Post Calculus Exam: Sonic Boom

I spent 2 of the class periods after the AP Exam exploring and expanding on a cool problem I found in Smith and Minton. The problem is about what a sonic boom is, and how you can visualize it graphically.

The first day we had to refresh our memories on parametric equations and graphing. Then the students looked up various things on the internet and wrote it in their notebooks as such:

We had some good discussion on the various speeds and if they are "exact" and what could change the values. Then I made sure they got what a Mach number is by the following "quiz" in their notebooks:

I had them look up the speeds of various vehicles and we tried to get a wide range of numbers and then they had to figure out the Mach numbers based on their speed of sound.

On the 2nd day we then read over the "yellow" paper from page one, and I had to make sure they understood what a unit on the graph was. That was fascinating. It was more of a struggle for them than I would have thought, but we eventually got to it, and again, good discussion.

Then the actual graphing began. We had to take it slowly and keep talking about what the units meant and how you made decisions and such. Here is the graph for a jet going Mach 0.8. We had to keep stressing that the "arcs" were at time 5 seconds after "start" of the 5 noises the jet made at various times:

 

Then we graphed the "same thing" but for the jet moving at Mach 1:

 

 The students were excitedly asking me question upon question, because really it is cool and wonder-ful ... and I kept mentioning that I'm not an expert, but that we should write their questions down to think about for later.

Then finally we did the same process for a jet moving FASTER than the speed of sound ... Mach 1.4:

 

We had to be cautious with scales and such and all sorts of great mathy things came up. Then class was over. 

I loved their enthusiasm and questions and wonderment at this actual topic.  

 

GrumpyCrabbyNess

Why are all these teenagers acting like ..... teenagers?! How old ARE you anyway? Behave and fly right!

Excuse me while I detox:

Our principal some time earlier in the year did away with bells for whatever reason. You were still required to show up to class on time, but you had to rely on yourself and your handy dandy watch/clock/cell phone. I let a ton of things slide in general (lie, but ...), but one thing I do not like is kids sauntering to class late. They started being 15 seconds late, then maybe a minute, then consistently 3 or so minutes. It got to be too much. So I instituted a "be in the room or get a demerit" policy last week. I hate giving demerits. Boo on being the bad guy. I know it's ultimately good for them, and I know I have to be consistent, and I know I still have a grumpy knot in my stomach for the about a bazillion demerits I have given out in the last several days. Kids have started coming to class on time. Shocker. I still have a grumpy teen that is consistently late. Yay! Have her for 2 classes. Twice the demerit fun.

AP Calculus Exam Studying. Hmmmmm. I think a good chunk of the kids are studying the way I think they should be studying. The rest are being, well, teens. I have carved out time in class to do released exams and have them discuss things. In my mind that's going to help the most. We will see in July when the scores come out.

AP Exams start this week. So do EOCs. And thus, so do tons of kids being gone from class in a sporadic fashion. Yay for being flexible and being able to roll with it. Or at least putting on my game face.

Good things: 

My CS class and I are going on a field trip to an apparently well-known local game developing business. We have spent some time playing their games and researching them and creating questions for the field trip.

The NHS group of kids I co-sponsor have done an amazing job this year with doing service and getting fund-raising ideas and actively participating.

My precal students are just a hoot, and even the not-so-strong-mathematically students are a treat to talk with.

Ice Cream.
 
 

What?!?! Me Study?!?!?

AP Calculus Exam coming up. Let's have the kids create a study calendar! That's the ticket. Because you know, if you fail to plan, you plan to fail.

I fell into the old Geometry Logic trap. Just because ~p --> q is true, it DOES NOT say anything about what p implies. Silly me. About a week after they all made their calendars, I checked in with about 3 or 4 of them. Sheepishly, they admitted that they were not adhering to their study calendars ... their beautiful calendars they set up.

We had a class powwow. We brainstormed. We came up with ideas. Who knows what will work.

Things I need to think about changing/adding next year: a part of the homework for the calendar that mentions what incentives they'll give themselves for studying ... maybe some strategies they need to write up for the times they DON'T feel like studying ... other?

I checked around with other AP teachers. Yup, their students (we all share) basically admitted to not doing extra studying outside of class ... much.

Okay.

Well, I've instituted some other motivations. Don't know what will work, so I'll do multiple ones of them. Here's one I thought of today after seeing something similar on Pinterest.

Today, I had them start a foldable that is due next class. I prepped for the insides by listing various things they need to memorize:

 

Then I made one myself (sort of) and made a flipped video for them to watch to see what goes on the inside. Here are the flaps:

 

 Here's a wee look on the inside. I didn't just want formulas, I wanted examples:

I'm SURE this will be the ticket. Girls LOVE pretty colorful things, right? They won't be able to tear their eyes away from it. They'll study daily.  

Making a Graph Updated...

A while ago, I used to make graphs for my worksheets in a way that, at the time, seemed reasonable. Hah! and Double Hah! I have seen the light. I don't know where I heard about this technique, but I am using it now, and just today, I enhanced it to be easier for me. 

Here is a finished graph that took about 4 minutes to make from a blank space:

I like this process because I can never seem to find my old "made" graphs, and if I do, they are never the right size.

Also, I used to make a similar grid using "tables", but then I would go and insert shapes with textboxes to do the scale. Tedious. I just realized today how I could do it all with tables. Viva la tables!

Here are instructions in case you are in need of graphs.

Quick PSA for Precalculus

We are now into our Logarithms and E Unit, but before that I wanted to review exponent rules and manipulations for a day. We did that, but I showed my students THIS Public Service Announcement. To set the stage for their project.

We went over 6 different exponent rules, and I mentioned that if everyone remembered them really well just from taking notes and practicing them, then we wouldn't need this review. I said that they each were assigned one of the 6 rules, and they had to make a PSA for that rule. 

We discussed that JUST restating the rule was not effective and sort of besides the point. We discussed that humor or shock value is effective. We discussed linking new things to things you know. We also discussed that the thinking of the actual content was the hardest part, and then you had to ink it out, so just use your "pockets of time" in the next 2 days to brainstorm through some creative ideas.

I also only gave them until the NEXT class to do it (8.5" x 11" paper, colored, correct, effective...). I also joked with them that if I had given them a week, they would have left it until the last minute anyway, so just pretend I assigned it last week.

Don't know if this will be effective or not, but I liked the project, and I liked seeing the wittiness and creativity of kids that I may not otherwise talk to that much because they're not the yappers in class. Here are some samples.

 

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.