Mrs Rowntree

Teach. Grow. Inspire.

about

Welcome! My name is Lisa Rowntree, the Aussie teacher behind Mrs Rowntree. Teach. Grow. Inspire. I have worked in education for more than 10 years and am a wife, mother of three, and passionate primary teacher with a particular interest in mathematics education. Before becoming a teacher, I worked in a credit union, where my love of numbers was already well established. While raising my family, I began studying teaching and discovered a passion for helping children make sense of mathematics. Today, alongside teaching, I design practical mathematics lessons, units and resources that focus on conceptual understanding, reasoning and meaningful learning. Through Mrs Rowntree, I hope to share the ideas, resources and approaches I develop along the way — helping teachers save time while creating worthwhile mathematical experiences for their students. My intention is simple: to continue doing what I love — teaching, growing and inspiring.

How often do you find yourself saying, “go back and show your workings?”

04/10/2026

The student stops to look at you and says:

“I can’t, I just know the answer!”

An argument follows about the teacher wanting the evidence and the student not knowing how to represent it.

Then comes the dreaded shrug!

Mathematical reasoning requires students to develop skills in representation. Representation is a skill set that needs to be explicitly developed and practised.

Providing students multiple opportunities to represent their thinking helps them learn how to show their reasoning.

Offering varied representations to explore and use also changes up the cognitive demand. Students begin to develop flexibility in how they think and communicate mathematical ideas.

Reasoning asks students to do more than follow a procedure. They need to interpret, connect, represent, justify and communicate their mathematical thinking.

A lot of numerical equations are abstract and require interpretation to uncover complex conceptual mathematical ideas underneath.

Let’s take the grid paper for example.

We can draw our manipulatives we have used to form concrete representations of groupings and then draw these on the grid as groupings.

The square grid shapes help students represent equal groupings and begin to develop connections between their concrete models and mathematical representations.

Array paper works in a similar way.

By having to represent concrete models via array groupings students are influenced to organise those groupings efficiently. They can see why organising the group helps. It makes their job easier because they can count efficiently, without having to recount every object by one.

Now numbers can label the diagrams and connections between the representation and the equation come to life.

This is how we can gradually move from concrete models, to representations, to mathematical symbols and increasingly abstract thinking.

So, if you need some handy grid paper and array paper to print and use for your lesson tomorrow, you can download these free resources from the link below.

I’ve even included some handy notes about what to watch for and how to use these representations.

Happy representing!