Maths IA guide
How to write a Maths IA, step by step
The Maths IA (the exploration) is a 12–20 page piece of your own mathematics, worth 20% of your final grade at both SL and HL. This guide walks through the whole process in the order that works — the same order Pete Bromfield, a practising IB Maths IA examiner, uses with his own students.
1 Understand how the IA is marked
Five criteria, 20 marks: Presentation (4), Mathematical communication (4), Personal engagement (3), Reflection (3) and Use of mathematics (6). Only 6 marks are for the mathematics itself, so a clear, personal, reflective exploration with course-level maths beats a complicated one you cannot explain.
2 Choose a question, not a topic
Start from something you care about and turn it into a question with an answer: not “the golden ratio” but “do credit-card proportions cluster near 1.618?”. Check that the question needs mathematics at the level of your course and that you can get the data.
3 Write a precise aim
One or two sentences that say exactly what you will find out. The aim is one of the most important sentences in the IA — every later section should help answer it. Include your reason for choosing it, briefly and honestly.
4 Plan before you calculate
Write a one-page plan: area of interest, aim, data (what, how, how much), technology, representations, the mathematics you expect to use, how it links to the aim, how your approach differs from a textbook question, and likely limitations. Show it to your teacher.
5 Collect or source data carefully
Primary data you measure yourself is often the most personal; secondary data must come from a reliable, cited source. Decide your sample size and sampling method in advance and say why. Record conditions so you can explain surprises later.
6 Describe the data before modelling it
Plot it first. Predict the shape, describe what you see using precise vocabulary (gradient, intercepts, asymptotes, periodic…), and say whether your prediction was right. Then propose an initial model and justify it from the context.
7 Build the mathematics up in stages
Start simple and improve: a first model, its residuals, a better model; a special case, then the general case. Show one full worked example of any repeated calculation, then use a table. Explain every step and every use of technology.
8 Reflect after every result
After each major result, add a few sentences: what does it mean in context, is it reasonable, what are its limits, and what will you do next because of it? This running reflection is what reaches the top of Criterion D.
9 Write a short, punchy conclusion
Answer the aim directly, summarise how well your methods worked (referring back to your reflections), state the limitations that matter most and their effect, and suggest a genuine extension. Do not introduce new mathematics.
10 Check against every criterion
Before your draft goes to your teacher, go through the checklist for each criterion: aim, structure, notation, definitions, labels, rounding, engagement, reflection, and correctness. Your teacher can give feedback on one draft only, so make it your best.
11 Use the single teacher draft well
Your teacher is allowed to comment on one draft, in general terms. Read the comments against the criteria, fix the issues yourself, and keep a record of what you changed. Acknowledge any tools (including AI) you used, in line with your school's policy.
12 Final checks and submission
Citations and bibliography complete, appendices referenced, page numbers, figure numbers, a title page that follows your school's instructions on identifying information, and a final read-through for calculator notation and undefined variables.
The five criteria at a glance
| Criterion | Marks | In one line |
|---|---|---|
| A · Presentation | 4 | The organisation, coherence and conciseness of the exploration as a whole |
| B · Mathematical communication | 4 | Whether the mathematical language |
| C · Personal engagement | 3 | The extent to which you engage with the exploration and make it your own |
| D · Reflection | 3 | How you review, analyse and evaluate the exploration |
| E · Use of mathematics | 6 | Whether the mathematics you use is relevant to the exploration and at an appropriate level for your course, whether you show understanding of it (not just results), and whether it is correct. At HL the top bands also expect sophistication and rigour. |
| Total | 20 | 20% of your final IB Maths grade (SL and HL) |
Frequently asked questions
How long does the Maths IA take?
Most students spend several weeks on it, spread over the months their school allows. Plan backwards from your school's internal deadline and leave time after the teacher's draft feedback.
Is the Maths IA the same for AA and AI?
Yes, the exploration and its five criteria are the same for both courses. The mathematics you use should be at the level of your own course.
Can my teacher help me with my IA?
Your teacher can discuss your topic, answer general questions and give written feedback on one draft. They cannot edit or correct your work for you. The same principle applies to tutors and online tools.