Outside The Box, Nov-Dec 2013: A Riddle Runs Through It

I run a monthly school-wide puzzle contest that I call Outside The Box. I’ve crafted a riddle for Nov-Dec’s OTB challenge. Some of you will recognize the important idea at work here. If you, interested reader, would like to participate, contact me with an answer and I will physically mail you something sweet!

Scotiabank Toronto Waterfront Marathon 2012

Here’s the OTB Challenge I posted for Nov-Dec:

Last month the Toronto Waterfront Marathon, a 42km marathon, was held. It had approximately 4000 participants.

Assume that it had way more participants, say 50000 runners, who all made it to the finish line. Would you be able to say, with absolute certainty, that at least two runners took the exact same number of strides to get to the finish line?

Complete reasoning of your answer is required to win this challenge. (i.e. If ‘yes’, explain why. If ‘no’, explain why not.) The winner will get something chocolaty. Ties will be broken by clarity, correctness, and completeness of the given solutions. You have about a month to submit an answer, until December 18th.

Happy puzzling!

Mr. Chow

I had two groups of students submit correct answers to October’s literal and spatial OTB Challenge. We’ll see how this one goes! 😀


Classroom Field Recordings: Music to My Ears

 I’ve been away for a month, not the best way to try to restart this blog, this year! Sorry I was quite wonderfully distracted for the last month, but I’m focused now! 😀

Last week, I was really pleased and proud of the hard work done by the students in my physics classes. They were tackling some tough kinematics problems in small groups, with little direct help from me. I was so happy that, on a whim, I started to record some of these sessions. This will give other teachers a sense of what my classes sound like. To me, it’s music to my ears! Students puzzling together over a new situation/problem, and figuring out the correct solution together. It reminds me of how climbers approach a new problem and work it out together. 🙂

1st Projectile Problem:

I’ll be back soon with more substantive posts about Growth Mindset, the Importance of Student Agency in the Classroom, and a post about Classroom Ambiguity (which I’ll purposefully leave ambiguous for now)… and all of their connections to climbing!

Braking with a Reaction Time 1:

Braking with a Reaction Time 2: 

Outside The Box, October 2013

I run a monthly school-wide puzzle contest that I call Outside The Box. October’s OTB challenge was the first of the school year, and I was testing the waters to see if there’s enough interest to keep it going for 2013-2014 (last year, I stopped around February, partially because of Robotics competition season and partially because of thinning participation).

Here is the challenge I posed to the school on Oct. 1st:

October’s OTB Challenge.mp4

Using (recycled) paper, create the two objects in the video. Your creations should have the same folding abilities as the ones featured.

All valid solutions will receive a prize. The size of that prize depends on the number of people who submit correct solutions.

(Apologies to Paul and Justin for removing important credit… I’m trying to make the solution ungooglable. I will include full credit when I give solutions on Nov. 1st!)

I’m happy to report that I received a collaborative solution from two S4 students today! (S4 = Grade 10/11 at my school)
Their awesome solution can be found here: October’s OTB Solution, Alev and Monica.mp4

So at least some prizes will be given this month, hopefully the first of many this year! 😀

Lazarus Post: SBG Collaboration Catalyst

Let’s dust this blog off a bit. It’s been close to 2.5 years since I’ve written here. This year (my 3rd in HS) is the first year I feel like I’ll have time to give back to my PLN in more than just ≤ 140 character snippets. Finally!

During the past two years, I’ve been meaning to write about the interesting connections between two of my passions: education and climbing, to illuminate the heathy aspects of both, in addition to adding a unique voice to both communities. This post is about increasing collaboration on SBG Objectives using inspiration from how climbers collaborate on boulder problems.

Background: I use small-group guided inquiry and an evidence-based (not test-based) SBG assessment system.

An important goal I have with SBG is for students to be working together on objectives, learning from and teaching each other. In previous years (and from what I remember from my high school experience), students are, for the most part, silo-ed and focusing on their own work. This is a disservice to them and their (our) future. Problems in society are only becoming increasingly complex and their solutions will likely be cross-discipline involving many different people with specialized knowledge working together (see: global warming).

To increase collaboration between my students I’ve implemented a Peer-Teaching mechanism this year. If students take advantage of this mechanism they will gain increasing control over the weighting of their course assessments (adding a bit of a gamification feel to the year). Full details are as follows:

Peer-Teaching Information

Summary: If you are teaching other physics students concepts, you may be eligible to improve your course grade.


  1. The teaching student must have mastered an objective.
  2. The learning student must have already attempted the same objective, or a very related objective if in another class (i.e. a grade 12 student teaching a grade 11 student).
  3. Both students must show evidence of earnest collaboration on the objective.
  4. The learning student must then obtain mastery on this objective.


  1. The learning student obtains mastery on the objective (and can now teach other students)!
  2.  The teaching student is allow to bank one percentage weighting credit for that objective’s unit.

Anytime during the year (and by moratorium week, at the latest) each percentage weighting credit may be used to move one total grade percentage point weight from any assignment to any other assignment within a unit. (i.e. within the Kinematics Unit, moving one percentage point weight from Unit Objectives [originally 6%] to Daily Inquiry Activities [originally 4%], so that your Unit Objectives are now worth 5% and your Daily Inquiry Activities are worth 5%. Grade percentage point weight breakdowns for each unit can be found in your grade spreadsheet.

Secondary goals of this mechanism are to reduce procrastination on objectives, remove any possible stigma from the students that quickly master ideas (instead seeing them as potential helpers), remove any possible stigma from the students that take longer to master ideas (instead now being win-win opportunities), and increase cross-class and cross-grade collaboration. There is also hopefully a self-sustaining cycle of teaching, where the newly taught student can now teach other students who are struggling with the same idea they previously were.

Going from confusion to obvious success is wonderful. Doing it within the context and support of a community can be game-changing.

For the climbers in the audience, you probably pick up on the influence from working on bouldering problems. These sessions are often marked by climbers of many different skill levels working together on a range of problem difficulties. Virtually everyone in the gym can be thought of as a teacher as well as someone who is learning. Success at all levels (beginning to advanced) is boisterously celebrated and climbers who learn new skills are excited to teach others. This is a major reason why I love climbing and climbers.

We’ll see how this goes this year and what improvements will be necessary. In the spirit of this post, don’t hesitate in sharing your thoughts and support! (It’s good to be back! :D)

Students Make the Best Presents!

So my final practicum has come to a close, I’ll have some time in the coming weeks to post more interesting thoughts here later…. but for now:

Thank You Students!

Students are the best. Seriously. There’s no excuse not to feel this way! Students are a joy to be with everyday!

I’m part of the lucky few new teachers who will have a full-time job this coming fall. I hope I never take for granted the amazing journey I’m about to embark on…

This emotional farewell card from my Grade 12 Math students will be an easy reminder. 😉

WYCDWT: Deal or No Deal

Another quick post, here’s another project I’ve used in the classroom… just today actually.

We’re studying Expected Values (Probability Distributions) and I found two powerful videos from the gameshow, “Deal or No Deal” where the issue of E(X) arises quite naturally. tbh, any video of Deal or No Deal implicitly deals with Expected Values!

Hint: Use Probability Theory!

How much is this worth?

The videos can be found here: http://nchow.ca/DorND-DB

The first video is of a contestent who has a $200,000 case left, and the $1,000,000 case left. The banker offers her $561,000 to stop playing the game. There is tons of drama, and it’s impossible not to get invested into the outcome of her decision, (Spoiler Alert: she declines the offer, and ends up with the million dollars, for a nice heart-warming ending.)

My setup: I would play the video up until Howie asks the natural hook, “So, Deal or No Deal?” and then pause the video. After the students stop groaning, get them to put themselves in the contestant’s situation and decide if they would take the deal or not (this isn’t hard :P). Have them form groups and then debate their decisions. Teasing out some math inherent in this situation is a plus, but really you just want them to invest in the problem. I used this as a nice introduction to expected values, a topic most people are unfamiliar with unless they’ve studied finite math before (or are professional gamblers!). After your students debate, play the rest of the video and ask whether it was a good decision. This segues naturally into the topic of expected values.

The second video is of a contestent who has a $0.01 case left, and the $10,000 case left. The banker offers her $5,500. This video acts as a nice consolidation at the end of the class to drive expected values home. You can ask similar questions, if she should take the deal or not. (Spoiler Alert: She ends up balking the deal and winning a penny.)

The beautiful part about these two videos is that the math works out. When the expected value is more than the offer, the contestent goes for it and wins the million. When the expected value is less than the offer, the contestent goes for it and wins a penny. It’s prudent here to talk about taking a $361,000 chance at coin flip odds. This is a life-changing amount of money, and I definitely would have taken the deal, even though I understand that the value is lower than my expected one… and I explained and justified this hypothetical decision to my students!

Just my thoughts, use as you wish!

On that note, how would you use this in your classroom?


Other notes:

1. Expected values resolve the question in my previous post, “Should Derren Brown be happy it took ~9 hours?”. Proof is again left to the reader, but the quick answer is probably not. 😛

2. Apparently I’ve won the UOIT Faculty of Education Tech Award! I didn’t know it existed, but I’m ecstatic to be the recipient! The cash prize of $500 is nice too. 😉

3. On that cash note, I’m almost done my B.Ed and ready to be certified come the end of April. I’m happy to report that I have two job interviews this Thursday afternoon. They’re both for Science and/or Math positions, and I’d be over-the-moon if I got either one. Wish me luck!

WCYDWT: Ten Heads in a Row (Hello World!)

I’ll have time to post my pedagogy and teaching philosophy later. I’ll also clean up the look of this site, pardon the dust.

I just signed up to share a project I made for a probability lesson (independent events), that could be useful for other teachers!

It’s famous UK magician Derren Brown flipping a coin and getting it to turn up heads, ten times in a row. The explanation is included: he was flipping coins for the better part of a day, until he finally got a string of ten heads together.

My Setup: Play the trick, then ask for explanations. Play the explanation video (with beeps) and get the students to try and solve for the amount of time and/or probability of this happening. If the students need to know how long a flip takes, you can play the original trick video edited with a timer. After groups have come up with solutions and explained their process, watch the full un-beeped video for the answers.

from Derren Brown, The System [2008]

The project files can be found here: http://nchow.ca/HorT-DB

(N.B. you may want to tell your students to make the simplifying assumption that there’s an average of 2.5 flips per trial. If you want to get more complicated you can get them to do the expected value calculation for 1 flip trials, 2 flip trials, 3 flip trials, etc… and reach the expectation of 2.5 flips per trial themselves)

Should Derren Brown be happy it took ~9 hours?

Use freely!

…oh, and hello and welcome to my teaching blog. My name is Mr. Nathan Chow. 🙂

Full Disclaimer: I do not own the rights to these videos. My intention here is not to break copyright law, but instead to teach students how to think critically and learn a bit of probability. If you own this video and take issue with this, please let me know and I will remove it. Also, I am heavily influenced by Dan Meyer, David Wees, Shawn Bullock, Steven Hurley, etc… I admit openly to taking their ideas and running with them!