I just finished the class - last period of the last day before Thanksgiving break, right after a special double-length lunch with music, dancing, and staff v. student volleyball and soccer. Given all that, the class went amazingly well. They were wound up at first and were having "focus problems" (my favorite euphamism), but when we got to the competition, they really got down to work. So the lesson..

After reviewing the homework, students did a warm-up of solving word problems with 2x2 systems. They still have trouble with converting from verbal statements to equations for things like "my second number is 3 more than 6 times my first number". To help them through those, I ask them to try a specific numeric example (reducing the level of abstraction by that step seems to help them see the relationship). I say "imagine my number is 10 - what is 3 more than 6 times 10?" They say 63, and then I ask them how they figured that out. That is usually enough to get them to write out the equation.

After this, we worked together on a word problem that uses a 3x3 system as its model. In this example, the last equation was in a different form (where one variable was already isolated), and they saw how substitution would let them create a 2x2 system, instead of just using linear combination as we had been doing. I'm trying to get them to be as flexible as possible in their problem solving; there are different methods, and you should pick the method that applies best to the given problem.

This left about 35 minutes for students to get into groups of 3 and do a word problem relay. Each group got problem 1 to start with; when they solved it, they brought it to the front for me to check. If they were correct, they got problem 2, and so on. There were 4 problems - I told them they'd get 5 bonus homework points if they solved all 4. At this point, most of the students worked really well (except for one chatty group) and most groups got to the third or forth problem, but none solved the forth in time.

For homework, I gave them a review packet for the Midterm, which will be next Tuesday, when they return. You can imagine how excited they were about that! It's five pages long, and I suggested that they do one per day to keep their math brains running.

It was a nice day today overall, and this little break always comes just in time to keep us all (teachers and students) sane and friendly.

A beautiful combinatorics argument

18 hours ago

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