Session 1, Part B:
Building from Directions

In this activity, you will work on both visualization and communicating mathematically.

The National Council of Teachers of Mathematics writes:

Communication is an essential part of mathematics and mathematics education. It is a way of sharing ideas and clarifying understanding. Through communication, ideas become objects of reflection, refinement, discussion, and amendment.... Because mathematics is so often conveyed in symbols, oral and written communication about mathematical ideas is not always recognized as an important part of mathematics education.

 Principles and Standards of School Mathematics, p. 59 Reston, VA: National Council of Teachers of Mathematics, 2000

This activity also works best when done in groups. Go to Note 3 for suggestions for doing the "Building from Directions" activity with a group.

If you are working alone, consider asking a friend or colleague to work with you. Otherwise, print the following final designs (PDF). Put the final designs aside without looking at them. Then begin with the first design description. Follow the instructions to build the described design with pattern blocks, or draw it on a piece of paper. When you are finished, compare your drawing with the final design for this description. Repeat this activity with the second and third designs.

Description 1:

The design looks like a bird with

 • a hexagon body; • a square for the head; • triangles for the beak and tail; and • triangles for the feet.

Description 2:

 • Start with a hexagon. • On each of the three topmost sides of the hexagon, attach a triangle. • On the bottom side of the hexagon, attach a square. • Below the square, attach two more triangles with their vertices touching.

Description 3:

 • Start with a hexagon. Position it so that it has two horizontal sides. • On each of the non-horizontal sides, attach a triangle so that the side of the triangle exactly matches the side of the hexagon. • On the top side of the hexagon, attach a triangle so that the side of the triangle exactly matches the side of the hexagon. • Take a square and place it above the top triangle. It should be placed so that the vertex of the triangle is at the midpoint of a side of the square and the sides of the square are horizontal and vertical. • On each of the two top vertices of the square, attach a triangle. Place each triangle so that the vertex of the square is at the midpoint of the side of the triangle and the side of the triangle makes 45° angles with the two sides of the square it touches.

Problem B1

When you were building from the given descriptions, what pieces were clear, and what pieces were unclear? What elements of the descriptions made it possible for you to picture (or not to picture) what was described and recreate it?

 Problem B2 How closely did your designs match the target? Describe any differences between them and why you think they occurred.

 Video Segment In this video segment, the participants discuss how they described their geometric designs. Watch this segment after you have completed Part B. What kinds of words did the participants use in their descriptions? Which descriptions were precise? Which descriptions were less precise? If you are using a VCR, you can find this segment on the session video approximately 9 minutes and 17 seconds after the Annenberg Media logo.

 Principles and Standards of School Mathematics (Reston, VA: National Council of Teachers of Mathematics, 2000), 59. Reproduced with permission from the publisher. Copyright © 2000 by the National Council of Teachers of Mathematics. All rights reserved.

Next > Part C: Folding Paper

 Session 1: Index | Notes | Solutions | Video