## Saturday, 23 January 2016

### Lattice Puzzle

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 2 blogging challenge is “My Favourite”. (You can find my Week 1 blog post here.) Now, I presented a “My Favourite” back at ‘Twitter Math Camp 2013’ - namely Unit Circle Estimations (for Trig). I’ve also droned on a bit about teaching the Sine Law. Those are more traditional topic centred posts, but I’m still feeling subversive, so let’s use this one to talk about this number puzzle I got at OAME 2013 instead.

I'll pause to give you a moment to scroll though all those other lessons and recaps I threw at you. Do I link too much? I probably link too much.

 Here is the puzzle.

The premise is simple enough. Fit all the numbers flat into the box provided. Note that the conference was in Toronto, hence the CN Tower in the logo. I don’t recall if everyone who attended that PD conference got one of these, or if it was something related to the fact that I presented there (Musical Mathematics - I’ve parodied 30 songs). But the puzzle has been surprisingly popular this semester! Does it fit into the curriculum? I don’t know.

Presumably, it’s got some spatial reasoning associated with it. After all, the only way to make the pieces fit is to create a full lattice, with no gaps or spaces. (In the image below, look in the lower right corner.) Now, if you think about it a bit longer, you might realize that symmetry is a useful tool. (For instance, lock the ‘7’ in with the ‘1’ - looks a bit like a ‘4’...)

 What it looks like on my desk this week.

I simply keep the puzzle on my desk at the back of the room, and students (Grade 11 students) who are finished work early or want a bit of a break can play around with it. I have sets of puzzle cards on my desk too, but for whatever reason, this is the popular thing. It started the semester fully assembled, when a couple guys would time each other for the fastest to assemble it.

Eventually, it spent well over a month fully disassembled, as people toyed with it and couldn't put it back together. One student wondered if there was a way to get/make her own. I had a teacher in my room for an on-call ask me about it the following day. I even played around with it a bit once, while catching up on “Supergirl” (while procrastinating from catching up on marking). There’s only been one casualty, the tip of the ‘5’ (2?) fell off - a student glued it back on.

 "How does it work? I MUST KNOW!"

So there you go - the favourite thing that has nothing to do with instruction. Though "a game your students love to play" was an option, so maybe I'm not as subversive as I think. Related, perhaps I should bring in a tangram next semester.

If you enjoyed reading this, I’m all about the writing. Feel free to check out some of my other posts:

-Meet Lissa Jous, over at my math webcomic.

1. I am getting ready to teach trig soon. I will definitely come back here and spend some time with your links.

1. Oh, thank you! I think the two links I posted here is about all I have for the trig though, aside from some offsite stuff. So, here's those links again:
-"TrigGate" for Unit circle estimations:
http://mathiex.blogspot.ca/2013/07/mat-triggate-r1.html
-I also mentioned my Sine Law post above:
http://mathiex.blogspot.ca/2014/07/unambiguous-sine-law.html

Offsite, my comic explained how the ratios fit together on the circle: