Yeah, when those trig questions come up for me, I just... oh, wait. That never happens.

Tonight I'm gonna have that nightmare where I'm in geometry class and I don't know any of the answers.

Emily! Did you get the Internet to work at home? I mean, you must have, but...

Laga hang in there. My holidays are routinely a source of a lot of pain due to my family.

Tonight I'm gonna have that nightmare where I'm in geometry class and I don't know any of the answers.

The other night I had that nightmare were I was running for Congress but forgot to campaign.

OK, not really a nightmare. But I ended up losing. To my brother.

Which leads to the question: is it really so important that EVERY student learn to factor ALL factorable quadratic equations?

If they are ever planning to take any college-level math classes, yes. Or at least learn that, if they can't factor something, the next step is the quadratic formula.

(The homework I was grading today has a problem where the had to find the roots of x^2 - 2x -4. A significant number of them wrote x^2 - 2x = 4, so x(x-2)=4, and so either x=4 or x-2=4. Most of the rest used the quadratic formula. A few graphed it on a graphing calculator and found the approximate roots. One completed the square.)

thanks Omnis and ND. It would have been a lot easier if Mom hadn't said that stuff about "we're just exchanging $50 bills" and then apparantly signed off the internet. I sent her three emails asking for clarification and got nothing back. I'm hurt and I'm worried and I'm sure not looking forward to Thanksgiving anymore.

{{{Laga}}} I'm sorry about the family craziness. I thought I was going to make it easy for my family this year for Christmas by telling them they could get TCG and I a joint gift from our registery. Apparently that is an awful idea and there is no way they will do it.

Laga, my family and two good friends are the only ones I get presents from, either.

My sister and I have always bought mountains of presents for each other and her two girls for Christmas. Only one or two that were expensive, "major" gifts, just a huge amount of small or funny gifts. Like, eight presents each with one silly sock and turns out none of them match, and then we'd all pick two socks and wear them. We'd pile all the wrapping paper in the middle of the floor. It would take four or five hours to open all the presents and play with them, and by the end we'd have a mountain of paper to play in. People who joined us for Christmas morning were often bemused by us.

This year, the girls are all grown up and one may not even be there for Christmas. And sis and I are exhausted and broke. We've talked and all agreed that Christmas needs to be small and simple this year. I'm glad, relieved really, but at the same time, I'm a little sad. I'll miss our craziness. Since her divorce, it's been the only time all of us get together and have fun. Maybe next year we'll have money and our spirits back, and we can do it again. Oh well. Everything changes, right?

I remembered that cosine was cozy so it had the adjacent side in the numerator, so sine must have the opposite, and tan=sin/cos was just easy to remember for some reason. Love the unit circle.

If they are ever planning to take any college-level math classes, yes. Or at least learn that, if they can't factor something, the next step is the quadratic formula.

Well sure, but that's just passing the buck. Why is it important that they learn that in a college math class, either? There are a very few students that are going to be regularly solving quadratic equations in real-world situations (engineers, physicists, etc) - but most of the people in both classes are learning that topic because people have always learned it.

Don't get me wrong: I think quadratic equations are super-cool in and of themselves. So do some of my students, and I think they should have the option of learning that stuff. But my sister doesn't grok them or care about them in general, and I can flat guarantee she can't factor one now. And you know what? She's going to do fine.

In an ideal world I would have a project for the students that love the pure math, that helps them through the idea of how to complete the square, then has them try to complete the square symbolically, and see if they can derive the quadratic formula on their own. Because THAT is good math, and I didn't even think to try it until I was a sophomore in college. But the students like my sister, who would just blink at that sort of thing? They can create an accurate budget for our school play, complete with ideal pricing for refreshments and tickets, instead.

ETA: I never learned the unit circle in class, but having seen it since, I like it. Also, Hil, I think you should look at the Foul Shot problem I gave up above - it is REALLY cool. I think you'd dig it.