Monday, November 17, 2014

Sine Graphs and desmos.com

We have finished all of the transformations for sine and cosine graphs, and soon I want to have an application day where they can write models for various data: blood pressure, tides, weather, oscilloscope readings.... but first I assigned them the following homework:

Think of a city in the world, maybe you want to visit, or it's exotic, or it's far away, or it's a place you have never heard of but searched for online. Then find weather data for a 12 month period for your city. We quickly logged onto desmos.com and they got accounts and we practiced making/plotting table data and changing window settings and such. They were to come back with their city weather data entered and saved.

The next class, we practiced on paper with "weird data":

I made them just draw a generic sine graph with no axes or numbers around it. I then prompted them for numbers, and then got (say) the "28" for the top x value and the max (71) and min (-31) y values. I made sure to wait until I heard things I wanted before I committed them to the paper.

Then they had to find the amplitude/vertical shift/horizontal shift/period. We talked it through and then got an equation. We did it again for a cosine graph. 

Then we went on the laptops and they brought up their weather data. I asked them to do what we just did to find an equation that would model their weather data. Most importantly, YES they could guess and check, but it would be WAY better to think things through and come up with an equation first and some justification for the 4 key values as we practiced and then play around.

It made for some interesting conversations about "not normal" data points (I picked Timbuktu, Mali, and the year's data had a cold snap for 4 months that should have been hot) .... and about north of the equator and south of the equator cities (one student's data was warm in January and cold in August) ... and cities that were near the equator (all the temperatures stayed basically the same all year). 

My Prague data worked out better than my Timbuktu data:

 

Tuesday, November 11, 2014

Hello (mid) November

I have nothing to blog about, so here I go blogging. Isn't that how it works? Is there a point in every year/blog/person where you start to think of something to expand on and then go, eh, been done, not interesting, navel gazing, ....

Some things I've learned so far this year:

* My "if you want help, you need to ask for it" policy was NOT working for all kids. Shocker! In my mind, I was all, "You're 11th and 12th graders! Ask for help!" But in reality, for whatever reason (apparently, I'm scary??), there were kids that were just fine with sitting there in class or after school and being stuck but not asking for assistance. When I finally picked the brains of some kids, I got various responses: well, I don't know how to phrase the question specifically .... well, you were busy .... well, I feel you judge me .... etc. This has caused me to reevaluate how I run class. Now I purposely stop at each table and kid and ask how it's going. It seems that if I'm the initiator, then I get more responses.

* For precalculus, I have a 100% or 0% quiz I give to the students so they learn the values of sine/cosine/tangent of special angles in the 1st 2 quadrants. They initially have 2 minutes and 10 questions, and if they get any wrong it's 0%. They can take the quiz as many times as they want in a grading period. Usually, this is enough of a motivator for my groups of kids to study. This year, not so much. I had the idea of having MANDATORY 15 minute conferences with me about 2 weeks into the grading period. I made a sign up sheet that basically said: morning, lunch, after school with 3 name slots for each and told the kids they HAD to come in at some point in their time frame. I loved it. This allowed me to talk to kids that would NEVER come in for help. I could see how they were tackling the problems and give tips on speed and patterns and strategies. Of course some kids were already fine, so I could just validate their awesomeness in this arena and move on. I'm thinking of having such a mandatory conference for all my classes (on what?) and all my kids at some point in the year. Am I the only one that hasn't ever done this? Some things I like about it are that I talk to kids I may never talk to in class. I also get to see their thinking and pick their brains one on one on how they are doing. I also get reminded that they are humans and not math-receiving vessels.

* In AP Calculus AB, the learning opportunities NEVER stop. I hear my kids learning AFTER an exam when I make them come in to do corrections one on one. I see them learning when they go through my detailed answer key where I give them extra tips on how to do things and what to watch out for. I sense them learning when they are helping each other through hard problems. Yay math.

* Humans are prone to be happy AFTER something is over and they realize it was not so bad after all. I saw some kids that were in calculus last year, and they are unsettled with the math they are learning this year. They said they "missed calculus" and they were surprised. Hah. I take this more as, now that calculus is over and they saw they were successful, they want that comfort level again because they know how it turns out. Now they are in a new situation with a new teacher and it's an unknown, which everyone knows equals SCARY. I'm guessing next year, they'll be all, "oh, I miss last year's math class!".

* I'm turning 50 this school year. Oy! So that's occupying a large space in my mind. I've decided to make this a year of "trying new things". So far that has entailed going out to eat at DIFFERENT restaurants, ordering a DIFFERENT smoothie than usual, cutting all my hair off into a short cut not seen since 1985, .... that's it so far: food and hair. Go me. 

Okay, maybe I did have some things to blather on and on about.

Thursday, October 23, 2014

Fraction Remix...

I had about 20 minutes after a test today, and RIGHT before the test, a high school student in precalculus was confused about how to divide 2 fractions, and she couldn't remember the method: "do you multiply the top and bottom?" were words that came out of her mouth.

So. I thought I'd give the following short lesson on why the "flip and multiply" that they seem to spout works.

First I asked them the following questions:

Simplify:   (7/3) / (4/5)

Then after they did that and checked, I asked them to discuss WHY it worked, and "my teacher said so" or some such thing wasn't an option.

Then we walked through the following 4 scenarios:

 So to recap, it basically boils down to seeing how many groups of the denominator fit into 1 unit (that's where the "flip" comes from), and then how many 1's fit into the numerator, and then you combine the 2 numbers and MATH.
 

Saturday, October 18, 2014

Boring Ceiling. Fixed That For You.


Something needed to change. I could no longer stand the travesty that was my ceiling. How could we spend day in and day out under such a boring mess? How was learning taking place? How did we all not just fall asleep under the endless white scandal that was looming over our heads?

After searching the internet for ideas and finding an art teacher that had her kids paint black and white designs ON the tiles and realizing I didn't want to go THAT far, I came up with:

 I am happy with the results. I still need more, as not all kids chose the opportunity. And as a side note ... for all the questions I get about bonus points, you'd think I'd be drowning under a pile of drawings, but, nope. Nada. I am not one for bonus points, and this was a rare instance, but, hah, go figure.

 

Thursday, October 16, 2014

Intermediate Value Theorem

I have never liked my unit as a whole for the Intermediate Value Theorem in Calculus. My explanations, I like, my homework and the time the kids spend thinking about it and then quickly forgetting it, I don't like.

Attempt this year:

 I like this first page because the kids have to stop and process the whole IVTh and think about the parts and then analyze the parts and see what goes wrong. I heard some good discussion.

I like this second page because for 5 and 6 they then have to start the thinking process graphically on how to apply the IVTh. Then problems 7-9 are what I just used to do by themselves. Hopefully, this year after they've processed things, then 7-9 should go better. We will see.

In other news, apparently I make kids feel dumb - based on a conversation I had with a parent. Oy! They interpret how I talk to them as just expecting them to know things already. Of course it's an obvious logical conclusion on my part that "one kid" implies THE WHOLE CLASS. Go me! Because of this, I made the following handout, and we had a discussion, and I asked them to tape this in their notebooks (or staple it to their hearts) to remember:


Monday, October 06, 2014

Trig Identity Match Up Activity

I'm on my quest to try different things for the Trigonometric Identities unit. They explored last class, and today I wanted to get them started on simplifying various trig expressions using identities. Here's what I did. I made this set of 2 sheets for every student, put it on colored paper, and then made them cut them up (my first class) when they started.

They're mixed up on the sheets, and there are FOUR total problems that start with the "squiggly" boxes, but I didn't tell them that first. I said they should look for 2 cards that pair up in such a way that they are ONE step away from each other either by an algebra law or by an identity. I did one example with them and took questions. Then they were on their way.
Since they sit at tables, and I didn't want to do different colors of sheets of paper (though I guess I could have), I had them draw dots in different colored pens (one per set) at the bottom right corner of their cards to avoid mix up.

Once they got as many pairs as they could, and I mentioned that depending on a variety of things they may not get pairs. Then I said they could try to find a "triple" pair for their remaining lone cards. After some time for this, then I asked if they can "pair up" the pairs to get a set of four .... Ultimately, I then said, or they noticed the "squiggle" cards, and we got to the point that there are FOUR separate problems, that each start with a squiggle card, so see if you can set up 4 different strings of "one steppers".

During all this they had their "notes" on pink paper that they were going to eventually tape in their notebooks.


This all took about an hour or so to give them think time, and not everyone was successful with all of them, but we came together as a class and talked it out and got the 4 sets of problems, and celebrated any successes they had. Some problems had 7 steps, some 6, some 4. Then students taped the notes in their books, and we copied down 2 of the problems into their notes with "reasons". Hopefully, this will aid in their homework tonight where they have to do a string of one steps for each problem.

Friday, October 03, 2014

Trig Identities

We have started our unit on Trigonometric Identities in precalculus. Every year is going to be THE YEAR where it all comes together nicely, and the sun comes out and the birdies chirp and the kids embrace their Identities. Yes. It will happen. Chirp. Chirp.

I took some extra time at the start of the unit this year for them to explore instead of me walking them through things and them nodding their heads pretending to understand.



This took most of a block period (2 pages), and it was a nice refresher of a few things: 
* proof rules from geometry
* fraction rules for adding/dividing
* exponent rules

Hopefully, the extra time we spent will be worth it in the end as we skip and hop through solving/simplifying various equations/expressions involving trig.