Numeracy

At Orchard Park Primary School, mathematics is more than getting the right answer — it’s about thinking, reasoning, problem solving and communicating ideas.

Our approach helps students develop the confidence, curiosity and flexibility they’ll need to use mathematics creatively and effectively — now and in the future.

The Ever-Changing World

The world our children are growing up in is very different from the one we experienced 20 or 30 years ago.
In the past, maths lessons often focused on neat working, memorising facts and following fixed steps — skills suited to predictable jobs that valued routine and accuracy.

Today’s world demands much more. Modern workplaces and communities need people who can:

Think critically and creatively to solve unfamiliar problems.
Collaborate and communicate effectively with others.
Use reasoning and evidence to justify decisions and make sense of data.
Adapt and show resilience when faced with challenges or change.
Work flexibly with technology, applying mathematical thinking to real-world contexts.

The World Economic Forum’s Future of Jobs Report (2023) identifies the top skills for the coming decades as analytical thinking, creativity, curiosity, lifelong learning, technological literacy, empathy, and adaptability.

Our mathematics program is designed to build these skills by encouraging students to investigate, reason, make mistakes, explain their thinking, and learn from others.

How We Teach Mathematics at Orchard Park

Today’s mathematics lessons look and sound very different from those many adults remember. Rather than rows of students quietly completing pages of sums, our classrooms are filled with discussion, problem solving and collaboration. Students work in pairs or small groups, using materials, drawings and digital tools to test and share their thinking. Traditional lessons often centred on the teacher showing how to solve problems and students practising that method repeatedly.
While accuracy and fluency remain important, research now shows that deep mathematical understanding grows when students are encouraged to think, reason and explain.

In our classrooms you’ll see:

Students discussing and comparing multiple strategies, not just following one method.
Questions and debate, not silence.
Visual models, drawings and hands-on materials, not just worksheets.
Mistakes valued as important learning moments.

This approach ensures that every student can participate and progress, regardless of their starting point. Lessons combine inquiry, collaboration and explicit teaching, with teachers carefully guiding discussion to connect ideas and strengthen understanding.

This approach helps every student to understand why mathematics works, not just how to follow steps.

By teaching in this way, we nurture confident, capable problem solvers who can reason, explain and apply their learning — skills that will serve them well throughout school and beyond.

Rich, Open Problems

In the past, a maths lesson might have focused on a question like:

6+5=◻

If students answered correctly, they were given ten more just like it. If they were incorrect, the teacher re-taught “the way” to solve it.

Today, we reshape that kind of task to promote reasoning and exploration:

◻+◻=11

Students are asked:

What could the missing numbers be?
How many different ways can you make 11?
How will you know when you’ve found them all?

This single question opens up dozens of possibilities. Some children might use blocks or counters; others might write number sentences or look for patterns. The teacher supports them to share and test ideas, building number sense and flexibility.

Rich, open problems like these encourage students to think critically, take risks and use reasoning rather than memorisation. They allow for many strategies, solutions and extensions — creating genuine engagement and deeper learning for everyone.

Multiple Entry and Exit points

Every student enters a lesson with different knowledge and experiences.
Our lessons are designed so all students can begin successfully and extend their thinking as they progress.

A multiple entry point means there’s always a way into the problem. For example, some students might start with materials or drawings, while others may use mental strategies or algebraic reasoning.

A multiple exit point means the challenge doesn’t stop once a student finds one solution. They might continue by looking for patterns, proving results, or connecting ideas to new concepts.

This naturally differentiates learning: every child is supported, challenged and extended at their point of need — all within the same rich task.

Mathematical Talk and Reasoning

Mathematics is a language, and learning it means talking about it.

Throughout each lesson, students explain, justify and compare their ideas — both with peers and their teacher.

These conversations help students:

Clarify their thinking and use accurate mathematical language.
Listen to and build on others’ reasoning.
Identify connections between different strategies.
Develop the four Victorian Curriculum proficiencies — Understanding, Fluency, Problem Solving and Reasoning.

Teachers plan for this “mathematical talk” using questions like:

“How do you know that’s true?”
“Can you show that another way?”
“Is there a more efficient strategy?”

By talking about mathematics, students learn to think like mathematicians — testing ideas, using evidence, and refining reasoning through discussion.

Visible Connections

Across each year level, lessons connect new ideas to those learned previously.

For example, a Prep student exploring ways to make 11 is laying the foundation for later understanding of addition, subtraction and place value.

In upper years, those same connections support multiplication, fractions, and algebraic thinking.

By making these links clear, students begin to see mathematics as an organised and logical system — not a collection of separate topics.