## If you teach trig, you need this post.

The reason you need this post is because Math Teacher Mambo has unlocked the secret to teaching radians so kids will understand.  YES IT IS TRUE. She posted this fabulous idea on cutting out radian pieces to use, like this:

Image from mathteachermambo.blogspot.com

How can I describe using them in class?  Well…

Exhibit A:  After two days of working with both, I informally polled all three classes about whether they prefer radians or degrees.  At least 25 – 50% raised their hands for radians, and many of them said it didn’t matter to them.  That’s right, a class where kids prefer or at least do not actively dislike radians.

Exhibit B: In one of my classes, after the poll, I told them I was so excited because this was a new way of teaching it and it actually worked.  One of the students asked, “so how in the world did you teach it before?” “We just thought about it.”  Their reaction:

Exhibit C: After that reaction, another student said that they were great to start with, but then after a while they didn’t even need them. Woohoo!

Since I use NoteTakerMakers® instead of INB, I modified my NTM from last year to accommodate Shireen’s circle files:

.doc file

We started with degrees. By “bow-tie triangle” I mean reference angle (we had done trig values at a point the day before and practiced drawing our bowtie) and by “type” I tell them short, medium, or tall.  We did the first five together and then I sent them on their way.  Yes, with greater than 360 and negative angles, which was great because everyone had a different way of thinking about where they were.

Ok, just so I’m not kicked out of the #MTBoS, I would love to do a radians activity where we discover what they are, and that one radian is the same for every circle, and it takes 2pi of them to go around, lalala discovery learning, but I have 13 class periods to go from 0 to translating sine and cosine graphs, so I showed them a quick animation from Sam and pi, 2pi, pi/2 and 3pi/2 using Math Teacher Mambo’s empinadas analogy. (except with quesadillas because our Moe’s actually asks if you want them cut in half or fourths). We had just enough time at the end of class to cut out radians out, label them, and put them in a pocket (hint: Give each student a third of a piece of paper. Fold strip into thirds. Tape two sides and you got a pocket with flap.  You can even tape it down to the NTM between the two circles, but it does over lap the chart a bit.  I could probably make it pretty so it doesn’t, but I didn’t.)

The next day we talked about the radian examples at the bottom of the NTM.  After the examples I asked them about what type of triangle we will have with denominator 6, 4, 3, and 2. I think next year, I’ll have them cut out the pieces like this:

Because lining up 7 or 11(!) of the wedges was time consuming and easy to land on the wrong space.  Plus hopefully this might help them think, “is this more than a whole quesadila?” when they are deciding which pieces to use.

I stamped the first five and ten as they were working to make sure they were on the right track.  They didn’t even balk at the last few that were greater than 2pi!

Warning: the rest of the post is less essential than those radian cut-outs. 🙂

The next day was the big intro to the unit circle.  I’ve moved away from “these are the coordinates, let’s memorize the unit circle and draw it on everything really quickly” because I realized when I started teaching precal we need to know sin 5pi/6 without having to draw the whole thing. So instead we talked about short/medium/tall triangles and just remembering 3 numbers: 1, 2, 3 and which one is short/medium/tall (or skinny/wide). I have them draw the triangle for each question. I think maybe I should also have them highlight the part we care about?  Or now I’m thinking (and I’m going to try this tomorrow with reciprocal functions) of sacrificing one of our wedges and making it a triangle we can label and move around.  I’ll report back.

We spent the next day practicing and me stamping off correct answers, which I need to find an equitable way to do. I normally go around the room and stamp, but I always seem to miss tables.  I need one of those numbered ticket things like at the butcher or Joann’s.  Anyone have any great ideas on that?

They are definitely not where I want them to be after 5 days of this, but I think they are getting there.  We shall see.  Maybe I’ll just throw in the towel and start doing timed unit circle quizzes again.

Category: Alg II, trig | Tags: , ,

## My Three Favorite Word Shortcuts for Math Teachers

I’ve shared these before, but not all in one handy video and not with SOUND before. It’s like I’m right there in your living room room controlling your every move on the computer. But like in a not-creepy way.

In other news, it seems I really like the word “WHAT?” especially when paired with “that just happened.”

I will certainly take requests for the next installment. Is there something you’d like to know how to do in Word? Make tables? Make drawings? Make shortcuts for pi/2 or square root of 2 over 2? Put in graphs? Or maybe you’d like to make a fancy powerpoint with equations and such? Leave me a comment or tweet a request!

Category: Tech Tips | Tags:

## The Limit of Limits

We finished up our limits chapter and the test results were….underwhelming? There were no HORRIBLE grades (not even a lot of F’s) but there were only a few outstanding grades.  On the other hand, the majority of them did great with graphical limits and algebraic limits except for one-sided limits approaching an asymptote.  Which, in retrospect, I may take out doing algebraically next year (or at least if I teach regular precal).  I mean, we end up just making a mini-graph anyway, so why not just keep it in the graphing section?  And at least no one gave this as answer:

Dude, that may be my favorite math equation pun, right after (sin x) / n = 6.

Also, the ant analogy (see my last limits post) worked a bit too well. At least 10 students “explained” that the limit was equal to the y-value of a hole “because the ants can still reach across” or “the ants will still be at the same place.” So if you’re an AP reader next year and see a lot of talk about ants, you’ll know why.

Here’s what the last half of the chapter looked like:

1) I redid the piecewise function worksheet to have more exciting piecewise functions.  This took them the better part of a 47-minute period. File here.

I have to admit I feel like I must not be doing my best as a math teacher when at least three students ask me “since 2x +10 doesn’t fit on the graph, can I graph x + 5 instead?”

2) Then we jumped into finding limits algebraically, with a chart that I think is fabulous (but I may be biased).  File here, and some homework just cause I like you.

(also, check out that amazing multiply-by-the-common-small-denominator action happening in #9).

3) I’m continually amazed at the fact that no matter how often I told them you need to SHOW me algebraically all three rules when I ask about continuity, I still had maybe 5 that were like, “yep, looks good to me; you can draw it without picking up your pencil!”  Here’s the file and some homework. Yes, the last two on the homework end up being beginning-of-the-next-class-period discussion questions.  Also, cut down the first part of the homework by half.

I also enjoy it when students put smiley or sad faces in the middle of problem because I do it.

4) To Infinity….and BEYOND! (Aw, sorry you got cut off on my scan, Buzz). . I think highlighting the biggest power really helped. This is also the first year we “plugged in” infinity and I think that helped, too. And trust me, just omit #20. Save that sort of heartache for Calculus.

(file here)They finished the rest for homework.  Be sure to talk about #43-45 the next day–how .02 difference affects the limit at infinity!  Also, this was funny: a student was asking about #40 (37^(1/x)) on the way out of class. So I was writing on the board 1/∞ then she said that was 0, so I wrote 37^0.  A kid from my next class walked in and said, so 1/∞ = 37 degrees? 🙂  I told them we should totally start using 37 degrees as our fallback answer for any question.

That was the last lesson before a couple of days of review.  And just to make sure I’ve covered all limit jokes and puns:

Done.

Category: Precal | Tags: , , ,

## #MTBoS presentation

So…this was a thing that happened. The Central Alabama Council of Teachers of Mathematics is trying to resurrect itself and is holding monthly meetings again. I didn’t know about the first one, went to the second one in February, and volunteered to speak about the #MTBoS for the March meeting.  Of course, as soon as I came home, I tweeted for other presentations and Sam linked this page o’ presentations.

But like I assume others are in the #MTBoS, why use something that someone has already perfected when you can cobble together something from everything that turns out to be less than the sum of its parts?

So here’s my presentation.  Some key slides:

So here’s the good:

People seemed excited about some of the other MTBoS sites that I shared (WODB, would you rather, etc).Many participants said they enjoyed the presentation.

I had planned for 45 minutes (talk for about 20, have them play around for about 20, share for 5), but ended up with 30 minutes and paid(!) wifi. I was able to stretch out the presentation but people didn’t get to play along and I haven’t seen any of them join twitter yet (or maybe they did and didn’t follow me which could certainly be the case).  Then again, I’ve been reading blogs for years and last year was when I finally made the leap to twitter. I will have to follow up at next month’s meeting.

At the end of the talk, I had one person ask “so what IS the MTBoS?” which is really hard to explain.  Maybe add something about how if you want to be a part of it, you are?

I seriously thought everyone at least knew about math blogs by now, but maybe 30% did? I should have added some screenshots of good shares from blogs.

Trying to get too much in? Focus just on blogs or just on twitter or just on the other stuff?

And here’s the handout:

Two things to note about the handout:

1) I hate putting my “favorite” blogs up in public because I know I’m going to leave someone out. Please don’t be hurt if yours didn’t make the cut when I put this together the night before the presentation after grading 70 Precal limits tests. Also, Math Teacher Mambo will always be my favorite forever and ever.

2) Google docs is THE WORST.  See those funny little pictures at the bottom of the page?  Yeah, they don’t print. They’re like a Google mirage. Don’t even get me started with “yeah, we’re going to put paste in the right-click menu, but don’t think that means you can actually, you know, PASTE by pressing it.” Oh, wait, you did get me started….  Ok, so if I have to ctrl+v to paste, why doesn’t ctrl+shift+c/v copy and paste formatting???  The. Worst.

So now maybe Sam will quit yelling at me all the time now I’ve that linked this to his page. And maybe I ended up getting one new #MTBoS member!  🙂

Category: Uncategorized