Tag Archives: Chromebooks

Fitting Periodic Functions Presentations

It’s been a while since we did presentations in Precalculus, so I figured it was time for a mini-project again. Learning from my past, I quickly doctored up an example presentation, mostly as a guide to how the format their presentations should take.

The students got really into the presentations. They had a bunch of ideas as to what “periodic” meant and they explored a lot of possibilities before deciding on one to study. I think the good thing about this project was my requirements were so open-ended that they were able to find one that interested them.

Here are some examples of presentations (with the names removed).

In this next one, the students actually got a jump-rope & meter-stick and measured where the jump-rope was as if they were jumping rope.

In this last example, the students really wanted to do something with square-dancing, but couldn’t find any videos of square-dancing that they could measure. So the first part of their presentation was slides showing where people (represented by circles and squares) would be.  Then their function is pretty nifty (they ended up fixing the “undefined” parts of their table, which was a great talking point in the class).

In the past I had the students come up with questions to ask their classmates. This time I honestly forgot about that aspect if I had to redo it, I’d ask them to include that in their presentations. Instead, I decided to pose questions to the class based on the presentations (which intimated the presenters a little, until they realized that they didn’t need to answer the question: they were supposed to help their classmates solve the questions). It wasn’t too difficult to ask a question of the students that really required that they understand what the graphs and equations represent.


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Stop-Motion Parametrics: Post-lesson Analysis

I posted recently about a lesson where students created stop-motion videos to model parametric functions.  Last year I did a similar lesson, but this year it went so much better because the activity was more structured, and I had them create presentations (on Google Drive so they could embed videos) rather than just creating a video. Here are just a few of the videos (in case they don’t work in the embedded presentations).

And here are some of their presentations, with names edited out.

Thanks to the questions that students had to create as a part of their presentations, the discussions that occurred around these questions were very good: students brought up misconceptions, and other students helped them out.  I didn’t always stop them at every little thing that was wrong, but after everyone’s presentations, I think we covered all the topics where students got something wrong.

Because this (students presenting and then asking questions) was a new way of learning (at least in this class), I had to push them to ask their peers the questions, and then wait for a good discussion to evolve.  We had good discussions and some of them posed great questions, but it took too much of me asking them for it.  I hope to do something like this again, soon, so they can get accustomed to teaching each other.

It also took a full 3 days of class to get through all the presentations (only 8 presentations), but I think it was worth it with the great discussions that were taking place.

Part of the reason students payed close attention was the fact that they had to answer their peer’s questions during the presentation.  The other part is that I had them fill out peer evaluations on Google Forms, which I hope to use and share with them. Here are just some of the responses (spelling errors included).

Answers to the request for: “One thing this group did well.”

they knew how their function worked pretty well.

What they said made sense and they had a good presentation.

the video was cool

explanation of domain and range

Understood her project and graph really well.

She did very well in finding a very unique parametric equation.

I really liked their video. They did a very good job in thinking about their questions. The questions are very well thought.

They really explained what the independent and dependent variables were. They also explained domain and range.

she knew allot about how her equation worked and knew how she got it, [1]

Answers to the request for: “One thing this group could work on or do better.”

They confused me when when finding the distance horizontally. They didn’t find the distance instead they found the displacement.

Be more ready for their question maybe go over them more before they presented so they could catch their errors before their presentation.

they were a little bit scared which made them uncertain of the equation

I think that they had okay questions but i felt that there could have been a few better questions.

They did not explain there X&Y values.

Answers to the request for: “One thing you liked about the presentation.”

I liked the fact that they went BACK IN TIME!!! WITHOUT HAVING TO GO 88MPH!!!

It was smart to have the equation before the questions because it was then easier to answer them.

She thoroughly explained her equation and its domains and ranges.

I liked the way they explained their answers so that i understood.

they kept the presentation going, no awkward pauses.

i really like the graph it was creative.

cool video


This kind of reflection is great, both for students to see their own pro’s and con’s, and to think about other groups as they presented.  If students are “just supposed to watch” a presentation, then there’s much less incentive for them to pay attention to the details.

[1] That’s a new way to spell it that I haven’t seen from a student.


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Using Sketchfab to view 3D Orbital Clouds

Go here to view the orbital clouds that I describe below.


I didn’t really learn about Blender until about this time last year, and so I was still very new at creating 3D objects.  Since then, I’ve been able to apply my hobby of creating 3D objects to my math and science classes just a handful of times.  The two ways in which I’ve been able to share my work with students is through an Augmented Reality App on the iPad and through Sketchfab, a website that will use OpenGL to render 3D images.  Both are very cool ways to view 3D objects, with the Augmented reality app being a little more hands-on for the students with a little more “wow” factor, and SketchFab being a little easier for me to upload my blender files and for students to access (doesn’t work as well on iPads because of Apple’s restrictions, but we got Chromebooks this year from grant, wohoo!).

The highlights have been:

Using 3D & Sketchfab

I used to stand up at the board and lecture on the Quantum Numbers.  I’d draw the 3D objects which wasn’t terrible, but definitely didn’t help students picture things in 3D. [1] It was teacher-centered, lecture-based, and (no matter how excited I made it sound) boring.

So I decided to spice things up with Augmented reality.  Unfortunately our network was being stupid and blocking everything related to the app, so I had to change gears and go with Sketchfab.  I created several of the orbital shapes, orientations at multiple energy levels.

After uploading them, I embeded them on my website.  Unfortunately you can’t embed iframes into wordpress.com websites, so you’ll have to go to my website to check them out.  There are 5 pages of them, so don’t miss the other ones.

I gave my students a packet to work through (see below), which worked better than I had hoped!  It involved students sketching various pictures, in addition to answer questions at checkpoints and requiring that they check with me before moving on.  I was worried I’d be swamped, but the checkpoints are so easy to glance and say “yes” or “no”, that there wasn’t a big backlog.  Students developed a sense of what the atom looks like, in addition to how electrons behave within the atom.  The activity was student-centered and hands-on: much better than how I used to teach it. I overhead students struggling with and debating on the problems, asking each other what an “energy level” was and what “orientation” means.  At one point students even sketched what they thought three different shapes, when put together, should look like in 3D, and could immediately check themselves by going to the next web-page.

I could definitely improve it in little ways, such as explaining that an orbital cloud at a given orientation means both sides of the p-orbital.  Or I could better explain what an energy level is.  And I didn’t like how I phrase the question where they’re supposed to “discover” where the numbers 2, 6, 10, and 14 are on the periodic table.  But those were minor hitches that went over fine because I was constantly walking around answering questions.

The following day, we even had a great discussion from some of the students about a way to provide a “house address” for the electrons.  A few students presented how they would give students a location, and I followed up with showing students the quantum numbers.  Even when I was lecturing (for only 10 minutes or so), students were much more engaged and invested in what I was saying because they had, in the back of their mind, the system they created to locate the electrons.

[1] How important is it, in the grand scheme of Chemistry to know what the electron orbitals look like? Meh. You’d be able to understand most of Chemistry without it, but I like to do it because (1) it helps students with their spatial understanding (which is often sorely lacking), (2) it’s quite beautiful the way that these orbital clouds exist in every atom, and (3) it reinforces ideas about electrons and “where they want to be” as I put it.  This idea of “where electrons want to be” comes up more in chemical bonding.

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The Day the Scaffolding Fell Apart (and Got Put Back Together)

The Setting

Being in only my 3rd year teaching at this school, my principal still wants to do semester observations on us “newbie teachers”, and so I decide I’m going to show him another 3 Acts lesson since the first one went so well. (Side note: this is not a nervous or bad experience for me, not because I think I’m an awesome teacher or anything like that, but because our principal is so approachable and dedicated to helping us teachers grow. He’s “on our side”.)

The Lesson

In Precalculus, we’re still getting used to (read: remembering) different functions and their various representations. After much debate with myself, I decided to use Dan Meyer’s “Will It Go In The Hoop”, where he shoots a basketball, freezes it halfway and asks the students to predict.

I’m learning how to better “hook” students, and this time I did it by record a simple “yes” or “no” next to each student’s name after asking them “Do you think the basketball will go in the hoop?”  Takes 30 seconds, engages them for the rest of the lesson–at least the first leg of the lesson.

I then put Dan’s Geogebra applet, complete with the picture of the ball, sliders, and parabola (he did all this), onto my website for students to access. Geogebratube wasn’t working the night before for me, so I didn’t want to take chances and actually had them download the .ggb file.  The downside is that it’s a few small steps to use that on the Chromebooks. Fortunately, Geogebra has a Chrome applet, so (1) the had to install Geogebra on their Google account, (2) download the .ggb file from my website, (3) open Geogebra (not just click on the file like they’re so used to), and then (4) go to “file–>open–>open”.  Not very many steps for any competent computer user, but as we all know, most teenagers are woefully incapable when using the computer doesn’t involve Facebook or Youtube.

Crash & Burn

So they open the file, and of course they’re all moving at different speeds: some figured out what the sliders do right away.  If you’re wondering, the variables in this particular applet are a, h, and k in the equation y=a(x-h)^2+k.  I decided I would remind them of parabolas & equations at the same time as teaching them to use Geogebra.

That was my first mistake.

The first two .ggb files had sliders already built, but I actually deleted Dan’s work so they only had the picture because I wanted them to want (and then create) the sliders and not just take them for granted. They need to understand what they do and why they’re so nice and helpful.  However, we ran into a few “speed-bumps”. (Hitting speed-bumps when travelling 60 mph isn’t smart, btw.)

  • Creating and using sliders is much tougher in the Chrome applet than with the desktop version. For one thing, I never figured out how to edit the max and min on the slider unless you create a new one.
  • Having to click the “mouse” button on Geogebra always throws students for a loop (although these were doing better than in the past).
  • Students’ understanding of variables is tentative at best, so connecting the slider to the equation via a variable almost always had to be explained explicitly (“Type in exactly what I tell you…”)
  • Even I find using a mouse much easier than a track-pad, especially if there’s no clear button to click outside of the touch-pad. Clicking and dragging items are trickier.
  • The screens on the Chromebooks are just a tad smaller than it seems the applet was created for, so they had to shift and zoom the sheet to see the equation, the picture, and all the lines.
  • One girl at the front became very flustered and frustrated with herself and her computer, which can quickly change the dynamic of the whole class.

I felt the class slipping away from where I had them when I recorded their guesses. We managed to get through two of the shooting videos fine, but when I took away the slider, they became “disengaged”.  I guess I should have known it was their first time using Geogebra as I’m the only teacher in the school to use it.  I just need to give them a better intro than one where they crash & burn so they come to appreciate how easy it can make things.

It really felt like I had pulled too much out from under them and they were collapsing under all that they were required to do. This is one of those cases where the technology was becoming a hindrance rather than supporting more dialogue and investigation.  On the one hand, giving them sliders felt like making it too easy for them. Yet taking away that simple tool made it much more difficult.  I’ll need to try to tread the line between challenging/engaging and frustratingly, pointlessly complex.

The Putting Back Together

I should have pulled these out sooner as a “recap” to help the students bring together their thoughts, but in the excitement, I honestly forgot about them at first.  (Fortunately in my 2nd precal class of the day, I corrected my error and they got this as a summary immediately). I attended a conference where I learned about these “Link” sheets.  This is excellent because it brings together four representations of a function: in this case (1) equation, (2) verbal description, (3) table, and (4) graph.  Sometimes I fill in some parts and they fill in others, but for this I wanted them to take their Geogebra & the video and put it onto the sheet. Here’s a word version (LINK-Blank Linear v 2)  if you’d like to edit it.

After all that technology, I think some students were honestly relieved to have a piece of paper in front of them that they could write on. This helped them to see what the goal of this activity was in the first place.  We’re still not to the point where they understand how to translate any given function, but we’re more used to seeing functions and connecting equations, graphs, tables, and verbal descriptions, which is not a bad block period. The afternoon went better, mostly because I never took the sliders away from that group.

My Analysis

I think I need to do a better job of deciding what I want the students to get out of my 3 Act lessons. I’m trying to remain flexible and “go where the students want to go” in case they mention some great ideas, but I also need to have a plan and something in mind that I want them to learn, rather than just generic “understand & play with functions”. That’s on me.  More planning than I am sometimes motivated to do, if I’m being honest.

And of course there’s also the technology aspect.  I am fairly comfortable with new technology (I find installing operating systems and customizing them fun, for example), so it is very difficult for me to understand how little technology some of my students understand. (One unfortunate girl started at me questioningly when I asked her to “reload” the current web page. My mind was blown, and not in a good way.)  Somehow I became good at being patient with them when they don’t understand math, but I get much more frustrated and tired when they are so slow with technology. Perhaps it’s because I’m not expecting it: they grow up with technology all around them, but they can’t transfer it, mostly (I suspect) because they don’t want to as badly. Figuring out how to find the most popular Youtube video is more essential to their lives than figuring out how to open a file through a program other than the browser you just used to downloaded the file. Ugh. Well maybe next time I’ll be more mentally prepared.

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