Logic and Reasoning

Posted by: rant84 on: February 3, 2010

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Eggs in the Basket (http://www.folj.com/puzzles/)

It is difficult for me to tell you how I solved this problem because I have done it before in another situation. I do know that with students I would probably tell them if they are struggling that they should think outside of the box. Sometimes we tend to try and make situations harder to solve than they need to be.

Manhole Cover  (http://www.mycoted.com/Manhole_Covers)

The problem made me think more about shapes. At first I thought the circle due to the fact that it would be faster to take off and replace. Without corners the shape would fit easier, doesn’t require turning or aligning sides. I also thought about ease of moving, rolling. Once I looked at the answer I felt foolish for not even thinking about the lid falling into the hole.

I think the “Manhole Cover” question is at the analysis level. Analysis requires that the person uses problem solving skills to determine the answer or solution to the situation. I also see this problem as an application. In order to solve the problem you must apply information that is known about the shapes (circle and square). It can also be synthesis because a unique solution may be expressed in verbal form or with a physical object.

When presenting this problem to my students I would present it while we were in a geometry unit. I would make sure that we had already discussed the fact that the diagonal of a square is longer than the sides. Once I know that we have covered all of these concepts I would feel comfortable giving the problem to the students. I would give the students a few minutes to work on the problem individually and then I would allow them to partner up and discuss the problem. As the students are discussing the problem I would walk around to listen to their conversations. As I am listening to their conversations I would ask questions such as

1) Prove to me that the _________ is the best solution.

2)  Compare the traits/characteristics of the two shapes.

After an allotted amount of time I would ask for someone to share their response as long as they explain mathematically why their solution is correct. Once the solution has been given I would allow the other students to ask questions for their own clarification. If time allows I might ask them to 3) Create a list of other shapes that would and would not be appropriate for manhole covers.