Math Investigations

Help with Opening PDF Files

Chapter 23

Part 1: For the problem in the Teacher's Edition, page 608

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

Ask the students to predict how the two figures will be the same and how they will be different, before they draw the second figure. Then have them draw the second figure and do a comparison. Finally, have them compare their descriptions to their predictions.

Possible Answer:

The shapes are similar triangles. The lengths of the sides of the second triangle are double the corresponding sides of the first. Corresponding angles are equal.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 2 on writing and solving equations.

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

If the students need help getting started, do the first question with the whole class. Draw the grid and the points given on the board and connect the points. Ask the students what the missing point is. Take one of the suggestions and graph it, connect the points, and see if the figure looks like a rectangle. Keep doing this until the correct coordinates are given and the figure looks like a rectangle.

Data Sheet

Answers for Data Sheet:

  • Question 1: (5, 3)
    drawing of a rectangle with the following coordinates in the first quadrant: (2,1) (2,3) (5, 1) (5, 3)
  • Question 2: (3, 5)
    drawing of a square with the following coordinates in the first quadrant:  (3,2,) (6,2) (6, 5) (5, 3)
  • Question 3: (1, 2)
    drawing of a parallelogram with the following coordinates in the first quadrant: (2,4,) (5,4) (4, 2) (1, 2)

Student Report

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

Extending the Investigation

Have the students create their own Coordinate Quiz questions for one another.


Houghton Mifflin Math Grade 5