## GECDSB School Based Learning Sessions (SBL)

### Monday March 6th, 2017

Thanks for inviting me to learn with you on your school based learning day! The group was energetic and excited to learn about meaningful manipulative use, spatial reasoning, some counting principles, visualizing numerical expressions, some multiplication/division and the importance of concreteness fading!

Here’s a summary of what we explored today throughout all three 100-minute blocks, noting that some groups went further in different areas than others:

## The GECDSB Mathematics Strategy

## Mathematical Proficiencies

The full GECDSB Mathematics Vision is here.

## Paying Attention to Spatial Reasoning

## 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.

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

## 3 Act Math Task: Donut Delight

After a good consolidation of the dot plate task, we explored the Donut Delight 3 act math task 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.

## Donut Delight [3 Act Math Task]

### How many doughnuts are there?

Sparking Curiosity to Promote Conceptual Understanding 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 cou...

Most of the groups recognized division as the opposite operation to multiplication and noted the Japanese multiplication method that has been floating around on Twitter recently. Here’s a summary of it below:

## Why Japanese Multiplication Works

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...

While we didn’t explore the progression of multiplication explicitly, the following post might be useful to extend some of the thinking from the donut delight task.

## The Progression of Multiplication

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...

## Progression of Division

We spent some time working with the progression of division in most groups as well. Here are some screenshots of what we looked at:

## 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.

Hope you folks found this professional learning experience useful.

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

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