Every Year 7 teacher knows the problem. Students arrive from five different primary schools with five different approaches to mathematics. Some have been taught one method, some another. Some have gaps nobody can explain. Before the year has properly begun, the class is already fragmented — and the teacher is managing twenty-five different starting points instead of teaching.

This isn’t a teacher problem. It’s a systems problem.

An Induction to Foundational Numeracy is a 36-lesson, 14-section structured teaching program that does something no other mathematics resource currently addresses: it gives an entire Year 7 cohort — regardless of their primary school background — a shared mathematical foundation, a common language, and a unified starting point for secondary mathematics.

One System. Curriculum, Professional Development, and Tools — Integrated.

Most schools buy curriculum, then budget separately for professional development, then wonder why the two never quite connect. This program integrates all three from day one.

Every lesson includes the student learning experience, the teacher professional learning, the mathematical background, and the pedagogical reasoning behind every concept. This isn’t just what to teach — it’s how and why, embedded into every lesson so teacher growth happens in real time, alongside the students.

Teachers don’t need to be mathematics experts before they begin. They become more expert as they teach. That is what makes this program sustainable — and what makes the investment justify itself year after year.

The Approach: Numeral Mechanics

At the heart of this program is numeral mechanics — explicit instruction in the grammar of mathematics, analogous to phonics in literacy. Through colour-coded descriptive arithmetic, students develop a meta-language for understanding how numbers work and interact. This is not remediation. It is not revision. It is a genuine induction — building the conceptual foundation that primary arithmetic assumed but rarely established.

The Linear Abacus® serves as the single unified tool throughout — the only manipulative that connects number and measurement in one continuous model, making abstract concepts tangible and visible for every student in the room.

What the program covers across 36 structured days:

Place value — whole numbers, beyond 1000, exponential notation · Renaming numbers · Decimals — tenths and hundredths · Fractions as measures · Informal and formal measurement · Metric units and unit conversion · Different number base systems · Connections to algebra — descriptive arithmetic, linear equations, coordinates on the Cartesian plane

What your school gains:

A unified mathematical language across the entire Year 7 cohort — so teachers can teach, not diagnose. A shared reference point that makes mathematical conversation possible in every classroom, regardless of what students encountered in primary school. Students who understand why the rules of mathematics work, not just that they work. Teachers who grow in expertise alongside their students — building confidence, reducing anxiety, and developing the kind of deep subject knowledge that stays. A structured, day-by-day program that teachers can implement with confidence from the first week of school. A mathematics culture your whole school community can see and feel — in the classroom, in the staffroom, and in your results.

Whether supporting developing learners or extending advanced students, the Linear Abacus® provides a consistent, clear methodology that works across every ability level in your classroom. Nothing is introduced in isolation. Every concept builds on the last.

What’s in the physical kit:

120 × student 100-bead Linear Abacus® strings · 10 × magnetic teacher demonstration strings · 5 × copies of An Induction to Foundational Numeracy (311 pages, paperback)

Each string is individually pouched and ready to distribute on day one.

A note on subscription support — coming soon:

Instructional videos, assessment tools, professional learning resources, and an educator community will be available through a Linear Abacus school subscription. We are building it now. Contact us to register your school’s interest and be first to know when it opens. This is included for free in in the first year.

Ready to talk?

This kit equips a cohort of 120 students. For larger cohorts, multiple year levels, or whole-school implementation, contact us for a personalised quote. We’ll make sure the solution fits your school’s size, timeline, and budget.

I have had the opportunity to read and review the Introduction to Foundational Numeracy,  The Linear Abacus Games Book,  and the Additive Thinking Flash Cards.

My first reaction is that the resources are structured to support students making sense of mathematics by emphasising the connection between the principles of arithmetic and the representation offered through the linear abacus bead strings.

My second reaction is that the resources, taken together, are a extraordinarily well compiled comprehensive set of resources that emphasise not only the mathematics but also the pedagogy of engaging students in thinking about the mathematics.
I would encourage teachers and principals to take advantage of any professional learning opportunities offered that illustrate the potential of the particular resource.

Emeritus Professor Peter Sullivan