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What It Is (continued)
For the next session, introduce the cantilever. A cantilever is a projecting
beam or other structure which is supported at only one end (e.g., awnings,
flagpoles, tree limbs). Challenge your students to build a cantilever
out from a wall or out from a tabletop. Use the same rules for building
as above with the following addition:
Challenge the students to do one of the following:
These challenges are scaled down versions of the Garden Poles--Building Out activities with all of the lengths and weights divided by six. Discuss with your students whether or not they think this is the proper way to scale down the challenge. The work on two scales is most instructive if student groups work on the same challenge on both the large and small scale. If they build on the small scale first, they could start on the large scale by trying to replicate their design. This is very instructive as it is usually impossible to replicate the small scale design exactly.
As with the garden poles, choose the difficulty of the challenge based on the age and level of building skills of your students. It is especially important in this activity to be sensitive to the issue of creating winners and losers. Student groups put a lot of time and effort into these structures and may feel bad if their structure doesn't measure up. Setting a challenge level which most students can meet and allowing them to go beyond this level is a useful strategy. Look for various criteria to judge buildings, including the degree of risk, stability, and innovation.
The question of rules and what is fair inevitably arises in these challenges. Typical questions are, "How do you measure distance from the wall or tabletop?" and "Are the structures allowed to droop, and if so, how much?" Setting rules by class discussion enhances sensitivity to these problems. "Where is it fair to hang the weights?" is another question that often arises. The place where weights are hung is critical for cantilevers. When we hear students protest "it's not fair" when a group hangs their weight in close to the wall or table, we know that they understand an important aspect of torque.
