Friday, August 21, 2009

Riddles and Reasoning and Math Teachers at Play 14

When is a carnival full of problems? Besides like every circus movie ever?

The new carnival is up, hosted this week by Susan Van Hattum at Math Mama Writes.

My favorites include the Math Recreation post on origami and a clever lesson using statistics to catch cheaters which also uses bad jokes.

The bad jokes thing reminded me of a lesson I use with riddles about reasoning.

Reasoning and Riddles
The framework David Coffey and I use for reasoning, based on the NCTM process standards of course, is:
Mathematicians are engaged in reasoning when they:
-Make sense of something (sorting, understanding a problem, interpreting a representation)
-Make a conjecture about something (initial answer, plan of attack, possible relationship)
-Make an argument for something (justification, verification, proof)

I then give the students a list of riddles and ask them to figure out the answers. As we look at their answers, and more importantly, how they got their answers, they generate lots of examples of making sense, making conjectures, and arguing for why their answer fits.
(General riddles and Halloween riddles are posted at my faculty page. Click the links for the pdfs.)

We then explore a more math-centric riddle (it's usually a geometry class):

Four Sided Riddle

1) Taking the clues for a mystery shape in order, put a checkmark next to the last clue you need to know exactly the type of shape that the mystery shape is. Then explain your answer.
1. It is a closed figure with four straight sides.
2. It has two long sides and two short sides.
3. The two long sides are the same length.
4. The two short sides are the same length.
5. One of the angles is larger than one of the other angles.
6. Two of the angles are the same size.
7. The other two angles are the same size.
8. The two long sides are parallel.
9. The two short sides are parallel.

2) Using one less clue than your answer to number (1), draw a shape that satisfies all those clues BUT is different than the mystery shape, or explain why this cannot be done.

There is also a nice Van Hiele connection here as students at different levels approach this task very differently.

Dinosaur Comics are perfectly qwantzian. Click the cartoon to see it full size, click the link to get to the web comic's home. (T-Rex does not always subscribe to human norms of taste and good form, obviously, so, at your own risk.)

Eventually I'll work all my favorite webcomics in here.

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