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MathUsing geometry

polygons

SciencePhysical science

forcesstructures

stability

Integrated ProcessesObservingComparing and contrastingCollecting and recording dataGeneralizingApplying

MaterialsLEGO ® elements (per group):

2 1 x 8 beams2 1 x 12 beams4 1 x 16 beams8 connector pegs

Background InformationThe names of the polygons in this activty are:

Sides Name

3 Triangle4 Quadrilateral5 Pentagon6 Hexagon7 Heptagon8 Octagon

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.

NRC Standards • Develop descriptions, explanations, predictions,

and models using evidence.• Use mathematics in all aspects of scientific

inquiry.

NCTM Standards 2000* • Recognize and apply geometric ideas and relation-

ships in areas outside the mathematics classroom,such as art, science, and everyday life

• Collect data using observations, surveys, and experiments

• Represent data using tables and graphs such as line plots, bar graphs,and line graphs

• Recognize and applymathematics in contexts outside of mathematics

BRICK LAYERS II © 2008 AIMS Education Foundatio204



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.




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Connecting Learning

1. Which polygons arestable?

2. Which polygons are notstable?

3. If you were going to make astructure and did not want it tobe unstable and move, what

polygons would you use in yourconstruction?

4. Explain in your own words whyyou think triangles are stable.

5. Where have you seen triangles

used to make structures morestable?

6. What are you wondering now?