Wednesday, December 10, 2014

12/9 Prime Climb

I've already tried a few different games out and they've always worked really well especially for drawing out kids who don't raise their hands as often. However, I've never used a honest to god board game. This week, Prime Climb, finally arrived in the mail and it seemed like a natural to test it in the group setting. Before starting I roughly thought that we'd review last weeks challenge problem, play 3 parallel games at once for maybe a half hour, and then introduce next week's challenge problem. I wasn't sure if that left a gap so I decided to talk about multiplying variable expressions and deriving the mental math trick of  using  (x + n)*(x-n)  == x^2 - n^2 to solve some problems as a backup to fill any extra time.

As usual, only some of the kids had solved the problem. See: November. The problem as defined is fairly trivially solvable via guessing and checking. Just start at 1 see if the answer works and by the time you reach 3 you're done so I asked a followup question: what if the side length was 16?  This requires fractional answers and more understanding of the problem structure. My hope was solving the easier version would be insightful for everyone.

With a little prompting that you could guess and check I guided everyone who hadn't already done so to the easy solution in a few minutes and then had the kids try to figure out the structure to solve the general problem. In the meantime I labeled the diagram with some x's for the missing portions. Adding 3x on the vertical would hopefully trigger some more thinking. Bingo, one girl stood up and declared how you needed to divide the length by five. I labelled some more and put the 3x on the horizonal side as well. When asked everyone could now say that you just needed to solve the equation 15 = 5x and changing the constant did not pose any further troubles.

We then broke out the raisin snacks and the new Prime Climb games. It turns out I had underestimated average game time based on my samples at home with my son. In groups of 3 the game actually took the entire rest of the hour. It was a total success though. All the kids were engaged, the boys in particular took to bumping each others pawns back to start. It was interesting to me as well, because the kids were trying to do calculations like is 24 * 7 < 101 and I received a peppering of questions asking me to do the mental math for them. I ended up talking them through the several examples like that. I'm going to need to find ways to subtly encourage more mental calculations over following weeks. Maybe I can find/invent a mental math tournament that we can warm up with.

Next week's challenge: 

This one is a word problem which I haven't really done yet. Its based on an AoPS one I saw that had a interesting trick to reach the solution.

Two football teams played a game with a combined score of 65.  All the points were scored via 3 point field goals or 7 point touchdowns.  One team scored 2 more touchdowns and 1 less field goal than the other team. What was the final score?

1 comment:

  1. Seems like a lot of field goals for an actual game, no?

    This doesn't tell us the variation from game to game, but is suggestive:
    Team stats field goals per game

    This link (average NFL game) paints a similar picture and also offers a new topic for exploration: why is 29 a much less frequent team score than 28?