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Teaching math: A question that worked well

December 4, 2009 am31 12:19 am

Algebra 2 and Trig this year are a little tricky in NY State. How do you teach a rich course, but also prepare kids for a state test? If you’ve never seen the state test? If you suspect the test will cover way too many topics, and do so poorly? And did I say, also teach a rich course?

So, this teacher squeezes in extras. Go off topic, and onto other topics of value. Challenge questions that preview what they’ll see in a few weeks. And better, challenge questions that help their analytical skills, without practicing current topics (math class is for thinking and doing and performing!). A little extra graphing to tie topics together (more on that, later. Who’s going to teach me to take screen shots from the TI?)

And some days, I just squeeze so I have time for something else. And yesterday’s lesson, how to handle a + n\sqrt{b}, not a killer for squeezing. I threw what could have been a quickie worksheet on the board:

Model A:
Add: (4 - 5\sqrt{10}) + (7 + \sqrt{10})
11 - 4\sqrt{10}

Model B:
Multiply and simplify: (4 + 3\sqrt{7}) (5 + 2\sqrt{7})
(4(5 + 2\sqrt{7}) + 3\sqrt{7}(5 + 2\sqrt{7})
20 + 8\sqrt{7} + 15\sqrt{7}+6(7)
62 + 23\sqrt{7}

Try:
A2. (1 + \sqrt{8}) + (5 - \sqrt{2})
A2. 11 - (11 + \sqrt{10})

B1.  (8 - \sqrt{6})(5 + \sqrt{6})
B2.  (3 + \sqrt{10})^2
B3.  (3 + \sqrt{5})(3 - 3\sqrt{5})
B4.  (5 - \sqrt{2})(5 + \sqrt{2})
B5.  (6 + \sqrt{5})(2 - \sqrt{20})

So they’re buzzing. I’m checking homework and walking around a bit. And I decide to use a question I’ve played with a little:

“What’s a question that someone else might get wrong?” followed by “Explain.” And then I got another kid to comment, or to answer the question, or to explain how to avoid the error. And back for another “question that someone else might get wrong?”

I ran, back to back, two of the best five minute discussions I have had all year.

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2 Comments leave one →
  1. December 4, 2009 am31 8:03 am 8:03 am

    I LOVE it when that happens!! And the screen shot thing is easy. You just need the TI Connect software that you can download from their website and your USB cord. I taught myself and I’m no technology whiz.

  2. December 4, 2009 am31 10:34 am 10:34 am

    Or… there’s a TI emulator (software that we got a free copy of somehow) that I was using, and so I could do screen shots, and also record steps, using that. I could show you some of what I made using that. Just email me.

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