1. I can construct an ellipse using only compass and straightedge tools in Geogebra. It took much longer to figure it out than I originally anticipated.
2. There is an app called "Plickers" that can be used as a low-cost quick response system that is similar to clickers. Each student gets a paper with a QR-like code on it and holds it in the air a certain way to submit their answer. The teacher then uses their phone or ipad to scan the room and collect the data. I haven't used it yet, but it sounds promising. Check it out: https://plickers.com/
3. There are many ways to check for student understanding, but the most important part is that it is planned and purposeful. One method is a variation whiteboard speed dating where students each receive their own problem, become an expert in that problem, then exchange problems with a partner. In case there is an issue, they can just ask their partner, the expert, for help. Other methods include two truths and a lie, or simple problems that target one conceptual understanding. Here's the original white board speed dating: https://kellyoshea.wordpress.com/2012/01/22/whiteboard-speed-dating/
4. If you're a farmer that has a scale with two sides, you can maximize the amount of corn you can weigh by using only weights that follow the powers of three: 1, 3, 9, 27, etc. This came from a solution to a problem posed during the "Pizza and Problem Solving" session. Oh, and I have the tendency to eat too much pizza.
5. Line dancing can be fun.