Math Investigations

Help with Opening PDF Files

Chapter 15

Part 1: For the problem in the Teacher's Edition, page 380

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

Have your students look at the chapter opener on page 380 to see an example of Rutherford Boyd's artwork. If you or your students can find other examples of Rutherford Boyd's artwork, show the examples to the whole class. Try looking on the Internet. However, students can still do the activity even if they don't see other examples of Rutherford Boyd's artwork.

Have students draw a shape and then use transformations on the shape to create their artwork. If students have access to computers and appropriate software, they could create a digital design.

When students have finished creating their artwork, have them write a paragraph describing the shapes and transformations they used.

You might want to display the artwork in the classroom so children can view and discuss each other's designs.

Answers will vary.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 8 on transformations in the coordinate plane.


  • rulers

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

Doing the Investigation

The students may need to estimate the area of their design if they have outside edges of the design going through squares on the grid.

Students will discover (if they don't realize it right away) that their initial design must be quite a bit less than between 95 and 105 square units because the area will increase when the initial design is transformed to one or more quadrants. Let students come to this realization on their own.

Display the designs in the classroom and let the students compare and contrast them.


Answers will vary.

Student Report

The Student Report gives students an opportunity to show what they have done.

Houghton Mifflin Math Grade 6