Chance helps us reason when outcomes vary. It asks what can be predicted, what remains uncertain and how evidence should change our expectations.
Uncertainty is not a failure of mathematics. It is the thing mathematics is helping you describe.
Chance
What can we know when outcomes are uncertain?
Flip a coin ten times, or imagine ten flips.
Would exactly five heads surprise you? Would eight? What would change if you repeated the experiment many times?
Try noticing
Notice 1
What outcomes are possible?
Notice 2
Which outcomes feel likely, and why?
Notice 3
How does a sample differ from the long-run pattern?
Notice 4
What evidence would change your mind?
Knowledge you may need
Tools and visualisations
RepetitionPatternChance
Cellular Automata Explorer
Explore how simple local rules create order, randomness and emergent patterns.
ExplorationChanceRepresentation
GCSE Probability Tree Lab
Build two-stage tree diagrams and compare replacement with no replacement.
ToolChanceRepresentationOptimisation
Linear Regression and Overfitting Lab
Compare training error, test error and model complexity.
Tool and explorationChanceRepresentationOptimisation
Monte Carlo Simulator
Estimate pi and area under a curve using random sampling.
Tool and explorationChanceRepresentationQEDReasoning
Normal Distribution and Hypothesis Testing Lab
See rejection regions, z statistics, p-values and conclusions.
ToolChanceRepresentation
Probability and Statistics Lab
Explore binomial distributions, sampling and sample means.
ToolChanceConnectionPattern
Random Graph Lab
Explore G(n, p), connected components and random network behaviour.
ExplorationQEDReasoningOptimisationChance
Voting Systems and Fairness Lab
Compare plurality, Borda count, instant runoff and head-to-head fairness.
ExplorationWhere this appears in school maths
Probability and statistics
Tree diagrams, distributions, sampling and hypothesis tests all turn uncertainty into something we can reason about.
Multiplicative thinking
Probability often depends on combining chances, proportions and repeated trials.