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# Queen Elizabeth Public School Professional Development

## Friday March 31st, 2017 – PD Day

Great learning with the Queen Elizabeth staff today. Please find some resources below:

## Mathematical Proficiencies

The full GECDSB Mathematics Vision is here.

## 3 Act Math Task: Solar Panels

We dug into math using a question called Solar Panels to engage in a notice and wonder as well as model different representations including number lines for proportions:

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## Fraction Constructs & Number Lines for Representations

Then, we dove into Fraction Constructs based on the work from the Paying Attention to Fractions document.

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### Paying Attention to Fractions

We then engaged in a 3 act math task that involved fractional thinking and using fractions as operators:

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Finally, we used some double number lines to help us make connections between fractions, decimals and percents, solving equations and even working with radicals like square-roots.

It was a pleasure working with you all and I’m excited to work with you all again sometime soon!

## 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:

## Paying Attention to Spatial Reasoning

We explored some quotes from the Paying Attention to Spatial Reasoning document. Download it in PDF form below:

We then explored a task called “The Airplane Problem” to introduce the idea of arrays and multiplication:

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## Daniel Finkel’s TED Talk: Five Principles of Extraordinary Math Teaching

We watched Daniel Finkel’s TED Talk:

## Tiny Polka Dots

We then shared 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. Visit the site to buy the game from Amazon or purchase the \$5 downloadable PDFs.

## Counting Principles

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

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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.

Some other links I promised to share are included below:

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.

## 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 and strategies shared, head to this post here:

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## Paying Attention to Spatial Reasoning

We explored some quotes from the Paying Attention to Spatial Reasoning document. Download it in PDF form below:

## What Do You Notice and Wonder?

We explored this image:

After taking some time to notice and wonder in your groups, participants shared out what they noticed and wondered. Quite a bit of excitement filled the room.

We then let you see this image:

These images are from Daniel Finkel’s Prime Climb game from his website, LoveforMath.com.

Math4Success offers some blog posts [here, here and here] involving ways that you might consider using these images in your classroom.

## Daniel Finkel’s TED Talk: Five Principles of Extraordinary Math Teaching

We then watched Daniel Finkel’s inspiring TED Talk: