## Fuel Sense Making Related Posts

## Counting With Your Eyes: Subitizing

Have you ever looked at a group of items and just knew how many there were without actually counting? This ability to "see" how many items are in a group without counting is called subitizing. The ability to subitize is an important part of developing a strong mathematical foundation and understanding of number (Baroody 1987, 115). Playing with dice, dominoes, and asking children to find a spe...

## Lower the Floor in Math Class

Making Math More Accessible Through Concrete Manipulatives and Visuals What comes to mind when you think back to learning math in school? It would seem that most people I ask typically respond with a negative or neutral response and very few with something positive. Since many of us were taught primarily using procedures and steps, it is unlikely that too many of us could see math as anything m...

## Gummy Worms

Early Addition and Subtraction With Part-Part-Whole Models In this task, we will start with something for our kindergarten to grade 3 friends focusing on early addition and subtraction with a part-part-whole model. In the first task, we will take it Estimation 180-style to spark curiosity and build number sense through estimation. However, in the sequel, we will fuel sense making by d...

## Using Tasks to Teach Lessons

Instead of Teaching Lessons to Do Tasks Over the past 5 years, I’ve been exploring the use of Dan Meyer’s 3 Act Math Task approach in my math classroom and share many of my own tasks when facilitating workshops. After participants experience these tasks in the role of the student, they quickly understand why 3 act math tasks are useful. After their own curiosity is sparked, it would seem reason...

## Cover It Up!

Last year, our district focused our system wide math content learning on number sense and numeration including counting and quantity principles, composing and decomposing numbers, addition and subtraction as well as multiplication and division while exploring these concepts through a spatial perspective. This school year, we continue to our work in number sense and numeration by deepening our unde...

## 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 Having spent the majority of my professional life teaching secondary math and mentoring intermediate (grades 7 to 10) math teachers, 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 se...

## 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...