Number Concepts & Systems
Every equation you'll solve later, every measurement you'll take, every fraction you'll simplify rests on knowing exactly what kind of number you're holding. This strand pins that down properly: which numbers are exact and which go on forever, how to represent huge or tiny quantities sensibly, how to round without lying about precision, and how to stop losing marks on double-negative sign errors. None of it is new arithmetic — it's making the number sense you already have rigorous enough to survive an exam.
Overview
Where This Sits
Number Concepts & Systems is the toolkit strand — nothing here is genuinely new mathematics, it's your existing number sense made exam-proof. Once this is solid, ratio, algebra and measurement units stop causing 'silly' sign or rounding errors.
- The strand splits into two halves: what a number IS (rational/irrational, place value, primes, factors) and how numbers BEHAVE (rounding, ordering, signed arithmetic).
- Almost every question in the exam bank for this topic uses 'Show that', 'Explain' or 'Compare' — a correct final answer with no reasoning typically scores close to zero on these command terms.
- The single idea that ties the whole chapter together: every number sits at an exact point on the number line, and every rule (rounding, ordering, sign changes) is really just a statement about position on that line.
The shape of the chapter
Command terms this topic actually tests
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | Give a fact or result with no working required | AO1 | 1 mark for the correct fact alone — extra explanation isn't needed but wrong justification can't cost you the mark |
| Identify | Pick out / name the correct item(s) from options given | AO1 | Mark awarded for correctly selecting the item — must match exactly (e.g. naming BOTH rational numbers in a list, not just one) |
| Show that | Prove a GIVEN result using full algebraic or numeric working | AO2 | The answer is already printed on the paper — marks go entirely to the METHOD (e.g. the 10x−x steps), not the final line |
| Explain | Give a reason, using connecting language ('because', 'since', 'this means that') | AO3 | A correct fact with no linking reason typically scores half marks; the reasoning sentence is what's being marked |
| Compare | State a similarity AND a difference between two things | AO3 | Describing only one number (e.g. only explaining why π is irrational) loses marks reserved for the comparison itself |
| Determine / Calculate | Produce a numerical answer, normally showing working | AO1/AO2 | Correct answer with no working may still gain the answer mark but loses all method marks if it turns out wrong |
Key point
Overview