LWB Level 2 Networks 2.5 Learning Workbook

The LWB Level 2 Networks 2.5 Learning Workbook is a specialized, write-on resource designed for the NCEA Level 2 Internal Assessment: Apply network methods in solving problems. This workbook introduces students to the branch of mathematics known as Graph Theory, providing practical tools to model and solve real-world logistical problems, from laying fiber-optic cable to planning the most efficient delivery routes.

Key Features

• Foundations of Network Theory: Introduces the essential vocabulary of networks. Students learn to identify and define Vertices (nodes), Edges (arcs), Weights, and Loops, and understand the difference between directed and undirected networks.

• Minimum Spanning Trees (MST): Master the techniques for connecting all points in a network using the minimum total edge weight. The workbook provides step-by-step practice for both Kruskal’s Algorithm and Prim’s Algorithm, essential for problems involving minimum cost or distance.

• Shortest Path Problems: Teaches students how to find the most efficient route between two specific points. It covers Dijkstra’s Algorithm, providing clear grids and templates to track working—a requirement for gaining Merit and Excellence credits.

• Traversability and Euler Circuits: Investigates whether a network can be drawn without lifting a pen or retracing a line. Students learn to calculate the Degree of a Vertex and apply Euler’s laws regarding odd and even nodes to determine if a path is traversable.

• The Chinese Postman Problem: An application of traversability where every edge must be covered at least once. Students learn how to "pair up" odd vertices to find the shortest route that covers the entire network.

• Hamiltonian Paths and Cycles: Explores routes that visit every vertex exactly once (rather than every edge). This includes an introduction to the "Travelling Salesperson Problem" and strategies for finding efficient, if not always perfect, solutions.

• Network Flow and Capacity: Analyzes the movement of "traffic" through a system. Students learn about Source and Sink nodes and master the Max-Flow Min-Cut Theorem to determine the maximum possible flow through a network with limited capacities.

• Critical Path Analysis (CPA): A vital skill for project management. Students learn to create activity networks to determine the shortest possible time to complete a complex project, identifying the "Critical Path" where any delay will affect the final deadline.

• Real-World Modeling: Features scenarios based on modern infrastructure, such as designing water pipe layouts, optimizing computer networks, or planning a multi-city flight itinerary.

• Achievement, Merit, and Excellence Scaffolding: Tasks are clearly graduated. Achievement focuses on basic algorithms, while Excellence requires students to choose the best method for a complex problem and justify their decisions with logical mathematical reasoning.

• Full Answer Appendix: Includes all completed network diagrams and numerical solutions at the back of the book, allowing for immediate feedback and independent study.

• Glossary of Network Terms: A guide to technical vocabulary—such as Algorithm, Bipartite, Bottleneck, and Tree—ensuring students use the correct mathematical language in their assessments.