Change is about following motion, growth, decay and accumulation. It asks how one quantity responds when another quantity moves.
If the motion feels slippery, freeze one moment and compare it with the next.
Change
How do things move, grow, shrink, decay or accumulate?
Write 1, 4, 9, 16, 25.
Look at the gaps between terms. What changes in the gaps, and what might that tell you?
Try noticing
Notice 1
What is increasing, decreasing or staying fixed?
Notice 2
Where is the change fastest?
Notice 3
Can you describe the change with a graph, table and sentence?
Notice 4
What would happen if you measured the same situation at smaller intervals?
Knowledge you may need
Tools and visualisations
ChangeRepresentationQEDReasoning
A Level Calculus Revision Lab
Revise tangent gradients, definite integrals and trapezium-rule estimates.
ToolChangeRepresentationOptimisation
Area Approximation and Integration Explorer
Compare rectangles, midpoint approximations, trapezia and exact integrals.
ToolChangeRepresentationRepetition
Differential Equation Slope Field Explorer
Explore slope fields, initial conditions and numerical solution curves.
ToolChangeRepresentation
Forces and Inclined Plane Explorer
Resolve forces, friction and acceleration on an inclined plane.
ToolTransformationRepresentationChange
Function Transformation Playground
Explore vertical and horizontal graph transformations across familiar functions.
ToolRepetitionPatternChange
Conway's Game of Life Explorer
Run still lifes, oscillators and gliders in a two-dimensional cellular automaton.
ExplorationOptimisationChangeRepresentation
Gradient Descent Visualiser
Watch optimisation move across a loss landscape.
Tool and explorationRepetitionChangePattern
Logistic Map and Chaos Explorer
Iterate a simple recurrence and explore fixed points, cycles and chaos.
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 explorationWhere this appears in school maths
Functions and graphs
Graphs make rates, turning points, gradients and accumulated areas visible.
Mechanics and calculus
Motion, forces, gradients and area all belong to the language of change.