McWilliam Public School Professional Development

GECDSB Professional Learning Sessions

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Friday February 3rd, 2017

Great learning with you all again today. Please find some resources below:

Learn More About the Progression of Fractions:

The Progression of Fractions

The Progession of Fractions from K-12

Exploring Fraction Constructs and Proportional Reasoning Fractions are a beast of a concept that causes struggles for many adults and students alike. While we all come to school with some intuition to help us with thinking fractionally and proportionally, the complexity quickly begins to increase as we move from concrete, to visual, to symbolic and from identifying, to comparing, to manipulatin...


Other Resources Related to this Session:

Paying Attention to Fractions

Paying Attention to Fractions


Gimme A Break [3 Act Math Task]

How many pieces of the whole are there?

Gimme A Break - Adding, Subtracting, Multiplying, Dividing Fractions 3 Act Math Task

Adding/Subtracting and an Intro to Multiplying/Dividing Fractions A colleague and good friend, Dave Burke, reached out to me recently for some ideas around adding and subtracting fractions. In particular, he was interested in trying to make the topic a little more enjoyable by adding some context. This was a challenge I was really eager to work on because working with fractions is such ...

Summary & Resources

Doritos Roulette: Hot or Not? [3 Act Math Task]

How Many Chips Are Hot?

Doritos Roulette - Hot or Not - 3 Act Math Task

Don't Get Burned By Doritos Roulette Spicy Hot Chips! Today, I was finally able to record some footage involving the mysterious Doritos Roulette chips when I was working with some colleagues from Tecumseh Vista Academy. If you haven't heard of the new Doritos flavour, here is the commercial: Special thanks to: Joey Demarse, Dan Frezell, Diane Gardin, Craig Gu...

Summary & Resources

Looking forward to working with you again in the next couple weeks!

Wednesday March 22nd, 2017

It was awesome to work with the Kindergarten team at McWilliam. Have a look below for resources from our time together:

The GECDSB Mathematics Strategy

GECDSB Math Strategy

Mathematical Proficiencies

The full GECDSB Mathematics Vision is here.

GECDSB Mathematical Proficiencies

Paying Attention to Spatial Reasoning

Paying Attention to Spatial Reasoning Document

Warm-Up: How Do You See the Dots?

We did a quick Dot-Card warm-up asking you to visualize how you saw a series of dots on the screen. We went around the table and it seemed that everyone had a different perspective.

Jo Boaler Dot Card Warm-Up

Here’s some of the ways you might have visualized the dots:

Tiny Polka Dots

We also explored Daniel Finkel‘s game, Tiny Polka Dots. We made some connections between the counting and quantity principles and the different card decks in this game.

Tiny Polka Dots - Math Game - Daniel Finkel

Also be sure to check out his TED Talk here.

Counting Principles

We briefly discussed the importance of counting and quantity principles like subitizing and unitizing. A full summary is below:

Counting Principles – Counting and Cardinality

Counting Principles - Principles of Counting and Quantity Featured Image

A Progression of Counting and Quantity Having spent the majority of my professional life teaching secondary math and mentoring intermediate (grades 7 to 10) math teachers, my new role as K-12 math consultant has led to a wealth of knowledge that I wish I had during my years spent in the classroom. My conversations about student learning needs with intermediate and senior math teachers always se...


We also discussed the difference between perceptual and conceptual subitizing. See this link for some more information on these ideas.

Pentomino Challenge

We spent some time working on the Pentomino Challenge and discussed ways that this activity could be modified for Kindergarten students to physically manipulate objects in space to activate their spatial reasoning.

Access PPT

Some other links I promised to share are included below:

Looking forward to working with you all again soon!

Monday March 27th, 2017

It was a pleasure spending time with three different groups for a full day, school-wide SBL at McWilliam! Here’s a summary of what we did with each group:

3 Act Math Task: Donut Delight

The main math task explored was Donut Delight where we played with multiplication to predict how many donuts there were in the “double hundred dozen” box and then used repeated subtraction to lead to a flexible division algorithm for division when we tried to find how many layers there were. To see all kinds of different representations and access all of the resources, head to this post here:

Donut Delight [3 Act Math Task]

How many doughnuts are there?

Krispy Kreme Donut Delight - 3 Act Math Task Screenshot

Sparking Curiosity to Fuel Sense Making of Multiplication and Division When one of our district math leads, Brennan Jones asked me to brainstorm some ways we could help his staff engage in some professional development around division and incorporate a 3 act math task into the learning, I immediately thought of some contexts where arrays, base ten blocks and area models could be used to h...

Summary & Resources

Pedagogical System

We then took some time with our Pedagogical System placemats to write down some elements from the Donut Delight task that fit into one of the four categories.

Based on work by Glenda Anthony and Margaret Walshaw, the Pedagogical System is the result of a meta-analysis of many studies which are summarized into four key components:

The Pedagogical System - Task Tools and Representation Non Threatening Class Environment Discourse

You can also see a “silent solution” animation of the pedagogical system in detail:

Japanese Multiplication

In some of the groups, one of the multiplication strategies we explored was Japanese multiplication. You can view the post below:

Why Japanese Multiplication Works

Why Japanese Multiplication Works - Using Lines to Multiply Is Not a Math Trick

Japanese Multiplication? Chinese Multiplication? Line Multiplication? Whatever it's called, it's only a trick if you simply memorize without meaning Have you ever wondered why Japanese multiplication works? I've heard some call it Chinese multiplication, multiplication from India, Vedic multiplication, stick multiplication, line multiplication and many more. While many might argue as to the...


Here’s a video that gives a detailed explanation of Japanese multiplication.

What a great day of learning. Can’t wait for the next one!

Thursday April 13th, 2017 – School-Wide SBL Day

It was a pleasure spending time with three different groups for a full day, school-wide SBL at McWilliam! Here’s a summary of what we did with each group:

3 Act Math Task: Toilet Paper Problem

The main math task explored was a modification of Todd Romien’s Toilet Paper Rolls activity where instead of determining how much less toilet paper we now get on a roll, we looked at ways to incorporate multiplication and division strategies when dealing with the number of packages that were on the shelf in the following image:

This gave participants an opportunity to explore multiplication strategies.

I hope to post the task in its entirety shortly, however you can access the slide deck for use in your own classroom here:

Download Task

Teams had an opportunity to discuss the tasks they brought to the table in an attempt to have an open discussion around how one might make the task more rich by using visuals, making it more open, or using some of the other “look-fors” explored during the session.

We then heard from mathematics education leaders Jo Boaler and Marian Small about their thoughts on open tasks and making tasks rich:

Always fun when I’m able to join the McWilliam Math Learning Team for some professional development! Looking forward to the next one!

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