Number Concepts & Systems
MYP Year 3 Mathematics — Number strand
Every number question you'll meet this year — 'is this rational?', 'round this to 3 sig figs', 'find the LCM' — is really asking the same underlying question: which set does this number belong to, and what are you allowed to do with it there? Get sloppy about whether is natural, or whether is prime, and every later argument built on it collapses. This chapter is about being precise where students usually guess.
Overview — The Number Landscape
Numbers aren't one big undifferentiated pile — they live in nested boxes, each box adding a new freedom the previous one didn't have. Natural numbers can only count. Whole numbers add zero. Integers add direction (negative). Rationals add fractions. Irrationals fill in every remaining gap on the number line. Almost every exam trap in this topic is really a boundary question: does this number sit just inside or just outside a box?
- Rounding, estimation and place value are about controlling precision — deciding how much of a number's information you actually need.
- Primes, composites, squares, factors and multiples are about structure — what a number is built from.
- Positive and negative integers are about direction — the number line extended both ways from zero.
- All seven subtopics ultimately answer one question examiners love: can you justify a classification or a rule with a specific example, not just a feeling?
The shape of the chapter
Command terms this topic loves
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State | Give a specific fact, value or name — no working or reasoning required. | AO1 | One mark for the correct fact; extra unrequested explanation earns nothing but wastes time. |
| Calculate / Determine | Obtain a numerical result, showing the method that produced it. | AO1/AO2 | Method marks are available even if the final answer is wrong — a bald correct answer with zero working can still lose the process mark. |
| Explain | Give a reasoned account of why or how something is true, using correct vocabulary or a specific example. | AO2/AO3 | A correct one-word answer ('true'/'false') with no reasoning scores 0 — the reasoning itself carries the marks, not the conclusion. |
| Justify | Support a stated conclusion with evidence — a calculation, a counterexample, or a named rule. | AO3 | Must reference the actual numbers or rule used; a general unsupported claim earns nothing. |
| Deduce | Reach a conclusion using information already given, without re-deriving it from scratch. | AO2 | Marks are lost if you recalculate everything instead of building on the given result — examiners want the logical link, not repeated arithmetic. |
Key point
Overview