

Ask the students to create designs where less than four colors are needed to color the design, so that none of the edges of a shape inside the design have the same color on each side of the edge.

Houghton Mifflin Math Grade 5