Optimisation asks what is best when there are limits. The best route, shape, choice or strategy depends on what you decide to value.
Before searching for the best answer, decide what best actually means.
Optimisation
What is the best choice when there are limits or trade-offs?
You can walk a short steep route or a longer flat route.
Which is best if you care about time? Which is best if you care about energy?
Try noticing
Notice 1
What are you trying to maximise or minimise?
Notice 2
What constraints cannot be ignored?
Notice 3
Can a good local choice lead to a bad final result?
Notice 4
What changes if the cost changes?
Knowledge you may need
Tools and visualisations
ConnectionOptimisationQEDReasoning
A* Search Visualiser
Explore goal-directed pathfinding with heuristics, g-scores and f-scores.
ExplorationChangeRepresentationOptimisation
Area Approximation and Integration Explorer
Compare rectangles, midpoint approximations, trapezia and exact integrals.
ToolConnectionOptimisationQEDReasoning
Dijkstra Visualiser
Explore weighted shortest paths, tentative distances and settled nodes.
ExplorationOptimisationChangeRepresentation
Gradient Descent Visualiser
Watch optimisation move across a loss landscape.
Tool and explorationConnectionQEDReasoningOptimisation
Graph Colouring Visualiser
Use greedy colouring and compare vertex-order strategies.
ExplorationChanceRepresentationOptimisation
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 explorationChangeRepresentationOptimisation
Projectile Motion Lab
Adjust launch speed, angle and gravity to explore projectile motion.
ToolChangeOptimisationRepresentation
River Flow and Flood Risk Simulator
Explore rainfall, storage, release decisions and flood thresholds.
Tool and explorationQEDReasoningOptimisationChance
Voting Systems and Fairness Lab
Compare plurality, Borda count, instant runoff and head-to-head fairness.
ExplorationWhere this appears in school maths
Graphs, calculus and modelling
Shortest paths, maximum points, minimum costs and efficient decisions all use optimisation thinking.
Algebraic thinking
Constraints can often be written as equations, inequalities or rules.