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.

Friday, 1 April 2016

Guessed Writing 2016

It happened again. Last April 1st, 2015, I wrote an ‘April Fools’ update for another serial writer, namely Jim Zoetewey at “Legion of Nothing”. (Here’s a link to that 2015 entry still on his site.) This year, the “Fools Swap” was again proposed in the “Web Fiction Guide (WFG) Forums”. Alexander Hollins again graciously organized it.

And so like last year, I’ve decided to write about my writing process. There’s spoilers here for my 2016 entry to “SyncPoint, if you wanted to read that first.


You may recall that last year, in 2015, I’d hoped to write something that wouldn’t immediately be recognized as fake. Ultimately though, I'd also decided I wanted my entry to act as a bit of a window into Jim’s universe - the main characters, the rules, that sort of thing. So those things were foremost in my mind when signing up for 2016.

I was given “SyncPoint” by J. A. Waters. When I did my initial check in on February 22nd, I noted the serial had been running for about a year, but less than 30 updates. (Of note, J. A. Waters has another serial going as well.) This time, I did not have years of backlog to consider using! So I decided to make it a project for my March Break.

I started reading on Sunday, March 13th, aiming for at least 5-6 parts per day. I quickly realized that the setting and style were up my alley, what with a “Back to the Future” reference early on. In fact, the way a multiverse played into the tale, it inspired me to re-categorize the links off my serial site - sending anyone keen on my “Epsilon Project” over to “SyncPoint” too.


Like 2015, I kept a text file to track what seemed like key details in the story. (Or even the little details, for the observant - like doilies). The funniest thing was how random “april fool” ideas I had while reading ended up being addressed by Waters himself. For instance, after Sidella left, I thought maybe I could pull her roommate back in... oh wait, he’s doing that. Actually, she’s a main character. So maybe the ex... oh, there she is.

Then Leonard showed up, and I thought, maybe I could have a scene with doubles... again, J.A. did that a few parts later, not only with the Solstons but also the Reis. Well, okay then. There were a couple little things though - like I wondered if I could get any mileage out of the fact that there were two “Greg”s, and my name is also “Greg”. Plus there was the bit with Bugsy and the “writers"... would it return later too?

I mean, I didn't worship Gadget like a
goddess... wait, this was a thing somewhere??
I ended up reading faster than I’d thought. Part 19 I was forced to walk away from the story for a while, because WOW, my character “Alice Vunderlande” and his “The General” were perhaps separated at birth and you did NOT just make a “Rescue Rangers” reference because Gadget was an idol of mine back when I was younger and I need to breathe properly. (I think that was on Tuesday.)

Incidentally, and I said this last year, it’s a good idea to read the comments on posts too - assuming they exist. Because (again) that’s the future audience, plus there’s usually extra remarks by the author. For J.A.’s Part 16, someone wrote “I literally start every chapter not knowing which version of which character I am dealing with, or when it is set”, which is great for me as far as fooling people goes. Also, I learned that J.A. had given a mini shout-out to other serials on JukePop, which was pretty cool.

At some point, the idea of a courtroom trial came to my mind. Hard to say when that was, but it stuck. I caught up completely on Thursday, March 17th, decided that idea still worked, and on Friday I started writing out the scene. Part of what I liked about that setting was how it would let me snapshot all the main characters at once - without necessarily having them at each others’ throats. And it was maybe just plausible enough to fit into the universe.


Aiming for about 2,000 words (roughly the length of J.A.’s entries and my own) I decided the first half would set up the location and key characters, and the second half would need to be Bridget, leading into a finish - likely with Bugsy. This worked well for breezing through Rena (I know nothing about Nalan, and cursory research didn’t help much) and Rippante (who swears a lot - and in my own writing, swearing is a bit of a microphone drop, so I wanted to save swears for the climax, if at all).

Alice Art
(Commission by Cherry Zong)
For other characters, having Talbot or Rebecca felt like it would be overloading the scene. At the same time, I couldn’t resist the paragraph cameo of Alice (from my “Epsilon Project”), because somehow she just FITS into that world. And I absolutely had to put in the line about Dwayne Johnson being “a pillar of the community”. (It’s actually my favourite bit, because it will be read VERY differently depending on if you know "SyncPoint" or not!)

The writing came together surprisingly quickly. I was already into editing by Sunday the 20th. I found I had to tone Sidella down from the first draft, she was a bit overly emotional. (I now wonder if I write excessively emotional characters, which is WEIRD, because at my core, I’m not that different from Sidella at all... so do I write terrible characters?) But there were only minor revisions aside from that.

The minor revisions became kind of constant over the following week (how about mushroom stools instead of regular ones!), so on Wednesday the 23rd, I send J.A. Waters a message saying I had something, in case he wanted the file. He said sure (thanking me for being timely), so I sent it to him on Friday the 25th, a week early. That stopped me revising it, and gave him time to make a little graphic, if he wanted. (He did - nice lego piece! It's below.)


I ended up being pleasantly surprised by how well my “extra” part can blend in, given how I (obviously) hadn’t read SyncPoint’s most recent Monday’s episode when I pitched this one to J.A. I also recommend you check out kaleidofish, who wrote my “Epsilon” entry here. Including link-outs! Extra props because my per-week-plot-vote caused a rather short time frame to write in. (Interestingly, kaleidofish’s regular serial also does interactive voting - find it at “Redwood Crossing”.)

So where are the doubts this year? Last year I worried about overthinking things with Jim’s entry, and whether I should have set things in the past with so many main characters. This year my doubts are on a more generic level. Such as, are my own characters interesting to anyone aside from me? Am I perhaps a better analyst than I am a fiction writer? Will anyone who finds me through this swapping actually stick around? (If anyone did last year, they’ve been shockingly silent.)

That said, I was also worried that J.A. Waters would see my entry as too irreverent. And he liked it! So, as last year, I guess it is what it is. Thanks for reading about my writing process! New voting for “Epsilon Project will occur Sunday morning, and my time travel serial will resume (on that same site) with Book 3 this summer.

Monday, 28 March 2016

Three Benefits of Obscurity

I spent the majority of my Easter long weekend writing the usual 2,000 words for my Sunday serial, followed by writing, drawing, inking, scanning and lettering for four new math comics for Mondays stretching into April. Why? Because April sucks for productivity time. More to the point, why bother?

That’s a good question. Since I don’t think anyone would notice a missed update. Oh, someone might wonder about the absence after a week. Maybe. But my serial is currently interactive, and it’s all I can do to scrape together 5 votes. (After updating for 88 consecutive weeks.) Meanwhile, my webcomic Facebook page is still limping along at 26 likes. (Began 2012, presently at 35 straight weeks.) Why not skip updates?

Nothing to see here, move right along...

I won’t address the question of regular scheduling here - but it did make me think that more flexible updating is a benefit to being obscure. Obscure as in, the opposite of popular, in that both popular and unpopular things tend to garner lots of attention. I’m talking about the usefulness of being lost in the crowd.

This post is more regarding fiction updates, but I think it can also apply to a non-fiction column (I did write one of those for over a year too). Will you agree with my choices? If you’re in a similar situation, can you take some solace in these benefits to obscurity? Consider, it could always be worse, right?


As I said above, if you have to miss an update, so what? No one will be sending you emails saying “hey, where’s the 7am update!”. You can publish late. (I did on Feb 22nd.) You can take a week off. (I don't.) Heck, you can publish whenever you like. If you don’t, you’ll only be disappointing yourself.

Pictured: Crowd scene! Because my sanity.
And if you don’t want to disappoint yourself? To avoid missing a scheduled update, perhaps your art has to suffer a bit. Again, there will be no complaints from viewers saying “why didn’t you draw backgrounds today?” or “this isn’t advancing the plot at all!”. Because when you’re obscure, you don’t tend to draw in ANY comments, let alone complaints.

I rank this third because, as a white cis male, maybe there’s a privilege element to this that I’m missing. Perhaps lower quality scheduling or art isn’t as tolerable (personally or otherwise?) when you’re fighting as much to be seen as equal, as you are to be seen at all.


In a similar vein, obscurity allows a person to play around more freely. Possibly even with touchier issues, such as race or sexuality. My quartic and parabola (both female) have been dating for quite a while, and trigonometry is now black. No one has ever remarked on those facts, aside from me.

When I started online stories in 2011, I shied away from such topics, things I felt I didn’t know enough about. But after years of public disinterest, I decided to toy around with it. Because why not? Most don’t know I’m doing it, and those who do, don’t seem to care. (And I’m pretty sure someone would tell me if something came across as deliberately offensive.) As Shakira sings in “Zootopia”, “Try Everything”.

Related, as one gets popular, there’s more of a tendency to pigeonhole. (Or so I imagine, anyway.) Conversely, while you’re obscure, you can play around more in a variety of genres. People won’t demand more of the same. Do you fear losing half your audience by trying out urban fantasy, instead of the usual science fiction? Hey, that’s only 10 people. You can probably build that up again.

And now my number one benefit to obscurity...


I see two possible outcomes from achieving sudden fame. The first is that you get one entry/comic/video with a couple dozen (hundred?) comments, followed by months and months of silence. Leading the creator to wonder if they’ll ever recapture that lightning in the bottle, worrying that they’re now “doing it wrong”.

Something I said? Or didn't say?
One can still experience this on a micro scale. There’s usually a bump to start a project; my webcomic started with 100 views per update, now I’m lucky to get half that. Similarly, a year ago, my fiction blog got 58 views in a single day! A record for 50 WEEKS, until week, March 21st, when it got 78 views in one day. (Someone binge read, thanks to a review by Maddirose at Web Fiction Guide.) It’s worth reminding yourself that a rise to fame isn’t immediately exponential, but more sinusoidal. Obscurity avoids this roller coaster.

That said, I see the second possible outcome from fame is that you stay popular, and start being regarded as knowledgeable in your genre. Then, as more people come, you’ll reach that tipping point where a percent of your audience is trolls and people baiting, rather than giving than constructive criticism. And your opinion on things outside your field suddenly matters to people too, individuals that you don’t even know!

Now, I don’t mind if I’m being approached about art technique, or in a professional capacity. I even volunteered to be an MTBoS mentor last January. I like helping people! But if the questions turn to my personal feelings about the refugee crisis? Or how I feel about the touchier issues I mention above? That’s problematic.

Because I don’t want my personal opinion to matter any more than someone else’s. I’ve always preferred to observe from the side, rather than become a talking point myself. Heck, as a teacher, any personal opinion can be problematic, as there are people out there who can believe you will push an “agenda” while on the job. Talk about my work, not me personally.

I saw a tweet the other day saying “celebrity status negates anonymity” - seemingly, once you’re enough in the spotlight, you need to consider the impact of everything you say before you say it. That’s what really strikes me as exhausting. Actually, I should probably do a column on “decision fatigue”. It shouldn't be normal to attack individuals, unless there's some connection to their creative output. Which is not a problem for me right now.


So my point is, so long as I am (we are?) obscure, there's no need to worry about schedules, pigeonholing or personal attacks. Sure, sometimes it’s lonely instead. But other times I can get two comments on a post - from different people - and it feels like my birthday!

Plus, perspective - I’m sure there are others out there in my position too. Right? So we’re all being lonely together. Not to mention flexible, experimental and troll-free.

Thanks for reading! Feel free to leave a comment. I should go, these papers won’t grade themselves.

Tuesday, 16 February 2016

Snow Days Are A Myth

You heard me. Snow Days are a MYTH! They don't exist! They're like unicorns or palm trees. I will fight you on this! (I may not win, but I will fight you.)

Bear in mind that I consider a "Snow Day" to be a day when the majority of schools in an area are closed. I think the last time that happened in Ottawa, Ontario was January 2012 (which was an exam day, not an instructional day, and I think it may have been principal's discretion).

It certainly wasn't a mythical "Snow Day" today, so let's "Day in the Life" my Tuesday for your amusement.


Monday evening, Environment Canada was warning that the city could see 20cm to 40cm of snow (8-16 inches) the next day. Woke up the next morning, and sure enough, busses were cancelled, schools were open. As you do.

The procedure at this point is to head to your school, if it's safe to do so. (If it's not, I believe you proceed the nearest school you can get to safely.) There was maybe 5cm (under 2 inches) on my driveway, I cleared it, looked safe enough.

8:20am: Arrive at school. Only 10% of our students are bussed. Looks like less than 90% of students in the halls though.

8:30am: First period. There's an announcement to let students arrive without a late slip before 9am. I end up with 6 of 22 students. My backup plan for Gr 12 data management was to talk some cryptography. It relates to the probabilities we're doing, and I can make a period of that.

9:50am: Second period. I end up with 8 of 28 students. I don't have a good backup plan for Gr 11 "Functions", so I show some new trig (which I'll be going over again next unit anyway), take up some work, show another video, and end by singing "Polar Plot". (Tune of "Let It Go", you can check it out here, if you're so inclined.)

11:05am: Lunch. Enter the attendance. Fight with people on Twitter about Snow Days being a myth. (Lisgar is legit closed due to a water pipe bursting. But I maintain one or two schools closed doesn't count - our school was closed some years ago due to heavy snow on the roof. That was only us.)


11:50am: Just before end of lunch, I check in with the librarian. She's doing a presentation about human libraries for a teacher today and opened it up to other classes. I figured my smaller college level math class might be interested.

12:00pm: Third period. I have 4 of 8 students. One would prefer math, so I get him into the blue room (a quiet work space), and off to the library with the others. At least one of them saw it in the morning; I say oh well, work on your computer.

1:20pm: Fourth/Prep period. Having been able to accomplish ZILCH thus far today, I try to figure out how to manage the rest of the week. I also make a phone call, leaving a message for them to get back to me at this number.

2:00pm: Vice Principal stops into prep room. Says we can leave, it's getting pretty bad out there. But I'm now in the midst of figuring out Google Docs related to last Friday's PD day, and I'm waiting on my phone call.

2:30pm: Teacher comes in, says she was out in the parking lot. Nearly hit by a car driven by a parent, who was trying to exit the queue of cars picking up students.

(Photo by a co-worker)
2:35pm: End of school day. Snow days are a myth. On the right, you can see what the parking lot looked like.

2:40pm: I get my phone call. I give my wife a call, and head out to the parking lot. Snow is up to the base of the doors, about 30 cm (12 inches) has fallen. It's still snowing.

3:45pm: Many of us are still helping students and teachers get their cars out of the parking lot. The little plow driven by custodians is also prone to getting hung up on the snow. Speed bumps are not our friends. Posted some fun quotes to my Twitter feed this eve. (Search #SnowDaysAreAMyth)

4:00pm: I'm on the road heading home. I try to avoid what I hear is an accident on St. Joseph by taking the 174. End up stuck on the off ramp for St. Laurent for over half an hour - an accordion bus is stuck in the right hand turn lane.

I hear on the CBC that Ottawa has hit a record snowfall for a single day, beating some record set back in 1947. One could imagine that if schools don't close on a day like THIS, they NEVER close.

5:15pm: Get home. Almost. I live on a small dead end street. We're lucky to get plowed at all, let alone on a day when they're doing side streets around 8pm. I gunned it, and got stuck at the bottom of my driveway.

6:15pm: An hour of shovelling has led to progress. But despite appearances, the car is stuck. I try clearing more snow. No. Scraping snow out from underneath. No. Some sand equivalent under the wheels. No use. I have to get my wife (who is sick) to come out and help.

Still nuts.

6:30pm: With the help of a neighbour, rocking the car back and forth a bit, able to get it up my driveway and into the garage. Now I need to clear snow from the front stoop, etc.

7:00pm: I'm home. (After accomplishing a three point turn in my driveway, heyo!) I remember I haven't had anything to drink since before 8am, and have some water. About the only good thing about this day is that my step counter, at about 5000 steps when I left school, is now at 11,222 steps.


Whew, almost lost out on an instructional day there! After all, we're legally required to have 184 of them, with no flex due to weather -- that was a close one. Non-sequitur, I need to remember to put the recycling out tomorrow.

So yeah, snow days are a myth. If you don't believe that, I guess you believe in palm trees too.

Saturday, 6 February 2016

Order the Fruit Salad

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 4 (and final) blogging challenge is “Share a Lesson”. (For my previous weeks, see “Questioning” here, “Favourite” here and “Day in the Life” here.) We were warned about this one in advance, since depending on where you work, there might not have been teaching this past week. So I had something in the back of my mind.

That said, I did teach - namely the startup of semester two, with new classes and students, while still finalizing marks for semester one. (I did mention January was the worst month...) But with the startup, I realized I should probably blog here about how I start off my Data Management class (aka Statistics) every year. Namely by making a run to the store to get an apple.


I’ve been doing my fruit lesson for at least four years. Probably longer, though I didn’t always start the semester this way. Mainly because I didn’t always start with the counting unit. I’m also cheating a bit, because this “lesson” actually spans three days.

Day One, I don’t immediately start with the fruit. My first example is the probability of getting the correct combination for a standard locker lock. Then definitions, some other simple probability examples, and THEN the fruit comes out. A grapefruit, a lemon and an orange.

With the objects, we can no longer repeat our choice (versus having a password of all ‘a’s). Once the grapefruit is down, I only have two options left. 3x2x1 = Six options total, the students are on board. That’s when I pull out the lime, as seen below. The total arrangements is easy. The number of arrangements where the lime is first requires a bit more thought.

From there, it’s into factorials, and we call it a day. The BAD news from this year, is that this intro was on a day when the busses weren’t running. And even though only 10% of our school uses busses, the bad weather means lower attendance. (Schools are never closed. Ever. We could get 20 feet of snow and they’d still be open.) So I had to do a little rerun the following day.

Day Two, we move from factorials to permutations. Here’s where the apple is added, to make things interesting. Normally I’d get all the way through my “how many ways with lemon and lime together” example - seen below. But with the “ice day”, I had to leave it with them to think about. This picture was actually taken to start off Day Three.

Oh, I physically move the fruit around too, to emphasize. (This arrangement is fine. Not this one, not this one, but this one... *I switch the position of the lemon and lime only* ...and this is fine. *groans are heard*) And normally the apple is green, to match the lime, but my wife happened to have an apple at home, so I took that one. I don’t like apples much, this is the only time I buy them.


Once the lemon/lime example is done, I don’t advance the next slide. I pull out a second orange. And they know what’s about to happen, and someone says “Sir, why would you do that to us?” THEN I advance the next slide. And sometimes someone will try to argue that the two oranges are different enough, and so I have other examples with letters and words, and they will grudgingly capitulate.

Thus the first part of Day Three is finalizing this permutations knowledge, but of course, I have one more trick up my sleeve. I pull out the grocery bag, and announce that I’m going to take three of these home for the weekend. And I grab the grapefruit, the apple and the lime, tossing them in the bag. But wait!

Does it matter that I selected the grapefruit first? It’s coming home with me, the same way as the lime is, even though I picked it last. Of course now order doesn’t matter, and so now we have combinations, to round things out. Factorials, Permutations, and Combinations, all taught with fruit.

The inspiration was in part due to the “Shad Valley” program I went to at University of Waterloo in 1993 (when I was in high school). Ed Jernigan used fruit in his math lecture, as a way of trying to categorize “fruit” for artificial intelligence. This is, by the way, the closest I get to a "3 act" lesson.

Things to watch for: Students tend to like the visual/physical presence of the fruit - two of them remarked on that aspect this time. Students also tend to ask if they can take the fruit home with them. (Someone wanted the grapefruit this time.) I’m more leery of that, in case bad things happen. Also, I like grapefruit; if they want the apple, meh. Along the same lines, one guy wanted to be in my picture (above) but while I applauded his enthusiasm, I said I probably shouldn’t do that.

Fun fact: At one point, some of them were talking about salad. I’m not sure why (this period was right before lunch), but it was easy enough to steer that conversation back to permutations and combinations. Fruit salad, anyone?


Quick bonus, the lesson I likely would have written up if I hadn’t been buying fruit this past week is the “painted cube” problem. You paint a cube, then disassemble it - how many of the component blocks have no sides with paint? One side? Two? Three? It’s a rather elegant way of having linear, quadratic and cubic patterning in a single activity. But it’s also one that educators are liable to find more familiar - maybe you’d already heard of it?

The plan is now to have lime tilapia at some point for dinner this week. But before Monday, I need to get my personified math comic coloured and uploaded! (I hit entry #250 last week.) Thanks for reading here, if you enjoyed, know that I’m all about the writing. Feel free to check out some other posts:

-Check out the Bola Fruit in the Conic Household with “Tea Leaves”
-The math song parody “Permute” is the one I use for this Data unit
-Here’s my reminder that, even in the face of other creative ideas out there, “You’re a Good Teacher” (too)

Saturday, 30 January 2016

The Quest in Question

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 3 blogging challenge is “Questioning”. (My Week 1 post at this link; My Week 2 post at this other link.) Nearly didn’t post this week, for reasons I go into below. But I’m an MTBoS mentor for three other math educators, so I decided I should set a good example. In no small part because my more “hands off” approach to mentoring has a tie in with this particular subject.

So, why did I nearly opt myself out of Week 3? And what did I come up with for a question in the end?


I am not very good at asking questions of others - I’m much better at giving responses. In fact, I’m really lousy at approaching others in general, even people I know (or teach). There’s this default mode in my brain, where I tend to assume people are just fine without me, so why should I interfere and possibly make things less clear or more complicated.

It’s probably the introvert in me. Coupled with the depressive.

The paradox is that I want people to approach me with questions - mostly about my recreational writing - yet perhaps they’re assuming I’m just fine without them too. It’s the same sort of thing with teaching and mentoring, I’ll sit here waiting for the questions, so that I can respond to them. Not always to give an answer, mind you, but to give options, start research, or to turn the question back on the poser. And sometimes I interpret body language as being a question. Point being, I rarely initiate.

Given that, I don’t believe I’m someone people should look up to. In fact, I can be quite self-deprecating. It occurs to me that this could be the reason why I’m reticent to take on any sort of student teacher. Is MTBoS mentoring even a thing I should be doing? ... I don't think that's a question I can answer myself.

Let’s focus back on the classroom.

What are you thinking about?
Breaking down the MTBoS assignment options: A question to get kids thinking about something? I tend to improvise off the cuff, or ask lame questions to give them processing time. An awesome/sucky test question? I feel pretty middle of the road. A student asked a question that sparked something? This happens a lot, but it’s pretty ‘in the moment’. And while I have a great memory in that I can remember details of the story I wrote 5 years ago, I rarely retain a memory of social interactions. Plus I’m SO bad with names.

In the vein of “a question I didn’t know how to answer”, I suppose I could get into the “why is it a greater than 5 check?” in statistics. (It’s a threshold for the normal and binomial approximations, it’s referenced as the lowest indicator for the coefficient of determination, and then there’s p values. Why 5?) It’s a question that almost always comes up, yet I never really have an answer aside from “let me know if you find out”.

But if I only put that out there, this would be a really short post, and as you may have noticed, I’m bad at those.


I haven’t been teaching this past week. It’s been four days of exams, and while there was class on Monday, that was fielding final review questions. Standard form stuff. (Or factored and vertex form stuff.) I did get an interesting email from a student on Wednesday afternoon though. It cycles right back to the idea of a problematic textbook question.

For anyone in Ontario with the Nelson 3M “Functions and Applications” text, follow along on Page 188. It’s a multiple choice in the cumulative review. Question 14 gives a quadratic area formula, asking what width option gives an area of 130. The student solved the equation, ending up with two answers of 5 and 13. And BOTH were listed as options.

She dutifully subbed both answers back into the equation - and they still worked. This was when she emailed me with a snapshot, stating “I’m a bit confused” and “I might not be doing it right”. I reassured her that she was correct... but I wasn’t content to leave it there. How could the text have misfired like that?

We take many words for granted.
Not content to leave it at “textbooks are stupid, yo”, I generated the lengths for the rectangles as well. This gave me a hint, producing 5 by 26 and 13 by 10. Which suggests to me that they had rejected the 13 because this would make “width” longer than “length”. After all, properly speaking, the English definition of “length” is “the measurement of something along its greatest dimension”. Did you know that?

It’s mathematics which muddies the waters, tending to use ‘length’ and ‘width’ interchangeably, depending on which way your page is oriented in front of you - and here we had no page, only a formula. There was a rather interesting discussion of the meaning of “length” with a sixth grade class on Ask Dr. Math from 1999. This is not a new problem!

So the textbook listed “5” as the correct answer for width. Since “13”, despite being a “width” that solves the formula, is technically a length. (And “10”, also given as a possible answer, would be a valid width but doesn’t solve their formula.) Now, do I think that was the INTENT of the text? No. And it’s needlessly confusing. But wasn't that journey interesting?

All this to say, I rarely initiate questions. I respond.

Thought from a prior post.

I also respond to every comment on my blog, if you’re so inclined. Both here, and on “Any Q-Bars”, my math webcomic which is a play on words for the popular “Any Qs” mixed in with “Q bars” denoting the irrational number set. I’ll also throw in a quick plug: If you’re an educator in Ottawa, Canada, check out #OttSlowChat on Twitter!

For now, I should get back to marking exams. Wheeee. If you enjoyed reading this, I’m all about the writing. Feel free to check out some other posts:
-There’s some fun math questions in this COMA Recap Post
-The Big Question: Me blogging about my depression
-And in the vein of better questioning, “Hinge Questions” by Nik Doran.

Saturday, 23 January 2016

Lattice Puzzle

 January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 2 blogging challenge is “My Favourite”. (You can find my Week 1 blog post here.) Now, I presented a “My Favourite” back at ‘Twitter Math Camp 2013’ - namely Unit Circle Estimations (for Trig). I’ve also droned on a bit about teaching the Sine Law. Those are more traditional topic centred posts, but I’m still feeling subversive, so let’s use this one to talk about this number puzzle I got at OAME 2013 instead.

I'll pause to give you a moment to scroll though all those other lessons and recaps I threw at you. Do I link too much? I probably link too much.

Here is the puzzle.

The premise is simple enough. Fit all the numbers flat into the box provided. Note that the conference was in Toronto, hence the CN Tower in the logo. I don’t recall if everyone who attended that PD conference got one of these, or if it was something related to the fact that I presented there (Musical Mathematics - I’ve parodied 30 songs). But the puzzle has been surprisingly popular this semester! Does it fit into the curriculum? I don’t know.

Presumably, it’s got some spatial reasoning associated with it. After all, the only way to make the pieces fit is to create a full lattice, with no gaps or spaces. (In the image below, look in the lower right corner.) Now, if you think about it a bit longer, you might realize that symmetry is a useful tool. (For instance, lock the ‘7’ in with the ‘1’ - looks a bit like a ‘4’...)

What it looks like on my desk this week.

I simply keep the puzzle on my desk at the back of the room, and students (Grade 11 students) who are finished work early or want a bit of a break can play around with it. I have sets of puzzle cards on my desk too, but for whatever reason, this is the popular thing. It started the semester fully assembled, when a couple guys would time each other for the fastest to assemble it.

Eventually, it spent well over a month fully disassembled, as people toyed with it and couldn't put it back together. One student wondered if there was a way to get/make her own. I had a teacher in my room for an on-call ask me about it the following day. I even played around with it a bit once, while catching up on “Supergirl” (while procrastinating from catching up on marking). There’s only been one casualty, the tip of the ‘5’ (2?) fell off - a student glued it back on.

"How does it work? I MUST KNOW!"

So there you go - the favourite thing that has nothing to do with instruction. Though "a game your students love to play" was an option, so maybe I'm not as subversive as I think. Related, perhaps I should bring in a tangram next semester.

If you enjoyed reading this, I’m all about the writing. Feel free to check out some of my other posts:
-How Teaching Is Different
-Meet Lissa Jous, over at my math webcomic.