Time for AP Calculus AB Review

I handed this sheet out too late last year, and so didn't promote and stress effectively enough this aspect of their studying:

This year, I took some time in class today to stress each bullet. Basically, the theme was, "do something that will realistically work for you", and "show me that you have put some thought into this", and "if you find it's not working, then revise your schedule on the fly".

I personally know how it is that time just slips away if I don't have a firm plan of action on what to do when.

Hopefully, this will help the little boooooogers.
 

Seven Segment Display

In all of my classes this year, for the most part (unless I'm thoroughly bogged down and re-use an old key or such), I am doing the homework assignments that I assign my students fresh each year, and if I assign a project, I do it with them. I think this keeps me honest and I can keep my skills fresh and each year I can see what the issues may be and also commiserate with the students if things come up. Maybe everyone does this.

Anyway, in Digital Electronics, there is a Seven Segment Display project that we do. Here is what an SSD looks like. The students are supposed to do the logic and circuitry either to light up their birthday mm-dd-yy or to spell out a word/phrase. My phrase is "Go run 26.2". I have been working on it off and on with the students from the outset. Then I got "all that" and expected it all to work swimmingly the first time I did the breadboard. Hah! I have had a pickle of a time tracking down my errors. Then there are the students in various states of distress or completion or such that I have to help or talk down from the cliff or push along to actually put out some effort.

Our current phrase to each other is, "I am smarter than a plastic board!" to keep us going. I also keep their motivation up by telling them, "I have NEVER had a student fail this project, and you will NOT break my record" whenever they start whining, "but what if I don't finishhhhhhhhhhhh?"

Well, well, well, I just finished mine, and here is my YouTube proof. Woot! What do you know, I AM smarter than plastic!

 

Italy...

We just finished our spring break and it's back to business as usual (or maybe unusual since we need to remember how to teach/learn again). I got to go to Italy for a week and LOVED it (how could you not). 

We went to Rome, Siena, and Cinque Terre. 

 

Cool Rome Things: 

* You can just walk around town and be simultaneously hit with modern and ancient structures. 

* Catacombs.

* Pantheon.

* A mix of tourists from ALL over and chic locals going about their business.

Cool Siena Things:
* Panforte Panpepato!
* Medieval Buildings.
* Gorgeous churches.
* Great streets to walk around and observe and see the doors.

Cool Cinque Terre Things:
* Views.
* Trails to walk on between towns.
* Water.
* Hills.
* Easy trains between the 5 towns.

Observations:
* I love Duolingo and promise to be Italian-Fluent soon .... you know, like my "people" (or future people ... or people wannabes).

* Hey Roman Bus Driver, just because it's the 1,000th time you've been asked this question, it's just my 1st time asking it. Sorry to make your eyes roll.

* Hey badly-chaperoned students coming back on the plane from NYC, no one wants to hear about EVERYTHING about you all the way back home. Use your inside voices so that only 2 or 3 people around you can hear.

* Dear US coffee sellers, I think a field trip is in order to learn how to make non-bitter coffee.

* Dear TexMex food, thank you for the tradition of being our first delicious meal back when we return from "non Texas".

Straight Line Motion and AP-Style Questions...

Last year, I broke up notes into 3 different days, and yada yada yada'd my way through things in this unit. I did examples. I put definitions. I did tables and graphs and stuff. Do you see all those "I"s floating around?

This year, I gave a flipped lesson on ONE page of all inclusive notes on Straight Line Motion. Then we did "Waldo". I think that went okay. Today I did something I learned of in an AP workshop where one person is in the role of either positive/negative velocity and a 2nd person is in the role of pos/neg acceleration. They walked it out, and we discussed how the forces either work together to speed up or against each other to slow down. Someone made a funny video of it in my class. Good times.

Then "we" did THIS. I think it's good because it mixes calculator and non calculator skills. It also asks specific ONE question each on pos/veloc/accel type things that I found on free response questions. I also like the answer bank because of the immediate feedback the kids get so that they work harder and more instantly on figuring out things.

 

Straight Line Motion: Calculus

I don't know if this was effective today. We had a late start day, and the kids are already in SPRING BREAK mode, and everyone was brain dead. Did I kill them, or are they just being teens? The second one. Yes. 

Anyway, this  is what my students worked on to get a sense of position, velocity, and acceleration. I think I need to follow it up with more of the same, just to get them in the right frame of mind.

 

Vector! Vector!

You would have thought by the scrunched faces and cries of "this is harrrrrrrrrd" a bit ago, that I was slowly poisoning my students with math torture tools and stunting their growth. I had this "brilliant" idea that I wanted to tie their initial vector learning to video game programming. 

The first day went fine with notes and stickers and basics. Then the next day I thought they could self teach through a packet. It was "fine" except they were to make their own graphs/grids, and then the numbers weren't nice integers, then the estimation was doody, then ..... Drama in the math class! 

I always go back and forth with the, "they're bad at fractions and get worried about "wrong answers" if they're not integers, so I should have fractions in EVERY lesson" versus "Oy! New Topic! Hard enough. Let's not complicate it with fractions."

Anyway. Here is version three of a packet for teaching vectors. I don't know if it seemed to work well because they'd already had exposure, or if it was just effective on its own. I do know that I had to walk around the room and monitor errors and such.

Here is what we did with vectors today. I think in the future (after more torture), I would then give a mess of practice calculations with an answer bank to make it stick in their heads.

 

 

Best.Husband.Ever.

My husband is the nice spouse in our relationship. He also gives thoughtful presents whenever we actually do exchange gifts (not a big thing for us). 

He is currently in D.C., and had some extra time before his flight home, and he's fascinated with flying, so, hello Smithsonian Space & Flight Museum.

Anyway, he knows I'm fascinated with "bathroom issues", as in:

- Camping ... where will you "go"?
- Marathon ... hope I don't have to "go"!
- Getting Older ... diapers!
- Old people ... they may smell like they "went".
- Babies .... ew! changing diapers!

You get the picture.

I also love Mary Roach's books, and "read" on CD her book: Packing for Mars. If you've never read any of her books, they are a treat. "Stiff" was fascinating. But I actually couldn't get through the Mars book, because she does such detailed research and describes things so thoroughly, and when she got to the part where your underwear started disintegrating on your body because of "things", well, I just had to "put the book down".

Anyway, he sent me this picture because, as I said, he gives great gifts.

Accumulation Functions, Day 2

I think the other worksheet/class work went okay. It is too soon to tell. I made a day 2 sheet HERE. Also, there have been so many crazy days and now I am at a PLTW conference, so I STILL don't know if it is effective. Oh well, sharing is caring.

Quote that is resonating with me: Be a voice, not an echo.

Precalculus: Triangle Areas

Sigh of sadness. We are now done with our trigonometry unit. But on the plus side, we get to move on to vectors and all sorts of other good topics.

I made up a valentine's sheet for triangle area problems. It was last minute, so I only got 6 problems. Here it is. 

I found the "net" online, and now I almost want to cut it out and make it.

Accumulation Functions

I didn't like the treatment I gave to Accumulation Functions and the "2nd part" of the Fundamental Theorem of Calculus, so I thought I'd change it up this year.

Me Last Year: Here! Look at some quick calculations of going "forward" and "backward" on derivatives and integrals all mixed up. Boom! Here's the formula and let's apply. Oh, and here are accumulation functions. Area! Let's do it.

Me This Year: Okay, okay, let's spend more than a day point 5 on these things so you really internalize them and can get the nuances in your sleep and go on to fame and fortune accumulating all sorts of calculus knowledge.

(or at least this way of teaching it is a step in that direction).

I am not even mentioning FTC-2 to begin with. I'm going to start with this packet I made up. I have seen similar things on my web search, but I did not come across any that gave the context of the problems. I feel that THAT would have led to the same short memory of the process problems I encountered last year. 

I came up with 3 types of problems. I wanted them to be ones where the kids wouldn't feel like, "well hold on a minute there. Why don't we just measure the volume. This it too made up." Don't know if I nailed it, but I guess we will see when I present it tomorrow.

I think I will have to stop them at several points along the way just to make sure they don't get the wrong answer and then keep going on and cementing that to their brain.

Also, I have some ideas on then how to do the integrals "backwards" from a larger limit number to a smaller limit number. Still working on that. Then I think I can introduce FTC-2 based on all these problems and POOF! Success! Or at least that's how it goes in my mind.

Also, also, just because it's my last chance to brag. Okay, that's not true. I'll totally milk it at school tomorrow. I completed my first marathon today. Woot! 

And "funny" story in the continuing saga of my students feeling I'm 1 foot in the grave at 49. A kid the other day said she thought about me when she was in the store looking at cards. One was, "do you know what we call old people running a marathon? Obstacles."

Hah. Hah.  Of course she reassured me that she wasn't referring to me as "old". D*@# whippersnappers.

Law of Sines & Cosines

In honor of Valentine's day this Friday, I made a sheet of mixed practice problems in which the students have to decide which law to use and have to know when to try for 0, 1, or 2 triangles. 

I tried to be all witty and make my triangle vertices have the "love" theme.

  

I had ΔSWT  and ΔHUN, ΔHRT. I feel I have to mention what I was going for: "sweet", "hun" as in "honey", and "heart". As I was walking around the room and a student asked me about the names, another pipes up, "oh! I thought that was SWT for Swastika or Swat and HUN like Attila the Hun and HRT like Hurt". 

Okay then.

Then a student was having trouble remembering which triangles gave the ambiguous case. So I pulled out my handy-dandy spaghetti and cut some angles out of construction paper:

 

And I started snapping off spaghetti and walking through SAS and ASA and such asking, "if you were given this information and it was fixed, could you make one or more than one triangle?" ... It was fast and I think effective.

 

Thank You Pinterest

I was browsing on the math section of Pinterest the other day and found a math activity for elementary school kids.  It was similar to this (but of course I can't find the pin anymore). If the link doesn't work, picture this: you have some number (say 23) and there is a box above it and a box below it, and the instructions are something like, "subtract 8 from the number and add 8 to the number". It seemed like a nice graphical organizer for notes and to practice. 

I made one for drilling derivatives and anti-derivatives.

Then I got all crazy and thought about colors. We are just starting u-substitution, and part of the issue for kids is to identify the "u" and the "du possibility". I made a sheet where they had to color the u one way and the du another. Here is a sheet with the key on it.

 

This was meant to be quick classwork. HAH!. What crazy person put 21 problems on the left? Next time less problems. Also, I THINK I like the right hand side, but time ran out, and I haven't asked the kids if either side was useful yet. 

 

Ice Day!

Yeesh, at this rate, school will be out in July or something. We had sleety drippy cold 27F weather this morning, and it started out as a two hour delay. Yay! I could go to school and torture teach children. I left early anyway to treat myself to breakfast out. Also, I live about 24 miles or so from school, so I wanted to leave with PLENTY of time for the icy road conditions. I did see some slipping and sliding, and here are my car tires when I arrived.

Then, what's this? School is canceled. Yeesh. Now I am killing time by surfing and blogging.

On a positive note, LOVE my mini iPad and the local natural foods place with free wifi and friends I can chat with on Facebook. I think it is almost warm enough to make the trek "back north" without fear of accidents. Maybe there is lunch out in my future. Must keep up the energy to come up with more teaching techniques ( and by teaching techniques, I mean gentle ribbing of the kidlets ).

Seniors, Workload, Responsibility

I'm mulling over recent events and trying to decide how to handle this next year if it comes up again. 

Background story. At our school, we do push the students to take full course loads every year. They get a little slack their senior year and maybe can have a flex period or such. But since our intention is to get them to college and to succeed in college and to look good on college applications, we push. Also, in Texas, our students basically have enough credits to graduate their junior year ... give or take some requirements. So basically they're hard workers.

The flip side of this is that depending on what courses the students take their senior year, and how they approach their scholarship applications and college applications, and what sports they play, and how far their daily commute is, the amount of time they have for homework and sleep and life fluctuates. Needless to say, there are stressed out little bundles of walking sleepless zombies.

Okay, back to me, which, of course it's TOTALLY about. I have (had) 3 seniors in Computer Science 1 along with juniors. So far this past week or so, 2 have stressed out and decided they needed the time during the school day to do their homework, so they dropped out of CS1. I didn't complain too much, just gave them the stink eye, but I go back and forth as to what's best for the student, and how I want to handle this in the future.

One part of me thinks, "you signed for a class ... or you made a commitment to something (anything in general), then you should follow through even if it gets tough. This is what defines your character."

Another part of me thinks, "there are times when you have to cut your losses and maybe decisions you made are not the best."

A third part of me thinks, "I don't want this to be a precedent. Kids will then just sign up willy nilly to look good on their college applications, and then drop the ball when things pile up too much."

A fourth part of me thinks, "if students get in the habit of quitting things when they get too hard, then they are teaching themselves the wrong lessons and are not letting themselves get the satisfaction of knowing they can do things or figure things out when things don't go so easily."

Oy! I have some ideas on how to broach this next year, but I can still stew about this year.

Related Rates Update

A while ago I mentioned that I wanted to get the students to create some more realistic related rates scenarios for calculus. I made up a sheet last semester and had them do just that. We talked a bit about how the "simple" and "cheesy" problems they see in the book are just SIMPLIFIED stand-ins for actual problems people really want to solve. I gave some examples. Here is the sheet with their assignment.

We talked about the "cheese" factor. And by "we" I mean "me". Apparently, that was not enough, because about 1/3 of the samples I got back were still "edible and fermented". Next year more "we" and less "me". (hah! as if!)

I made sure to share the wealth and divide the types of problems "evenly" by birthday.

I made sure to get them to talk to someone who is NOT from calculus about the problem and ask if it was something that looked like someone would care if it was solved.
 

AP Calculus Wall

Last year or so I saw our AP English teacher had pictures (with AP Exam score) up of previous kids who had passed the AP exam. I thought it was a great idea and could be an archive of our history and an incentive and reminder for the "current" students. My issue was that I couldn't see how she managed to get pictures of the students after July. Nothing seemed efficient or manageable. Yes, I could have asked her, but there it is.

My vision is that after each exam is finished, the following year the "Wall of Fame" is added to with new pictures and new scores. I know this is not a new idea, and I'm sure I saw this idea somewhere before.

I'm thinking that the following may work for me. Some time in the beginning of each year school year, when students are still well rested and fresh, and we're not too into curriculum, I take everyone's picture with a blank placard, something like this:

Then after I see who passed the exam, I print those pictures and write their score with a sharpie .... or HOLD THE PHONES ... I could even edit the pictures, so not everyone has a white ball face (joke). 

Anyway, I'm excited about this, and soon the little cherubs will be in my camera roll.

Calculus Graphical Organizer

Okay little Calculus Kidlets, maybe THIS will settle things in your mind.

After reading my end-of-semester surveys, too many students were mixing up what to do when and why when finding the maximums and minimums of functions. I created this graphical organizer to put in their notebooks. This is how I picture it in my head and how I remember it, so maybe it will help some students.

End of Semester Surveys

Our administration reminds us every semester that every class must give a survey to every student and then share the responses with our department chair. I think this is a great idea, and I love to sift through the student reflections, and I'm SO HAPPY the admin reminds me WAY ahead of time. This is because without fail, I always forget to give the survey, and then I'm scrambling to hand them out on paper to the students either on a finals review day or GASP maybe even one time during the final (no! that can't be true can it?).

Anyway, my clever department chair mentioned doing the surveys online, and I tried that this semester. We did it in class, since I have laptops. I don't know if I would have had 100% responses if it was a homework assignment. SOLD! I think the students took more time to answer the questions, and I couldn't distinguish their handwriting, so it was pretty anonymous (though some revealed themselves on purpose), so maybe that helped. I do take some time, though, no matter how I give them out, to talk about the great life skill of giving constructive criticism versus negative feedback that is not helpful.

Blah blah blah. Dear Google Docs Forms, Thank you for being easy to create and send out and read anytime anywhere.

Here were my AP Calculus Questions for the Form, and some of the answers with my thoughts.

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1. Things you liked/disliked about calculus and class in general (think about daily activities or the class as a whole).

I liked being able to discuss with peers while doing homework because it gave us the opportunity to work together on harder problems instead of giving up. The ability for me to be motivated and actually have intriguing discussions completely depended on who I was seated with. For this last section of the semester, I was next to two people who generally got the concepts so if I was stuck on a homework or didn't understand a concept I didn't feel like I would ask them about it.

This is a problem I haven't mastered yet. I totally get not feeling comfortable asking your table mates  for help because you feel stupid. Part of me wants to say, "figure out a solution" and part of me wants to jump in and spend lots of time on seating arrangements and part of me wants to do a warm fuzzy table bonding activity so there is love spread all around. 
  
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Some questions on flipped lessons (good/bad) and improving the Haiku experience.
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5. What surprised you about calculus?

It is nothing like Pre- Calculus. Although it is math Pre-Calc is like the thinnest base ever for what you do in calculus.
 
Agreed! It does seem to me that labeling the class we teach as "precalculus" is a misnomer. I mean basically everything then would be precalculus because it comes before calculus. I love precal, and maybe a better name would be "all the cool stuff that you haven't learned in the other math classes and you won't see in calculus but we want you to be exposed to math", though I guess that wouldn't fit on the schedule box size.

I was surprised at how difficult calculus was for me. Previously, I was able to succeed in math by putting in extra work effort and simply working hard. In calculus, though, it doesn't seem to be enough - I don't understand why most of it is used or when to use it until several weeks after the class, when we've moved on to other subjects. Because of this, calculus has been a class I really struggle with. 

Oy, part of me is feeling like I dropped the ball here because, HELLO! I do mention why people would need to know about rates of change and how they're useful. But I guess I do it only a smattering of times at the beginning of a unit and then we go over all the various derivative rules and maybe the students don't realize that it's still all based on the cool stuff. I guess I could keep mentioning this every other class and change some problems to be application problems (now that I think about it, I don't have many. eek!). 

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6. What topic(s), if any, do you think I need to change my strategy on AND HOW/WHY? (see your table of contents)

This was revealing. Many people answered about jumbling up some concepts because we went through them "so fast". Good to know.  

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7. General suggestions you may have for my teaching of this class in the future.

Not so many abstract hand motions, more drawings and patty paper. The hand motions just confuse me.

Hah! And here I was patting myself on the back for using CLEAR hand motions. Who knew.  

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8. If you could give yourself advice for the 2nd semester, what would that advice be?
 
Shockingly, they give themselves the same advice I'd give them. Imagine that :).

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9. What are some things you feel you’ve learned really well (and why do you think you did)?

Interesting answers and mixed. Some felt they learned some things well where those were the very things other kids felt they suffered with. Hmmmm. 

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10. Anything else you think I should know.   

If I had one hour left to live, I'd spend in this class because it feels like an eternity ................................... I'm just kidding I love this class and math loves me (most of the time) but also maybe more AP question exposure?  

Best answer yet!


 

Calculus: f and f ' graphs

Happy New Year! Happy New Calculus Activity. 

I'm not 100% (okay, even 60%) sure my students fully grasp the challenging topic of how y = f(x) and y = f ' (x) graphs can be looked at to give you information about the "other" graph, so I just made this activity to welcome them back to the first day of Second Semester. 

I'm all for using technology, but I think (maybe everyone does and is rolling their eyes now) that putting their chubby little hands on pencil and paper and manually creating things will take the "magic" out of things and allow the kidlets time to process what's happening and what it means.

Also: Dear Spaghetti, thank you for being an awesome math tool that I can use over and over for a cheap cost and effective tool not only for math but for bad jokes about eating the tools afterward and such.

 

 

Semester Wrap Up

I could be grading finals, but ... phawwwww, maybe I'll blog instead. You're supposed to take brain breaks, right? RIGHT?!?!

The Good:
 * Thank you to whoever (whomever?) I read who wrote about answering questions with, "that's a good question!" and walking away. It's my favorite technique, now, especially on tests. Of course, I gauge whether or not it's something I want/need them to figure out on their own first. 

* My Precal Teaching Buddy and I are working on a project to do with sine waves and their graphs and applications. We (I) usually don't like math "projects" that are "meaty" because they end up not seeming meaty and taking away too much time for the students to learn the basics. We structured it so that there is class time and explore time and lots of check points. It's not perfect yet, but here are some questions the students came up with as a result of the project:

1. Is there a relation between where a color is on the wavelength spectrum and how often it appears in nature?

2. Can gamma waves cause hallucinations? 
3. Can frequencies cure mental illnesses? 
4. Does manipulating your brain waves during the day affect your dreams?

5. Can other cellular components of our body be regulated by a sine function and is this information useful for doctors?

* I'm actually following through with my Marathon Training Schedule, and have been into it since school started. My long run/walks on the weekend are now up to 13 miles. Toot toot goes my horn!

* My Computer Science kids are happy, and the administration is now seeing that this is an good class to have at school, especially an all girls school, and they want to expand it somehow. 

* Our first-time-graduating-class kids have started to trickle back and visit. Even the ones I had trouble with were all smiles and happy to say hi. They are thriving at college, so that's a win.

The Bad:
 * What is UP with my right shoulder! Tendonitis? Bursitis? Pinched Nerve? Some stubborn person WON'T go to the doctor, but she may soon have to.

* There are STILL a smattering of kids choosing to fail. I don't know why I still am annoyed by this. It's a pattern and their choice and I see it every year, and it usually works out for the best because it puts a fire under their butts. But people, grow up already and figure it out, so I don't have to have these heated conversations with you inside and outside of my head, full of scrunched faces and wild gestures.

The Ugly:
* Lack of enough sleep. Crow's feet. Bad home situations for various students.

Okay. Break over. Calculus and DE finals ... here I come.