Networks are everywhere in modern society: roads, wires, water and gas pipes all connect one place to another. Computers are built of networks at many levels, from the microscopic connections between transistors in a chip to the cables and satellites that link the internet around the world. People who build networks often need to work out the most efficient way to make connections, which can be a difficult problem.

This puzzle shows students the decisions involved in linking a network between houses in a muddy city. It can lead on to a discussion of minimal spanning tree algorithms for optimizing networks.

Other Resources

• Wikipedia: Spanning Tree
• The Mathmaniacs web site has a similar activity (lesson 13).

Curriculum Links

This is a great problem-solving exercise that can lead from a focused goal to a discussion of general principles of network design.

New Zealand Curriculum Achievement Objectives

• Mathematics Level 1: Position and orientation
  • Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
• Mathematics Level 1: Statistical Investigation
  • Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting and counting, and displaying category data; discussing the results.
• Mathematics Level 2: Position and orientation
  • Create and use simple maps to show position and direction.
  • Describe different views and pathways from locations on a map.
• Technology Level 1: Planning for practice
  • Outline a general plan to support the development of an outcome, identifying appropriate steps and resources.

ACM K12 Model Curriculum

• Level I (Grades 3-5) Topic 11: Develop a simple understanding of an algorithm, such as text compression, search, or network routing, using computer-free exercises.

Great Principles of Computer Science

• Computation
• Coordination