As students develop, their mathematical understanding and thinking also develops throughout early numeracy. Through the research of Alex Lawson and her team, two continuua (addition & subtraction and multiplication & division) have been created to help support educators as they uncover numeracy development and work with students to build flexibility and proficiency within number sense. The continuua focus on strategies and key ideas used during operations.

 The continuums by Alex Lawson are divided into 4 increasingly complex phases of development; 

Direct Modelling and Counting

Counting More Efficiently and Tracking

Working with the Numbers

Proficiency 

Each phase has a variety of strategies that you may see students using when demonstrating their thinking.  

The strategies within each phase are aligned so that the earliest strategies are on the left and more efficient and complex are on the right. However, as the overall progression is forward from left to right, it is not strictly linear. Students can jump forward and backwards depending on the problem type and numbers used. Students will develop different paths towards proficiency. They do not necessarily need to develop and apply every strategy to be flexible thinkers. 

You can learn more about each strategy by hovering over the title and opening a webpage that describes the strategy in more detail.

Teachers are encouraged to learn more about each strategy by clicking on the links for videos and descriptors that explain each strategy.  Teachers can also access more information and sample think alouds they can use in the classroom at each of the following areas of the site:

Using the Website

Hover over and click the name of each strategy on the continuum image to learn more about it.  There is also a 'Where to Next' for students who have mastered the strategy.  Sample Think Alouds for some strategies have also been provided to support the exploration and/or practice of some strategies.  Keep in mind, the games and where to next are only suggestions to help guide individual feedback. This is by no means exhaustive nor the only way to support students. The key is to know your students and use observations, conversation and products to provide intentional feedback, supporting ‘where to next’.