Maths IA guide
Maths IA structure and format: a section-by-section template
The IB does not prescribe headings for the exploration, but the IAs that score well on Criterion A (Presentation) almost always share the same shape: a short introduction with a precise aim, a body that builds the mathematics in stages with reflection along the way, and a conclusion that answers the aim. Here is that shape, section by section, with outlines you can adapt for modelling, statistics, optimisation and pure-maths explorations.
The sections, in order
| Section | What goes in it | Typical length | Criteria it feeds |
|---|---|---|---|
| Title page | A title that is a question or names the question (“How long does a cup of tea take to cool?” beats “Newton's law of cooling”). Follow your school's instructions about names and candidate numbers: many schools ask you to leave identifying information off the pages the moderator sees. | A few lines | A |
| Introduction and rationale | Why this question matters to you, in two or three honest sentences, then any context a classmate needs to follow the rest. Do not announce all the mathematics here, and skip long histories or biographies that do not serve the aim. | About half a page to a page | A, C |
| Aim | One or two sentences that say exactly what you will find out, precise enough that a reader can tell at the end whether you succeeded. It is one of the most important sentences in the IA: every later section should help answer it. | One or two sentences | A |
| Data or method | What you collected or used, how, how much and why; the sampling method, units, conditions and the source of any secondary data (cited in a footnote). For a theoretical IA: the approach you will take and why. | About a page | A, B, C |
| The exploration (body) | The mathematics, built up in stages: describe the data, propose a first model or method and justify it, test it, improve it. Show one full worked example of any repeated calculation and put the rest in a table. Graphs and tables sit next to the paragraph that discusses them, each labelled and referred to. | Most of the IA: roughly 8 to 15 pages | B, E |
| Reflection, throughout | After each major result, a few sentences: what it means in context, whether it is reasonable, what limits it, and what you will do next because of it. This running commentary is what separates the top bands of Criterion D from a single “limitations” paragraph at the end. | Short paragraphs after each result | D, C |
| Conclusion | Answer the aim directly, summarise how well your methods worked (pointing back to your reflections), state the limitation that matters most and its likely effect, and suggest a genuine extension. No new mathematics. | Half a page to a page | A, D |
| Bibliography and acknowledgements | Every source, dataset, image and piece of software you relied on, in a consistent style, with footnotes on the pages where you used them. Acknowledge any tool, including AI, that helped you, and say what for. | As long as it needs to be | A |
| Appendices | Raw data, long tables and code. Anything the reader needs in order to follow your argument belongs in the body, not here. | Optional | A |
Lengths are what we typically see in well-organised explorations of 12–20 pages, not IB rules. See how long a Maths IA should be.
Outlines for four kinds of IA
Adapt one of these to your question. They are structures, not content: every sentence under each heading must be yours.
Modelling IA
- Introduction: the situation and why you care
- Aim
- Data: how it was collected, a table or summary, a first plot
- First model: why this family of functions, the fit, residuals
- Reflection: where the first model fails
- Improved model(s): justification, fit, comparison with the first
- Testing on data not used to build the model
- Conclusion: the best model, how good it is, its limits, an extension
Statistics IA
- Introduction and aim (a question about a population)
- Data: population, sample, sampling method, cleaning decisions
- Descriptive statistics and graphs, each interpreted
- Hypotheses stated in context; choice of test justified; conditions checked
- The test, with one calculation shown and technology explained
- Interpretation in context and the effect of your sampling
- Conclusion: the answer to the aim, and what a better study would change
Optimisation IA
- Introduction: the real object or decision
- Aim
- Measurements and assumptions, stated and justified
- The function to optimise, derived step by step
- Finding and checking the optimum (and that it is a maximum or minimum)
- Comparison with reality: why the real object differs
- Refinement: an extra constraint or a better model
- Conclusion
Pure maths / proof IA
- Introduction: the pattern or problem that caught your attention
- Aim: the result you want to prove or understand
- Special cases and conjectures, explored with examples
- The general result, proved step by step, every step justified
- Checking the result and its limits (where does it break?)
- Conclusion and a genuine next question
Format checklist
- Typed, with an equation editor for all mathematics (never calculator notation such as ^, * or E).
- A readable font and size, double line spacing: the page guidance in the IB guides assumes double spacing.
- Headings for each main section; page numbers; figures and tables numbered and referred to in the text.
- Graphs with a title, labelled axes, units and a sensible scale; tables with units in the column headings.
- Citations as footnotes on the page where you use the source, plus a bibliography at the end.
- A consistent rounding rule, stated once with a reason, and ≈ (not =) for rounded values.
Notation rules in detail: Criterion B guide. Organisation and conciseness: Criterion A guide.
See the structure in a real exploration
Every one of our annotated exemplars follows this shape, with an examiner's comment on how each section is organised.
Frequently asked questions
Does the Maths IA need specific headings?
No. The IB guides do not prescribe headings. Clear section headings make the exploration easier to follow, which helps Criterion A, so most strong IAs use them.
Do I need an abstract or a contents page?
Neither is required. A precise aim in the introduction does the job of an abstract. A contents page is optional; for a 12–20 page exploration with clear headings it is rarely needed.
Where should the reflection go?
Throughout, not only at the end. Short reflections after each major result, plus a summary in the conclusion, are what the top bands of Criterion D look like in practice.
Can I use a template from the internet?
You can use a structure like the one on this page, because a structure is not content. You cannot copy text, analysis or mathematics from any template, exemplar or other IA: the exploration must be your own work.
See this structure in ten complete IAs
The IA package: nine full annotated exemplars (three written to a top-band standard) and a mid-band draft, 5 AI feedback credits for your own drafts, and saved planner projects. €39 once, 12 months' access, 14-day money-back guarantee. It helps you write your own IA; it never writes it for you.