## Thursday, September 29, 2011

### Fractals

It's been kind of a weird week. Everything was going well and (fairly) normal until yesterday when I got a call after school that I needed to pick up my girl at her school.  Turns out their bus (which none of the kids were on yet, thank goodness) had been in an accident and wasn't drivable.  Something little, but it threw off my whole afernoon.

Today I got a call at school around 12:30 saying that my boy had fallen at recess (while going after a ball during his kickball game, I later found out) and hit a permanant tooth on the blacktop.  The tooth was bleeding and kind of loose and he was really upset.  I arranged for a sub for my last class and headed out. After a trip to Dairy Queen for a milkshake (he'd missed lunch!) we headed to the dentist to get it checked out. Nothing was obviously wrong but we were told to keep an eye on it. I'm just hoping it doesn't turn gray/black!

This year I'm on a quest to do fun/applicable/new stuff in precalc. I saw in my precalc book (which I've used for probably 9 years and never noticed before) a lesson on fractals and thought I'd give it a shot.  It took me a while to figure out how/what to do, but yesterday I decided to give google sites a shot.  Here's my first attempt - check it out to see what you think! I'm using it basically as a webquest - I set up different pages with information/videos/activities for the kids to complete and write their responses on a separate page.

Here's what I'm planning to give them:
Fractal

## Tuesday, September 27, 2011

### A cubic pattern

I don't post much about the actual math that we do in class, but I gave my precalc kids an assignment yesterday  that showed this (what I thought was) cool pattern in cubic functions.

It started with a function.

f(x) = $5x^{3}-33x^{2}+58x-24$

Their paper showed a graph and asked to find the zeros.  We picked out 2 and 4 (checked with synthetic division) and ended up with 3/5 as our last.

Then it went through a process to build the cubic polynomial if you know the zeros (without doing all of the messy binomial multiplication).

Step 1:  Factor out the 5.  (This only works if the leading coefficient of 1).

$f(x)=5(x^{3}-\frac{33}{5}x^{2}+\frac{58}{5}x-\frac{24}{5})$

Step 2.  Find the product of the zeros. $(2)(4)\left ( \frac{3}5{} \right )=\frac{24}{5}$
(Which is the opposite of the constant term.)

Step 3.  Find the sum of the zeros. $2+4+\left \frac{3}5{} \right =\frac{33}{5}$
(Which is the opposite of the quadratic term.)

Step 4.  Find the sum of the pairwise products (this totally confused most of the kids... ) which is $z_{1}z_{2}+z_{1}z_{3}+z_{2}z_{3}$.
$(2)(4)+(2)(\frac{5}{3})+(4)(\frac{5}{3})=\frac{58}{5}$  (Which is the same as the linear term.)

So if you have the zeros of a cubic polynomial with leading coefficient of 1, you can use these patterns to find the polynomial itself.  I thought that was pretty cool (and I found a couple of kids that agreed with me.  The others not so much.).

The next problem was to find a cubic polynomial with zeros at 5, $2\pm \sqrt{3}$. (It ends up being f(x) = $x^{3}-9x^{2}+21x-5$ if you're playing along at home. :)

Oh, and a couple of other things happened today:
1.  Got a new girl in my honors precalc 1st period class. She just moved in from a school on the other side of the city.  She "didn't have a clue" as to what we were doing and had been solving linear systems in her old school.  I gave her a copy of the summer work that the precalc kids had done for her to look through; she asked if there were notes somewhere that she could use because she didn't remember any of it.  Oh my.  I actually emailed a friend who happens to teach at the girl's old school to do some checking; she said she should be fine (is just kind of "flaky") and was going to check with the Honors Alg2 teacher to see what they'd been doing.

2.  Had my first "I'm overwhelmed" crier in another precalc class.  This student had been absent for a couple of days and hasn't made any effort (that I've seen) to make things up.  She told me when looking at their review for tomorrow's quiz that she didn't know any of it.  I told her to come after school and we'd work through some problems; hopefully she'll have calmed down enough to realize that she does know it and was just stressed out.

## Saturday, September 24, 2011

### Things I've Tagged (weekly)

• announcing PATTY"S CALCULUS VIDEOS! free, in-depth explanations on all the important topics! http://t.co/urvOM0td pls RT

• Target Practice - Game time. Keep track of what you notice as you play. a. Warm up. Show a target function.... http://t.co/Oh4XYlTR

Posted from Diigo. The rest of my favorite links are here.

## Wednesday, September 21, 2011

### Freshmen.

I wasn't excited last year when I heard that I would be teaching the Honors Algebra 1 class this year. I tend to like the upper classmen more... but going from my Integrated (aka general) Algebra 1 to Honors was a move up.

I'm formally admitting that I was wrong.  Today in class we were able to review some problems, take a quiz, and go over a new lesson.  Do you think I could've done that last year?  Ha!  The new lesson was on Solving One-Step equations, which all of the kids are familiar with and I probably could have skipped.  Tomorrow's solving two-step equations and I'm not going to be here, so I'm trying to decide what kind of notes/assignment to leave them.  I'd like to leave an assignment on which they can check their answers... I need to check my puzzle/pun worksheets to see what I have.

What really has amused me is the seriousness in which they take correcting their homework answers.  Someone asked me the other day if she should mark a problem wrong on her assignment because she wrote a number in a different form that I did (maybe she didn't reduce a fraction or something - I don't know).  I told her not to mark it wrong but to make sure she reduces (or whatever) in the future.  She was relieved.  And they're really concerned with how to organize their notebooks... I feel like I should have some sort of set method, but I know every student is different and I don't want to tell them one set way to do it.  Is that bad?  As long as they're organized and keeping stuff I'm happy.

(Oh, and I just noticed today that they all have graphing calculators.... gotta love it!)

## Saturday, September 17, 2011

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

## Thursday, September 15, 2011

### How big is your foot?

I've done some crazy stuff in precalc so far this year (and I'm sure it's driving some of the by-the-book kids nutso just like it would've driven me nutso when I was in high school).  Today I threw a couple of questions at them to see how they would react.

1.  How long would it take to pass a ball down a line of 457 people?
2.  The world's tallest man was 2.72 meters.  How big should his foot have been?

It was fun to see the changes in the classes (3 of 'em.)

Question #1
First period really got into it.  They quickly arranged 10 people in the front of the room and passed the ball (which I conveniently had in my car... thank goodness for soccer practice last night!) down 5 times.  Then they averaged their values,  figured out their time/person, and multiplied to figure out 457 people.  I think their final answer was something around 3 minutes, 23 seconds.  And then as we moved on, 2 boys sat next to each other and passed the ball back and forth 457 times (yes, really).  They were off the time by 2 seconds.

Third period took a different approach.  They started with two boys about 5 feet away from each other throwing the ball back and forth 10 times.  (Their interpretation of "pass".)  Some of the other kids from the class intervened and decided they wanted more people in a line... they started out with 10 people in the room then asked if they could go in a hall. We ended up with 25 people in line passing the ball a variety of ways (hand to hand, rolling on the floor).  Very funny to watch... and noisy, too.  Sorry to my neighbors!  After averaging all of the times they came up with something under 3 minutes.

Fifth period (Remember how boring they are?  I'm still going with that.) was blah.  A couple of kids were involved and had to drag others in to participate.  Eventually we ended up with 22 people in a line in the hall passing a ball.  In almost near silence.  They did it a couple of times, were content with the results, and headed back to their desks.  Wake me up when it's over, please.  I forget their final time...  I think I was sleeping.

(It was funny to me, though, that for the most part the kids were really concerned about getting the fastest time possible.  The question mentions none of that.)

Question #2
Again, a winner.  I showed a picture of Robert Wadlow (the man who I was referring to) and gave the kids free rein.

 Gotta love the socks!
In first period, everyone got up to start measuring.  They made a big chart of height, footsize, and ratio and went from there.  My idea was for them to do a linear regression (and I gave out directions on how to do that) but their numbers were so crazy that they ended up with a negative slope and 25 cm as their final answer.  (Then we got off an a discussion of his weight and BMI.  A couple of kids had me checking their BMIs, too.)

Third period ended up at about the same point (with fewer people contributing their values), got a much better equation, and a final value of 51 cm.

In fifth period not too many people were jumping up to measure (surprise!) and they were all boys of about the same height and footsize.  We decided we needed some variance (but they were determined to stick with people of the male persuasion) so we sent a couple of girls down to a freshman health class to grab a couple of little freshman boys.  Very funny.  The data ended up kinda crazy and they ended up with a 43.74 cm foot.

(In case you're wondering, I found some information saying that he wore a size 43AA shoe, which we looked up and determined that was about 49 cm.)

## Tuesday, September 13, 2011

### Random today stuff.

1.  I arranged my desks in groups today.  Kinda liked it!  It gave me much more room to wander about.  I think I'll do that more often.  (My Algebra 1 kids loved it, but they were also noisier than usual.  Hmm.)

 2nd class
 1st class
2.  We broke out the trashketball in precalc.  Two classes were pretty successful at it, one was kinda boring (but it's also hot and kids are seeming kind of drained).  I had them make up team names, which is usually pretty fun.  The boring class was boring - Team Jeff, Team 1, etc.  Bleh.  But one boy in that class did ask if we could play every day.  Um, let me think about it.  No.  In one class someone hit a 3-pointer from the corner to win the game at the last second - very exciting!
 boring class

3.  Our network was down about 4 hours this morning so I was happy not to have anything planned that I needed to get online for (except the normal access to our gradebook, attendance, email, etc.).  And luckily I'd even planned ahead a bit and got my Algebra 2 test printed yesterday afternoon... if it had been earlier in the day (instead of last period) and I hadn't been able to print anything I would've been hurting.  Instead, the only thing that affected me was not being able to print out notes for the Algebra 1 kids.  They'll live.

4.  Had a walk-through type visit today from our assistant principal.  I realized later that I'm not even on his observation list, so I guess he was just wandering around to see what was going on.  It was during the first trashketball class and we were having a good time (while learning!) so I'm hoping he got a good impression.

5.  Early dismissal tomorrow and a precalc test.  Those two don't normally mix well.  I made up the precalc test to be what I think of as pretty short, so hopefully time isn't an issue.  Then Thursday I have another short day because I'm going to a district tech-type meeting.  At least the non-normal schedule changes make the week go quicker!

## Sunday, September 11, 2011

### My Week...

Last week was really a mixed bag for me.

Personally, the death of some friends' 3 year old (from drowning in a pool) really threw me for a loop. I felt so horrible for them as a family but also tortured myself with the thoughts of "What if that were me?".  The funeral on Friday afternoon was especially tough, of course.  I know their healing will be a long time coming, but I'm glad the week is over.  I spent some time over at their house this evening and was comforted to see that they're doing a little better.  The mom is still taking the little girl's blanket with her everywhere she goes and is only eating a few bites a day, but she's also not constantly wracked with sobs.  Baby steps.

Professionally, I had a great week at school (considering).  I felt really good with my classes and finally know (almost) everyone's name.  I don't know why I've struggled with this so much this year... maybe it's the bigger-than-normal classes?  Maybe it's just not trying as hard?  I don't know.  But I think I'm good now.  I also felt better prep-wise; there were actually a few nights where I didn't do any work and didn't regret it the next day!  Until tonight, of course... I just typed up a review for my precalc classes (which I'll need 1st period) and didn't do any grading or Algebra 1 prep.  Oh well.  So tomorrow I may be regretting this!  (But I was glad to be able to spend time with friends who need all the support they can get right now.)

I also fit in a 9+ mile run this afternoon... I'm so ready for this hare-brained idea of running a half-marathon to be over. One more month. What was I thinking?!

## Saturday, September 10, 2011

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

## Saturday, September 3, 2011

### Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.