Scott Farrar:

But we also convey something a little dangerous: that the math expert (the teacher) has a trick, and knowing the trick solves problems. Does this lead the student to construe math as the magic spellbook that must be memorized?

I think we’re doing the opposite here.

I typically play this game to begin with for something like a “free homework pass.” As you can guess, this is modular arithmetic where you need to get to a multiple of (X+1) +1. When you first start out, you can randomly subtract things as a teacher to try to stimulate different student thinking. I typically pick the first interval to be 1-5 so “key numbers” of the game are 1,7,13,19,25 and 31. I always ask the student if they want to go first of if they want me to.

It typically takes a few times playing the game before students really catch on, but it is great to see them create ideas and want to test their theory against the teacher. It is also great to see them realize their theory is wrong, and try to create a new one while playing the game. I typically get numerous requests to play the game during the year, and I will let their thinking cool down for a month or two before accepting the challenge again- but I normally throw in the twist that I pick the student to play against. It keeps them all on their toes and accountable for remembering the mathematics behind the game.

Based on “The Best Card Trick?” from this site (http://nrich.maths.org/1479), I created a Geogebra file to be projected on the Smart Board, and I tell my students to take five cards. Then I drag for cards in the proper order on the board, and computer can guess the fifth one reading my mind….

http://ggbtu.be/m63806

I made a video of this, but I did it in Dutch, so the bonus is that you learn how to count in Dutch: een, twee, drie, vier, vijf, zes, zeven, acht, negen, tien ;-)

Always a bunch of students figure out the trick, but the hardest part is writing the equation. Every year I have students totally stumped writing x+y+a+b. It’s really a reframing for them to think about the *relationship* between the numbers and express that algebraically.

Finally I ask them to write a rule for three consecutive numbers, but I don’t say which number you should find and inevitably someone has a rule for finding the first number and someone has one for finding the middle number. I love that!