Monday, May 7, 2012

All Tied Up - a Geometry Classic Challenge

For exercise, a prisoner was chained  to one corner (lower) of a 10 ft concrete cube located in the center of the yard. If the chain was 16 ft long and was not obstructed except for the cube, over how many sq ft of ground could he roam?

Ans: 210π sq ft

1.  Give the students the diagram or have them draw it themselves?
2.  Have them work individually or in groups?
3. How much time would you give them to work on this in class?
4. After discussion, how would you know if they 'got' it? Assessment?
5. Makes more sense to give them a variant of the problem for HW or ask them to design their own and solve it?

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Kathleen Hodik said...

I like this problem. I think I would not give the students a diagram to start with. I teach Honors Geometry so I would want to see them work it out with just the basic information provided.

Dave Marain said...

Thanks for the thoughtful reply, Kathleen.

An even bigger issue for me is:
What strategies would one try with a non-honors class?

Ask intro questions like, "If the prisoner were only chained to a spike in the middle of the yard, would it be easier? What would the region look like then?"
Have students make mini-models of the problem in class or for homework with appropriate incentives?
Working in groups of 2 or 3?
What kinds of hints/cues to provide and when?
Would most teachers be receptive to what I am asking or suggesting?
Would many math teachers think it folly to even attempt a problem with complexities?