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Mathematics experiments and science fair projects

Hands-on mathematics projects covering probability, patterns, geometry and statistics. Each one lists the exact materials, the time and cost involved, the variables to control and a data table you can fill in — so it works as a class activity or as a full science fair entry.

12 published projects in this collection

Choosing a mathematics project

Maths projects live or die on sample size. Plan for enough trials that your averages stop jumping around, and show the raw data alongside the summary.

What every project includes

A research question and hypothesis, an independent and dependent variable, the variables you hold constant, a materials list with costs, numbered steps, safety guidance and a reproducibility score based on how completely the method is documented.

Projects to try

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Does the Fibonacci sequence appear in real plants?

Count petals, seed spirals and leaf arrangements across many plants and compare with the sequence.

Beginner
Elementary +3
Several days
$5 materials

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Is a dice game fair when you change the winning rule?

Play a two-dice game under several rules and compare observed win rates with calculated probabilities.

Beginner
Elementary +3
30–60 minutes
$5 materials

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Does the Monty Hall strategy really win more often?

Play hundreds of rounds by hand and by simulation to test a famous counter-intuitive probability result.

Intermediate
Middle School +2
1–2 hours
No-cost materials

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Is the ratio of circumference to diameter the same for every circle?

Measure many round objects and test how closely the ratio clusters around pi.

Beginner
Elementary +3
30–60 minutes
No-cost materials

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Do real-world numbers follow Benford's law?

Collect leading digits from populations, invoice totals or river lengths and compare with Benford's prediction.

Intermediate
Middle School +2
Several days
No-cost materials

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Does the shape of a graph change what people conclude from the same data?

Show the same numbers on differently scaled charts and measure how readers interpret them.

Intermediate
Middle School +2
Several days
$5 materials

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Does the birthday paradox hold in real classrooms?

Survey many groups of different sizes and compare the observed rate of shared birthdays with theory.

Intermediate
Middle School +2
Several days
No-cost materials

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Does a longer survey get fewer complete responses?

Hand out surveys of different lengths on the same topic and compare how many are finished.

Intermediate
Middle School +2
Several days
$5 materials

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Does the number of coin flips bring results closer to 50/50?

Flip a coin in growing batches and watch the running proportion settle towards the expected value.

Beginner
Elementary +3
30–60 minutes
No-cost materials

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Which shape holds the most area for the same perimeter?

Build shapes from equal lengths of string and compare the areas they enclose.

Beginner
Elementary +3
30–60 minutes
$5 materials

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Can you estimate a crowd size accurately by sampling?

Estimate the number of items in a big jar using sampling methods, then count them for real.

Beginner
Elementary +3
1–2 hours
$10 materials

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Does rounding change the total of a long list of numbers?

Add long lists of measurements with different rounding rules and measure the accumulated error.

Beginner
Middle School +2
30–60 minutes
No-cost materials

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Physics Chemistry Biology Earth Science Environmental Science Astronomy Engineering Computer Science Mathematics General STEM

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Preparing for a fair? Read the science fair guide or record your data in the lab.