One was on the history of pi, and the presenter, Janet Teeguarden, set it up as a game of Risk (her own version). We got a sheet with 25 multiple choice and short answer questions, and put our answers down. As she presented, she'd stop at each question and ask us to put down how many points we wanted to risk. We started with 100 points, and each question allowed us to increase that if we were right. One person was sure of his answers on ten questions and didn't try any others, so he got 102,400 points. I was only sure on a few answers, but tried a bunch. I got up over 10,000 points. The game kept me listening much more intently to a presentation that I might have mildly enjoyed otherwise. (And I'm not good at listening to presentations that don't have audience participation, so I might have drifted away, even though it was interesting.)
Although this presenter used Powerpoint for her presentation and the game (it made a cool swooshing noise as each answer was shown), I think I could do something similar with just a worksheet and the board. I think I'll try this when we're reviewing for the final exam. I could give them a practice final to do as homework, and then play Risk with them as I go over it.
[Edited to add...] Here are the first few questions of the 'Risk Your Knowledge of Pi' game:
100 1. What is the formal definition of pi?
2. In what book will you find the following? “Also he made a molten sea ten cubits from brim to brim, round in compass, … and a line of thirty cubits did compass it round about.”
3. What ancient Greek mathematician determined that 3 10/71 < pi < 3 1/7?
4. He used circles with inscribed and circumscribed polygons to make this estimate. How many sides did his final polygons have?
I risked 100 on question 1, got it right, and entered a total of 200. I risked all 200 on question 2, got it right and had 400. I think I risked all 400 on question 3 and got it right, for a total of 800. I risked 50 on question 4, and got it wrong, for a total of 750.
The next session was something about improving antiquated word problems. The presenter (a textbook author) talked about how silly some problems are, and how he tweaks them to make them more relevant. He said: "Functions are the heart of intermediate algebra." I've been looking for a way to tie all the topics together, and thought that might work for me. I'm excited to look at the text again, and see whether a function focus would tie most of it together.
The problem we worked longest on started out something like:
The 10,000 seat stadium will sell out for the rock concert. The better seats are $65 and the cheaper seats are $45. How many of each ticket type must be sold to bring in revenues of $500,000?
Silly question. Why do we want that revenue in particular? If we change it to a function question, it becomes more interesting: Create a function that takes number of
- Graph this function.
- What does the y-intercept represent?
- What does the slope represent? (Hey, the slope is negative. More tickets means less revenue? How's that possible?)
- What x and y values make sense?
On Thursday (backing up), I went to a fun workshop on using the abacus. Now I'd like to spend some time trying it out with kids.
I also visited a math circle on Sunday morning and had a great talk with one of the presenters afterward, just before I caught my plane home. The woman I sat next to on the plane liked to talk, and that made the time go faster for the first half. After 3 hours, she'd run out of stories and neither of us was looking forward to the 3 hours left to go. I offered to show her some math, and she said sure. I showed her binary numbers by starting with a magic trick. (Hey, I think I have to revise my post on binary. I left that out!) You normally start with 5 cards, each showing some of the numbers from 1 to 31. I just wrote them on my paper. She got into it, and I showed her a way to subtract by adding (decimal first, then binary). Our flight wasn't over yet, and she said she liked algebra, so I showed her some of the Pythagorean triple patterns. We were landing as we finished that up. Thank you, Helen, for being an eager student - you made my flight so much more fun!
It's good to be back home, and I'm pumped up for the last few weeks of the semester.