York 4 Mathematics Assocation (Y4MA) Workshop


York 4 Mathematics Association Math Professional Development Workshop

May 2017

Thanks for inviting me to learn with the York 4 Mathematics Association Chapter of OAME for an evening of math professional development! The group was energetic and excited to learn about meaningful manipulative use, sparking curiosity and building conceptual understanding across the grades.

Here’s a summary of what we explored today. Looking forward to connecting again soon!


After a brief presentation about avoiding the rush to the algorithm, we took some time to explore a 3 act math task with a very low-floor and high-ceiling, called Toilet Paper Rolls. The resources are not yet posted on the web, but I hope to do this soon!


Counting Principles

We briefly discussed the importance of counting and quantity principles, but focused on the importance of unitizing. A full summary is below:

Counting Principles – Counting and Cardinality


Counting Principles - Progression of Counting and Quantity

A Progression of Counting and Quantity As a former secondary math teacher and intermediate math coach, 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 seems to come down to gaps in student understanding, however rarely wer...


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Exploring the Progression of Multiplication

We made a leap from counting principles and unitizing to multiplication and specifically, using arrays and area models.

The Progression of Multiplication


Progression of Multiplication - Area Models and Standard Algorithm Featured Image

Arrays and Area Models to The Standard Algorithm Did you know that the words "array" and "area model" appear in the Grade 1-8 Math Curriculum a combined 22 times? Not only do arrays and area models help to support the development of proportional reasoning when we formally introduce multiplication in primary, but they also help us understand how to develop strategies that lead to building numbe...


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As an aside, you might consider looking at the “Japanese Multiplication” or “Stick Multiplication” which is derived from base ten block representation:

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...


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Concreteness Fading

We attempted to summarize the use of manipulatives on a continuum called “Concreteness Fading”. While the name suggests that concrete manipulatives fade away over time, it is important to remember that they fade away with one layer of abstraction and then reappear as a new layer is “piled” on.

Applying Concreteness Fading to Progression of Multiplication

3 Act Math Tasks: Curious Math iTunes U Course

Access over 30 tasks with all resources downloaded directly to your iOS Device to avoid streaming media in your classroom through the Curious Math iTunes U Course:

3 Act Math Tasks - Curious Math iTunes U Course

Enrol in Course

Other Useful iTunes U Courses to Check Out:


Learn Pythagorean Theorem Through Exploration – Kyle Pearce
Stacking Paper Tasks – Kyle Pearce
Beautiful Functions – Jon Orr

OR, you don’t want to download Jon’s Beautiful Functions book? Check out all of the links here on his blog.

Hope you folks found this YCDSB math professional development experience useful.

I’d be delighted to come back and learn alongside you all again sometime soon!

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