"40 millimeters does not equal 6 meters!"

David was interesting with math this week. One set of problems we worked on related to proportions and used the notion of map scale. David uses an online math program called ALEKS. He read the problem, said, "I don't understand" and pushed the "Explain" button. He went right to the mechanics of doing this problem - I could see he didn't really understand. He (and his brother) are very good with patterns, so he can learn "how" to do a problem without learning the underlying concepts. The Evil Math Grandma made him stop looking at the screen so we could talk about What Was Going On in this set of problems.

Starting out with 40 millimeters = 6 meters caused him enormous angst and discombooberation. He raised his voice (not yelling; this is his I'm-going-to-talk-fast-and-loud-because-this-disturbs-me voice). "Forty millimeters is not 6 meters! That's stupid! I don't get it! You're trying to make me to busy work!"

I tried, "David, do you know how wide the United States is?" "No." "About 3,000 miles. If we were to draw it that big, you wouldn't be able to see it. So when we draw it, we ...." Let's just report now this approach did not work.

This did - well, it did enough for today. I have a sneaking suspicion this is a concept we'll go through again.

"I'm going to draw a picture of David. [standard stick figure here; I'm not an artist, and won't pretend to be one!] Does this look like you?"
(Giggles) "Yes!!"
"Let's see, this figure is about 1-1/2". How tall are you?"
"Five feet."
"Ok. This 1-1/2" represents th 60" tall that you are. How tall is Mom?"
"She's 5' 10"."
"Ok. So if I want to draw Mom in the right proportion to you, how tall would she be?"
We then went through the example and drew "Mom" and were able to understand the math problems.