Monday, December 19, 2011

Finishing Up

We have some crazy two days ahead of us at school and I'm just hoping to hang on long enough to make it to Wednesday at 2:15!  (And then another couple of hours until my 2nd grade basketball team's practice is over... always an exhausting exercise!)

I'm not seeing one of my precalc classes tomorrow and am determined to get a quiz in (solving right and oblique triangles) so I needed a day that isn't vital but isn't a throwaway day, either.  Today during my tutoring period in the library I found a cute little map of the North Pole.  I wrote in some values on the map, came up with a story to match Santa's trip around the village, and hopefully it will work well enough that the kids can practice their solving triangle skills while determining Santa's distance traveled.  Here's what I ended up with:





We'll see how it goes!

My Algebra 1 kids are taking a test (I'll get them started on some exam review stuff on Wednesday) and Algebra 2 kids are reviewing for their Quadratics Quiz on Wednesday.

Two more days....

Friday, December 9, 2011

Loooong week.

I swear it should be January by now.  This week has taken forever to get through!

Kind of a weird day today.  They held a breakfast during first period today for all of the kids who are "Anderson Achievers", which means their gpa is above a certain value, they are involved in school activities, and they have no discipline referrals - basically all of my precalc kids.  I had 8 kids left in a class of 30 and that was because they forgot to turn their application forms in.  We had a quiz yesterday over graphing trig functions and I didn't want to start anything new without the majority of them here, yet I have 2 more precalc classes later in the day to deal with.  I refuse to bow to the pressure of the "Freeday Friday Funday" (which seems to be a staple at our junior high) and was searching for something to do.

Here's what I ended up with. It uses the idea of a person's biorhythms to create sine curves showing their cycles of intelligence, physicality, and emotion.  We had a discussion about this being only a theory (so it's not something you'd bank on) but the kids enjoyed plotting the sine curves to determine their "high" and "critical" days.  (There are gobs of them online if you want to check them out.)

A couple of comments:
1.  One girl said her dad had had a long talk with her about this - she was skeptical (thank goodness) but was excited to show him what we'd done when she got home.

2.  Had a lot of discussion amongst the girls about the emotional cycle (28 days) matching their periods. (And by that I mean their periods.)  Oh, the things they'll talk about.


Had a quiz today in Algebra 1 about solving systems by graphing and using substitution. We've been working on this all week and everyone seemed fine.  Until they got in class today and did the typical pre-quiz freakout. I'm seriously tired of that one!  I posted all of the worked out answers on the class blog last night and I'm guessing maybe 1 girl actually checked her answers on it.  The others decided to wait until today to check in class.... and then of course had questions.  Sometimes I wonder why I do the extra work!  Just hoping that it helped out that one girl.

I got a new student in Alg1 this week. A move in. From China.  Who speaks no English.  She's 17 and I'm sure has taken this level of class before, but because of the language issue they didn't want to start her in anything higher.  We've exchanged "hi"s and when I said "How are you?" she stared blankly at me.  Poor thing.  Had a discussion with the kids about how isolated she must be feeling; they're being extra-nice to her... or at least as much as they can be!

Introduced imaginary numbers in Algebra 2 today. I'm guessing that 7th period on a Friday wasn't the best time for that; they were pretty much freaking out and in major resistance mode.  Monday should be fun. (Not.) We didn't get to the idea of using the conjugate to simplify fractions, which is probably a good thing.

Lots of grading to do this weekend; precalc graphing quizzes from yesterday and Algebra 1 quizzes from today.  I'm totally graded out - having 90+ precalc kids kills me when I grade assignments.  I just finished up their temperature regression equations from last week and a sine/cos graphing applications packet that was due on Monday. And now the quizzes. Ugh.

8 days until Christmas break!  Hope I make it.


Friday, December 2, 2011

What's the temperature in Denver today?

Happy December!

It's my goal in precalc this year to have the kids apply knowledge whenever possible. We haven't been able to do that a whole lot (at all?!) so far in trig, so it was nice to get to graphing sine and cosine curves.

We've spent a couple of days graphing with periods, amplitudes, and horizontal and vertical shifts, so I'd assume that 90% of the kids could do that without a problem.  Give 'em an equation and they can graph it.

Yesterday I gave each student a strip of paper with the name of a city and their average daily high temperatures for each month (found them here).  I also gave them a full size piece of graph paper and a half-sheet of directions/questions for them to complete.

It was amazing the thinking they had to do.  Everyone seemed comfortable with having 12 as the period of the graph, but how exactly do you fit that into the equation?  (Some kids put 12... or 1/12...)  What happens if you set January as month 1?  Uh oh - a horizontal shift!  And what trig function is it showing?  Sine?  Cosine?  Has it been reflected?

Something that had become almost automatic for them turned back into a thinking game.

Nice.

Today I told the kids (after they'd turned in their results) that I didn't want to grade them all.  After being accused of being lazy, I passed the graphs and equations out (making sure that no one got their own) and told them to grade it for me.  (Had to give them some directions, too, of course.) They plotted the data points on their calculator, typed in the equation, and had to figure out what was wrong.

More thinking?!  Oh my goodness.

First were the problems actually graphing the functions on the calculator. Check your mode. Did you remember to type the variable?  Adjust your window?

Then the identifying of the equation errors.  Graph isn't wide enough?  So what's the problem?  Could you fix it?

Graph isn't tall enough?  Is in the wrong place?  How could you fix it?

I also had the kids rate the equations on a scale of 1 - 5.  I was pleasantly surprised to see that they were very generous with their scores. Someone who hadn't even included a sin or cos in their equation (or a variable...) was given a 4 out of 5.  Wha?!  And then one girl was given a 4.5/5 because (although her equation was virtually perfect).

I'm happy to say that I think most kids have a better understanding of the different transformations of a sine or cosine equation and what exactly they do to a graph.  Hopefully.

Tuesday, November 22, 2011

Trig stations

I'm at the point in Precalc where I would normally give a quiz over trig values without using a unit circle. But with today being the last day before Thanksgiving I didn't want to cram in a quiz without knowing they were ready. And I definitely didn't want to move on with something new!

So I pondered.  I have a unit circle turkey coloring page that I could give, but that would've taken about 10 minutes... and I definitely didn't want to leave them 35 minutes of free time!  I also had a couple of other fun-type stuff that I could give, but again, nothing that would take the whole period.   So I decided to set up some stations and give the kids some options.  They had to choose at least two options plus one required one.  I gave each of them a quarter-sheet with the stations listed so that they could keep track of what they'd done (and I could make sure that they did what I asked them to do!).  Here's what I ended up with:

Station 1:  War
I copied a deck of cards (cut them with the help of a student aide - thank goodness for her!) and set up 3 stations of max 3 kids each.  Standard War rules apply.  (Some of the boys had a bit of an argument during 1st period and a bottle of water was thrown. Silly boys.)

Station 2: Radian, the Turkey
This used to be Radian, the Snowman, but that was when we didn't get to the unit circle until December. I altered the picture a bit so that the kids could make a turkey out of it. I'm going to post a bunch of them on the wall so that they can enjoy the pretty pictures. :)



Station 3: Trig Dice Game
Several years ago at an OCTM conference I picked up several sets of 1" foam dice. On half of them I taped the 6 trig functions and on the other half I taped special angles.  The kids roll one of each, answer the question (correctly, hopefully) and move along the game board. I usually give them pieces to move around (or have them use a coin) but today I pulled out my white-board crayons which erased awesomely on the laminated game boards.

Station 4: Trig Dot-to-Dot
In theory I like dot-to-dots, but this one didn't work out so well.  There are unrationalized and rationalized answers on it, so the kids weren't sure which ones to use (eventually we figured out it should've been the rationalized ones).  And the answer is a picture of a barn.... not quite so obvious.

Station 5:  Row Game
I definitely like the row games - it's basically two columns of problems but each set of problems has the same answer.  The kids didn't think they were so much fun, though.

The required station that everyone had to do was to fill out a unit circle in less than 4 minutes.  It's amazing at how quickly they're able to do this now!  So cool.  And very neat to see how proud they are of themselves when they get it done the first time (or faster than the last time).

Two other activities that I thought about including:  a Trig Crossword Puzzle and some Trig Cut-Ups.  Maybe next year.


Saturday, November 19, 2011

Things I've Tagged (weekly)

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

Friday, November 18, 2011

Two more days...

It's felt like months since we've had a day off of school (except for weekends, of course, which are normally so crammed full of stuff that I am able to relax more during the week!).  That Labor Day to Thanksgiving stretch is certainly a killer!  But can you believe that it's almost Thanksgiving already?!  Yikes.

Working on trig in precalc and it seems to be going pretty well!  I've taken a page out of Ms. Cookie's book ( I referenced it here) and have been giving them a unit circle every day to practice with (writing degrees, radians, ordered pairs).  I don't know if I'll go so far to "grade" it, but they are definitely appreciating the value of knowing all of the points and angles around the circle.  On day 1 I had 3 kids (one in each class) complete the entire unit circle in 4 minutes.  On day 2 I was up to about 12.  Niiiiice.

Yesterday was when I introduced reference angles for the first time... but I let the kids come up with their importance.  After our unit circle 4-minute frenzy, I gave them this half sheet:

I was really pleased with some of the relationships they saw in the angles.  Recognizing the reference angles with our special radian angles was a piece of cake (and I'm embarrassed to say I'd never made the connection before!) and in two of my classes they saw that all of the degree answers were the same value from the x-axis.  Hopefully that will help the idea of the reference angle stick!

I'm heading to my alma mater tomorrow (Miami University!) for a math competition.  Our calc teacher takes a group of kids each year and I've never been able to go until this year. I'm not going as an official chaperon, but I am riding the bus (ew) because it's totally out of the way for the calc teacher to come to school then drive to Oxford (she lives halfway between the two).  Should be a fun time - I know most of the kids she's taking (I think there's 9 of them) and it's supposed to be a pretty day.  Besides, any day that I can get a bagel at Bagel & Deli is a banner day!

Just gave a factoring quiz in Algebra 2... I feel like I've rushed a lot this year with them, but it's so hard to slow down because they're all doing so well!  I'm almost 2 weeks ahead of where I was last year and feel like they haven't missed out on anything.  My plan is to include factoring on everything we do now so that they don't forget it when the time comes when we actually need it.  We'll see how that goes. :)

Wednesday, November 9, 2011

Trig! (almost)

Pam Patterson just sent me a link on twitter that's AWESOME. It's a list of assignments (with linked activities) that a teacher named David Pleacher gives to his precalc classes (who just coincidentally are using the same book that I do!).  Heaven.  I actually have quite a few of the resources he uses, but it's always nice to find some new ones!

We talked about the unit circle today in precalc - it's nice to be able to bring together all of the "random" things we've been doing the past week (like radians/degrees/special right triangles). I always like the kids to know where the ordered pairs on the unit circle come from, so I hand out notecards, we draw the special triangles to fit in our unit circle, label the sides, and voila!  The ordered pairs.  There's always the awkward moments where the kids are trying to see through their notecard to find the 30 degree angle so that they can draw the triangle.  Today (after doing this twice already... and multiple times for the past 10+ years) I had a revelation.  WHY NOT USE PATTY PAPER?  We have a ton of it (so I'm not scrounging up note cards) and it's see-throughable.  I can't believe this wasn't obvious to me years ago.  I grabbed a box from the math department office and used it 5th period without a hitch.

My Algebra 1 class finished up Barbie Bungee today... and boy, them working with Barbies was quite different than my Algebra 2 class. They looooved it.  Barbie had quite a few more accidents, though - and that was just on our walk to get to the final bungee location!  Needless to say, they were quite excited about our "field trip" to the football field for the big drop.

Factoring today in Algebra 2!

What a big day it's been.


Monday, November 7, 2011

Missing students

I've had three types of students miss multiple days here lately. I've broken them down into three categories...just because I like to think like that. :)

 1. The ones who disappear without word for 3+ days. I later find out they've gone on a vacation. These are the type that, upon return, are shocked to find out we moved on without them. Had one of those return today... he didn't even dare ask me if he'd missed anything, thank goodness. He was out for all of last week.

2. The ones who are gone for 3+ days and ask for assignments in advance (and continue to remind me about it, because my memory isn't the greatest when it comes to stuff like that). I like them even better when the work's all done when they come back! One of my students went on a cruise in the first month or so of school and came back with every assignment done. Little did I know that he would not complete another assignment! (Ok, that's a stretch, but it's not too far off!) Related to that is the students who contact me about assignments after being out several days - those are emails that I welcome! One of my freshmen was absent for 3 days last week and emailed me asking if I would send her what she'd missed. She came in today without missing a beat.

 3. The students who are gone unexpectedly for long stretches (either from illness or some other emergency). I found out over the weekend that the father of two of my students passed away unexpectedly from a heart attack. You really just have to feel so badly for the family. One of the students already arranged for a friend to pick up the work (and I guess was concerned about getting behind). I'm not sure what will happen with the other. I hate to think of them spending time on their schoolwork right now (honestly) but it may be a nice way to feel somewhat normal. Hope they're ok!

Tuesday, November 1, 2011

Pumpkin pi!

Math tweeps

I created a gdoc today to try and organize the math people on twitter.  I'm leading an inservice session next week (along with @mseiler and @dhausberger) and thought it might be helpful to have a list of people on twitter for math teachers who want to get started.

Please add yourself to the list if you're not there already!  Thanks! :)

Monday, October 31, 2011

Happy Halloween!

Pumpkin pi, anyone? :)



(It's amazing what kids will do on the last day of the quarter for extra credit!)

Saturday, October 29, 2011

Things I've Tagged (weekly)

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

Friday, October 28, 2011

One class down...

Just finished first period and I wanted to make some notes on it before I forget what happened. It was truly a whirlwind!  I'm thinking that half of the class walked out without a clue of what had gone on.

1.  Started out showing my facebook powerpoint.  When looking at the quartic regression slide, one of the boys (let's call him Fred, because he'll be back!) brought up the idea of Myspace, which I had intended to address as well (thanks to @DaveLanovaz last night, who made the same comment!).  Someone else questioned why the logistic regression equation didn't give a correlation coefficient.  I told him I didn't know why; I'd looked into it last night and couldn't find out. Fred (who is taking AP Stats) told us that the correlation coefficient is found by taking the log of something (he lost me here) to turn the equation into a linear equation. Because the logistic equation had already been taken a log of, you couldn't do it again.  Hence no correlation coefficient.  Or something like that.  (@druinok let me know (late!) last night that maybe my regression equations weren't the best as the calculator uses least squares regression which would affect the vertical aspects of the equation.  I decided that instead of redoing all of my slides I was just going to let it slide. Ha. :) )

2.  Flip the paper. The other problem they were to work on last night (thanks to @JackieB!) was to find the area between f(x) = e^x and g(x) = ln x in the interval [1/2, 1].  We talked through strategies... plot some points, draw a graph, cut up the shape into shapes we know to find their area.  Fred kept referencing integrals (I kept putting him off), other ideas were a trapezoid and a triangle, a big rectangle minus two triangles, and two triangles. Then I let Fred talk. He's a great kid - the kind who is constantly running up to the board to do his "thinking".  He's very very interested in all things mathematical and is currently taking AP Computer Science, AP Stats, and Honors Physics (in addition to Honors Precalc).  He explained the "idea" of integrals (dividing up the shape into smaller trapezoids of which you have an infinite number of pieces) and was very theoretical. Then another girl (who had asked me yesterday if this was an integration problem) came up to the computer and talked through something more "concrete". She showed an integral, made up a function, showed exactly what it was she was finding in terms of the area, and found her area.  Did I mention she's a sophomore who's come up through college prep and was just added to my class a few weeks ago because the trig teacher thought she needed more of a challenge?  And did I mention that she takes extra classes on the side because she likes math?  Anyway.  The other kids in the class were stunned.  Some totally tuned out because they had no idea what was going on and some were interested and amazed that they were seeing a classmate do this.

3.  New stuff - modeling exponential functions.  Not so exciting, but I was able to get the rest of the class to tune in.

Crazy class.

Phew.

(A year ago this never would've happened because I wouldn't have given them the opportunity to think this way.  Shame on me.)

Thursday, October 27, 2011

Facebook regression

It turns out that using an exponential function to model the facebook population wasn't the best choice.  Check out the results!




(Can you tell I had fun making this? I love the results of this question!)

Wednesday, October 26, 2011

Catching Up

So a few days ago I was happy that I was all caught up in everything.  Today?  Not so much.

Friday's the last day of the quarter and I've got a stack of papers thiiiiiis high on my desk.  Projects (kinda) that I collected from my precalc kids today, Algebra 2 systems of equations quizzes that were taken yesterday (which I should've graded last night but just couldn't bring myself to do after spending almost two hours carving pumpkins with the kiddos), and a myriad of make-up and late work that needs to be added in.

[side note: There's just something about random papers that annoys the heck out of me and I hate trying to figure out where they go and why.  I was actually considering this summer coming up with a half- or quarter-sheet for the kids to staple to their late/make-up work saying when the assignment was due and why it is being turned in late.   I might consider that for next quarter.]

And so I can avoid actually getting any real work done, there are a couple of things that went well today.
1.  My principal stopped in during my 3rd period class for what I guess was a formal observation (although I thought that we were supposed to be notified about them, but oh well.... I'd rather be surprised so I don't stress about it).  It was probably the best class for her to be here for, which was nice.  We spent quite a bit of time reviewing last night's assignment (solving exponential and log equations), took a little side trip to Wolfram Alpha to see if it would tell us about the origins of the term "natural log" because one of the kids was insisting they were abbreviated ln as a result of being Napier's initials (um, no), then went to google translate to check the translation of natural logarithm into French and Latin.  Hey, you know it's all about 21st century learning, right?

Then we went over a couple of the questions they still had about the Risky Business project that was due today (and that was seriously all for show - I never intended to do that with them but thought she'd appreciate the assignment.  She did!  She loves that kind of thing) so we did a bit of that before I gave them tonight's assignment.

2.  One of the days I dread the most in Algebra 2 is the day when we first start Linear Programming.  It's such a process that the kids really don't like it... and today was that day!  After a bit (ok, a lot) of whining about how long it was going to take them, the kids really settled down and hopefully will do ok on the problems I gave them to try tonight.

3.  Over the summer I'd put together what I could about the number of people on Facebook through the years.  I found something like this and typed up a list showing how many active users were on through the years.  Today (as we're finishing up with exponential functions and logs) I finally checked the values that I had and was delighted to find that the numbers are almost a perfect exponential function!  Nice.  So tomorrow I'm going to ask my precalc kids to come up with the date when Facebook has 1 billion active users. Should be interesting!

I'm out of stuff to say.  Guess I should get to work!  Boo.


Monday, October 24, 2011

Musings....

I'm actually somewhat caught up on work tonight right now, so wanted to jot some things down that I found tonight (while cleaning up my 1000+ google reader. Sigh.).

1.  Another gem from Ms. Cookie. Love her. I'm so happy that she's back to teaching precalculus this year!  Love this idea....

"I'm also going to start the 100% or 0% quizzes soon. I want them to have quick and accurate access in their heads to the sine, cosine, and tangent of all the special angles given in radians (including on the axes). I give them a 10 question (14?) quiz and I take it with them the 1st time. I tell them that I'll give them twice as much time as it takes me, and they have to get 100% or it's a 0%. They can take it as many times as they want throughout the 6 weeks. This forces them to have a super fast grasp of it."


2.  A salary/when-are-we-going-to-have-to-use-this pic from Dan Meyer.  Love the coordinate plane involved.  (And you have to love Dan's comments, too:  Good news about learning second-year algebra and trigonometry, though. It seems you're well-positioned for a career teaching second-year algebra and trigonometry. (See also: careers in physics.))


3.  I gave my precalc kids something like this the other day in which they found a quadratic equation relating the drop and speed of roller coasters.  While whittling down my reader, I saw this post shared by Kate Nowak that I'll definitely (try to remember to) pull up if I give that again next year.


4.  It seems as though I didn't learn last year when giving a project the last week of the quarter. On Friday I handed out a "Risky Business" activity (not really a project) in which they kids will use logs to determine the risk factor involved in several different activities (which I have been waaaaay too helpful on. Seriously need to stop that!).  I've had several students ask about watching/acting out the Tom Cruise underwear scene from the movie... I've denied that, but I think I'll show the Alf version tomorrow. I wonder if they'll know who Alf is.


5. Got an email from our district tech-type lady about leading (helping? who knows) a Twitter PD session on our next inservice day. I detest speaking in front of people so this is already causing me anxiety, but I agreed. Now I'll just need some help from you all in trying to decide what to say. Luckily there are some other math teachers at school (@mseiler and @dhausberger) talking too so I won't have to go solo.  I'm thinking of trying to find Sam Shah's talk he did a while ago about the blogotwittersphere and showing it... :)
[Found it!  And he called it the Blogotwitterversphere]

Friday, October 14, 2011

End behavior!

Blogging is so not on my list of things to do today... but I had a comment that I couldn't resist posting!

My Honors Precalc kids did their Polynomial Photo project last week (or so) where they used geogebra to fit a polynomial function to a picture they'd uploaded.  (Links here and here.)  I added some requirements to it this year - instead of just finding a polynomial, they also had to find its zeros and end-behavior.  When I entered the grades for the project on our online gradebook, I included in the comments what they'd left out so the kids could see why they didn't get some points.

One of the girls came in today saying that her parents sat her down last night to have a "talk" with her. They'd seen "end behavior" as a comment and thought that it referred to her behavior in class.  She then had to explain exactly what end behavior is and why she missed her points.

I thought that was hysterical!  (Keep in mine that this is a good kid who LOVES math and wants to be some sort of mathematician in the future.)

***************

Another "Fun Fraction Friday" in Algebra 1 today!  Although they complain about fractions, I honestly think these silly freshmen would be disappointed if we didn't do them.  When I see kids in the hall before class on Fridays they always ask if we're going to do Fun Fraction Friday.  So funny.

And to make it even better, today I gave them a bunch of word problems, too!  (like, "this train left point A at this time traveling this speed... when will it meet the other train")  It was a momentous day for us.  And yet they still had fun, thought that solving the consecutive integer problems was "cool", and the other word problems were "so easy".  Seriously?  Who are these kids?!

**************

Looking through the results of the fractal activities from last week (I know, I know.  I'll never catch up.) The last question they were to answer was "What's the relationship between fractals and complex numbers?"

One boy's answer:
It's complicated, but they're trying to get it together. Fractals has a problem with commitment but he loves complex numbers and wants the relationship to work out. Complex numbers loves fractals just the same as she did when they first met, every kiss to her feels just like the first again, she wants fractals to put a ring on her finger but she doesn't want to rush him.

Total BS?  A funny way of getting around finding the real answer?  He's lucky that it's Friday and I'm in a good mood. :)


Saturday, October 8, 2011

Things I've Tagged (weekly)

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

Wednesday, October 5, 2011

A few comments.

I'm actually ready for 7th period today (this is my plan period, and I'm usually getting ready for my last class of the day!) so I thought I'd post a couple of things I've been thinking about.

1.  I had a nice comment from a fellow math teacher yesterday while I was running on the treadmill (less than 2 weeks until my half marathon!).  He said that as a football coach he talks to a lot of the guys about their classes and how they're doing and has never heard anything bad about my class.  The guys all enjoy it and think I'm a great teacher and explain things well.  So nice to know!

2.  In precalc we just finished up the fractal unit that I put together (here).  The kids enjoyed it; some got into it more than others, of course, but it was at least something new for most of them. A few people said that it's changed how they're looking at their surroundings, checking to see if things are forming fractals at all. I thought that was pretty cool!  I scrambled and found some of the long skinny balloon-animal balloons (on clearance at Target!  woo hoo!) and several groups made a tetrahedron balloon fractal (check out Vi Hart's instructions here) that I hung from the ceiling.  Just in time to look good for conferences. :)  Or not so good, in some of the cases!

3.  One of my Algebra 2 girls (who is totally rocking it right now... somewhat surprising to me because I had her older brother last year and he really struggled) asked me the other day if I was the only person who teaches the Honors Precalc class.  She was kind of upset that I am because she said it's making her want to take the class.  (I think there's a compliment in there!)  I told it was really early to be deciding that and we'll talk about it later in the year, but at this rate I think she's a shoo-in.

4.  Parent conferences are tonight, so it's one of those 13+ hour days that you only dream about (or have nightmares about!) over the summer.  We went to all appointment times this year (as opposed to our normal division of some walk-ins and some appointments) and mine are all full.  I'm not looking forward to the constant  talking but at least the evening will go quickly!

5.  I keep getting emails that people are adding me on Google+.  I'm honestly wondering why (and where these people are coming from!).  I haven't been on Google+ since it first came out and have posted a total of probably 2 comments.  Anyone else this way?  I'm perfectly happy with Twitter as a professional resource.

Saturday, October 1, 2011

Things I've Tagged (weekly)

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

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) = 

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).



Step 2.  Find the product of the zeros.
                  (Which is the opposite of the constant term.)

Step 3.  Find the sum of the zeros.
                   (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 .
  (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, . (It ends up being f(x) = 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)

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!)

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

Tuesday, August 30, 2011

Precalc box project

What's the biggest box you can make out of an 8 1/2 x 11 piece of paper?  Go.

That's the question I posed to my precalc classes yesterday.  The first class kind of just stared at me for a minute, then thought of some questions.
1.  What does biggest mean?  (we decided volume, not surface area)
2.  What's a box? (um....)
3.  Does it have a lid? (we decided no for simplicity's sake... but today figured it out with a lid)
4.  What shape?  (we went with a rectangular prism, but one boy wanted to do a cylinder, so he did!  love him.)

As a class we came up with a net of the box on the board, labeled some values, and came up with a formula for its volume.  But how do you find the maximum volume?  Someone suggested graphing the volume equation... but then what?  What does a cubic look like?  How does it have a maximum if it goes up forever?

That lead us to a discussion on the domain of our volume.  The polynomial itself will go to all reals, but that's not applicable for our box.  Once we had a good window, we talked about how to find the maximum value (without tracing on the calculator) and what that ordered pair represented for our box.

At this point, everyone grabbed a piece of cardstock (cut in different sizes so they had to work independently), measured, and proceeded to maximize their box.  (Question - what do I do with 90+ small open-lidded boxes?)

Today I had them do some checking for me.  Everyone grabbed a constructed box from yesterday, measured it, and entered their values into a google spreadsheet that I'd set up.  It was a little crazy with 14 people trying to enter their numbers all at the same time (because they kept typing over each other) but it was fun to see all of the data come in.  Then they were to come up with the maximum volume for a lidded box (after we drew a net and found a volume formula together)... though I'm not sure the net we came up with would maximize the paper, it was fun to see them think through what it would need to look like!

I actually did this project at the end of last year when we were doing limits and derivatives in precalc.  They then had to find the derivative of their volume function and determine where it would have a maximum (by setting = 0).  I'm going to keep one of the pages they filled out leading them through the process and give it back to them in May so we can do the limit and see that it's magically the same value that the calculator gave us!  Crazy how that works.

(Much thanks to Luajean Bryan, who showed us this project at NCTM!)

Thursday, August 25, 2011

Two down... how many to go?!

Two days down, and I think my body's in shock.

Ok, so maybe I'm exaggerating.  I'm feeling my feet and legs ache... I'm feeling my tummy rumble (lunch was at 10:15!)... and I'm feeling my body all yucky and covered in sweat - gotta love having no a/c when it's 90+ outside!  I literally was dripping around 7:45 this morning (but it actually got a little better as the day progressed because the humidity subsided a bit).  And did I mention that I could totally go home and go to bed?  5:20 am is inhumane.

But my first two days back have gone pretty well.  The kids seem nice (except one boy in a precalc class who I can already tell is super annoying... and I knew that after the first 10 minutes in my room!) and have been working for the most part. I assigned summer work for precalc and it was nice to jump right into factoring, solving, graphing, etc. without the normal foray into "here's what you should know" stuff.  I'm giving a quiz tomorrow which could be interesting (especially after grading all of the kids' summer work!)... honestly, what kind of "honors" kid doesn't do half of their assigned work? Or just writes answers (which I posted online for them)?  Maybe this will help my classes decrease in size a bit - I've got 32 in two of the classes and 27 in the other.

One thing that hasn't gone well is the technology component.  (I know - shocker!)  I had a wireless hub in my room which didn't seem to be working well except for the 5 minutes after I unplugged and replugged it.  Our tech people came in and determined that the hub was causing problems all around me, so it's now gone.  Yesterday was actually ok without it, but today's been a disaster.  I wasn't able to wirelessly connect to my projector and have lost my connection to the network numerous times (which means I haven't been able to print or get online). The tech guy was just back in the room and tried a new hub to no avail.  He said the engineer is supposed to come in on Monday and hopefully will get things back up like they're supposed to be... but I'm sure we all know that that's doubtful!

I'm a little at a loss with my Algebra 1 class.  There are only 22 kids and mostly girls and they all seem very sweet.  I gave them a fun problem to start class today (there are so many girls with cats and backpacks, etc. How many legs?) that they seemed to enjoy, then I handed out a skills review page just to see where they're at.  It had adding and subtracting with negatives, order of ops, and some simplifying/distributing with variables. We got through most of the first two sections without a whole lot of problems although there was some surprise that yes, sometimes you will need to divide before multiplying, but what I heard from them with the algebra section let me know that we'll basically be starting from square one with variables.  At least I know where they're at!  Kinda.

I'm done rambling and I want to find some a/c.  And a snack.

Saturday, August 20, 2011

Things I've Tagged (weekly)

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

Tuesday, August 16, 2011

Ask and you shall receive

It amazes me how generous people can be when you just take the time to ask.

Case #1.  My previously-mentioned paper folding escapade with my Algebra 2 kids last year. All it took for me to get 2 large (!) pieces of paper was an email and a special trip to pick them up. For free.

Case #2. I've been doing some searching this summer to find new projects I can use in Precalc. I've had a little luck finding stuff online and have run across a book called Projects for Precalculus every time I search.  Unfortunately, this book doesn't seem to exist in any stores.  I did, however, find the email address of one of the authors of the book and decided to write. I said I was a precalculus teacher and was interested in his book but wasn't able to find it for sale anywhere. He responded back today and said that it was out of print and then he sent me a copy of the book on pdf.  Can you imagine?!  Twenty-six precalc projects now at my fingertips. For free.

Case #3. One of my twitter friends sent me some files today that I'll be able to use in precalc to help the kids get ready for the AP Calc format.  Twitter.  I can't say enough.  If you're not on twitter, get on it. If you're not hooked up with a good group of teachers to help you, let me know.  You're seriously missing out.  And you know what? It's free.

Sunday, August 14, 2011

Memory loss

With opening day just a little over a week away, I'm trying to get a little more specific with what I want to do starting out in each class... and yet when I sat down to do that, I couldn't remember exactly how I'd opened last year.  Thank goodness for this blog!  Just checked out the archives and found my description of what I did last year (it's here).  Whatever did I do before blogging? :)

****

I typed that a few hours ago with the best of intentions to get some work done tonight for Algebra 1 (my kinda new prep). And then I got distracted with my first day stuff.  Last year @lmhenry9 made up a prezi to show the kids the answers to her Quiz about her and I thought about doing that but it would've taken me forever to make (I'm not the most proficient with prezi).  So I fell back on the good old powerpoint.  And 3 hours later, it's done!  (Seriously?!  Obsess much?!)




It was fun to make, though, and hopefully the kids will enjoy it. :)

Saturday, August 13, 2011

Things I've Tagged (weekly)

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