Whew! Almost the Weekend

This week had cr*ppy written all over it. So I'm just going to detox and purge the "bad" stuff:

* Tired from too little sleep.
* Drink too much coffee to make up for it.
* Can't sleep the following night because of the excess caffeine.
* Rinse. Repeat.
* Patience at an all time low due to sleep issues.
* Weird Schedules due to state testing.
* Don't read one of the bazillion e-mails about the schedule and get called out for it.
* Snap at children due to lack of patience.
* Feel bad and remember I don't have to say EVERYTHING I'm thinking.
* Have conversations in my head saying the sleep-deprived snotty things I shouldn't verbalize (also visualize snotty facial expressions I'd make with words).
* Skip yoga and tap and Lindy Hop due to sleepiness.
* Feel worse physically due to less exercise.
* Make up for "stuff" by mainlining huge chocolate chip cookies.
* Feel worse physically due to bad eating habits.
* Take on more work for next year in the form of an "inventing 'contest'".
* Hear about various ones of our/my students putting down our school.
* Take it personally.
* Wake up at 3am Friday to make a test I have to give today.
* Excited about the faculty meeting this morning taking up 1 hour of my planning time.
* Excited about being "tired stupid" today.

Off to go "running" at 4:30am before I get ready for work. Woot! At least I got my geometry test done. I envision caffeine and a cookie in my near future. Breakfast?

Logarithmic Graphing

In precalculus we finished our unit on logarithms by seeing what/why/how log graph paper is used. I showed them the crazy-uneven-looking paper and we got to it with:

this sheet.

Things that came up: name of our galaxy, how to do the work for the 2nd blank, giggling about Uranus, caution and care of units when you just see "58", number of feet in a mile, how much is a billion, how many millions in a billion, ...

I also love the type of examples that we used. Their homework that night was to find a sort of "show and tell" example about anything to do with astronomy. They came back with some cool facts, and we had fun sharing and being amazed at it all.

Trigonometry Word Problems

We finally got to the cool section in geometry where the students FINALLY can figure out what those crazy "sin" "cos" and "tan" buttons are on the calculator. After practicing *basic* problems in class, I assigned this "word problem" homework.

A sample problem is:

1. For a 50 foot pole to be stable, engineers have decided that 3 equally-spaced guide wires (running from the top of the pole to the ground) have to create a 75deg angle with the ground.
a. How much total wire should they plan for?
b. How far from the pole should each wire be attached to the ground?

I tried to make "sensible" problems that weren't of the "shadow" or "kite" variety ... because at the end of the day, I guess I don't care how far out the kite is or why I would even want to know my shadow's length (and you know, students don't grasp this whole shadow thing anyway :) ).

Also, I found it was a good idea NOT TO ASSUME they knew what sonar was or what guide wires looked like, so we had a discussion before the end of class as to what the pictures might look like (with them doing most of the work, of course).

Also, spring break? why si, I did enjoy it, gracie.

Shadows on Planet Earth....

We just finished our unit on similar triangles, and as par for the course, there were the typical shadow problems. I know from past experience that students have problems with these: they draw shadows going in 2 different directions .... they don't know how to set things up .... etc. BUT. I thought it was a geometry misconception problem. No. From deeper questioning of various students today, I see that some students have no concept of shadows.

Various questions/answers:
* What makes a shadow ... or how is it made?
- shrug.

* How would you make your shadow longer if it's coming from a light post?
- move closer to the light?

* Draw the picture and point to the shadow.
- points to the hypotenuse.

How did I miss this scary fact in 12 years of teaching geometry? I guess I just made assumptions on why they were struggling, and didn't probe deeper.

Eavesdropping Assumptions

In geometry we are learning the special right triangles, and I wanted to give the students time to come up with memory tools for remembering which ratios went where on the 2 triangles. Having taught geometry for 12 years, most of the tools are repeats for me, but every so often I get some surprises that stick in my head.

I gave the students time to discuss, and it was a class late in the day, and I was observing who was doing what. I eavesdropped on 2 students and thought I overheard, "she was hung over, so that's why she didn't come to school". And then they both snickered and continued talking. "Great!" I thought. First of all someone is drinking, second of all these kids are off task. Third .... who's absent today ??? Fourth, do I make a big deal of it? Which part? The drinking or (more seriously :)) NOT talking geometry when they should be.

Then I asked for volunteers to share their memory tools. Here are some repeats (for me) and some refreshing new ones:
* The 30-60-90 has 3 different angles, so that's the one with 3 different numbers (1, 2, root 3).
* The 45-45-90 has twin angles, so the parents are the x's and the root 2 are the twins
* For each of them, the hy-pot-TWO-nuse has a 2 involved on the hypotenuse side.
* the root 3 is by the 30

Then one of the "drunk talker" students raised her hand:
* On the 30-60-90 triangle, the bottom one has one X boyfriend, one has 2 X boyfriends, and one has 3 X boyfriends, and she's still HUNG OVER HIM, so that's why there's a radical hanging over the 3.

I clarified that she really meant "hung up" on him, and I was the only lush thinking about alcohol, but then I had to laugh at myself for assuming the students weren't doing what I'd asked them to do when all along they were.

Logarithm Applications

I shuffled around my precalculus curriculum (was eager to get to intense trigonometry in the fall) and am JUST almost through logs and ln and e. My class spent a day on applications, and we had some fun conversations about the following scenarios. My last day will be spent showing them log graphing paper and log-log and semi-log and 1-cycle and "how do they get the partitions" and why would someone graph on log graph paper and all that. Sheesh! The year (as always) is whizzing by.

Here's what we did (heavily borrowed from a TON of math books: