## Friday, July 16, 2010

### Student-Art Combinatorics

Pretty momentous: Yesterday, after Geoff's morning run, he came back in and said nonchalantly while laying out his towel for doing situps, "Happy 1 year in El Salvador!" --Wow! He's totally right!

On a funny expat note, just the other night when I was making tea for the both of us, I had asked Geoff what type of tea he would like. For a brief moment, his face went blank and he mumbled after a bit of hesitation, "Manzanilla." I started to giggle because I realized then that he had remembered the Spanish word but not the English word for chamomile!

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I don't teach combinatorics, but a fun lesson idea occurred to me while I was skimming through a discussion online, and I thought I'd sketch it up for the possible benefit of others.

The idea involves setting aside a day when the kids would each create/bring in a full-body, colored cartoon drawing of a person, and we would cut them into three parts (head, torso + arms, legs), and make three piles in the front of class, one pile for each "body part".

The kids would then each randomly pick a head, a torso, and a pair of legs out of the respective piles, and paste them together on a page, no matter how funny it looks, and write about the combinations / probabilities involved in this problem:

Assuming that no student has yet gone up to pick from the piles...

• How many combinations of body parts are possible?

• What are the chances that you would pick out an "entire" (contiguous) paper person, with all three parts that belong together?

• What are the chances that your paper person would have at least one mismatching body part?

• What are the chances that your paper person would have exactly one mismatching body part?

• What are the chances that you would get all three parts of your own original paper person back?

• Let's say that Jenny is the first student to go up to the front of class to pick out three parts at random, and James is the second. Explain why and how the results of Jenny's paper person might impact the probability of James to then pick three parts that belong together.

• Compare the chances of piecing together an "entire" (contiguous) paper person for the first student of the class (Jenny) vs. the last student of the class (you). If you go last, will it be "unfair"?*

*This question is my favorite, because it sounds deceptively simple but it begs an intuitive wrestling between what is commonly perceived as unfairness ("I am the last person to go up; by the time it gets to me, I've got no influence over whether I can piece together a contiguous person!") and a different story told using numbers (All participants, regardless of eventual order, had an equal chance of winning prior to the picking).

It could be a fun and light activity, while still keeping the rigors of a combinatoric lesson -- and it may also contribute towards decorating your classroom! ;) Obviously, the kids would write an explanation for each question in addition to showing the math work...

--But, sadly, I don't currently teach combinatorics, so if you have stumbled upon this entry and happen to enjoy this idea and decide to implement it in your (future?) classroom, I would love to hear how it goes! Let me live vicariously through you.

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Off to the highlands of Peru! WOOHOO. :) See you back here in 10 days or so.