I’ve been reading Out of the Labyrinth: Setting Mathematics Free, by Robert and Ellen Kaplan, who are the founders of “the Math Circle.” As I understand it a math circle is where you get a bunch of people together, ask a couple of provocative questions to get them thinking, and then get out of the way and let them create mathematics.
I decided that I would try something akin to their math circle with my kids. I settled on using the opening example from the book: draw a number line with 0 and 1 labeled, ask if there are any other numbers in there, and step back to see what numbers the kids can find. The idea is that they start marking fractions, get comfortable with those and eventually come up with an irrational number.
A was easily distracted tonight. She kept wanting to put in numbers beyond 1. B put in 1/2, then 1/4 in approximately hte right places. Later he moved them so that he could fit more numbers in. He ended up with 1/2, 1/3, 1/4, etc. down to 1/13 spaced approximately evenly. A added 1/14, 1/15, 1/16. I asked how many more there were. ” I can’t say how many. Lots more. Infinity many.” Is what B replied. He ended up writing “infinitely many numbers like these” between 1/16 and 0. We also ended up with 1/1 somewhere between 1 and 1/2. For now I’m letting that persist until they figure out that its the same thing as 1. A wanted to put in 0/2, but B told here that that was the same thing as 0.
A also said that one thousand two hundred thirty four was her favorite number and wrote it out: 1234, with a box around it.
Next week we’ll pull the number line out again and since 0 has so many friends next to it, I’ll ask whether 1 has any.