1. When sand, snow, or any other loose material is piled on top of a polygon, the pile will have ridges equidistant from the nearest sides (also known as angle bisectors), and peaks at the center of an inscribed circle (also known as the incenter).
2. Written feedback is often difficult to write well and not read by students. Carol Dweck’s famous study on growth mindset suggests that we should not score or evaluate student’s work, but instead give specific feedback that relates to their effort or methodology on a particular problem. Such feedback should also move a student to think or reconsider their error rather than giving hints or being evaluative. It may even be useful to give feedback on correct answers to extend student thinking. Research has shown that these techniques increase desire to attempt difficult tasks, allow students o recover more quickly after setbacks, and increase academic achievement in the long run. Of course, the source: http://mindsetonline.com/
3. James Tanton has a series of eight books called Thinking Mathematics that run from basic arithmetic through AP Calculus and AP Statistics. My roommate Matt describes it as, “A bit long, but very easily accessible. He provides many examples and develops concepts intuitively before putting a name and a formal definition on them.” He also publishes curriculum letters monthly. If your interested, take a look at his philosophy: http://www.jamestanton.com/
4. Collaborative Mathematics is a website by Jason Ermer that posts mathematical video challenges and encourages users to discuss their successes and failures both in chat form and in video response form. These are great problems for teachers and students alike. As Ermer puts it, "one of the goals of Collaborative Mathematics is to help cultivate a productive attitude toward challenging problems: one of creativity, resourcefulness, self-confidence, and perseverance." Take a look here: http://www.collaborativemathematics.org/
5. Just three sets of one minute planks before lunch will get you ripped abs in no time! Or at least, that’s what Samantha and Alice told me.
6. (Extra Credit) The Uinta Mountains in North East Utah are beautiful. I went backpacking for two nights with Matt; pictures are below.