I covered a couple of Precalc classes today and got to teach about polar coordinates. I started with a clip of Crimson Tide (remember that movie? It's a great one!) so they could "see" some math.

"Math!", one of the kids yelled.

Then I handed out a couple of polar coordinate grids and told them there was an enemy sub right there. (I drew it on my projected computer.)
Where are we? (the origin)
How far away is the enemy? (they counted the circles)
In which direction? (we discussed using east of north vs an angle (measured from where?))
And then,
Is there any other way we could describe this location? (Yep, with +360 angles, negative angles, etc)
So then we plotted a couple other points and came up with all kinds of different ways to get there.

Then, we got to the teacher's notes. Because I spent so much time on the intro stuff, I didn't get completely through what she wanted me to. But I like getting them to think about what they're learning instead of just showing them, so hopefully she's ok with it.

My son is currently finishing up 5th grade (only 12 more days for him!) and last week forgot to bring home his math workbook. I mean, it's not like having homework has been a habit for him; maybe once every other week does he have an assignment.

I put a plea out on facebook to see if anyone could send me a picture of the page and was thankful that a friend of mine obliged. (He was too, considering that the punishment for not having an assignment is 50% off and having to sit during recess. Grr.)

I normally don't check over his assignments too closely because he does so well, but because I was copying from a picture that my friend sent onto a separate sheet of paper I obviously knew exactly what the problems were.

#1 - 4 were multiplication.
The next section went to this:

(Point E was drawn in by my friend's son.)

My guess is that they were working on plotting points.

The page finished up by asking the students to plot Point E so that BDEC was a square. (FYI, my boy was able to do it correctly. :) )

And the kicker? Find the area of the square.

This caught me off guard. I don't think the kids have done Pythagorean Theorem or (most definitely) the Distance Formula. So when my boy looked at me with a blank look on his face, I decided I'd talk him through it.

I started by asking him what shapes he knows how to find the area of. The answer? A square/rectangle and a triangle. We drew a big square around BDEC so that he could see some extra triangles. He figured out that the big square was 5 x 5 and each triangle had a leg of 1 and a leg of 4. Taking the area of the big square minus the four triangles, he ended up with area 17.

Perfect.

I followed up the next day and asked how his math had gone (I basically wanted to make sure that she accepted the homework even though he'd written it on a different piece of paper.) The first thing that he told me was that "my" answer of 17 for the area was wrong. It was supposed to be 16.

Um, what?! [You know what she did, though, right?]

I tweeted it. (Of course.)

I was happy that everyone agreed with me. And Mike Lawler even YouTubed his son solving it!

I sent the video to my son's math teacher (thought it would be a nicer way than saying nyah nyah nyah) and haven't heard anything back. [I did put it nicely; said it was such a great problem that I tweeted it and this guy made a video!]