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This activity is copyrighted by the AIMS Education Foundation. All rights reserved.
No part of this work may be reproduced or transmitted in any form or by any means—includingphotocopying, taping, or information storage/retrieval systems—except as noted below.
• A person or school purchasing this AIMS activity is hereby granted permission to make up to200 copies of any portion of it, provided these copies will be used for educational purposesand only at one school site.
• Workshop or conference presenters may make one copy of any portion of a purchasedactivity for each participant, with a limit of five activities per workshop or conference session.
• All copies must bear the AIMS Education Foundation copyright information.
AIMS users may purchase unlimited duplication rights for making more than 200 copies, for useat more than one school site, or for use on the Internet. Contact Duplication Rights or visit theAIMS website for complete details.
The triangle is the only polygon that is intrinsically
stable (does not change shape). If one vertex is moved,all its other vertices must move with it. The length of one side cannot be changed without changing at leastone of the others. This unique stability makes thetriangle very useful in construction. It is used to formstable structures and to reinforce unstable shapes.
TopicStructures, Polygons
Key QuestionWhat polygons can be used to make a stable structure?
Learning GoalStudents will build polygons and test them to see whichones are stable. Guiding DocumentsProject 2061 Benchmarks • Some shapes have special properties: Triangular
shapes tend to make structures rigid, and round shapes give the least possible boundary for a given amount of interior area. Shapes can match exactlyor have the same shape in different sizes.
• Design usually requires taking constraints into account. Some constraints, such as gravity or the properties of the materials to be used, are unavoid- able. Other constraints, including economic,political, social, ethical, and aesthetic ones, limit choices.
Management1. Allow 20 to 30 minutes to complete this activity.2. It is best done in groups of two.3. Before doing the activity, it may be necessary to
demonstrate how the beams can be connected witha connector peg to make a movable joint.
4. Students will need to know the names of the sixpolygons used in this activity.
Procedure1. Discuss the Key Question .2. Ask students to take three beams and connectors
pegs to form a triangular shape.3. Have them place the structure so it lies flat on the
table. Tell them to hold one of the beams securelyto the table while they push and pull on the shape todetermine if it is stable (does not change shape).
4. Direct the students to record the number of sides,the name of polygon, and if it is stable or unsta-ble.
5. Have students repeat this procedure after adding
another beam to the polygon. Have them con-tinue adding beams until they have completed theoctagon. (The polygons formed will not be regularsince beams of different lengths are used.)
Connecting Learning1. Which polygons are stable? [triangles]2. Which polygons are not stable? [all but the tri-
angle]3. If you were going to make a structure and did not
want it to be unstable and move, what polygonswould you use in your construction? [triangles]
4. Explain in your own words why you think trianglesare stable.
5. Where have you seen triangles used to make struc-tures more stable?
6. What are you wondering now?
Extensions1. Have students make a list of different structures
they observe around them. Have the students iden-tify the geometric shapes and make inferences asto why the structure is made with this shape.
2. Have students explore ways to make unstablepolygons stable (see Angle Fixer ).
* Reprinted with permission from Principles and Standards for School Mathematics , 2000 by the National Council of Teachersof Mathematics. All rights reserved.