IB Mathematics Internal Assessment
Your commute, the school bus, a bike route, a flight you took last summer. Travel is a context every student knows from the inside, and the data is everywhere. That is the attraction and the trap: it is very easy to produce a tidy page of journey times and call it an exploration. Here is how to give the mathematics a real job.
You have lived the problem, so engagement feels free. But a moderator is not scoring how often you catch the bus. They are asking what you decided, what you calculated and whether the mathematics could have told you something you did not already know.
Keep one question in front of you: what would I not have known without the mathematics? If the answer is "the average journey takes twenty-two minutes", you have a statistic, not an exploration.
Three routes, a few timed trips each, a mean for each route. One technique, applied once, with a conclusion everyone expected. At HL it sits well below the level, and at SL it leaves nothing to reflect on because nothing could surprise you.
Costs added up from a fare table and a fuel price. This is arithmetic. The mathematics only starts when you model something uncertain, such as how the cost changes with distance, parking, ticket type or how often you travel, and then justify the choices you made.
Textbook kinematics dressed in a travel setting. If every formula is given to you and you substitute, the context is decoration. It is also a physics exercise, and the mathematics is routine.
A map app finds the shortest path, or a spreadsheet add-in solves the timetable. If you cannot explain how the answer was found, what it assumed and where it could be wrong, the software did the mathematics and you took screenshots.
Treat a set of stops or junctions as a network with weights, and find the best route yourself rather than asking an app. The decision is what the weight means: distance, time, cost or crowding. Change it and the best route changes, which is a result you can reflect on. This suits students who like algorithms and structure.
Arrivals are random, buses are not. Collect your own counts at a stop or crossing, decide what distribution describes the arrivals and test whether it fits. Then ask what would happen if the timetable changed. You have a model, a check and a prediction, all from data you gathered.
Take the relationship between speed and the distance needed to stop, build the model from the reasoning behind it, and compare with data you can justify. The interesting work is in the assumptions: road surface, reaction time, braking. At HL, calculus can do real work if you derive rather than quote.
A school trip, a delivery round, a set of errands visiting several places. Define what you are minimising, list the constraints that genuinely apply, and compare a sensible hand strategy with something systematic. State what you could not check, because the number of possible orderings grows very fast.
Why does a flight between two far-apart cities curve on a flat map? Work out the distance on a sphere, compare it with the straight line on a map and explain the gap. Trigonometry and vectors do honest work, and you can test your answer against a published route.
Take "does my bus run late" as a starting idea. Left alone it is a list of times. To turn it into an exploration, keep pushing.
None of that needs advanced mathematics. It needs a question you can defend and an honest account of what the data did.
Reflection comes naturally when a real journey disagrees with your model. Record those moments properly: what you expected, what you found and what you changed. They are worth more than a further week of identical readings.
Got a travel idea and not sure it can score?
Send me the question and what you plan to do with the mathematics. I read real submitted explorations every year, and I will tell you honestly whether it has enough to do, while there is still time to change direction.
Get the IA sorted with meMore like this: all Maths IA guides. Related: using your own data in the Maths IA
These pages are free and stay free, but they are general and your IA is not. Send me your research question, or whatever exists so far, and I will tell you in writing whether the topic has a ceiling on it, where the marks are going, and what to change first. That costs nothing and it comes back within 24 hours.
Written by a serving IB Diploma and Career-related Programme Coordinator and Head of Mathematics, who reads internal assessments across every subject group every year. If you then want the whole draft reviewed properly against all five criteria, that is the paid one, and it is refunded if it does not name at least three specific things to fix.
Get a free verdict Full written review, $99
I never write any part of it. Not a sentence, not a calculation, not your data. Under 18: a parent buys this and the thread is with them. I do not work with students at my own school.