Favorite Problem Solving Activities

My absolute favorite problem solving activities are the ones where my students have challenged me to learn new mathematics. I associate some with a particular group of students, who I often remember years later. Other activities are favorites because they reliably engage and challenge students, they’re interesting, and there are many ways to solve them.

Clock Buddies — A Round Robin Tournament Activity

This is a great first day of class activity, which works well with math phobic students (I use it in a math for elementary teachers class). Students make a list 1:00, 2:00, etc. on a piece of paper — however many times I assign — and then they have to make an appointment with a different student in each slot. Students move around the room making appointments and learning each other’s names. If there are an odd number of students, I passively participate, accepting appointments whenever students come and ask me.

At some point a student or a few students will announce that they are done, and I tell them they aren’t done until everyone’s schedule is filled in. It’s an interesting question to figure out a good number of appointments to give them so that they will get stuck, but not overwhelmed; I usually go for a few more than half the number of students (12 for a class of 20). Read more >>

Pool Table Math with Excel (includes a Video)

This is a classic problem solving activity that I first saw many years ago in Mathematics: A Human Endeavor.   The NCTM has a nice applet to test cases one at a time.  

Since I like playing with Excel and trying to extend what it can do, I wrote a spreadsheet to represent the problem.  The end result is much better than expected — this representation uses a slider to show many cases in a short period of time, and with it I noticed patterns that I never had before (e.g. if you start at (1,0) on a rectangle whose sides have GCD=2, you get a loop that goes through all squares). Read more >>

The Biggest Product

I start this activity by handing out buckets of tiles (any small objects will do) and asking students to take 10. They can sort their ten tiles into any number of piles, and their “prize” is the product of the sizes of their piles — so if they sort them into piles of size 5 and 5; their prize is 5 x 5, and if they sort into piles of sizes 1, 2, 3, and 4, their prize is 1 x 2 x 3 x 4. The goal, of course, is to get the highest possible prize, and then to generalize for other numbers of tiles. Read more >>

The Handshake Problem

The handshake problem is an old chestnut — if everyone in the room shook hands with everyone else, how many handshakes would there be? Then generalize. What I have to add to teaching the problem is a handout (doc version, pdf version) with different (fictional, but based on reality) students’ strategies for solving the problem. This handout is good for homework after students have worked on the problems themselves and listened to their classmates’ strategies. Read more >>