Category: Mathematics

March 14

It comes every year on this day.  March 14.  It’s better known as Pi Day.

I can remember first learning about Pi.  3.14 or 22/7 was good enough to solve the problems presented in class.  And, beyond that, why would you want to learn more?

Then, I had a real mathematics geek who got us more excited and encouraged us to learn more about Pi and to memorize more than just two digits of decimal places.  So, I went as far as 3.1415926.

The game changed with the calculator and this magic button.


And, of course, your favourite programming language has a value of pi built into it.  Have you ever wondered to how many digits of accuracy?

The worlds best URL is located at “

The website is called Pi to 1,000,000 places.  Visiting and actually finding the million digits are two different things but hey…

Or, cheat and visit this site.

And get a poster here.

Or, write your own program.

I’ve been keeping track of interesting things about Pi for a long time.  The current collection is here.  I supposed collecting links for this is irrational but it keeps me occupied and I enjoy solving the challenges and read that there are so many mathematicians fascinated by documenting their experiences.


It’s a shame that Pi Day appears during the March Break.  But, you could always celebrate when the students come back or, get ahead of the game, like Alice Aspinall did.

Update 2018 

Kyle Pearce spent some time at Walkerville Collegiate before the March Break to celebrate.

And, of course, I’ve tucked away even more stories about Pi in the Flipboard references to above.  Knowing me, I’ll probably continue to do so all day today.  You can’t have enough of this stuff.  22/7 indeed.


Big data and lost towns

We don’t think about it much these days but Ontario went through a whole bunch of amalgamations a few years ago and literally changed the map of the province.

In terms of me, you may remember this post – My Childhood Community.

We actually knew the perimeter of our town from riding our bicycles around the streets at its outer limits.  We also knew the names of the townships that surrounded the town – Goderich, Hullett, Tuckersmith, and Stanley.

But, no more.  Towns and townships had been amalgamated into new communities or adminstrative entities.

I ran into this terrific resource recently.  It was a Fusion Table resource of Canadian Administrative Boundary data.

As you can see from the visited link colour, I checked out Ontario.

Screenshot 2018-02-25 at 12.17.51

That’s when it got real for me.  I set the Filter to filter by name.  Then, when I searched for “Clinton”, I got nothing.  Why?  Because it’s not an administrative place any more!  Then, I remembered the new name which covered more than the traditional town.  They named it after my old high school “Central Huron”.


Then, it gets educational, a bit nerdy, a bit mathematical, and big time geographical!

From the Fusion table, there’s the KML data that defines the area.

Screenshot 2018-02-25 at 12.23.32

How’s that for your above average polygon?

Here’s a piece of it.  Ideas about how to use that or plot that abound.

Want to see that on a map?  Of course, that’s possible.  This is Google after all.  All the jagged edges reveal the extent of the KML entries that define the place.

Screenshot 2018-02-25 at 12.24.26

Let’s zoom out to get a better look…

Screenshot 2018-02-25 at 14.47.00

How’s that for an n-gon?

It was actually kind of fun after that.  I started poking around looking at other administrative areas.  I learned very quickly that the process is additive so I had to reset if I just wanted to look at one area.

If you’re interested in exploring and doing a little geographic inquiry or if you’re in search of some raw data for a project or two, this is the place for you.

This Week in Ontario Edublogs

It’s time for another wander around the province, checking out the great thinking from Ontario Edubloggers.  As always, there’s some great, relevant professional learning just a click away.

Reframing Resistance

This post, from Lisa Cranston, provides an interesting insight about how to handle push back when delivering a professional learning session – through a self-registration lens.

Stephen Porgues talks about the need to feel safe in order to learn – how do we create an environment that fosters a sense of safety?

In a typical professional learning session, there’s often a real mixture of participants.  When the participant is there through their own choice, there’s bound to be a greater sense of safety.  It’s easy to see the opposite when the session is laid on and your attendance is required.

We talk about the rule of two feet and often attribute it to selecting based upon interest; perhaps an eye towards safety should be considered a factor as well?  What can be done to make a safe place to learn?

What Brings you Joy?

I kind of think that Paul McGuire’s thoughts about joy tags on nicely to Lisa’s thoughts about safety.

Paul sees a sense of joy in

Working with accepting people who appreciate your work and the time devoted to creative projects.

In terms of projects, I think he describes a perfect condition for joy and safety.  What’s even more interesting is to imagine the opposite.  In Paul’s case, he sees the opposite of joy as “mired in negativity” and goes on to make the reference to organizations.

Anything come to mind?

I also thought of opportunities to experience pure joy on a personal level – winning a football championship, finally reaching a student, birth of a child, meeting a childhood friend, and more.

I find myself not necessarily wanting to analyze it but I really appreciate the prompt from Paul to think about what brings me joy.  It’s been wonderful; I hope that you take a moment to reach Paul’s post and experience the same.

Les 4Ps d’un état d’équilibre

For the record, when you have Google Chrome set to automatically translate text, the 4Ps that Joel McLean identifies in French don’t all become Ps in English.

  • Pourquoi – Why
  • Perspective – Perspective
  • Priorités – Priorities
  • Progrès – Progress

I found the four points in the post interesting to think about.  It’s also intriguing to consider their order.

If you think, cause and effect, the last three make for a good starting point for reflection.  Then, I turned to the “Pourquoi” which helped with the context.

Since my word for 2018 is “Balance”, I found Joel’s post of particular interest.  If I can understand that there never will be perfect balance, understanding everything else and then challenging myself to understand the “Why” makes so much sense.

This is a great leadership post put in very practical terms.

Technology is a Church

So, Royan Lee freely admits that:

We’re an Apple family.

Watch the family that unboxes a non-Apple device!


It’s a great family event, I wish I had fast internet access like them (I was in awe of the download speed) and being photobombed by the family dog puts it over the top.

Now, their goal is to let Siri win them back.

Flipgrid for the camera shy

Jen Giffen runs into a challenge that seems so unintuitive to me.

People wanting to use Flipgrid but they don’t want their camera pointed at them.  C’mon, Flipgrid users, isn’t that the point?

I remember the first time that I saw Flipgrid in action.  It reminded me of the screens from the Brady Bunch show!

To solve this situation, Jen goes with the flow and offers some alternatives to your beautiful countenance.  Each comes with instructions.

  1. Voki
  2. My Simple Show
  3. Stop Motion with Google Slides
  4. Chatterpix 
  5. Sock Puppets 

Sock Puppets?  Can you take anyone seriously if they’re talking using this app?  <grin>

Counting With Your Eyes: Subitizing

We all do it, don’t we?  I guess I’ve just never thought about it as deeply as I did while reading Kyle Pearce’s post.

I also don’t ever recall being explicitly taught the concept either.  But, after reading Kyle’s post, I absolutely know that I do it.  If you’re interested, he has a free download of resources from this post.

All the time.

I especially found his talking about clumping interesting when thinking about my use of the concept.  Depending upon the objects, I either clump by 3s, 5s, or 7s.  Why all odd numbers?

It also brought me some fond memories of playing cards – they’re not all what we think of today – check these out.

If we had these in common use today, the concept of subitizing would take on a new level of importance.

Why do we have numbers on modern playing cards but not on dice or dominoes?  Personally, I blame Omar Sharif.

Learning factories

This post, by Jim Cash, was totally different from the sort of writing that I’ve come to expect and enjoy from him.

He draws a very visual description of a factory assembly line.

Imagine you have a new job in a busy factory, on an assembly line where parts continuously come down the line that you need put together. They come really fast but you are new and can’t keep up. Just to reduce your anxiety and embarrassment, you quickly pile a large number of the parts into a big box beside you.

I couldn’t help but think of the classic Lucille Bond segment.

In Jim’s post, he describes the desire to search for a new job, in search of a different criteria for success.

He paints a very interesting parallel to education.

His scenarios may just give you pause for how you’re going to teach something today.

Don’t you just love Fridays around here?

It’s a day of inspiration from these fine folks.  Please click through and read/share their original posts.  Your learning network will appreciate it.

And, make sure that you’re following these great bloggers.

Join Stephen Hurley and me on Wednesday mornings on voicEd Radio and repeated throughout the week for the radio version of This Week in Ontario Edublogs.  All the shows are archived here.

A fruitful activity

Who doesn’t know about the power of Desmos in the teaching of Mathematics?  The images, activities and everything make learning cool.  It’s one blog for Mathematics that you have to follow for inspiration and ideas.

There’s a wonderful collection of activities that will get you and your students thinking and analysing … fruit!  It’s called Pomegraphit.  Log in to your Desmos account and do a quick search.

Then, the learning gets juicy.


It starts easily enough in the collection of activities.


And, as you work your way through things, the opportunities for learning get really interesting.


And, of course, there’s a teacher’s guide to help you work your way through the Mathematics and the activities.  I never really thought about fruit as being difficult.  But, when you think of the pomegranate – maybe.



Who doesn’t like a good puzzle?

I often think that part of the reason why I did so well in Mathematics and went on to study it was that I had great teachers.  One of the commonapproaches that seemed to run through all of them was not to assign “problems” but to present each activity as a puzzled to be solved.  When they solved them in front of the class, you could see the joy they had in the solution.

I can’t say that the same approach would work for everyone but I know that it did for me.  I can actually remember the names of just about every teacher or professor that had that sort of impact on me.  The most recent was Ross Honsberger.  In fact, I was so inspired that I remember dipping into the very shallow coffers of a university student to buy books from his series Mathematical Gems.  I see now that they’re available to view online if you’re so inclined.

Now, those puzzles or gems might be a little intense for K12 schools but SolveMe Puzzles certainly aren’t.


I played around with all three categories of puzzle and will confess that “Who Am I?” really caught my fancy.

Each of these broad categories takes you into a section where you actually play the puzzles.  But, it’s more than that.  Check out the Bingo area for each and then, impressively, you can make your own puzzles.  Or students could create their own to challenge their classmates.

You can sign in to keep track of your progress or play anonymously.


However you use it, just don’t call them “problems”.  They’re mathematical puzzles at their finest.

This Week in Ontario Edublogs

Happy February and Groundhog Day (updated)…

For this Huron County boy, there only is one weather predictor – Wiarton Willie.  But I understand there are others.

While you wait for the sun to rise, check out these posts from Ontario Edubloggers.  I usually refer to this link but I also keep a Scoopit collection here.  I refer to that because


It’s now at a gold level.  That’s a lot of blogging.  Way to go, folks.

I’m sorry, but the world needs more real apologizing

Heather Swail has an interesting take and insight on a Canadian trait – being nice.  I mean, who among us hasn’t apologized without any real need?  I smile when I think of a lady who wasn’t paying attention at the store the other day and ran her grocery cart into me.   I apologized to her.

What can I say?  I was raised to be polite.

Heather’s take is that an apology should be …

A real heartfelt – not intellectually or strategically manufactured – apology involves reflection and thought on the part of the apologizer.

My action, I guess, could best be described as a reflex action.

We know that learned behaviours can be modified.  Is the reflex on my part worth the time and training that would be needed or is there a problem with being overly apologetic?

A $50 Million Gift Horse

This post, by Anne Shillolo is actually a copy of an email that she wrote to the Minister of Innovation with respect to the $50 million that has been allocated to the CanCode project.

The CanCode program will invest $50 million over two years, starting in 2017-18, to support initiatives providing educational opportunities for coding and digital skills development to Canadian youth from kindergarten to grade 12 (K-12). It also supports initiatives that provide K-12 teachers with the training and professional development they need to introduce digital skills, coding and related concepts into the classroom.

Anne correctly identifies the lay of the land, at least here in Ontario.

  • Not enough young women in technology,
  • Not enough computer science (CS) teachers in Ontario,
  • Most teachers’ colleges are no longer training CS teachers,
  • Teacher candidates are not choosing CS as a teachable.
  • High school CS and engineering courses are not offered province wide.

Then, she proceeds to share her thoughts about outsourcing professional development for teachers.  It’s a letter that will get you thinking.

The CanCode details can be found here and the list of winning companies here.

Precarious Absences – The impact of teacher intervention truancy systems

Deborah Weston tagged me in the announcement of the release of this post.

It’s a standing joke in the educational profession that it’s easier to come to work sick than to plan lessons for someone else to teach while you are under the weather.  Creating lessons is difficult enough when you’re healthy.  Being sick makes it even more difficult.

I see you nodding your head.  We’ve all said that.

Yet, there are times when you have to take time off.  It’s very seldom to get a doctor’s appointment in other than school hours.  Society generally likes people working from 8-5.

Now, I like a computer to do all kinds of administrative things for me as much as the next person.  Deborah talks about teacher truancy systems that track days off and then performs some sort of action for excessive time off.

As Deborah notes, it does cast a wide net.  Wouldn’t the principal of a school be in a better position of knowing if someone is potentially taking advantage of days off?

In the bigger scheme of things, the days are laid out as a matter in a collective agreement.  At what point does this become a violation of that agreement?

ok go

For the record, I don’t own a Google Home device.  But, I do have an Android phone with the Google Assistance installed and I’ll admit that it’s darn handy at times to just ask a question and get Google to try and respond with a a useful suggestion.

I’ve even trained Google to know that my dog’s name is Jaimie.  It was just a case of fooling around, asking Google…

“What’s my dog’s name?”

And the first time, Google didn’t know.  So, I taught it.

Now, when I ask “What’s my dog’s name?”, Google will respond correctly.

Chris Cluff shares a combo blog post, podcast with Chad Reay about Google Home.  Both the blog post and the podcast are entertaining and insightful.  I recommend both.

As for Google Home, my son got one for Christmas and we did have some fun with it.  But, when you put your tinfoil beanie on, you do realize that it’s listening all the time waiting for you to say “Hey, Google”.

The podcast did get me thinking about whether or not it is a welcome member of the household or classroom.  What do you think?

The Essential Catchall

When I read the title for this post by Tim King, I didn’t know what to expect.

It turns out, he’s reflecting on his teaching of an Essentials class.  This post is a powerful look inside the classroom and shares with us just how students end up in this course.  With Tim’s description, it’s quite obvious that a course geared for a particular type of student certainly takes a turn for the worse when it becomes a catchall.


I found Tim’s description quite disturbing.

I would have thought if anyone could reach out and design a course to engage students, it would be him.  He embraces technology and learning at an inspiring level.  And yet, he reports that equipment in his shop gets broken.

You can’t help but speculate that success would only be achieved if the catchall philosophy is abandoned and student needs become paramount rather than the current reality.

Taking the step: Vertical Non-Permanent Surfaces in my mathematics classroom

When you close a blog post with

The richness of the mathematics and the thinking that resulted from it was well-worth the challenges though. Moving forward we will use this strategy for some logic puzzles and number challenges, and then transition into specific curriculum content.

you know that you’re onto something good.

Melissa Dean’s post is interesting and got me thinking just about “how” we do mathematics.  Typically, it’s done by yourself flat on a desktop.  After all, the school board paid a lot for those desks.

Occasionally, you get called to write your solution to a problem on the black/white/green board in the classroom.  It’s different; you’re writing in a different direction but you now have a potential audience looking at your work.  She describes a problem solving situation that involves a triad and the role of the scribe.  (You have to read her post to see why I used that word!)

What I think is particularly noteworthy is for her to step back and view the students as mathematicians.  This whole activity is certainly worth trying out in your classroom.

Knowledgehook Math PLC Planning Tool

Kyle Pearce takes us through a very thorough walkthrough of the Knowledgehook PLC tool.

The product is made by a Kitchener based company and claims a few Ontario school boards already as clients.


It’s an interesting walkthrough with Kyle’s comments as your guide to what’s happening on the screen captures that he shares.

Clicking through Kyle’s post takes you to the Knowledgehook website where there are a number of mathematics tools running the gamut from free with a few features to a subscription model with much more utility.

In case you missed it, I had a chance earlier this week to interview Helen DeWaard.

Thanks for sticking with this post to get to the bottom!  I hope that you’ll click through and read the original posts in all their glory.  There’s lots there for learning and reflection.

And, don’t forget to add these bloggers to your learning network.

This Week in Ontario Edublogs

You know, in the week between Christmas and New Year’s, nobody would be blamed for not blogging.  Fortunately, there have been a number of bloggers who keep fighting the good fight and we’re to benefit.  Check out some of what I’ve read recently.

The Education Corporation
Paul McGuire makes an interesting connection from the book “The Corporation” to real corporations to the governance by school districts in the province.  As a result, I’m on the lookout to get a copy of that book for a read.

The big message here is about control and he gets you thinking

Will any educator make the connection that apart from the pursuit of profit, there is little that separates the modern corporation from the traditional school board?

Read on to see his thoughts about this.

Given that corporations are certainly in the news all the time, it’s an interesting ponder.  Start your pondering with Loblaw admits to bread price-fixing scheme spanning more than 14 years.

Mathematicians We Should Know More About: Ada Lovelace

This post, from Matthew Oldridge brought a smile to this old Computer Science teacher’s face.  She’s a compulsory mention in class because of her importance.  There’s much more than Computer Science to consider though….

  • Mathematics
  • Collaboration
  • Visionary
  • Solving a Problem of the Time
  • Patterns and Designs and modernization of the textile industry
  • Women in History/Mathematics/Computer Science

Studies like this are important for students to know.  It’s important to know how we got to where we are in any discipline to honour the work that went before and to inspire for the future.

I know that it can raise the ire of those who have studied the past when an “innovation” gets touted as something new when it’s actually built on years of vision.

#onewordOnt Introduction

So, what was your one word for 2016?  If you check out Julie Balen’s post, you’ll see that she has a collection of blog posts from around the province of bloggers who wrote a post about theirs.

Blogging, in this case, is the perfect tool to:

  • set your goals for the year ahead and
  • to reflect at the end of the year as to how well you did

Julie’s looking to collect posts for 2018; there’s a link where you can add yourself if she doesn’t catch you.  She promises to visualize all the information that she receives.

The post is an interesting amalgam of 2016, 2017, and 2018.  What stands out though is that her list of bloggers are all women.

C’mon, guys, let’s level the playing field.  Paul McGuire has already written his.

Knowing Your Readers and Literature Circles

If I was teaching potential educators at a Faculty of Education or an Additional Qualifications course, I would make this post from Jennifer Aston required reading.

She talks about the concepts of Literature Circles but adds an interesting and important twist – knowing the readers in your class.  There’s lots of good stuff here.

The absolutely biggest thing though is the large list of suggestions about how to make it all work.  I’d bet if you had any other suggestions, she’d appreciate reading them in a comment or two.

There’s also a great deal to see as she models good technology practice in here with a collection of surveys that she uses to collect the data that she needs.  (I’d “borrow” her questions and customize if I was doing it).

In honouring student voice, she uses a Padlet to collect their reflections.

It’s a wonderful process modelled and makes a good read for anyone.

Relationships Matter…I cannot stress this enough

I don’t know that I can add much to Jonathan So’s post than what he states in the title to the post.

An observation inspired by reading Stuart Shanker’s book …

There is no thing/ concept as a Bad Child

I’m reminded of a statement from Wayne Hulley.  “Parents send you the best kids they have; they don’t keep the good ones at home”.

Schools and teachers have a unique relationship with young people.  Parents still have the bulk of the time to be spent with them but the time in your classroom is unique and very special.  There’s a great deal written about the way “we” were taught – in classrooms, facing forward, memorizing, testing, etc.  We know the concepts are dated but …

… parents grew up thinking about education in the same way.  That’s what they remember when they think about their school years.  So much has been learned about learning over the years and often.  It can seem like a treadmill with school districts taking on the latest and greatest approach while ignoring the past.

The one thing that truly endures is the relationship with students.  “You can’t stress this enough.”


From the TESL Ontario blog, here’s an opportunity to catch up on what you may have missed.

Screenshot 2017-12-28 at 11.23.43

For me, I’ve got some new bloggers to add to my Ontario Edublogger list!

Math is Visual

Especially if you use purple triangles as part of your logo.

This latest project, from Kyle Pearce is a collection of videos demonstrating mathematics concepts.

It’s starting with a clean and usable interface.  Nicely done, Kyle.

This website was created to assist in building a better conceptual understanding of mathematics through the use of visuals. The images, videos and resources shared here are intended to help all teachers, parents and students understand that Math Is Visual and we should take every opportunity to teach it that way.

This is the last post for #TWIOE in 2017.  I’d like to take the time to thank all of the great Ontario Edubloggers who continue to write and to share their thoughts, learnings, experiences, and inquiries.  Recently, I created an alphabetical listing of all the bloggers who I’ve made reference to in this weekly post.  Check them out here.

Please take the time to support all of these terrific bloggers, by leaving a comment on their blog, sharing their post, or sharing this post.

For this week, make sure that you’re following:

Here’s wishing you a great blogging 2018.