MYP Maths: Mathematical Proof & Justification (MYP 4-5)

You answer them by stating what you're proving, showing every algebraic or logical step with a reason attached, and finishing with a concluding statement that links back to the original claim. Markers reward the reasoning chain, not just a correct final line — a bare answer with no working scores almost nothing under Criterion B.

Justification explains why a specific step or answer makes sense, usually in a few words or a short calculation. Proof is a complete, general argument that a statement holds for all cases, not just the one you've checked. MYP tasks often ask for justification within a solution and proof as the final deliverable.

A valid MYP proof shows a general argument, not a specific example — algebraic proof using variables like n or 2k+1, a logical deduction, or a documented counterexample that disproves a claim. According to the MYP: From Principles into Practice guide, mathematical reasoning is assessed under Criterion D, which rewards generalising patterns and justifying results, not just verifying one case.

Because one example only shows a statement is true for that specific case — it doesn't prove it's true generally. A proof needs to work for every value in the set being considered, so 'testing n=4 and it worked' isn't a proof, it's a check. Markers call this the single-case fallacy and it's the most common Criterion D deduction.

Yes — take 'Prove that the sum of any two consecutive integers is odd.' Let the integers be n and n+1. Their sum is 2n+1. Since 2n is always even, 2n+1 is always one more than an even number, so it's always odd. That's a complete general proof.

You find one specific case where the statement fails, calculate it clearly, and state that this single case is enough to disprove a general claim. For example, to disprove 'all prime numbers are odd', you only need n=2 — it's prime and even, so the statement is false.

'Prove', 'show that', 'justify' and 'verify' each demand a different depth of response, and mixing them up is a common way students lose marks. 'Prove' needs a general argument for all cases; 'verify' only needs you to check a given case works; 'justify' needs reasoning behind a specific step or choice.

Full induction (base case, inductive hypothesis, inductive step) is a DP technique, not a formal MYP 4-5 requirement — but the underlying logic, testing a base case then showing a pattern extends, does appear in MYP extension problems. If you meet it, state the starting case, assume it holds for n=k, then show it must hold for n=k+1.

Mathematical proof and justification is assessed mainly under Criterion D: Applying mathematics in real-life contexts, and Criterion B: Investigating patterns, depending on the task. Criterion B rewards recognising and describing patterns and generalising them; Criterion D rewards selecting and applying appropriate mathematical strategies to justify a conclusion.

MYP markers award most marks for the reasoning shown, not the final answer — a correct result with no working, or with a single example instead of a general argument, typically scores in the lower mark bands of Criterion D. It's worth asking your child's teacher to point to exactly which strand of the criterion they missed.

Consistent practice with past MYP-style tasks and the actual assessment criteria in hand works better than more textbook exercises — the skill being tested is communicating reasoning clearly, not just calculating. On RevisionPrep, our MYP Mathematics Revision Notes and Topical Worksheets include worked proof examples matched to Criterion B and D language, so students can see exactly what a full-marks answer looks like.

Yes — proof-style reasoning appears across nearly every MYP Mathematics unit, from number theory to geometry, so the skill compounds rather than sitting in one isolated topic. Getting comfortable with the structure now also makes the shift into DP Mathematics AA or AI proof-based questions considerably less jarring.