TOK exhibition
29 TOK exhibition object ideas from mathematics
Each idea is a kind of object with angles worth exploring. None is tied to a particular IB prompt: test it against the prompt you have chosen, and make it specific and personal. These are ideas to think with, not commentaries.
Knowledge and the knower
Your IB maths formula booklet
The booklet of formulas you are given in maths exams.
- Using a formula is not the same as knowing why it is true.
- Someone decided what you need to remember and what you may look up.
Make it yours: Choose one formula in it and explain whether you could derive it. Related question: Can you know a mathematical result without understanding its proof?
A lottery ticket
A ticket for a national lottery.
- Millions of people buy tickets despite knowing the odds; knowing a probability does not always change behaviour.
- It separates mathematical knowledge from personal belief and hope.
Make it yours: A ticket bought by someone you know, with their reasons, adds a real perspective. Related question: Why do some correct mathematical results feel wrong, even to experts?
A print of the Mandelbrot set
A picture of the fractal produced by one simple rule.
- Its endless detail was fixed by the rule before anyone drew it: discovered or invented?
- Computer images made a mathematical object visible for the first time.
Make it yours: Generate your own zoom with free software and say which part you chose and why. Related question: Is mathematics discovered or invented?
Three cups and a coin
A home-made Monty Hall game.
- A correct answer that feels wrong to almost everyone.
- Simulation persuaded people when proof did not.
Make it yours: Record the results of playing it with friends 30 times. Related question: Why do some correct mathematical results feel wrong, even to experts?
A medical test leaflet
The leaflet that comes with a home test kit, with its accuracy figures.
- A 'highly accurate' test can still give mostly false positives when a condition is rare.
- It asks how we should update beliefs on evidence.
Make it yours: Work through the numbers for one realistic case in your commentary. Related question: Should new evidence change what we believe according to a fixed mathematical rule?
A school report or results slip
A report with marks, averages or predicted grades.
- A single number stands in for months of learning.
- Averages and boundaries are choices that shape what a grade means.
Make it yours: Use your own report and remove anything private. Related question: Can a single average represent a group fairly?
A completed sudoku
A puzzle solved by pure logic, with no arithmetic needed.
- Every step is forced by the rules: a small model of deductive certainty.
- Guessing and checking also works; is that knowing?
Make it yours: Use one you solved, and mark where you guessed. Related question: Is a mathematical proof a stronger kind of justification than the evidence used in the natural sciences?
A pack of playing cards
A standard 52-card pack.
- Bayer and Diaconis showed in 1992 that about seven riffle shuffles are needed to mix a pack well; most people shuffle less.
- It asks what 'random' means and how we would know.
Make it yours: Record how many times your family shuffles before a game. Related question: What does a probability mean when an event happens only once?
A sunflower head or pine cone
A seed head whose spirals often come in Fibonacci numbers.
- Real patterns sit alongside exaggerated claims about the golden ratio in nature and art.
- Beauty can make claims feel true; how do we test them?
Make it yours: Count the spirals on one you found yourself. Related question: Is beauty a reliable guide to mathematical truth?
Knowledge and technology
Your graphic display calculator
The calculator you use in IB maths lessons and exams.
- You trust its answers without knowing how it computes them.
- It changes what you need to know: which skills does it replace, and which does it make more important?
Make it yours: Describe one moment it gave an answer you did not expect, or one you could not have found by hand. Related question: How far should we trust tools whose workings we cannot check?
A weather forecast with a percentage
A forecast saying, for example, 70% chance of rain.
- What does a probability mean for a single day?
- Forecasts come from many model runs because the atmosphere is chaotic.
Make it yours: Screenshot the forecast for a day that mattered to you. Related question: What does a probability mean when an event happens only once?
A slide rule or book of log tables
Calculating tools that use logarithms to turn multiplication into addition.
- A mathematical idea became a physical tool that shaped science for centuries.
- It makes you ask what calculators have changed about knowing.
Make it yours: Borrow one from a grandparent or teacher and record what they used it for. Related question: Does mathematical notation shape what mathematicians are able to think?
A map coloured with four colours
Any map coloured so that neighbouring regions differ, using only four colours.
- The theorem behind it was the first major proof to rely on a computer.
- It asks whether knowledge needs a human who can check every step.
Make it yours: Colour a real local map yourself and keep the attempt. Related question: Can we know a result is true if no human can check every step of its proof?
A fitness tracker summary
The daily summary from a watch or phone app.
- It turns a body into numbers using estimates and models you cannot see.
- Does more data about yourself mean more knowledge about yourself?
Make it yours: Use your own (or a family member's) summary, with permission. Related question: Does big data make mathematical theory less necessary?
A recommendation feed
A screenshot of 'recommended for you' videos or products.
- An algorithm decides what you see, using mathematics you cannot inspect.
- It asks whether a mathematical process can be biased.
Make it yours: Compare your feed with a friend's and comment on the difference. Related question: Can an algorithm be biased if it only follows mathematics?
An AI chatbot's attempt at a proof
A printout of an AI tool's answer to a proof question, clearly labelled as AI output.
- It can sound convincing whether or not it is correct.
- Who knows the result if a machine produced the argument?
Make it yours: Check the attempt yourself and say what you found. Acknowledge the tool as your school requires. Related question: If an AI system produces a correct proof, does anyone know the result?
A barcode or ISBN
The barcode on a book, with its check digit.
- A small piece of modular arithmetic catches errors millions of times a day.
- We rely on hidden mathematics we never see.
Make it yours: Check the digit on a book you own by hand. Related question: How far should we trust tools whose workings we cannot check?
Knowledge and language
A newspaper headline about risk
A headline saying something 'doubles' or 'halves' a risk.
- Relative and absolute risk can both be true and tell different stories.
- The wording shapes how readers act on the knowledge.
Make it yours: Find the original study and compare its numbers with the headline. Related question: How should we judge a statistical claim reported in the news?
A ruler
An ordinary 30 cm ruler.
- The metre is defined by international agreement, now tied to the speed of light.
- Every measurement has limited precision, so measured knowledge is always approximate.
Make it yours: Use your own ruler and compare it with another one; do they agree exactly? Related question: Are units of measurement discovered in nature or decided by agreement?
A thermometer below zero
A thermometer or weather display showing a negative temperature.
- Negative numbers were rejected as absurd by many European mathematicians for centuries.
- What made an idea once rejected become ordinary knowledge?
Make it yours: Photograph a real reading on a cold day near you. Related question: How do new mathematical ideas come to be accepted as knowledge?
Knowledge and politics
A Mercator world map
The familiar classroom world map, designed in 1569 for navigation.
- It is mathematically exact about one thing (compass directions) and badly wrong about another (areas far from the equator).
- It raises whether a representation can be neutral, and who chooses which one we see.
Make it yours: Use the actual map from your classroom or atlas, and say where you met it. Related question: Can a representation be accurate and misleading at the same time?
A census form
The questionnaire a government uses to count its population.
- Its categories decide which groups exist in official knowledge.
- Counting has consequences for funding and representation.
Make it yours: Pick one question on the form and focus your commentary on it. Related question: What is gained and lost when a state counts its people?
A COVID-19 graph from 2020
A news graph of cases or deaths, especially one on a logarithmic scale.
- The same data looks very different on linear and log scales.
- Graphs influenced public behaviour and policy, so their design had consequences.
Make it yours: Use a graph you remember seeing, with its source and date. Related question: Can the same data support opposite conclusions depending on how it is shown?
A ballot paper
A specimen ballot, or the paper from a class or school vote.
- Different counting rules can choose different winners from the same ballots.
- Mathematics can show that no system meets every fairness condition.
Make it yours: A ballot from a vote you took part in makes this personal. Related question: Can mathematics tell us what a fair voting system is?
A loan or savings statement
A statement showing an interest rate or repayment schedule.
- Compound interest is simple mathematics with large consequences.
- Who is responsible when people do not understand the mathematics in a contract?
Make it yours: A sample statement from a bank's website works if you do not have one. Related question: Who is responsible when a trusted mathematical model fails?
A bar chart with a cut-off axis
An advert or report chart whose axis does not start at zero.
- The numbers are correct; the impression is not.
- Is visual presentation part of the knowledge or just packaging?
Make it yours: Redraw it with a full axis and compare the two. Related question: Can the same data support opposite conclusions depending on how it is shown?
Knowledge and indigenous societies
A clock face
An ordinary analogue clock.
- Sixty minutes and sixty seconds carry Babylonian base-60 mathematics into daily life.
- It shows how conventions travel across cultures and centuries.
Make it yours: Use a clock from a specific place, such as your school hall. Related question: Is mathematics the same in every culture?
A woven textile with a repeating pattern
A fabric, rug or basket with symmetric patterns made by a traditional craft.
- Makers use symmetry and counting expertly, often without writing anything as a theorem.
- Is this mathematics, and who decides?
Make it yours: An item from your own family or community is ideal. Related question: Can knowledge built into practices such as weaving, building or navigation count as mathematics?
* Theme names from the current TOK guide as we understand it. An object can suit more than one theme; check which theme your exhibition must be linked to with your teacher.
Next: the planning checklist, and knowledge questions to sharpen your commentary.
IB Math Revision is independent and not affiliated with or endorsed by the IB. These pages are our own writing. They do not reproduce the IB's exhibition prompts or prescribed essay titles: your TOK teacher or IB coordinator has the current ones.