Here’s what I did. I taught this lesson today, and I had mixed results. For the record I’d say that kids in the second group that got the lesson where really into it, whereas the first group gave it a “so-what-else-did-you-cook-up-for-us?” rating. I started this post thinking I’d tell you what I did, but I kept thinking things like “if I’d only done this it would have gone better,” so here’s the if-I-would-have-done-this-then-it-would-have-gone-better version of what I did today. I know, too much hyphenation for one day.
At the end of this lesson, students will be able to
- Work backwards to solve a complex problem
- Use patterns and inductive reasoning to extrapolate data (logo positions on a large grid)
- Apply software to investigate (potentially) algebraic relationships
- Construct a rule for the corners problem
Setup: Show kids office clip #1 (see post). Then open up the 5 min. gridded version and play that in the background while acting like you’re trying to give directions. Get the kids to make guesses about whether or not it will hit a corner. Then after they’re done shouting about the epic moment at 1:43 (.333) when it does, get them to predict the next corner. It doesn’t happen. At least, not in the 5 minutes that Dan provided.
Distribute copies of the warm up below
As kids graduate from this, ask them if they’d like a bigger version (the desired answer being: “YES!”). Then hand them the first page of this sheet.
The answer here being that it doesn’t matter all starting squares result in a corner hit after varying numbers of steps. This can be shown with the software or through a pattern that many kids will notice after they have traced out sufficient numbers of steps. Talk about the patterns, ask them if they have any theories about how this might work on grids of varying dimension.
If you have access to a set of Mac’s you’re in luck. Ask the students if they have developed any general theories about these types of problems. How does the path to the corner depend on the starting location and grid dimensions? Allow students to work with the software to investigate and develop their theories. Use this sheet and have students download office-grid-basic.py, the simulator I designed.1
I leave off here at this incomplete point, because I’m not sure of a good way to finish this off.
Any ideas? How would you finish this lesson? Would you do anything differently? I’d love to hear, as I might be doing this again with different classes in a week or two.