N1.1: Networks

Students:

• identify and use network terminology: vertices, edges, paths, the degree of a vertex, directed networks and weighted edges

• solve problems involving network diagrams AAM

  • • recognise circumstances in which networks could be used, e.g. the cost of connecting various locations on a university campus with computer cables

    • given a map, draw a network to represent the map, e.g. travel times for the stages of a planned journey

    • draw a network diagram to represent information given in a table

N1.2: Shortest Paths

Students:

• determine the minimum spanning tree of a given network with weighted edges AAM

  • • determine the minimum spanning tree by using Kruskal's or Prim's algorithm or by inspection

    • determine the definition of a tree and a minimum spanning tree for a given network

• find a shortest path from one place to another in a network with no more than 10 vertices AAM

  • • identify a shortest path on a network diagram

    • recognise a circumstance in which a shortest path is not necessarily the best path or contained in any minimum spanning tree

AAM: Application and Modelling opportunities

Computation with Integers - basic weighted edge calculations, budgeting/minimal cost connecting problems

Ratios and Rates - converting between speed, time and distance when given map information (e.g. speed limits, length of road)

Length - distance units (m, km)

Time - time travelled (s, min, h, days)

Network Concepts (Standard 2) - practical Network problems explored

Critical Path Analysis (Standard 2)