area games geometry investigation pattern reflection scale

Upscale Pattern Blocks

Update: April 13th, 2022

Upscale Pattern Blocks are now available!

Now you can get your hands on a set of blocks through the amazing and creative folks at Math for Love. Click here for details!!

(If you are not familiar with Math for Love, poke around the website. Along with the Upscale Pattern Blocks, there are numerous other curiosities for home-based and school-based mathematical exploration.)


First off, I hope you are well. This post represents a portion of my attempt to remain “well enough” in the midst of tremendous uncertainty. Most of my time is spent talking about the teaching and learning of mathematics, something that seems to have ground to a necessary halt in recent days. Given our collective circumstance, the time feels as good as ever to talk about a little project I’ve been working on, and ask for a smidge of help.

The Blocks

Recent access to a laser cutter and a kindergartener got me wondering. I began to play with a few possibilities. One of the fun things that fell out was a set of scaled pattern blocks I’m calling, “Upscale Pattern Blocks”. Essentially, they are pattern blocks scaled in three different sizes. The sizes interacted in some very interesting ways, and after some test cutting and multiple trips to the craft supply store, I ended up with a really fun result.

investigation scale surface area volume

Experiencing Scale in Higher Dimensions

A colleague and I have often bemoaned our attempts to teach the concept of scale factor in higher dimensions. A topic that has such beautiful and elegant patterns and symmetries between the scale factors consistently seems to sail directly past the experience of our students. I have tried enacting several tasks with the students including some favourites from the #MTBoS (Mathalicious 1600 Pennsylvania and Giant Gummy Bear). Each time, the thinking during the task seems to dissipate when new problems are offered. It just seems like students have a hard time trusting the immense rate that surface area and volume can grow (or shrink). In the past, I had used digital images of cubes growing after having their dimensions scaled by 2, 3, 4… etc.; students seemed to grasp the pattern yet under-appreciate the girth of 8, 27, 64… etc. times as many cubes. 

ratios scale tasks volume

The Scale of Coffee Cups

A colleague is a religious McDonalds’ coffee drinker. One day she showed up with a medium coffee and a cream on the side. It was in two separate cups:

I asked her for her cups when she was done. (She is also a math teacher so understands that this is not a creepy request. It is no weirder than the time I bought 400 ping pong balls, or 1500 bendy straws). I then made her a request to buy a large and small coffee in the future and save me the cups.
area scale tasks

Basketball Golf Task

The other day, a future teacher asked what one piece of advice I would give to a soon-to-be mathematics teacher. I immediately had several. I settled on one that I felt encapsulated my belief both in and out of class:

Honour curiosity

In class, this finds me wandering through student suggestions and constantly posing new problems that create relevant challenges. Curiosity (both student and teacher) keeps a vibrant ecology going, and I would argue that the intellectual tension so often provided through curiosity is necessary for a positive ecology to thrive.

On a Smaller Scale

I was watching Saturday morning cartoons when this commercial was aired.

High energy music and neon flashes of light are often used to sell car related toys on these stations, but this commercial caught my eye. Upon first viewing, I thought I saw them advertise speeds of 

classroom structure scale tasks unit analysis whiteboards

Gummy Bear Revisited

The giant gummy bear problem has been floating around the blogosphere for a while. When I first saw it, I knew I wanted to use it. I finally have the perfect opportunity in Foundations of Mathematics 20 this year. (Saskatchewan Curriculum).
History of the Problem (As far as I know)
  • Originally presented by Dan Anderson here. Included original Vat19 video and driving question about scale.
  • Adapted by John Scammell here. Edited video and new driving question.
  • Dan Meyer provided a 3Act framework for the problem here.
  • Blair Miller adapted his own 3Act structure here.
My apologies go out to anyone else who played with or re-posted an original interpretation on the problem.
estimation measurement probability scale tasks

Merit to Mathematics Labs

There is widespread turmoil among teachers and students when it comes to the practicality of mathematics. School mathematics, at the middle and high school levels, has moved out of the elementary niche of rudimentary skills, but has yet to make it into the realm of complexity necessary to apply it back into the world. Our happy compromise, as teachers, is to go with a two-pronged attack:

1. Tell the students that the practicality comes later
2. Create word problems about trains leaving stations or people tossing balls off cliffs