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.