Connect the Dots for Math Geeks
December 1, 2011 8:56 PM Subscribe
Help me make an awesome connect-the-dots for middle school math nerds. I'll take care of the math, you take care of the art. Don't let these poor kids be stuck with my cat/walrus.
This weekend I'm co-teaching a workshop for 7-8 graders in which we explore math topics not in the curriculum. Up this week: Prufer Codes. A Prufer Code is a really crafty algorithm for encoding a graphical tree as a sequence of numbers. The entire tree structure can then be reconstructed from the string of numbers. It's super fun (for us math types that is.)
What I want to do is give the kids a sheet with just the numbered nodes for a graph, along with its code. Then, they'll use the code to draw in the edges - revealing some kind of whimsical/seasonal picture! (So yeah, its connect-the-dots for nerds.)
So what's the problem? The math won't work with just any old connect-the-dots picture. I need something special. Here are the constraints required by the encoding mathematics:
* The graph must be completely connected. No stray nodes, or sub-shapes hiding out inside.
* The graph must be a true tree: there can be no loops / cycles, so that each pair of nodes has a unique path between them. (This is the tough one.)
* The reconstruction is more interesting to carry out if most nodes have more than two lines, but single or two-line nodes are fine.
And here are the constraints required by common decency:
* It can't be one of those lame things where you know it's a stupid snowman before you draw any lines.
* It should be well, you know, cool for kids. What are kids into these days? Pirates? Owls? (Chicago-related things might be cool.)
* Probably shouldn't have a bajillion dots. Even with bonus math, dot-connecting is only fun for so long.
If you're not up for drawing a whole graph for me, that's fine. I'll take ideas too. What's the coolest connect-the-dots you've done? Where's the best online repository of connect-dot-pictures? Is this whole plan going to fail spectacularly?
I'm most definitely not above borrowing from the web, or changing something around to fit the math if it's really cool otherwise.
This weekend I'm co-teaching a workshop for 7-8 graders in which we explore math topics not in the curriculum. Up this week: Prufer Codes. A Prufer Code is a really crafty algorithm for encoding a graphical tree as a sequence of numbers. The entire tree structure can then be reconstructed from the string of numbers. It's super fun (for us math types that is.)
What I want to do is give the kids a sheet with just the numbered nodes for a graph, along with its code. Then, they'll use the code to draw in the edges - revealing some kind of whimsical/seasonal picture! (So yeah, its connect-the-dots for nerds.)
So what's the problem? The math won't work with just any old connect-the-dots picture. I need something special. Here are the constraints required by the encoding mathematics:
* The graph must be completely connected. No stray nodes, or sub-shapes hiding out inside.
* The graph must be a true tree: there can be no loops / cycles, so that each pair of nodes has a unique path between them. (This is the tough one.)
* The reconstruction is more interesting to carry out if most nodes have more than two lines, but single or two-line nodes are fine.
And here are the constraints required by common decency:
* It can't be one of those lame things where you know it's a stupid snowman before you draw any lines.
* It should be well, you know, cool for kids. What are kids into these days? Pirates? Owls? (Chicago-related things might be cool.)
* Probably shouldn't have a bajillion dots. Even with bonus math, dot-connecting is only fun for so long.
If you're not up for drawing a whole graph for me, that's fine. I'll take ideas too. What's the coolest connect-the-dots you've done? Where's the best online repository of connect-dot-pictures? Is this whole plan going to fail spectacularly?
I'm most definitely not above borrowing from the web, or changing something around to fit the math if it's really cool otherwise.
How about a celebrity's face? A scene from Charlie Brown's Christmas? The Grinch's face? Superman's face apparently has a very recognizable structure that could lend itself to connect the dots...
posted by carpediem at 10:43 PM on December 1, 2011
posted by carpediem at 10:43 PM on December 1, 2011
Response by poster: Ooh yeah, constellations are great fun. Not all of them work, but there's enough that would to get a start.
posted by Wulfhere at 11:46 PM on December 1, 2011
posted by Wulfhere at 11:46 PM on December 1, 2011
How about as they connect the dots, it's not obvious to them what it's going to be, and they think they're about to find out as they connect the last few dots and then... huh? I still don't get it.
And then you say "And now if you take your page home and cut out you shape and assemble it, you get a Futurama robot like this! (as you hold up a little model robot).
Ignore the robot idea, my point is to make the art a simple papercraft design instead of the tired and expected crude illustration. I think it would be a bigger payoff, and it's more mysterious and unexpected.
Depending on their age, maybe draw some red-herring background art on the page, just to be a bastard. :)
posted by -harlequin- at 2:29 AM on December 2, 2011
And then you say "And now if you take your page home and cut out you shape and assemble it, you get a Futurama robot like this! (as you hold up a little model robot).
Ignore the robot idea, my point is to make the art a simple papercraft design instead of the tired and expected crude illustration. I think it would be a bigger payoff, and it's more mysterious and unexpected.
Depending on their age, maybe draw some red-herring background art on the page, just to be a bastard. :)
posted by -harlequin- at 2:29 AM on December 2, 2011
Given that you're providing the dots, and presumably the labels for each dot, your edges can cross (though there won't be a node at the intersection, per the definition of a tree). You could take something like a line drawing of a wrapped gift, and cheat like crazy in constructing the tree to hide the object as long as possible; e.g., avoiding intersections as long as possible.
posted by bfranklin at 7:43 AM on December 2, 2011
posted by bfranklin at 7:43 AM on December 2, 2011
Oh, man, I need to write a prufer code exercise for my exam next week. This is such a cool idea!
Seems like you would need to be working with an awfully big tree/sequence to get anything reasonable, though...how many nodes were you anticipating? I'd be a little daunted by a 40 node prufer code.
On the other hand, making a tree in the shape of a tree is kind of funny.
(yeah, I got nuthin')
posted by leahwrenn at 9:12 AM on December 2, 2011
Seems like you would need to be working with an awfully big tree/sequence to get anything reasonable, though...how many nodes were you anticipating? I'd be a little daunted by a 40 node prufer code.
On the other hand, making a tree in the shape of a tree is kind of funny.
(yeah, I got nuthin')
posted by leahwrenn at 9:12 AM on December 2, 2011
How about if you use the dots to spell out words? You could jam a bunch of letters closely together, and not be able to tell what they spelled out until you connected the dots.
posted by ErikaB at 11:25 AM on December 2, 2011
posted by ErikaB at 11:25 AM on December 2, 2011
This thread is closed to new comments.
posted by littlesq at 9:02 PM on December 1, 2011 [1 favorite]