Welcome — Start Here
You looked at what was happening to your child — the confusion, maybe the anxiety, maybe the quiet feeling that something wasn't working — and you decided not to wait. Not to hope next year would be different. You stepped in.
That takes courage. And it comes with its own particular fear: what if I get this wrong too?
Here is what I want you to know before you look at anything else. You already know your child better than any curriculum, any school, any program ever will. What you are looking for is not someone to replace you. You are looking for tools that make it possible for you to do what you already do best — sit beside your child, think together, ask questions, and follow the thinking wherever it goes.
This page will show you exactly where to start — not by grade level, but by what your child understands right now.
Most mathematics resources give you activities. Some give you a curriculum. A few claim to do both. What you will find here is something different — and, as far as we know, something that does not yet exist anywhere else in mathematics education. Every book, every card set, every game, every lesson in the Linear Abacus system was built to connect to every other. Not loosely, not thematically, but precisely — through the same tool, the same language, the same underlying structure, building from the same first principles. A child who begins with the Games Book is already holding the thread that leads to place value, to fractions, to the metric system, to algebraic thinking. Nothing here is a detour. Nothing is a one-off activity that happens to be about numbers. Every idea your child encounters in this system is one idea — seen from a different angle, at a different depth, in a different year. That is what makes it possible for understanding to be genuine rather than patched together. Where other systems give you eight different tools for eight different topics, Linear Abacus gives you one — and it works across seven domains of mathematics, from Foundation to Year 8. And it is, to our knowledge, the first time it has been done this way.
Where to begin
Not by grade level — by what they actually understand. Four pathways, one system. Find your entry point below.
Pathway 1
Counting feels uncertain. Big numbers feel random. Your child can say the numbers but isn't sure what they mean — or why they are built the way they are.
This is the right place to start. The abacus makes numbers physical — something to hold, to build, to see. Your child will not be told how numbers work. They will discover it.
Start here: The Linear Abacus + Master Place Value: The Essential Guide (Book 1) — five activities, the full foundation. Accessible from Grade 1.
Easy first step: The Games Book On Amazon — playful, confidence-building, and the gentlest introduction to the abacus. Grades 1–6.
Pathway 2
Your child can add and subtract, but isn't sure why the method works. Multiplication feels like memorisation. Word problems feel like guesswork.
Here they will learn not just how to calculate, but how to read a mathematics problem the way they read a sentence. Operational arithmetic has a grammar. Once your child sees it, the guesswork stops permanently.
Start here: Master Place Value: The Essential Guide (Book 1) + Place Value and the Metric System (Book 2) + the Linear Abacus. One bead. Two books. The same big idea — from ones and tens to the full metric structure. Grades 1–8.
Add when ready: The Additive Thinking Flashcards — 108 word problems that teach children to read, decode, and solve — not just guess. This is the moment to delve into the grammar of mathematics. Every number sentence has a structure. Every word problem has a type. When your child can name both, the confusion ends. Grades 2–6.
Pathway 3
The place value foundations are there. Your child is ready for the full picture — arithmetic through to fractions, the metric system, measurement, number patterns, and the thinking skills that carry into secondary school and beyond.
This is where the Manual becomes the spine of everything. The Pocket Books extend it naturally. The Flashcards deepen the grammar work that is already underway.
The spine: A Concise Instructional Manual for the Linear Abacus — the complete curriculum for number, arithmetic, and fractions from primary through Year 7–8. With comics that model mathematical thinking from the inside. Grades Prep–8.
Natural extension — Pocket Books 1 & 2: Master Place Value and Place Value and the Metric System — concentrated, complete, and directly connected to the Manual's place value work. Grades 1–8.
The grammar goes deeper: The Additive Thinking Flashcards — this is where word problem types become explicit, number sentences are read like sentences, and your child develops a genuine meta-language for mathematics. Grades 2–6.
Pathway 4
Your child is moving from primary arithmetic into the world of algebra, abstract thinking, and higher mathematics. This is the most critical juncture in a child's mathematical education — and the one most programs handle worst.
The gap between primary and secondary mathematics is not about harder numbers. It is about a fundamental shift in thinking: from calculation to structure, from specific answers to general principles, from arithmetic to algebraic reasoning. An Induction in Foundational Numeracy was built precisely for this moment.
The bridge: An Induction in Foundational Numeracy — a 35-lesson structured program covering whole number place value, decimals, fractions as measures, metric units, other number base systems, and connections to algebra. From counting to the Cartesian plane. Grades 3–8.
Extend with Pocket Books 3 & 4: Measuring the World and What Numbers Hide connect directly to the Induction's metric and number base work — investigations into measurement, primes, patterns, and other bases that take the Induction's algebraic thinking further. Grades 2–8.
Already using the Manual? The Induction complements it. Both use the same tool, the same language, the same conceptual thread. Together they carry a child from their first number through to linear equations and coordinate geometry.
The full picture
Your curriculum — the complete system
Every product connects to the Manual at the centre. Nothing is a standalone add-on. When you enter the system at any point, you are already inside a complete curriculum.
The Pocket Book Series
Extend your understanding of place value and measurement
Books 1 & 2 — One bead. Two books. The same big idea. Place value from the ground up, then the metric system as its natural extension.
Books 3 & 4 — Measurement in the real world, then the hidden structure of primes, patterns, and other bases.
4 books · Grades 1–8The spine of everything
Complete curriculum — counting through fractions — to Year 7–8. Comics that make thinking visible. The centre your curriculum is built around.
Your CurriculumThe Grammar of Mathematics
Deepen your word problem understanding
Operational arithmetic has a grammar — just like language. The Flashcards make that grammar visible. 108 word problems that teach children to read, decode, and solve — not just guess. Turn confusing mathematics language into clear thinking, every single lesson.
108 word problems · Grades 2–6Fluency & Reasoning
Build real fluency — through play
18 games. Four operations, fractions, and growing patterns — all covered. Children build real calculation fluency while they play. Parents get lessons that run themselves. The gentlest entry point — and the right first step for most families.
18 games · Grades 1–6 · On AmazonPrimary to Secondary Bridge
Fill every gap. Build every bridge.
35 structured lessons from counting to algebraic thinking. Whole numbers, decimals, fractions, metric units, number bases, and connections to algebra — all built on the same tool and the same language. The transition program that actually closes the gap.
35 lessons · Grades 3–8Everything connects. Everything progresses.
How long will you use it?
One of the most important things to understand about the Linear Abacus system: you are not buying a resource for this year. You are buying a resource that will be in use for years. Every product spans multiple grade levels — because genuine understanding, once built, keeps going deeper.
| Resource | AU Year Levels | US Grade Levels | What it covers across those years |
|---|---|---|---|
The Linear Abacus Games Book Fluency & reasoning through play | Years 1–6 | Grades 1–6 | 18 games covering all four operations, fractions, and growing patterns. Returns deeper as fluency builds. |
Additive Thinking Flashcards The grammar of mathematics | Years 2–6 | Grades 2–6 | Word problem types deepen across the years. The same cards yield richer mathematical conversations as understanding grows. |
Pocket Books 1 & 2 Master Place Value · Metric System | Book 1: Years 1–6 Book 2: Years 2–8 | Book 1: Grades 1–6 Book 2: Grades 2–8 | Book 1 revisited at Grade 5 looks very different from Grade 1. The same five activities open new questions as the child's thinking deepens. |
Pocket Books 3 & 4 Measuring the World · What Numbers Hide | Years 2–8 | Grades 2–8 | Investigations that grow with the child. A Grade 3 child and a Grade 7 child ask genuinely different questions of the same activity. |
A Concise Instructional Manual The complete curriculum | Prep–Year 8 | Pre-K–Grade 8 | Counting through fractions. The spine of the system across the entire primary journey and into early secondary. |
An Induction in Foundational Numeracy Primary to secondary bridge | Years 3–8 | Grades 3–8 | 35 lessons from place value to algebra. Primary focus is Year 7 transition, but individual lessons begin as early as Grade 3. |
What you get
Here is what you actually have at the kitchen table.
Build real fluency — through play.
18 games. Four operations, fractions, and growing patterns — all covered. Children build real calculation fluency while they play. Parents and teachers get lessons that run themselves. Includes the Games Book, a free parent planning guide, a session planning table, and access to blogs with worked examples for every game.
Pick it up on a Tuesday afternoon with no preparation. Put it down an hour later with a child who has been genuinely thinking.
Additive Thinking — available now · Multiplicative Thinking — coming soon · Fractions — coming soon
The grammar of operational arithmetic. The first structured resource of its kind.
Operational arithmetic has a grammar — just like language. Every number sentence has a structure. Every numeral in that sentence plays a role: it is either a count-number (how many things) or a verb-number (how many more, how many times). When children confuse these roles, they don't make conceptual errors. They make grammatical ones.
The Additive Thinking Flashcards are the first structured resource to make that grammar explicit. 108 word problems, sequenced across 36 triples. Each triple contains three numerals, three stories, and three number sentences — one structure, three entry points. Children learn to move between them fluently.
Two word problem types are taught explicitly: I have/you have (two actors, change through space) and before/after (one actor, change through time). A child who can name the structure of a word problem before calculating it will never again treat a word problem as guesswork.
Multiplicative Thinking Cards — coming soon. Fractions Word Problem Cards — coming soon.
The complete curriculum. The spine of everything.
Full curriculum from counting to fractions — through to Year 7–8. Comics that show your child what mathematical thinking looks like from the inside — not illustrations, but a second curriculum running alongside the activities, modelling how a mathematician thinks. Microwriting prompts. Additive and multiplicative tables. Everything in one place, built to be used together.
Coming soon: an interactive AI section that answers your questions in real time as you work through the curriculum.
Proven in schools: following Linear Abacus implementation, St Albans Heights Primary School recorded a 16 percentage point improvement in student mathematics proficiency — from 38% to 54%.
Master Place Value: The Essential Guide · Place Value and the Metric System: Unlock the Full Story
One bead. Two books. The same big idea.
What takes six years of primary school instruction to consolidate — place value, from ones to thousands — most children genuinely understand within a few weeks of working with Book 1. Not because the book rushes. Because for the first time, the structure is visible.
Book 2 is the natural next step. For families in the United States, it is also something more specific: the first introduction to the metric system designed from first principles for home use. Centimetres, metres, and kilometres are not a foreign system to memorise. They are the decimal structure your child already understands from Book 1, made physical. Four activities. The complete picture.
Short books. Lasting understanding. That is not a coincidence — it is what happens when the noise is stripped away and only what genuinely matters remains.
Measuring the World: Perimeter, Area and Volume · What Numbers Hide: Patterns, Primes and Other Bases
Investigating what numbers can do.
These two books ask bigger questions. Book 3 takes the bead string into the physical world — measuring around things, covering surfaces, filling space — and shows that one bead has three completely different measurements depending on the question you ask.
Book 4 goes deeper still, into the hidden structure of numbers themselves. Children discover that every number has a unique prime code name, explore what happens when the rules of grouping change, and find patterns that have occupied mathematicians for centuries — through a bead string and good questions.
You do not need to know the answers in advance. Neither did the ancient mathematicians.
Fill every gap. Build every bridge.
A 35-lesson structured program that takes a child from whole number place value through decimals, fractions as measures, metric units, number base systems, and all the way to connections with algebra — including linear equations and coordinate geometry. Day-by-day lesson plans. Precise conceptual overviews. Detailed guidance for every session.
This is not remediation. It is the establishment of a shared mathematical language — a common foundation that means your child arrives at abstract mathematics already knowing how to think, not just how to calculate.
Built for Year 7 transition. Reaches back to Grade 3 for the foundations that were never fully built. Adaptable to every child's pace — and one-on-one instruction at home often means faster progress than any classroom setting allows.
A note on grade levels
The year level guides in our resources are exactly that — guides, not gates. Both Australian year levels and US grade levels are included throughout.
Use the year level columns in the Games Book sequence table as a reference point, not a rule. A child who needs to consolidate earlier understanding never feels like they are going backwards. A child who is ready for more will always find genuine challenge ahead.
The entry point is understanding. The pace is your child's.
Where to begin
The abacus gives your child something to hold. The Games Book gives you both a reason to pick it up together. The gentlest entry into the system — and from there, you will know exactly where to go next.
The best memories most of us have of learning — the ones we actually carry — are not the worksheets. They are the conversations. A parent who sat beside us. A question that stayed open long enough to become interesting. A moment when something clicked and someone we loved was there to see it.
That is what this is for. You are not just teaching your child mathematics. You are showing them what it feels like to think — and they will remember that you were the one who showed them.
