Vectors, Proof, and Various Other Rabbit Holes


I’m still waiting for my lab supplies to come in so I continued my unit on vector addition. Since students did so good last time with the graphical addition of vectors and the topographic map activity we did, I decided that we could move on to adding vectors using components, trig, Pythagorus, etc. This was a tough topic to teach primarily due to the differing mathematical background of my students — some are currently enrolled in college trig and others have yet to take geometry.

However, when we were discussing how to solve triangles something magical happened.

As I was walking a couple of students through the process of solving a triangle, one of my highly math-literate students asked HOW the first person came up with that. Several students actually began to discuss the question — some more serious than others, but nevertheless I was thrilled. He might have been slightly inspired by an off-topic discussion we had had earlier about the origins of the word “hypotenuse”.

A million thoughts were running through my head about how we could turn this into an awesome learning experience, but I never could quite figure out the best response. So I did what any under-paid state employee would do, played a video. .

Some enjoyed the video, others didn’t, but after it we got into some pretty deep discussions. I showed them a few of the proofs I think are cool (Cantor’s Diagonal ArgumentThe Square Root of 2 is IrrationalInfinitude of Primes, etc.); sadly, the one they found the most intriguing was .999… = 1 which is somewhat interesting, just not as much as the others, in my opinion. They also had some fun with QED, so much so that I had to get the letters put up on the wall. It has become somewhat of a class motto. I was reminded of this XKCD comic but kept that to myself.

I was so inspired by this that I wanted my geometry class to jump in on the fun as well. So I went home and did some research and ultimately created this for my geometry classes (NOTE: I just googled “Easy Sudoku Puzzle jpgs” for the puzzle shown and never worked it since the real goal of the activity is for students to practice proving things. I later realized that the puzzle is impossible because there are already two 1’s in one of the columns. I just told students to move the one on the bottom over a spot and a couple of them managed to work it fine) It did alright with the class my upper level kids, but most of my lower level kids didn’t even know the rules of Sudoku. All-in-all I like the activity for an upper-level class of math or science, but the lower level kids will need some serious scaffolding.

##setbacks ##rainydayactivity


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