Tuesday, May 12, 2015

5/12 Dog + God

I have a lot of interesting observations from math club today. First up, for the warm up I went with some decoding problems:

    D O G                  
+  G O D          
  D E E P

This one we mostly solved together on the whiteboard in order to give everyone a sense for how to do this class of puzzles. I asked everyone to raise their hands if they had an idea what to do next. First came the suggestion that D must be 1 since that's the only value you can get from a carry. Next someone noticed that means G can only be 8 or 9 or there won't be a carry at all. A few moments later there was the idea that either E was 1 or 0 with those values but we had used up the 1 so only zero was left.  Things went fairly quickly from there.

One lesson for me: My handwriting is messy and I should be careful to always read the problem aloud slowly to avoid kids thinking my G's are 6's.

Then I went for the slightly harder one courtesy of fivetriangles:

   A B C D E F               A B C
x                6   and    + D E F
-----------------            ---------
  D E F A B C                9  9 9

The group exercise was very helpful here. Everyone solved the problem within 15 minutes with only a little prompting for some of the later kids on my part. Better yet: I had hit my internal time budget for this section.

I then proceeded to give out the triangle number worksheet I wrote a week ago:

Second lesson for the day: I should have reviewed this one more closely or written some of the answers down originally. As a result I was a bit rusty and had to do more off the cuff recalculations like what is 1 + 2 ... + 685?  than I would have if I had done it last week as intended.

Most kids derived the basic triangle sum number on their own. About a third needed a hint to try regrouping the sums to make them easier.

Another consistent observation I saw was a weakness in notation. I noticed a lot of  samples that looked like : N + 1 x N / 2  missing the parentheses. This didn't seem worth correcting today since my main goal was to walk them through the derivation of the formula.

Also because I started the kids at different times I never regrouped everyone to do the proof without words I had originally intended. That's still pretty neat and worthy of a mention next week.From there most kids made it to 2 or 3 of the problems. If I repeat this next year it could probably be done as the entire activity for the hour.

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