## GECDSB Professional Learning Sessions

### Jump to Professional Learning Sessions:

- Friday March 31st, 2017 – PD Day
- Thursday April 20th, 2017 (AM) – Kindergarten/Primary SBL
- Thursday April 20th, 2017 (PM) – Junior/Intermediate SBL

## Friday March 31st, 2017 – PD Day

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

## The GECDSB Mathematics Strategy

## 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:

## Solar Panels [3 Act Math Task]

### How much greenhouse gas emissions can they offset?

Proportional Reasoning With Green Energy This is a 3 Act Math Task that focuses on "Green Energy" proportional reasoning questions related to solar panels in order to address proportions both visually using area models and proportions written as equivalent fractions. Special thanks goes to Dave Raney from CPE Inc. for allowing us to use his video and photos as well as Kathleen Quenneville, ...

## Fraction Constructs & Number Lines for Representations

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

## The Progression of Fractions

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...

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

## Gimme A Break [3 Act Math Task]

### How many pieces of the whole are there?

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 ...

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!

## Thursday April 20th, 2017 (AM) – Kindergarten/Primary SBL

## 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:

## Airplane Problem – Trip to Toronto [3 Act Math Task]

### How many seats are there?

From Subitizing and Unitizing to Multiplicative and Algebraic Thinking This 3 act math task was designed specifically to have a very low floor in order to be useful from primary grades and a high ceiling with an opportunity for many extensions so the task can be used in junior and intermediate classrooms. While I believe this task can touch on many different specific expectations at man...

## 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:

## Counting Principles – Counting and Cardinality

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...

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:

- Why Kids Should Use Their Fingers in Math Class – Atlantic Article By Jo Boaler
- Finger Discrimination vs. Finger Counting – A White Paper & Discussion – YouCubed
- Math Learning Center – Web Based Apps for SMARTBoard / Computer
- Mathies.ca – Interactive Math Apps and Math Resources

## 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.

## Thursday April 20th, 2017 (PM) – Junior/Intermediate SBL

## 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:

## 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...

## 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:

## 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.

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