Explorations in Mathematics Activities (or how to stay sane after the AP exam)

Here is one of the deepest truths about me as an AP teacher:

I can't convince myself to show movies every day. 

Let's be clear: I don't care if YOU are one of those teachers, I really don't! I often walk by your classroom and gaze in, longingly, at the students who are quietly on their phones as you grade papers and get s*** done in the dark corner with 21 playing on your Smart Board. I want to be you....I just can't do it.  

I do a bunch of different things after the exam, including teaching some Calc II topics like Integration by Parts and Partial Fractions.  My biggest successes have come from trying to dive into some upper level mathematics and fun logic puzzles in a fun and non-intimidating way. 

I'm gathering a collection of all the activities I use here, feel free to steal or modify any of them! I will add more as we progress- more to come!

The Josephus Problem

The Zebra Puzzle





The Four Color Theorem


The Collatz Conjecture

The Lagarias Problem

Others I've used in the past but haven't formally written up. Many of these are adapted from Numberphile videos. I'll work on writing up what I've done in the past!

The Secretary Problem & Optimal Stopping

Discrete and Bounded Envy Free Cake Cutting Protocol

Card Tricks & Modular Arithmetic

Optimal Shoe Tying Method & Knot Theory

When to Shoot In a Duel & Game Theory

The Imitation Game & Cryptography