Connection turns separate things into a structure. It asks what is linked, what can be reached and which paths matter.
Networks become clearer when you stop looking at everything and trace one path.
Connection
How are things linked, and what paths are possible?
Draw five dots. Join some pairs with lines.
Can you get from every dot to every other dot? What is the shortest route between two chosen dots?
Try noticing
Notice 1
Which points are connected directly?
Notice 2
Which connections are missing but would change everything?
Notice 3
What is the shortest, safest or most flexible route?
Notice 4
Can you remove one link and keep the whole network connected?
Knowledge you may need
Tools and visualisations
ConnectionOptimisationQEDReasoning
A* Search Visualiser
Explore goal-directed pathfinding with heuristics, g-scores and f-scores.
ExplorationConnectionOptimisationQEDReasoning
Dijkstra Visualiser
Explore weighted shortest paths, tentative distances and settled nodes.
ExplorationConnectionQEDReasoningOptimisation
Graph Colouring Visualiser
Use greedy colouring and compare vertex-order strategies.
ExplorationConnectionRepresentationQEDReasoning
Graph Theory Visualiser
Build a graph and step through breadth-first and depth-first search.
ExplorationConnectionQEDReasoningPattern
Planarity and Map Colouring Lab
Explore planar graphs, Euler's formula, crossings and map colouring.
ExplorationChanceConnectionPattern
Random Graph Lab
Explore G(n, p), connected components and random network behaviour.
ExplorationWhere this appears in school maths
Discrete maths and modelling
Graphs, routes and networks are useful models for maps, relationships and decisions.
Geometric thinking
Diagrams can reveal structure even when the distances are not the main point.