math them

As an undergraduate, I stumbled upon Jim Propp's Self-Referential Aptitude Test and spent a couple hours working on it. That experience stuck with me and I have since made smaller-scale versions and variants for students. This is a hard activity to pin down to an age group, but it can skew a little more abstract and occasionally arithmetic, so I'd peg it around 7th grade and up but have definitely had some luck with advanced elementary school children.

This problem was sparked by a question asked by a student in the JRMF Community Math Circle featuring Colored Loops, an activity based on Gord Hamilton's Stirring Paint.   While it can be used an an extension to Colored Loops, I'll present it as a stand-alone activity.

In this activity, students design bingo cards based on their impressions of which sums will come up first and most often when two dice are rolled repeatedly.  This activity is a nice introduction to discrete probability distributions and some of their conceptual pitfalls.