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Exploration Ideas

All Algebra (11) Functions & Equations (26) Geometry & Trigonometry (71) Statistics & Probability (41) Calculus (20) Mathematical Modeling (5) Applied Mathematics (1) Graph Theory (9) 41 ideas Clear filters
Height, Marriage, and What "Random" Would Predict
Height, Marriage, and What "Random" Would Predict

If height didn't matter at all when people paired up, the gap …

Sorting Speeds Into Bins
Sorting Speeds Into Bins

Four hundred balls bounce around inside a spinning drum, then shoot one …

Physics Normal Distribution +3
The Sprinkler's Secret Pattern
The Sprinkler's Secret Pattern

A rotating garden sprinkler throws water along a parabola — so why …

Trigonometry Modelling +3
The Guinness Question: Is the Difference Real?
The Guinness Question: Is the Difference Real?

Run any experiment with two groups and the averages will differ — …

Data Collection Experimental Design +3
Is Anything Actually Normal?
Is Anything Actually Normal?

The bell curve appears throughout statistics textbooks. This exploration tests it against …

Data Collection Sampling +3
How Many Goals on Saturday?
How Many Goals on Saturday?

Goals are rare, sudden and unpredictable — yet the number of goals …

Data Collection Probability +3
How Many Fish Are in the Lake?
How Many Fish Are in the Lake?

You can't count every fish in a lake — so ecologists tag …

Data Collection Experimental Design +3
Stuck at Deuce
Stuck at Deuce

You win 60% of points on your serve — so how often …

Probability Sports Mathematics +3
Monopoly Is Rigged (and You Can Prove It)
Monopoly Is Rigged (and You Can Prove It)

Some Monopoly squares get landed on far more than others — it's …

Probability Matrices +3
Do Tall People Earn More?
Do Tall People Earn More?

The Guardian reported research claiming every extra inch of height is worth …

Data Collection Statistics +3
Oxford's 33.7°C: How Unusual Is a Record-Breaking Day?
Oxford's 33.7°C: How Unusual Is a Record-Breaking Day?

In May 2026 Oxford hit 33.7°C, beating a record that had stood …

Statistics Data Analysis +3
Blue Seven: Are Humans Bad at Being Random?
Blue Seven: Are Humans Bad at Being Random?

Ask people for a random colour and a random number, and the …

Data Collection Statistics +3
The Secretary Problem: When Should You Stop Looking?
The Secretary Problem: When Should You Stop Looking?

You interview candidates one at a time and must hire or reject …

Probability Decision Making +3
Has the Elizabeth line led to a rise in rental prices?
Has the Elizabeth line led to a rise …

Compare rental prices near Elizabeth line stations before and after opening, against …

Statistics Applied Mathematics +2
Mathematics of Card Shuffling
Mathematics of Card Shuffling

How many shuffles does it take to randomize a deck of cards?

Probability Combinatorics +2
The House Always Wins
The House Always Wins

Investigate common casino games.

Probability Statistics +2
Spinner Games
Spinner Games

Make your own and investigate fair games.

Probability Statistics +2
Skyjo
Skyjo

A game about scoring the lowest score with negatives

Randomness Game Theory +2
Efron's Dice
Efron's Dice

The idea for non-transitive dice has been around since the early 1970s

Randomness Game Theory +2
Sicherman Dice
Sicherman Dice

Sicherman dice, invented by Colonel George Sicherman in 1978, are a non-standard …

Randomness Game Theory +2
Zipf's Law
Zipf's Law

Zipf's law describes a striking pattern in the frequency of words in …

Linguistics Power Laws +2
Do Left-Handers Die Younger?
Do Left-Handers Die Younger?

A famous 1991 study reported that left-handed people die younger than right-handed …

Hypothesis Testing Critical Thinking +2
Line Judge vs Replay: How Good Is the Human Eye?
Line Judge vs Replay: How Good Is the …

Slow-motion replay clips show many close line calls are wrong. Collect clips …

Probability Statistics +2
Same Average, Different Spread: What Standard Deviation Hides
Same Average, Different Spread: What Standard Deviation Hides

Two housing markets can share the same average price and tell very …

Statistics Data Analysis +2