March 30, 2012

The Escape from the Textbook! community was started by Henri Picciotto, a mathematics teacher at the Urban School of San Francisco. This is a network of math educators who want to teach innovatively and not be constrained by following the textbook. Teachers can collaborate in an online forum or in person at their quarterly meetings.

I attended the Escape community’s last meeting on March 24 in Berkeley. About twelve other educators and I explored the game SET and how we can use it as a classroom activity.

SET is a deck of cards with four characteristics:
1. Shape: The shapes drawn on the cards are either ovals, diamonds, or squigglies.
2. Number: There are either 1, 2, or 3 of the aforementioned shapes drawn on each card.
3. Color: The shapes are colored either purple, red, or green.
4. Shading: The shapes are either hollow, solid, or shaded with stripes.

The objective is to create a “set” of three cards such that each card differs from the others by the same number and type of characteristics. For example, if a card differs from another in its set by shape and shading, it must differ from the other card by shape and shading, but nothing else. In other words, for each characteristic, all cards must be the same or all cards must be different. Further clarification can be found at the SET website under “How to play” and then “Basic puzzle rules.” Once you understand the rules, try the daily puzzle!

After playing the game in groups, we discussed the following questions.
• How many cards are there in the deck?
• How many possible sets are there in the deck?
• How many different sets can one card be part of?
• How many different sets can two cards be part of?
• What is the largest number of cards you can have that will not contain any set?

See if you can figure them out.

Next, we shared ideas on how we might use SET in the classroom for different grades. SET definitely poses fantastic combinatorics problems, but not too difficult for high school or even middle school students. The last question above is certainly challenging and probably suitable for advanced high school students.

I greatly enjoyed the meeting. It was fun, collaborative, supportive, and stimulating. To learn more about Escape from the Textbook! and to join the online community, visit the website.

One thought on “The Combinatorics of SET

Leave a Reply