## Alg II Files: Let’s All Translate Some Graphs!

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[More files and FAQs on my Algebra II files page!] One big change I made in Algebra II was making an entire graphing chapter. Usually, we would learn a function, solve it, then graph it, repeat. Now, using Jonathan’s model, they all got mushed together in one unit, which actually really helped them with (a) things that are similar with all the graphs (shifting, stretching) and (b) things that are different. It also solved the issue that I had before where if we were in the quadratics chapter, they would just write y = (x – 2) + 6 for the equation, leaving off the most important part! Now they realized why that was so important! I was reeeeeealy pleased with how well the students did on this unit. I needed to keep spiraling back to these through the rest of the year, though, because when you graph all at once it’s a long time before you graph again!

When we last left our intrepid reporter, she had just finished translations of linear functions, so now we’re ready to jump into absolute value. The first part that they did mostly on their own:

Second part where we made sure everyone was on the same page:

(file and a practice WS file) I REALLY liked those questions on #1 that I stole from some worksheet; you’ll be seeing them for the rest of the chapter! Like on the quadratic NoteTakerMaker!

(file and homework) Again, we were just focusing on graphing by translating in this chapter. Let’s try translating some square root functions!

(file) And then it’s time for some John Travolta!

(file) This was the last function we were going to study, so we spent a day doing a Desmos “Match My Function” Activity Builder:

You can find it here. I think this was the first activity builder I made all by myself, so it’s not very elegant (it was before hidden folders so I had to monitor students not scrolling down to the answer!). I also had some students say it was too easy to just use sliders until it matched, so next time I would definitely add some Desmos-style questions like “Here is Addison’s (wrong) equation and graph. What would you tell her to correct so it matches?” and “How would you explain to your friend how to move a function left or right?”

Then a group speed dating day:

(file and yes the graph answers are included!) Some sort of dry-erase graph is a must for this activity so partners can see work! If you don’t have individual graphing whiteboards, take Tina’s (@TPalmer207) suggestion of buying a pack of job ticket holders and printing off graphs to put inside.

Then it was study guide day:

(file and video key part 1 and part 2) As I said at the beginning, for the most part the score were GREAT on this test! Was it because we ended up going pretty slow through this unit? Or because they had graphed most of these before in Algebra I? Or because all the graphs were together? I don’t know the reason, but I will definitely put this portion of restructuring Algebra II into the “win” column!

## Desmos Activity Builder Success

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This summer I was so excited when Activity Builder was revealed at TMC. About the second week of school, I made a really quick one that involved the students graphing their names with lines. I reserved the mobile laptop cart that our school has just for Math and Science to use, wheeled it into my room, and was ready for the excitement to begin.

Oh, wait, except my classroom is in some sort of wifi blackhole, so it was taking students 10-15 minutes to be able to log in to the computer and open the activity, and even then only about 4 kids got to that step. It was the Friday before Labor Day; I didn’t have any backup plans, so I just threw in the towel and they had a chill day. I, on the other hand was not chill.  I was Over Technology. I was at Unstackable-Cups-Otter level of Not Chill.

It took me two months to venture into trying it again. This time I reserved the computer lab, where the computers are wired to the Internet. It went much better. Here are the two activity builders that I made:

Algebra II:

Writing Equations of Transformed Parent Functions

We are graphing 5 different functions (lines, absolute value, quadratics, cubics, and square roots) and the students were having a lot of trouble writing equations from given graphs. Enter in Match My Functions Activity Builder!

Issues: Students still do not know how to find the slope of line. This makes me sad. So they just tried decimals and then were upset because it seemed “like random decimals for the slope.” At least they were trying something, I guess? Also a couple students said it didn’t help them because they could just guess until they got it right. But all in all I would probably do it again; they actually did very well on their test writing the equations and recognizing the functions.  Also, a student who is in two math classes bragged about how fun/cool it was to his other math teacher. 🙂 Plus when it came to study guide day, at least a few students broke out the app on their phone to check their equations!

PreAP Precal

Introduction to Polar Graphs

I had actually done this activity last year as just a regular Desmos file paired with a worksheet that asked them questions about the graphs. It didn’t take too long to create an activity builder based off of it. We had graphed polar points and graphed a couple circles by plugging in values of theta, but they had not seen any other type of polar graph. I set them loose (in pairs) to work on Polar Graph Exploration.

I had them play around with sliders for each graph; then submit “I notice…” and “I wonder…” On the more complex ones, we then looked at each part individually (like the slide above that just focused on the n value). Trying to learn from the feedback from Algebra II, I made a few “quick check” text questions where they couldn’t just guess (although some just went back a screen and played around with the sliders until it matched)

The fact that, with no direct instruction, most of them realized there had to be a 3, 6, and sin involved in the graph above is pretty amazing. I really loved the notice/wonder part as well (I’ve actually never used it before in class #MTBoSDirtySecret).  I always had an issue with the petals on a sine rose alternating between positive and negative y-axis. One student noticed that if it is positive, more petals will be above the x-axis. So clever!

I did get a few complaints on the feedback, “why didn’t you teach us?” but I’ve come to expect that.  The other complaint was not being able to know if their work was correct on the quick check. Maybe I should add a screen after that with the graph that says, “check your work” or “how close were you?” (but then I also don’t want to discourage them if they were wrong–I only wanted to see how much they had learned from the activity).  The best part was the last screen where I told them to have fun!  They made so many cool graphs, and then I was able to show them off the next day in class.

Now I know Desmos gets a lot of love around here, but let’s not forget about Geogebra, which is powerful and useful in its own right. For example, this beautiful, awe-inspiring, oh-so-that’s-why file that compares the two versions of a trig equation (made by Mark Fowler):

(Which I found the morning after we had done the Desmos activity, and now I’m debating if I want the Ss to play with this instead of the Desmos one! Or if Desmos could make this into a split screen activity with sliders that controlled both graphs?!?!) I used it as we talked about each graph, and was able to reference their responses from the day before, “Some of you were wondering what causes the inner loop…”

All in all, a fun week using technology in class. 🙂

## 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.desmos.com:

But 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):

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: ,

## Precal Files: Polar Coordinates and Complex Numbers

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A quick aside before I start sharing: in one of our tours in Iceland, the tour guide mentioned that 3 Miss Worlds have come from Iceland.  Since there’s about 320,000 citizens, and about half of those are female, it means that you have a 1 in 50,000 chance of meeting a Miss World in one of the bars (there was also a side note about the Vikings choosing all the pretty women from Ireland and Scotland to take and leaving them with….). Then the punchline: “Iceland: where everyone is statistically exceptional.” How could I not like this country? Plus over half the population does not discount the fact that there could be elves. Oh, and they eat ice cream all the time.

One thing they do not have in Iceland is polar bears. But if they did, wouldn’t that be an awesome segue into polar coordinates?

Alas, I guess we’ll just have to start with some Polar Coordinate Battleship then these notes:

And some equations, and a hint of graphing by hand:

The first year I did polar equations, we just did them all by hand and did some noticing. If you’d also like to, here’s a worksheet:

This year, I did a desmos exploration (read more about it here):

Sadly, the title is cut off of the next worksheet, it’s labeled as “The Greatest Polar Graph NoteTakerMaker Ever.”

Does the fact that a negative rotates a lemniscate 90 degrees make you freak out because HOLY CRAP THAT’S WHAT IMAGINARY NUMBERS DO ON A NUMBER LINE WHAT THE HELL, MATH??? or is that just me?

File here.

We did some practice with matching (from Mastermathmentor) and some practice sketching worksheets (from another teacher).  Also a wee bit of “where do two polar graphs intersect?” I’d also point you to Michael’s Reason and Wonder polar posts for some more ideas on introducing and graphing.

Then some complex numbers:

File here.  I did a lot of stuff in class (this actually took us two days) from the Better Explained website: here, here, and here.

Finally a study guide:

File here. And study guide videos: #1-16, #17-26, and #27-37 (even though it says 17 as the first problem-doh!)

Find more precal files and FAQs here. Hope you’re finding these helpful! 🙂

## Sunday Summary: I Love Transformations

3-2-1 Sunday Summary:

3 Resolutions for 2015

1. Blog more. Remind self that I don’t have to type a novel every time, nor does anyone want to read a novel on a blog.  Keep up with short 3-2-1 summaries.

2. Exercise more.  I joined the #500in2015 challenge and did pretty good the first week.  To motivate myself, if I keep my goal of ten miles a week in January, then I get to buy the new Jessica Smith walking workout video set. (Right now I’m using this DVD from her. The Nike+ app seems to record the walk pretty accurately and I’m not going outside when it’s below freezing! 55 degrees!)  If you’re looking for a good indoor workout, check out her website–she has TONS of free full-length workouts posted, with special appearances by her dog, Peanut.

3. Leave school at school. This has been one of the more trying years I’ve had as a teacher and I’ve been bringing a lot of that home with me. I’m going to try to be better about shutting that part of my brain off.

2 good lessons this week!

1. One day this week, I ended up with four out of eighteen students in class. Instead of calling the day a loss, we got together in a group and worked through the notes together. It was so nice to talk with them one-on-one through the lesson and then we all worked together on the homework.  I need to remind myself to sit down with more groups as they are working, instead of just helicoptering around the whole room.  (Side note: I did use the exam study guide days to do this as well: each group got 5 minutes of Mrs Craig time to ask any questions; it worked really well!)

2. We started transformations in Precal this week. Coincidentally, Shelley Carranza (@stcarranza) asked if she could link to a previous post I had made about transformations and of course I said yes. (Here is her post.) As a bonus, she gave me a sneak peek of her desmos graphs which inspired me to change up my introduction graph:

(Note: there is no table for the absolute value functions because my coteacher and I wanted them to thinking about those on their own for a bit).

Next year, I think I will use up some extra paper and recopy the table next to each graph.  Because being able to mark it up adds a wonderful visual to what happens when we affect the input, for example, f(x – 2).

THIS TOTALLY BLOWS MY MIND EVERY YEAR.  We are “reaching back” 2 to find the output value, which will “pull up” to where we are.  SO THAT’S WHY IT SHIFTS TO THE RIGHT WHEN SUBTRACTING.  We then talked about the “bonus” point of (8, -2) we could get from the original (6, -2).

Ok, are you ready for super mind-blowing?  Check out f(2x) (The green boxes are more “bonus” points.  A good question to determine these was, “where would this -8 output project to?”)

HOLY COW YOU CAN TOTALLY SEE THE GRAPH BEING PULLED IN!! We need to go out twice as far, then pull that answer back in to our x-value.

We spent two days on this, then did some more practice. Monday we’re doing a super-thoughtful-hope-they-all-ate-their-wheaties worksheet combining transformation, average rate of change, and area of the curve.  I will report back as to its success and/or not-there-yet-ness.

Here are the files: Table Worksheet  Table Desmos File

1 Thing I’m Looking Forward to This Week

More transformations!!!  Seriously, I love these.