Saturday, 30 April 2016

Math Gets Physical

This year, our school’s learning plan (SLP) wants teachers to include instructional strategies to focus on “intentional movement within a lesson”. Most of that information was discussed at the staff meeting at the start of April, with the idea that implementation of five consecutive movement days would follow before the end of the month.

The month of April. Report card month. Play month. The month where there are literally only 3 days when I am not at the school, sometimes working 12 out of 24 hours, and now I have to do unconventional lesson plans on top of everything else. Perfect. (Say that with the same inflection as Marty McFly in “Back to the Future III”... Clara? Perfect. We’re going past 60mph, I’ll never make it.)

Honestly, part of my frustration stemmed from me feeling like this is a good idea, and so I wanted to be able to do it right. Furthermore, this idea of physical activity having a positive effect was reinforced twice during the month.

Once was when I was at a teacher directed PD event, when Bruce McLaurin stated that some years ago he’d had his math class taking free throw shots in the gym (to determine where on the court one had the greatest chance of scoring). After that, the students worked quietly for half an hour without being aware of it. The second time was in talking with a colleague, who said that her first period class had seemed very tired, so she had two students lead a “body break” which included jumping jacks. Even the student who hadn’t participated had seemed more energized afterwards.

Ergo, after being at school for 25 straight days, and with only five remaining teaching days in April, I finally bent my mind towards how I could at least attempt this within the recommended time frame. Because I’m a teacher, and I think doing the impossible is in our job description. Please be understanding if the implementation is somewhat lacking.


I was giving tests in my 3U and 4U classes last week, so that meant I was trying this with my MCT 4C class. Which wasn’t necessarily a bad thing, as they’re my smallest group (only 9), and I’ve been having to revamp a lot of that course material already (it’s been 4 years since I taught the course, and there’s a new text). The unit we’re currently in is Polynomial Functions. Specifically, the expectation “recognize and evaluate polynomial functions, describe key features of their graphs, and solve problems using graphs of polynomial functions”.

Sample graph. Personification not included.
So, I went into Desmos and screen captured ten different polynomial graphs, with their equations. Then I decided half of the room was for “even” functions, and the other half for “odd” functions. On the diagonals, “positive” leading coefficient and “negative” leading coefficient. Ergo, a “four corners” activity (roughly corresponding to a Cartesian Plane). I created ten slides, starting with both equation and graph, then shifting to some with only one or the other. (Current technology did make implementation easier now than it would have been four years ago.)

We were doing a quiz on Monday, last period. I did this beforehand, in the hopes that it would remind the students of what we did last week better than ten minutes of study time with their notes. I would call it a success - when I saw uncertainty in terms of where to go, I could ask for clarification. A couple students were caught by a graph in standard form, choosing odd instead of even. At the end, one student said “I think I get it now. But I would have preferred pointing.”

Moving on, Tuesday/Wednesday we were looking at difference tables, the “a” value, and the points required to define a quadratic versus a quartic, etc. My plan? Construct a line through a point. So there should be lots of variations. (Indeed, one student picked the zero slope.) Then add a second point. Now everyone has the same line. But there could be different parabolas. Now add a third point, and so on. I even worked out equations in advance, in Desmos. Here’s that link, if you want to see.

I was hoping for some discussion, and comparison of different - or not so different - graphs. But the students simply held their sheet up into the air, or shouted out a value for slope, rather than actually incorporating movement. I adapted by having people raise hands if they had “concave up” versus “concave down”, and getting a volunteer to come up to the board to draw before showing my Desmos as a possible matching equation. Repeat for cubics, and so on. So, some of them were out of their seats.


Wednesday, I gave them all graphs when they entered. (The same graphs from Monday, retooled on a different sheet that I cut out.) I asked them to try and create an equation. After a minute or two, I handed out equations at their desks, but for someone else’s graph. Most of them (six) got up and moved around to compare of their own volition, without me saying anything. (One absence, and two stayed seated.) This led into a handout on the “a” values, and finding them from the y-intercept using factored form.

I’m not quite sure how to classify that - collecting materials for an activity? Anyway, it’s something I might be able to do again, and seemed more successful than Tuesday. Thursday I went very low key - it was a requiz of Monday’s material (I take the better of the two results). After giving them time to look at solutions, I covered them, and said they could take the new quiz from my desk whenever they thought they were ready, as I circulated for any other questions. I think only one student asked his friend to bring him the quiz.

Friday... was kind of a wash. Five students would be away for a host of reasons (field trip, family trip, religious day...) and I wasn’t sure what I could do with only four present. I decided to teach the “Graph Dance” moves. (Oh, FYI, there’s Graph Dances stretching back into 2011.) But then only two students actually came, one of them not a fan of my musical efforts, the other not keen on dancing.

Well, they both had to use the washroom, and the nearest one was locked (likely due to vandalism), so I guess the trip to the other side of the school counts as a win? Even though part of the idea behind including movement was to “have fewer washroom breaks”. Alas. If I remember to, I’ll try the “Dance” thing again in the coming weeks.


As I said initially, I do think there’s something to this “intentional movement” concept. It’s the main reason I’m blogging - so that I have something I can refer back to later. The preparation time wasn’t much more than a half hour each day (Mon to Wed), but granted it was a small class. The secondary reason for this post is to see if any of you, the readers, have thoughts about this. Or improvements I could implement in the future. So feel free to comment below!

And with that, April is done. As a bonus, I had a head cold for a couple days in there too. I am starting to think that April is indeed a worse month than June, even if it can’t top January for sheer hideousness. Of course, it may not help that my own personal calendar ticks over an additional year at the end of April. My tens digit is now a perfect square! Huzzah, peace out.


  1. Hey Gregory,
    my name is Anne and I am studying in Germany and will become a teacher soon. I am reading your blog for a few months now and I really like it. The blog posts are very interesting. I like the idea of “intentional movement within a lesson” and wonder if it was possible with a bigger class, beacause you were practicing it with a small one. Do you think that would be possible? I thought about separating the class into smaller groups...but was wondering if they made the same learning progress. Do you have other ideas for bigger classes?
    Thank you! Greetings Anne :)

    1. Wow, thanks for letting me know! Hope the studies are going well; I have a cousin who got married in Germany, I liked what little I saw over there. As to the larger class idea, I think it should be possible -- my choice of the small class was more driven by necessity than intent. The main thing is the buy-in. Let me divert for a moment, then elaborate.

      I did attempt the "Dance" thing a couple weeks into May, but it didn't go over well with that class. A couple of the students were game to try, but the rest were either indifferent or against it. After about five minutes, I gave up and moved on. In retrospect, perhaps I should have tried it with one of my other classes, but there's that tendency to slip back into old habits instead, I suppose.

      What I'm getting at there is I think there's a tipping point, where if you can get a majority of students on board, the others will join in too -- and likewise if a majority won't, you're kind of stuck. Peer pressure. And the sort of activity they'd prefer will likely depend a bit on who is in any particular class. For instance, most of my set were keen on the graph comparisons, just not the dancing. Of note, that colleague who did the "body break" had a class of about 20, and I'm sure others in the building tried with more students -- I simply haven't had cause to talk to them.

      Smaller groups might work too. It depends on what sort of activity you're trying to do.... for instance, I think the "four corners" of the room is best done with a whole class, but you can then have follow up discussions. (There's also "Which One Doesn't Belong", where each corner can be correct in some way.) One simple suggestion we were given for movement was simply to have quiz solutions or some sort of activity posted up at the back of the room, which students would need to get to, and class size seems irrelevant there.

      Hm, that got a bit long winded. In brief, I think it would be possible with a larger class, and can't really speak to small groups, since it's not my style. I'll see if I can turn up the handout we got on other ideas. Thanks for the comment!

    2. Hey Gregory,
      thank you so much for your answer! Yeah, the studies are going well and I hope I will pass all my exams in july.
      Good to hear that you think it's possible. I'm looking forward to try different sort of activities.
      Do you have any idea or tip how I can get the majority of the class on board, how you said, how they can be motivated?
      It would be really nice if you could talk to the colleagues who did it with bigger classes, but only if it's no big effort for you!
      So you mean it wouldn't be supporting to seperate the class??!
      I'd be very happy if you answer again!

    3. In terms of getting the class interested/motivated, there's a lot of factors at play. Two of the main ones that come to mind would be regularity, whether it's something you elect to do every Friday for instance, and rapport, whether the students accept that you have their best interests at heart. Both, I fear, being more long term requirements. Hence why something may not work on a specific day.

      As far as the colleague discussion, I fear it's the worst time of year right now (exams and other final evaluations), so I don't think it's in the cards. Separating the class into groups might work fine though! I only meant it's not something I have much experience with; I'm a bit "all or nothing", for better or worse. Find the style that works for you.

    4. Hallo Gregory,
      Thank you for your answer! It’s really nice that you always have time to respond! You have such a great experience and it’s great that you can share it with us! I like your Idea of regularity! I should try to do it once a week! Also, I will try to separate the class into groups! I hope it will work fine!!
      You are absolutely right, I just need to try different sort of activities and find my own style that will work for me!
      Thank you for all your comments and your tips! It was a new experience for me and it was really useful!!I will follow the news in your blog and I will suggest the blog to all my friends!
      Best Wishes, Anne.

    5. When you take the time to comment, I try to make the time too! Thanks for your thoughts and your enthusiasm. I appreciate the referral as well - I know I can get a bit random here. All the best back at you!

  2. Hey Anne, I think your idea about separating a big class into smaller groups is a good solution. Maybe you can think about methods which are less interactive but more include the whole class? But I'm not really sure either…
    I would be gratetful for some suggestions. Thank you!

    1. I found the list of strategies for "intentional" movement that we were given, some of them less interactive, some that might be ways of creating smaller groups. Here you go, hope these suggestions are of some use?

      1. Carousel/Activity stations (individual or in groups)
      2. Comprehension cards/Sticky notes (things student understands or doesn't, move to place on a bulletin board)
      3. 4 Corners (strongly agree/agree/disagree/strongly disagree)
      4. Fold the line (put students in a row then fold, so people on the ends partner, people one in from end partner, etc)
      5. Head-Bandz (there's a graph/equation on your head, you need to identify it by asking questions, without looking - could make groups this way)
      6. Moments of curiosity (something in the room, a puzzle or solutions or other, that students can look at when unoccupied or finished)
      7. Whiteboards or other vertical surface interactions
      8. Collecting materials for activity (could be gathering data points by shooting hoops, or simply having to go to a place to pick up rulers)

  3. Thank you so much for all these ideas, Gregory! I'm curious if it will work.
    Especially the third point sounds good to realize and I like the moving aspect about it.
    What are your experiences with comprehension cards? I would be interested in how you integrate it in the lesson.
    Thanks a lot!

    1. I am more of a "4 corners" guy myself. The only thing I've done similar to "comprehension notes" was in the first couple weeks of school, having students write down (on a post-it) 2 things they understood, 1 thing they were working on, and 1 thing they were wondering about (be it something about a topic we covered, or an extension). I had them stick it to their desk for me at the end of the class (on Fridays), trying to use it to guide my teaching more than incorporate the physical movement.

      I kind of lost the thread a couple weeks in, and then forgot... pity, I'd meant to do more self-evaluation like that this year. I should remember it for the future.