Number Concepts & Systems
MYP Mathematics Framework — Number strand (Key Concept: Form; Related Concept: Quantity)
Every number you will ever meet — from the 3 apples in a basket to the in a circle's circumference — belongs to a nested family of number sets, and MYP examiners build entire questions around whether you know exactly which family a given number belongs to and why the boundary matters. Zero is the number that catches almost everyone out at least once.
Overview — The Shape of the Number System
Why number systems are nested, not separate
Number sets in MYP aren't eight unrelated categories — they're one set built inside another, like Russian dolls. Natural numbers sit inside whole numbers, which sit inside integers, which sit inside rational numbers, which sit inside real numbers. Irrational numbers are the only set that sits OUTSIDE rational numbers but still INSIDE real numbers. Once you see the nesting, questions like 'name a whole number that isn't natural' stop being tricky — you're just looking for the extra doll added at that layer.
- (natural) → + zero = whole numbers → whole numbers + negatives = (integers).
- + fractions/decimals that terminate or recur = (rational numbers).
- + non-terminating, non-repeating decimals (irrationals) = (real numbers).
The shape of the chapter
Command terms this topic tests constantly
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Name | Give a specific word, number or example — no explanation required. | AO1 | Naming the wrong level of specificity (e.g. 'a number' instead of a stated value) scores zero — precision matters more than length. |
| State | Give a short, direct fact without justification. | AO1 | Adding a paragraph of explanation when 'state' is asked earns no extra credit — the mark scheme only rewards the fact itself. |
| Identify | Select or point out the correct item, symbol, or answer from given information. | AO1 | For symbol questions (e.g. choosing ) the bare symbol is enough; over-explaining costs time but not marks. |
| Describe | Give a full-sentence account of a feature, relationship, or process. | AO2 | Writing only a symbol or number for a 2-mark Describe question caps you at 0–1 — a relationship sentence is required. |
| Calculate | Produce a numerical answer, showing the relevant working. | AO1/AO2 | No working shown on a 2-mark Calculate item caps the mark at 1, even with a correct final number — the method mark is lost. |
| Compare | State a similarity AND a difference (or a numerical comparison) between two quantities. | AO2 | Giving only a difference when the mark scheme wants a numeric comparison (e.g. 'bigger by 9') loses the comparison mark. |
| Explain / Justify | Give reasoning or evidence that supports a stated conclusion. | AO3 | Restating the conclusion without new reasoning ('it's correct because it's correct') earns zero — a counterexample or definition must be cited. |
Key point
Overview