IB Mathematics Internal Assessment
Tilings, domes, logos, buildings, packaging, fonts. Geometry gives you things you can see and hold, which makes engagement easy and the final document attractive. It also makes it very easy to produce a lovely set of diagrams with almost no mathematics behind them. Here is how to avoid that.
A visual topic feels safe. You can draw it, photograph it, and explain it to a friend in one sentence. The trap is that a good picture can stand in for a good argument. A moderator reads the page, not the picture, and asks what you worked out that was not already obvious from looking.
The question to hold onto all the way through is this: what did the mathematics tell me that my eyes could not? If there is no answer, the topic is a presentation, not an exploration.
A photograph, a ratio read off with a ruler, and a sentence saying the building is "mathematical". This is a survey. Nothing is derived, nothing is decided, and there is no result that could have gone differently.
You measure until the number comes out near 1.6 and stop. The danger is that you chose where to measure after you knew what you wanted, which is the opposite of an investigation. Unless you test the claim honestly, including the cases where it fails, it is decoration.
Surface area of a bottle, volume of a roof, perimeter of a garden. Substituting measurements into formulae you were handed is routine, and at HL it sits well below what the course expects.
A drawing package or a 3D tool produces the shape, the angles and the areas. If you could not reproduce any of it by hand or explain why it works, the tool has done the mathematics and you have done the screenshots.
The cheapest container for a required volume, the strongest frame for a given amount of material, the layout that wastes least. State what "best" means, set up the function, find the optimum, then show what happens when the constraint moves. This is not the textbook box problem if the constraint is genuinely yours.
Why some polygons fit together with no gaps and others cannot, and what happens to the angles at each corner. You can establish the conditions yourself, test them against shapes you try, and explain a result that surprised you. Keep the claims small enough to prove or check honestly.
Describe a pattern, such as a border, a mosaic or a textile, using reflections, rotations and translations, then classify what you find. The strength is in the classification and the justification, not in collecting pretty examples. This suits AA students who enjoy structure.
The profile of an arch, the shape of a hanging chain, the curve of a ramp. Measure it yourself, choose a family of functions with a reason, and test the model against a second set of measurements. Decide what the curve tells you about strength or stability rather than stopping at the equation.
Roof pitch and rafter lengths, the lines of sight in a theatre, shadows through the day, the angle a ramp must not exceed. Take your own measurements, build the model in two or three dimensions, and compare predicted values with checked ones.
Take "the best shape for a drinks can" as a starting idea. Done as a one-line calculus exercise it is the most common optimisation in the school, and it will read that way. To turn it into an exploration, keep pushing.
Nothing there needs advanced mathematics. It needs a question you can defend and an honest look at your own result.
Reflection is easier here than in most contexts, because a real object will often disagree with your model. Record those moments properly, with what you expected, what you found and what you changed. They are worth more than another well-drawn figure.
Got a geometry or design 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: modelling 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.
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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.