About fifteen people participated in The Math Club on Monday, April 7. For our regular "fancy name tag" activity, we created spirolaterals. Basically, you select a few numbers and make lines of the corresponding lengths, always turning a certain angle. We used times tables (e.g. 2, 4, 6 or 5, 10, 15) and the right angles on graph paper. Much confusion occurred about "always turning one way" in drawing, but eventually people figured out how to make these beautiful representations of number sequences. You can see some beautiful exemplars here. Using different number sequences and different angles will produce different fancy results.


from BitArt Gallery

Then we looked at some proportions in human body and cartoons. A kid's height is about six of his head's lengths, but Garfield has very different proportions! What proportions make a character into a chibi? Proportion in art is a very rich topic, from Barbie's deformities to the golden mean. For a take on classic realistic drawing, go to The Drawing Lab page about proportions. Weird, unrealistic proportions are often funny. Once I went through the complete collection of the Far Side cartoons and selected all those based on "wrong proportion" as the main source of humor. I think I found about fifty of them. The Math Club spent the next hour or so measuring Caleb's proportions using multiple copies of his head as a unit, in Adobe Photoshop, and creating their own weird proportion cartoon characters for a poster children named "Mutant World of Random Caroons, Inc."

We also looked at some math jokes as possible sources of comic strips, but this will have to wait for the next meeting. Carol found a good site with printable cartoon strip blanks in various shapes. Here are a few jokes we laughed at:

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Teacher: Who can tell me what 7 times 6 is?
Student: It's 42!
Teacher: Very good! - And who can tell me what 6 times 7 is?
Same student: It's 24!

When calculators were first invented, the costs could quickly add up.
But then their prices came down, and they soon began to multiply.

What animals are the most proficient at math?
- rabbits, because they multiply
- cells, because they divide
- snakes, because they're adders
- beavers, because they work with natural logs
- flamingoes, because they balance
A mathematician wandered home at 3 AM. His wife became very upset, telling him, "You're late! You said you'd be home by 11:45!" The mathematician replied, "I'm right on time. I said I'd be home by a quarter of twelve."

There are 10 kinds of people in the world: those who can count in binary and those who cannot. And by the way, never trust a man who can count to 1024 on his fingers!
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If you know a good one, bring it to the club next time.

For the snack time, we mixed cocktails, with milk and chocolate, and also with banana and juice. The initial proportion of 1 squirt of chocolate syrup to 2 cups of milk to 1 drop of maple syrup did not taste right, so children changed it to 2:1:0 instead. This worked perfectly! At the previous meeting, we used time lines to figure out cooking time, not worrying as much about proportions, because they aren't as important for soups. For cocktails and other mixed drinks, there is no timeline, because all ingredients are added at the same time, but proportions make a huge difference.

We also played some games in-between, such as Human Knots (got separate circles this time, yay!) and Live Mirrors, and Picture By Phone. The Silly Robot task of drawing a square by description still proves to be a challenging quest, with frustrations cropping up now that we can't quite do it for the third meeting in a row. Next time, we will bring heavier machinery to help with the task. I feel particularly good about some amount of struggle with some of the most ancient and most fundamental math tasks, because by trying the task for themselves without any tools first, children appreciate the tools (such as formal geometry construction rules!) much, much more. The tools are seen as helpful, because the tasks are seen as problematic. If you do not see something as a problem, and a difficult one at that, you won't appreciate tools that help to solve the problem. It is a fine balance, though: you do not want to offer tools right away, before children have a chance to notice there IS a problem; but you also do not want to withdraw tools and leave children to struggle too long without help of the previous generations. My take on it is that you don't want the kids to reinvent the wheel, but you sure want them to have loads heavy enough that they will very much want to use wheels for help!