Tag Archives: Flipped Classroom

[2016 Blogging Initiative] Week Four: A Lesson Introducing the Unit Circle

My Relationship with Textbooks: “It’s Complicated”

My first several years of teaching I avoided the math textbook as much as possible[0]. One year I even waited to hand out textbooks to students until the second quarter. I assumed (incorrectly) that using the textbook would make me a lazy, bad teacher. However, at the start of this year I decided to embrace the textbook for the good resource that it can be: a bank of practice problems[1] not a replacement for my teaching[2].

Background: My Classroom 

One other thing I’m doing this year is flipping my classroom. The flip, however, isn’t just lecture. I’m trying to challenge my students do problem solving through the vidoes, and I hope to show how I’m trying to achieve that in this lesson. For one thing, I provide guided notes for the students to fill out as they watch the lesson. I also don’t do every problem: I ask them to pause the video and try some in the middle of the video. To that end, I’m also using EDpuzzle which pauses the video and asks them questions that I’ve created at a variety of levels.

When we get back together in class the following day, the students are randomly assigned into groups of 3 or 4. Students spend about 10 minutes going over the notes and making sure each students’ notes agree with one another and that students understand the topic. After that students work on practice problems, from the textbook, on the same topic. [3]

The Challenge

So we’re chugging along and we get to the Unit Circle. This is the first lesson that I disagree with how Blitzer (our textbook) approaches it. I’ve had success with students in the past by teaching special right triangles first because students see them in the Unit Circle. So I decided to create my own “chapter” and left the textbook, like old times.

The link below is a short (<13 minute) video so you can see what the students will do for HW prior to class. But you should watch it because that’s the interesting part of my lesson. 🙂


Here’s the handout:

As you can tell from the video, I show students the special right triangles and where the values come from. My hope is that they use the Pythagorean theorem if they ever forget the shortcuts in the future, but most students will, unfortunately, probably forget that. I’m not sure how to share that with them differently.  However I only give students a few points from the Unit Circle, and ask them to “figure out the rest”. If they can figure it out on their own before coming to class, and they understand the special right triangles, then I think that it will be more likely that the Unit Circle will stick.

Since I’ve deviated from the textbook here, I had to find practice problems online, but that wasn’t too difficult. Students will go to my website and simply click on the worksheet links (complete with answers) to practice this in class. I’ll only print out the sheets for those students who want more practice beyond class and have no internet at home.

I’ve assigned the video (only 2 students have watched it so far), but we’ll meet in class Monday to see how well they did filling out the rest of the Unit Circle.[4]

Request for Feedback

How can I improve this approach? How can I teach special right triangles in the video so that they do more of the “heavy lifting”?

How are the quality of the questions in the EDpuzzle video? Are there others you thought of that I could do?

Is there a better way to approach the Unit Circle that you’ve seen/used other than special right triangles?

If you could answer any of the questions above, I’d greatly appreciate it. Thank you for reading! (and watching??)


[0] I still avoid it in Physics–I haven’t handed out a textbook in 3 years, with the exception of one student who begged for it. It didn’t help her.

[1] It’s also a good resource for ideas for 3-act lessons.

[2] I’ve seen some teachers teach how to read a textbook, which is a valuable skill, but one that I’ve decided pass on for now. I want my students to understand the math first and foremost. I’m still not sure how I feel about not teaching students to use a textbook effectively and efficiently.

[3] Because I believe that HW is practice, earlier this year (before I flipped), I don’t grade HW. Students also didn’t do the HW (with very few exceptions). Now, I still don’t grade that they watch the video, but I’m not afraid to email or call home if students are missing it chronically. Also when students get to class, they recognize that they’re responsible for learning the material at home, and so will work harder at the start of class to understand what they didn’t watch. It’s amazing how much more “HW” (practice) they’re doing now just because it’s happening during class.

[4] And if I’m on my blogging game, I’ll blog about how it went. Unfortunately it’s tennis season, so I probably won’t find time to soon.



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Flip the Class?

I’ve heard pro’s and con’s of “flipping” a classroom (basic idea: having students watch videos of lectures at home and doing “homework” or practice problems at school instead). Here are a few that come to mind:


  • Low student HW completion rate, but students are more likely to watch a video than do actual work.
  • Students need help when they’re doing the work, but if it’s homework that’s when you (the expert) are not with them.
  • More time in class to do practice or other things, rather than students sitting there listening to you lecture.


  • For teachers that do Project Based Learning or some other sort of exploratory work where students are working with peers, not much lecturing is happening anyways.
  • Lectures with feedback (Plickers, anyone?) is the best way to lecture, but students don’t get that sort of feedback on videos.
  • Students don’t learn much (or worse!) with lectures OR math videos (great explanation here!) so it’s bad pedagogy at school or at home.
  • Roughly 20% of my students don’t have internet at home, and that’s a large enough chunk to cause headaches when requiring students to watch videos online.

After hearing another good speaker at a conference on flipping the classroom, I decided to give it another shot, but with some significant differences.

Students watch the video while filling out “Take Home Notes”

Here’s my first attempt at this. The idea is that if students are filling out notes, they’re more likely to pay significant attention to the video.

I periodically ask students to pause the video and attempt problems on their own.

Similar to the previous point, if students are doing the problems on their own, they can then check their answers against what I have in the video. I then ask them to follow that up and complete a few more problems before coming to class. This makes them pay attention to the video in a way that they otherwise probably wouldn’t, and provides good feedback during the video.

Students begin class by checking problems from the “Take Home Notes” with others in their group.

I’m still undecided whether to split students into “filled out the notes” and “didn’t fill out the notes” groups when they get to class. Part of me wants to do random grouping, but part of me wants to reward students for doing work at home. That time at the start of class (sharing notes) could become “the few who do the work always filling in the majority who didn’t”, which would be bad for many reasons.

This year we have mandatory Study Hall, so any student has, twice a week, built-in time to watch videos.

This takes care of the “I don’t have internet at home” problem. As I’m the only flipped class in the school, if they don’t have internet, they’ll have to prioritize watching my video over whatever else they wanted to work on. If they don’t, their parents will hear about it.

We still do 3 Act Lessons and Projects in class.

The things I find important–problem solving, communication of math ideas, applying math to real-world situations, building ideas and math concepts before introducing them via lecture–can all still happen. I just need to find a balance between “practice days” and “3 act lesson days”.

Now the only “con” is making the guided notes and the videos. When will I find time for that?!?

Here’s my first video. Please tell me what you think!

Some other Notes

I was worried about how long the video would be when I finished–I didn’t want long videos (longer than 15 minutes) to deter students from watching. When I finished my first video above, as you can see, it was 8 minutes and 45 seconds. Condensing all I do in a 45 minute period [1] into 8 minutes is ridiculous. Of course, students should be pausing the video to work out practice problems, so the actual time to watch the video should be between 15 and 30 minutes. But it made me realize how slow I lecture because I want to make sure that a majority of students follow what I’m saying. The ability for students pause and replay parts of the video help tremendously. The other incredible thing is ideally [2] that I now have a full class to devote to the questions that slowed down the lectures before. But since students will be working in small groups, the entire class doesn’t have to wait for the questions of the few.

I am using Doceri–something you should definitely check out if you have an iPad, regardless of how you teach. Before flipping, I used Doceri primarily for projecting notes to the front of the room from wherever I stood in the classroom.  In my opinion it is vastly superior to the technology that Khan uses for his videos. It took me about 1 hour to make the “Take Home Notes” (Google Drive), and almost another hour to write out all the work on Doceri, during which time I wasn’t recording, simply marking stopping points for the writing. Then I hit play and recorded my voice while pressing “play” at each stop. I thought I’d have to constantly pause and hit play again to recollect my thoughts, but I was able to dictate 8 min and 45 seconds straight through the entire lesson because of all the setup I did.

One more advantage of doing it this way is that I put way more thought into what I wanted to say and how I wanted to say it than I would in a normal lesson. I have a bad habit of “winging” lessons more than I should, mostly because I (in my own mind) want to retain the flexibility of responding to student questions. [3] However, when I have no students in front of me, it forces me to choose my words carefully ahead of time. During class I’ll often forget to do something, such as show students how they can check their work. I did a little better on the video with that, though hopefully it’ll continue to improve as I do more and more of these.

Thanks for reading all of this and let me know if you’ve tried something like this and/or have thoughts on it!


[1] That’s assuming I get through everything, which doesn’t always happen! I would probably actually spend ~2 days on this.

[2] This all works great in my head. I’ll try to remember to blog when I’ve actually done it.

[3] Yes, I know that the more prepared a teacher is, usually the more ready they are in responding to student questions, and therefore the more flexible they are. That’s why I put “in my own mind”. Ha.





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