Pure Mathematics + Cybersecurity
Break a secret with number theory: how RSA works
Encrypt and decrypt a message with small primes by hand, then in code, and see why large primes matter.
- Advanced
- 1–2 weeks
- Free
606 projects · 13 streams · every class
Mathematics projects 31
Investigations, models, simulations and visual proofs that show mathematics at work, from school topics to university-level modelling.
31 Mathematics projects
Applied Mathematics + Sociology
Model the spread of a rumour
Build a logistic model of how a rumour spreads through a school and test it with a class game.
- Intermediate
- 1–2 weeks
- Free
Pure Mathematics + Biology
Explore the Fibonacci sequence in nature
Count spirals on pine cones, sunflowers and pineapples and test whether they are Fibonacci numbers.
- Beginner
- 2–7 days
- Free
Pure Mathematics · Trigonometry
Measure heights with trigonometry
Make a clinometer and find the height of your school building, a tree and a tower.
- Easy
- 1 day
- Under 250
Statistics and Probability · Probability
Estimate pi by dropping needles
Drop sticks on ruled paper, count how many cross a line and get an estimate of pi.
- Easy
- 1–3 hours
- Free
Applied Mathematics + Finance and Banking
Study compound interest and inflation
Model how savings grow with interest and how inflation changes their real value.
- Easy
- 2–7 days
- Free
Pure Mathematics · Geometry
Prove the Pythagorean theorem five ways
Build paper dissections and algebraic proofs of the theorem and compare how each convinces.
- Easy
- 2–7 days
- Under 250
Pure Mathematics + Fine Arts
Explore tessellations and design your own
Find which regular polygons tile the plane and create an Escher-style tile.
- Beginner
- 1 day
- Under 250
Applied Mathematics + Civil Engineering
Model traffic flow with cellular automata
Simulate cars on a ring road and show how jams appear from nothing above a critical density.
- Advanced
- 1–2 weeks
- Free
Applied Mathematics + Behavioural Economics
Analyse a simple game with game theory
Play repeated prisoner's dilemma with classmates and compare what they do with the theory.
- Intermediate
- 2–7 days
- Free
Applied Mathematics + Physics
Derive and test the formula for a pendulum by dimensional analysis
Predict how period depends on length using only units, then confirm the power law with a log-log graph.
- Intermediate
- 1 day
- Under 250
Statistics and Probability + Biology
Estimate the size of a crowd or a population by sampling
Use capture-recapture with beans to estimate a hidden total, then judge how accurate the method is.
- Easy
- 1 day
- Under 250
Pure Mathematics · Calculus
Find the best shape for a container
Find the dimensions of a can that hold a fixed volume with the least material, and compare with real cans.
- Intermediate
- 2–7 days
- Under 250
Statistics and Probability · Probability
Design a fair spinner game and prove it
Invent a spinner or dice game, test whether it is fair and fix it if not.
- Beginner
- 1 day
- Under 250
Statistics and Probability · Data Analysis
Predict cricket scores with a simple model
Use the score at 10 overs to predict the final total and measure how wrong you are.
- Intermediate
- 1–2 weeks
- Free
Statistics and Probability · Statistics
Analyse whether a class's exam marks are normally distributed
Plot anonymous marks from several tests and check how well a bell curve describes them.
- Intermediate
- 2–7 days
- Free
Pure Mathematics · Algebra
Make and analyse a magic square
Build 3×3 and 4×4 magic squares and prove why the centre of a 3×3 must be 5.
- Beginner
- 1–3 hours
- Free
Applied Mathematics + Finance and Banking
Study the mathematics of loans and EMIs
Derive the EMI formula from a geometric series and build a full repayment schedule.
- Intermediate
- 2–7 days
- Free
Applied Mathematics · Simulation
Simulate a queue at a bank or canteen
Measure real arrival and service times and simulate how the queue changes with one more counter.
- Intermediate
- 1–2 weeks
- Free
Statistics and Probability · Data Analysis
Survey and model how students spend their time
Collect time-use data from 50 students and compare school days with weekends.
- Easy
- 1–2 weeks
- Free
Pure Mathematics + Geography
Investigate the four-colour theorem with maps
Colour maps of states and districts with as few colours as possible and link it to graph colouring.
- Easy
- 1 day
- Under 250
Pure Mathematics · Combinatorics
Find patterns in Pascal's triangle
Build 16 rows of the triangle and discover at least six patterns hidden in it.
- Easy
- 1–3 hours
- Free
Pure Mathematics · Algebra
Create a mathematical card trick and explain it
Learn three self-working card tricks and prove with algebra why each works.
- Easy
- 1 day
- Under 250
Applied Mathematics + Political Science
Investigate voting systems with mathematics
Collect ranked preferences from your class and show that different voting rules pick different winners.
- Intermediate
- 1–2 weeks
- Free
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