Southwood Public School – Gr 4 & 5 Math Professional Learning

GECDSB Professional Learning Community (PLC) Sessions

Thanks for inviting me to learn with you over the past few professional learning community days! This group is always energetic and excited to learn about meaningful manipulative use, making mathematics visual and concreteness fading!

You can scroll down to see our past sessions, or consider jumping to the specific session you’re looking for:

Tuesday December 6th, 2016

Here’s a summary of what we explored today:

The GECDSB Mathematics Strategy

GECDSB Math Strategy

Mathematical Proficiencies

The full GECDSB Mathematics Vision is here.

GECDSB Mathematical Proficiencies

Pedagogical System

Based on work by Glenda Anthony and Margaret Walshaw, the Pedagogical System is the result of a meta-analysis of many studies which are summarized into four key components:

The Pedagogical System - Task Tools and Representation Non Threatening Class Environment Discourse

You can also see a “silent solution” animation of the pedagogical system in detail:

Tools and Representations

We discussed the importance of tools and representations to help students see mathematics from different perspectives. These quotes help us better understand some of the other important reasons tools and representations are so important:

Tools and Representations Quote - Kilpatrick


 Tools and Representations - representations are critical to understanding


Marian Small gives her perspective on representations in math class:


K-12 Process Expectations: Representing

We very briefly discussed the 7 Process Expectations in mathematics that are embedded throughout our K-12 Mathematics Curriculum and looked in particular at the expectations for Representing:

K-12 Process Expectations

Task: The Sandwich Problem

With manipulatives on the table (square tiles, relational rods, cubes, pattern blocks and fake money) we attempted to find concrete and/or visual representations that could help us solve and justify the following task:

The Sandwich Problem

Original task was shared at a Ministry SIM Session. Here’s the slide deck.

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

Friday February 24th, 2017

Today, we explored the progression of division including partative and quotative division, using manipulatives to divide numbers including square tiles and base ten blocks when the numbers are two digit or greater.

I am still working on a post that will have all of these visuals and problems included in them, so hang tight or check back soon.

Wednesday March 1st, 2017

Here’s a summary of what we explored today:

Extending to Multiplication and Division

After spending some time doing some more division with base ten blocks and arrays / area models, 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?

Krispy Kreme Donut Delight - 3 Act Math Task Screenshot

Sparking Curiosity to Fuel Sense Making 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 could be used to h...

Summary & Resources

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

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...


Friday March 10th, 2017

Today, we had an opportunity to begin looking at Fraction Constructs based on the work from the Paying Attention to Fractions document.

The Progression of Fractions

The Progession of Fractions from K-12

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...


Paying Attention to Fractions

Paying Attention to Fractions


Tuesday March 21st, 2017

Today, we continued our work with Fraction Constructs (Part-to-Part, Fraction as Quotient, and Fraction as Operator).

To access the fraction visuals and a full detailed post about the Progression of Fractions, click here.

While we didn’t get to multiplication of division of fractions, here is a pretty cool task that would be easily modifiable for a grade 4 and 5 classroom looking to play with more contextual situations with fractions:

Gimme A Break [3 Act Math Task]

How many pieces of the whole are there?

Gimme A Break - Adding, Subtracting, Multiplying, Dividing Fractions 3 Act Math Task

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 ...

Summary & Resources

Looks like the next time we meet as a group will be at the Southwood Staff meeting on April 12th where we plan to do more Exploring Fractions as a staff, look at number lines with fractions and other numbers, and how one might monitor progress in the classroom.

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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