MATHEMATICS EXPERT · READER LIBRARY
Mathematics Knowledge Warehouse | Primary to JC
School years divide Mathematics for teaching and assessment. Mathematics itself is more connected. This library organises important ideas by mathematical object so that readers can see what an idea means, what usually comes before it, how it grows, and what later learning depends on it.
Stage tells us where a student is. The Mathematics object tells us what they are working with.
The Mathematics object spine
Number → Arithmetic → Fractions / Decimals / Percentages → Ratio / Rate / Proportion → Algebra → Functions & Graphs → Geometry & Measurement → Trigonometry → Calculus → Vectors & Coordinate Geometry → Probability → Statistics & Data.
The order is not a claim that every learner follows one straight line. It is a useful map of major mathematical ideas and some of the connections that make later work possible.
| Object room | What readers can explore |
|---|---|
| Number & Place Value | Quantity, counting, magnitude, ordering and number sense. |
| Arithmetic & Operations | Operation meaning, properties and calculation control. |
| Fractions, Decimals & Percentages | Part-whole relationships, equivalence and conversion. |
| Ratio, Rate & Proportion | Multiplicative comparison, scaling and rates. |
| Algebra | Variables, expressions, equations, structure and generalisation. |
| Functions & Graphs | Relationships, mappings, graphs and models. |
| Geometry & Measurement | Shape, space, measurement and geometric reasoning. |
| Trigonometry | Angles, ratios, triangles and periodic relationships. |
| Calculus | Change, rate, gradient and accumulation. |
| Vectors & Coordinate Geometry | Position, direction, displacement, lines and geometry through algebra. |
| Probability | Uncertainty, events and probability models. |
| Statistics & Data | Data, distributions, sampling and interpretation. |
Why connections matter
A student may be studying a current chapter while the real difficulty sits earlier. Algebra can be affected by weak arithmetic structure. Functions depend on algebraic fluency and the ability to interpret relationships. Calculus becomes difficult when functions, graphs or algebra are not secure enough to carry the additional load.
That does not mean every mistake should send a student back through years of work. The useful question is which earlier idea, if any, is actually preventing the current Mathematics from working.
What each public object page is designed to show
- What the mathematical idea means.
- Common ways it can be represented.
- How it develops across school stages.
- Typical misunderstandings or errors.
- Earlier ideas that may matter.
- Later Mathematics that may use it.
- Ways students can practise, explain and verify their understanding.
Use the library with the learner in mind
The Warehouse is a map, not a diagnosis. A topic name alone does not tell us why a student is struggling. Actual student work, explanations and changed questions provide much better evidence.