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# Hanover School Division (HSD) Math Workshop

## HSD Math Professional Development Workshop

### May 2017

Thanks for inviting me to learn with you at the Hanover School Division (HSD) for a day full of math professional development!

THIS PAGE WILL BE UPDATED AFTER THE SESSION TO REFLECT MORE ACCURATELY WHAT WAS EXPLORED

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 the Airplane Problem:

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In the airplane problem, we made predictions and made connections to multiplication and the order of operations by writing expressions. There are extensions to this task that we did not explore today, but are applicable for grade 9 applied.

## Counting Principles

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

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## Would You Rather?

After break, I shared Would You Rather?, a website created by John Stevens that provides all kinds of great warm-up problems for a range of grade levels including grade 9 applied:

Here’s a visual animation of the second problem we did involving fractions:

## Exploring the Progression of Multiplication

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

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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:

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## 3 Act Math Task: Donut Delight

After lunch, 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.

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## Progression of Division

We didn’t have time to dive into division with base ten blocks, but I thought I’d put that here for you to reference:

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.

Here are some other tasks we explored as well:

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The Stacking Paper Tasks are also available on iOS as a multi-touch book for iBooks:

Or, consider accessing these tasks in an interactive way via Google Sites.

# 3 Act Math Tasks: Curious Math iTunes U 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.

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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!