Angleatron Failure and Distance Formula Game Success

I taught the lesson on angleatrons that I previously posted about and it was not very successful at all.  I'm reluctant to write about my failures because I'm already the type of person who doubts everything I do and even my most successful lessons leave me feeling like I'm not the teacher I wish I was.  This is also why I'm a terrible blogger.  In my most insecure moments, I can't help but compare my teaching to these fantastic teachers I so admire and aspire to me more like.  I hope the fact that I am constantly striving to be better makes me a better teacher, but it also makes me very uncomfortable in my own skin much of the time.

The lesson was unsuccessful for several reasons beyond my control.  My speakers broke partway through showing the video so the students couldn't hear Vi Hart's narrations.  I then tried to paraphrase what she was doing with paper folding but students grew bored watching a soundless video.  This made me rush through the video to move on to the activity, but then students were confused about how to do the paper folding.  Their confusion reinforced my reasoning behind doing the activity because if students couldn't grasp the idea that the corner of their paper can be used as a 90 degree angle, then they really did need to practice basic angle drawings.  About half the class did take off doing drawings and folding angles.  A couple of them produced really beautiful designs and I think all of them did grasp what 90 degree and 45 degree angles are supposed to look like.  The other half of the class adamantly refused to draw, or refused to draw precisely (sloppily drawing 90 degree angles that looked more like they were 100 degrees because they refused to use the corner of their papers to guide their drawings.)  Their reluctance and difficulty only convinced me that they did need to practice, but the activity didn't work for the students who needed the practice.

I did try some other games this past week and they were much more successful.  For me, the simpler the game, the easier it is for me to pull off because I have a very minimalist classroom (I have to buy all my own supplies, the students have tiny desks and we don't have a white board, only a smart board which allows only one student to write on it at a time.)  I came up with a game to practice the distance formula which worked beautifully mostly because it was so simple.  First, I had to bribe the students to play because playing games involves more thinking than taking notes and they actually wanted me to keep lecturing so that they could passively copy/ sleep.  Then I asked them to group into threes and told them they were competing against their group members to convince them to work with people other than their best friends.  Finally, I just displayed four numbers on the smart board.  The students could rearrange the numbers into two ordered pairs however they wanted and could add negatives if they wanted.  The person in their group that was able to organize the ordered pairs in such a way as to maximize distance won and earned a candy.  I started with 0,0, 4, 12.  Then gave them 2,3,4,5.  Then started giving them bigger numbers.  At first the students just paired the first two digits and the last two digits and used the distance formula.  But after a round or two they started figuring out how to add negatives and rearrange the bigger numbers with smaller numbers to get larger distances.  They also were doing a good job of checking each other's work because they only earned candy if they did the calculations correctly.  By the end of the game, every student had figured out how to maximize distance and they were all tying and I was going bankrupt on Jolly Ranchers.  My favorite part was when one person in a group announced their largest distance was 13.2 and students from a different group came over and clustered around asking the person from the first group how they'd gotten such a big distance. I think the game worked very nicely because it was simple, strategic, competitive but not so competitive that students who were "losing" became disheartened.  By the end everyone was winning.

I didn't like the game because I don't like the distance formula.  I would much rather students use the Pythagorean theorem enough that they could then extrapolate the distance formula by picturing triangles on the coordinate plane without needing to graph.  Unfortunately I just didn't have the time to reinforce this method of calculating distance so I caved and taught them the distance formula (but at least I did show them how it came from the Pythagorean theorem, though half my class fell asleep or glazed over when I tried to show the derivation to them.  I've tried having them do the derivation themselves but their algebra skills are too weak.)  At least though, they did do some critical thinking in terms of figuring out how to maximize distance.  That was the saving grace of this game.