Learning tools & simulations
Make a mathematical idea visible. Work through fractions, test birthday coincidences or compare the two Monty Hall strategies.
Fraction visualizer
Add, subtract and compare signed fractions. See common-denominator working and aligned number-line jumps; download the diagram as SVG.
Birthday-paradox simulator
Inspect a random group, spot shared days and compare theory with seeded trials. Contrast any pair matching with a match to one fixed date.
Monty Hall simulator
Choose a door, see the host's reveal and decide whether to switch. Run paired trials with repeatable seeds and download the experiment.
Use the model, then check its assumptions
Fraction results use exact integer arithmetic within the stated bounds. Simulators separate mathematical probabilities from observed frequencies and state the randomization rules. Generated birthday groups use equally likely day labels, and Monty Hall uses an informed host who always offers a switch.
No account or real student data is needed. Downloads are generated in your browser. For tabletop probability questions, use the dice-pool comparison calculator; for pulse patterns, try the polyrhythm visualizer.