## Fuel Sense Making Related Posts

## The Progression of Division

Division From Fair Sharing to Long Division and Beyond Over the past school year, I have had an opportunity to work with a great number of K to 8 teachers in my district with a focus on number sense and numeration. As a secondary math teacher turned K-12 math consultant, I’ve had to spend a significant amount of time tearing apart key number sense topics including the operations. While I often he...

## 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...

## 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...

## 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...

## 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...

## The Progression of Proportional Reasoning From K-9

The Foundation and Development of Multiplicative Thinking Proportional Reasoning is a big idea that is connected in some way to all mathematical strands and stretches across many grades in the Ontario mathematics curriculum. While many focus on the importance of proportional reasoning for students in junior and intermediate grades, I believe that we can see the early development of proportional r...

## Connecting Relationships to Multiple Strands

Exploring the Relationship Between Diagonal Length and Side Length of a Square It's been a couple weeks since posting, so I thought I need to get back in the swing of things. I've been enjoying a really busy start to semester 2. I'm loving the implementation of the gamified assessment approach I've modified off of Jon Orr and Alice Keeler's work, the spiralled approach to teaching grade 9...

## MFM1P – 3.1 – Intro to Scatter Plots & Relationships

MFM1P - Foundations of Mathematics - Grade 9 Math Applied Learning Targets: Interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant. Carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate me...

## MFM1P – Unit 6 Review Videos – Solving One Variable Equations

Here are two quick videos to help you before you write your Unit 6 Test - Multiple Representations of Linear Equations. Please note that I created these videos in the hospital, the day my daughter Taliah was born. Please disregard any noise in the background, including baby cries! :) Solving Simple One Step Equations Your browser does not support the video tag Problem Solving Involving Solv...

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