Monthly Archives: September 2015

Life-Size Sine Curve

Last weekend, there was some twitter chatter about making life-size graphs so students could explore points/transformations/what-have-you. That got my wheels turning, and after a quick trip to the dollar store and about an hour’s worth of work I ended up with:

trig graphSteps:

1) Buy four shower curtains at the dollar store. Bonus if they are prelined!

2) Tape together with packing tape. (hint: tape them down to the floor with washi tape to hold them down, then tape the seams on the front. When done with the whole thing, flip over and tape the back)

3) Use duct tape to mark the x-axis. Print labels (file here), cut out, measure your axis, and tape down with packing tape.

4) Apply colored masking tape for 1/2, root 2/2, root 2/3. (see next picture since the masking tape was at school)

Total cost depends on how much tape you have around the house. I used almost 3 full rolls of colored masking tape, but the good news is I bought it from Have you heard of this site? One of the teachers at school shared it with me. Basically companies donate overstock and you get to buy it for the cost of handling. You do have to spend at least $25 and shipping takes about 2-3 weeks, but holy cow, can you get a lot of stuff for $25!  My first shipment I got 8 rolls of patterned/colored masking tape, 2 packs of 12 small post-its pads, 8 post-it pop-up cubes, 12 correction tape thingies, a pack of sharpies, 3 sets of dividers, 2 packs of post-it labels, and I think some other things I’m forgetting. It’s crazy!

Anyway, in class, I handed out dry-erase pockets with a sheet that had an x value in it (0, pi/6, pi/4….2pi) (file here) and told the students to find sin x, 2 sin x, sin 2x, sin1/2x, and cos x. Holy moly. We could have easily spent the day doing that. No, if x = pi/3, sin2x does not equal 2pi/3. Once we got that sorted, we went out into the hall. I had all the students stand on their x-coordinate, then step to the y for the function I called out. It was very easy to find people who made wrong calculations! 🙂  Here’s what cosine looked like:

cosine curveAnd sin 1/2x (with an outlier!)

sin half x

By third time I ran through it, I had worked some of the kinks out:

  1. In my first class, I had more people than x-coordinates, so I gave coordinates that were more than 2pi. This did not go well. They were way far down and we couldn’t really see the pattern continuing. The next class I handed out 2-3 points per group and had them work together to find the values, then as we graphed we substituted people in who hadn’t graphed yet.  (The class shown had just one person extra.)
  2. I only did each graph once. We talked about max/mins, who didn’t move and why, how many cycles fit on the mat, etc. I think it would have been beneficial to do sin, then cos, then switch back and forth faster and faster. Then do the same for 2 sin x and sin x, sin 2x and sin 1/2x, etc. And also positive and negative. The last class we even tried sin x + 2 (“oh, that means we need to all step up 2!”)
  3. Have them write down noticing/wonderings as we are doing it, or a quick sketch of the graph (maybe have some axes printed on the back of their point card?) to help solidify the concepts.

The next day, when we went to graph, I asked them if it helped to visualize what we did yesterday. Only a few raised their hands. I told this to Mr Craig, wondering if I would do it again or if it would be more efficient to just jump into graphing then practice. He said, “Hey, you helped those 5 kids see it better! Plus sometimes it’s about the experience, not about being efficient.”  Sometimes that Mr Craig can be pretty smart. (Don’t tell him I said that, his head is big enough already.)

In other news, this happened on Twitter the other night:

8,006 tweetsDo you think I will hit 1,000 followers or 10,000 tweets first?

Category: Precal, trig | Tags: ,

Haaaaave You Met Desmos?

So the first day back from summer, I asked my department if they would be interested in a Desmos workshop. At least two people asked, “What is Desmos?”

Obviously I had to remedy this situation as soon as possible (or six weeks later). I asked Michael (@mjfenton) for his bingo card from TMC15 and he replied with some new desmos awesomeness: go check out

learn desmosBut it turns out that I have this issue that I can’t just use what someone else has made. Why? I don’t know. Maybe I secretly feel like it’s cheating? I told myself this wasn’t *exactly* what I was aiming for in my session, so I made my own bingo card, borrowing quite a bit from the TMC version (because “borrowing” isn’t cheating?. I can’t explain):

desmos bingo(file here)

Only a few people were able to show up due to conflicts, but we had a really fun time!  I started them with this activity builder so I could have it running and show them the teacher dashboard on the projector. Then I let them loose on the bingo card. We got through the first three rows in about an hour (and the time seemed to just fly by!). We also did lots of brainstorming and bouncing off ideas to use in class. There was of course lots of “where was this last week/last year/when I was in college!?!?” comments. 🙂  Oh, and is there anything better than that gasp when someone uses a slider for the first time?

Now I just need to figure out how I can get a job going around to schools and playing desmos bingo with teachers. Basically, I want to be Barney and replace “Ted” with “Desmos”:

But that would be weird if I randomly started emailing schools and offering free desmos bingo, right? Yeah, I’m pretty sure that would be weird. 🙂

Category: Tech Tips | Tags: ,

Hold Onto Your Hats: Algebra II Unit One

At the end of last year, my fellow Algebra II teachers agreed with me to try a modified version of Jonathan’s Pivot Algebra II. Basically turning a class I’ve taught some version of about 10 different years into an entirely new prep. Just like a new prep, I’ve had a lot of grand ideas that have resulted in some successes and A LOT of notes of what to modify for next year.

Side note: Because of some weird geometry class issues, my students are much more all over the board than previous years. I normally have about 90% juniors with 10% sophomores (who should be in PreAP). This year I have about 70% juniors, 20% sophomores and 10% seniors. And compared to previous years when 27 or 28 was a big class, these are 29-30. Also, we have 47 minute classes three times a week and 52 minutes two times a week.

Ok, let’s get started. The first real day of teaching, I thought I’d hit on all the mistakes students make, “Hey, if we learn this now we won’t make them later!”  Um, yeah, what that turned into was “Hey, these are all the things you struggle with and are hard to understand and remember, so let’s talk about them all on the first day!”

Starting with this card sort. Determine if these are true or false.

Alg II Unit One files from here)

Oh holy cow. This went horribly. They had no idea how to determine if they were true or not. I suggested using a calculator to check, but imagine them trying to put some of these in a calculator. Frustration mounted. Then we checked and I was trying to use this as a big “ta-da” moment to introduce the GERMDAS house that Kent Haines suggested (more about this below).  “See, we don’t have to memorize all these different rules!  We can just use this one big rule!”

Alg II Unit One files from here)

The worst part was, after a few example problems, I never really went back and used those rules again with the types of problems they saw on the cards. I don’t know if I’d just scrap the entire idea next year or spend a day just focusing on those types of problems, or what. I’m also getting really frustrated with the fact that it’s like we’re starting from scratch every year in math. Should I really have to be covering order of operations again?

But do take a moment to embrace the beauty and simplicity of the GERMDAS house. I’ll let Kent explain it:

I showed it to the other teachers at school and one of them who works with lower level kids said the kids really liked it and understood it. Another teacher is planning to show it to her Calculus students (and she showed it to her 5th grade son as well with a really good explanation–when you clean a floor of a house, you don’t just jump from room to room to room, you go in an order. So don’t jump around to addition and then subtraction, but just clean up in order!).  Thanks again, Kent!

And because throwing all that at them wasn’t enough, let’s practice plugging in values into the un-simplified and simplified version and see if we get the same thing!  Or next year, I’m thinking probably not because it was just too much going on in one problem. Instead we’re going to spend a day on the difference between 3 – (x + 7); -3(x + 7), 2(x + 4) – 3(x +7) and 2(x + 4) – (x + 7). BECAUSE SERIOUSLY WHY IS THIS SO HARD. DID I MENTION THIS IS ALGEBRA II? Then I would spend a day on the last third of the notetakermaker: with a caveat that after today, if anyone tells me *I’m* wrong because my answer doesn’t match theirs because you didn’t put parentheses around a negative when squaring, then you have to do ten pushups. Because I’m over it.

Ok, so now we’re onto day three in what actually happened. It’s like when I was planning this unit, I got caught up in all excitement and forgot everything I’ve learned about teaching math. Because I thought what would make things really exciting would be to introduce a new, somewhat confusing (it turns out) method to solve equations, as well as adding writing out tedious steps! It’s going to come as a shock, but it did not go over well. (Note: this NTM ended up taking two days)

Alg II Unit One files from file available and I don’t really want to talk about why.)

After the entire chapter, I am IN LOVE with the flowchart method. But a lot of kids struggled with it to begin with (I think it was “so easy” for me to see that I didn’t take into account that (a) they don’t know the order of operations (see day one) and (b) it is something completely new that needs some soak time).

Learn from my mistakes! Here’s how I’m going to go about it next year:

  1. Save the variables on two sides for a different day.
  2. Save writing the justification for another day.
  3. Work on just the flowchart for a few problems.
  4. THEN say, well, we’d like to make this a bit more “mathy” and “formalized” so here’s what we’re going to do: draw the top half (the building part) of the flow chart in short hand, with just the arrows and operations above them, and not each intermediate step. Now work with the actual equation algebraically, check off each arrow as you go. That epiphany came to me at the end of the week, and it seemed to make all the difference. They were a bit frustrated (rightly so) that I was making them solve the equations twice (oh, and write out each step). But they didn’t mind drawing a little flowchart to help them. And again, the flowchat is MAGICAL. Just wait until the next post when we use it for 5+3|x – 2| = 14. (Or read more about it here)

If you’re still not sold on the flowchart’s worth, just check out these literal equations:

Alg II Unit One files from here)

I *almost* want to make them solve these with just the flowchart. I would say the students got them right 90% of the time with the flowchart. It was beautiful. One type of problem I need to add is something like x/b – a = c, where they can see the need for parentheses for the answer: c + ab was a common answer on the test instead of (c + a)b.

Speaking of test, I decided to stop here, review and quiz:

Alg II Unit One files from here)

Also, I’ve been trying mixed and lagging homework to mixed results. The biggest problems are (a) at the start of the year there was only so much to mix in (b) making homework for the entire week, but getting behind so it’s not lagging anymore and (c) students really lagging their homework, i.e. only doing it the day before the quiz. But I guess it makes a good review that way! Here is the homework for the week:

Alg II Unit One files from here)

Ok, so that was just the first half of Unit One but I think I’m all reflected out. As always, any comments, questions, or suggestions for improvement are welcome in the comments or on twitter!

Trig Addendum: Modified Radian Fraction Cutouts

Read about the awesomeness that is Radian Fraction Cutouts in Shireen’s original post (and my implementation). After using them in Algebra II last year, I made one little modification that made them even better (one of last year’s students that I have again even said so!):

unit circle fraction cutouts dotted

File here.  The secret? Cut only on the dotted lines!!!  So easy to see the whole enchilada (or em”pi”nada as Shireen also says) divided up into sixths, thirds, fourths, etc, then seeing if you add one, take one away from one, or take one away from two.

Comments I heard from the first class I showed it to (the others will see it tomorrow):

“This is so easy!”


“Why did no one teach it this way earlier?”

“These are really great!”

[In response to another Ss question about 7pi/6]: “Use your cutouts!!”

Not one person wanted to convert radians to degrees!  Woot woot!!!!!

Timing wise: In one 53 minute class, we cut them out, made a pocket (fold a half sheet into thirds [like a letter] and tape down the sides to the back of the NTM, leaving the top flap untaped), talked about degrees, talked about radians, and finished the front of this notetakermaker. The back has more practice that they had for homework:

degree radian WSFile here

DO NOT LET THEM LABEL THE UNIT CIRCLE!!!  Otherwise they won’t have to work at any of the rest of the worksheet. 🙂

And since it is the first day all week that I’m finished will all my homework before 9:00, I’m going to go read a real book!  That’s not about math! Or teaching! Take that, SCHOOL!!!!!