If you are using this site with your class, you might want a large supply of this exercise sheet, which is reused for all four exercise sets - just the instructions change.
Please feel free to use this site however you wish, with the provisos that:
If you have resources you can contribute, suggestions for improvement or anything else to add, please get in contact. I would love to collaborate, especially with anyone with the programming knowledge to make some kind of automated problem generator that included Dijkstra's algorithm and a minimum spanning tree algorithm.
I wrote this website because I wasn't entirely happy with the commercially available resources. In particular, most seem to do one or more of these:
You may also want to read this about free sharing of resources.
Please contact me if you have other useful websites that could be included. These are in no particular order.
Useful building networks of flights between airports.
Visual demonstrations of LOTS of computer science algorithms, including network methods for this standard.
Atom Smasher have a nice site that generates highway sign text for a bit of lighthearted fun.
Generates lots of different (but somewhat similar) distance tables and node diagrams. Look under "Networks" in the top left drop-down box.
The Dr Seuss practice assessment uses some free fonts that are available here. (Most Dr Seuss books use Garamond for the story's text, which you probably already have).
Giphy takes images (or videos) and makes them into gifs.
Demonstrating two of the three methods is sufficient for Achieved in this standard. Ideally assessments have several opportunities to demonstrate extended abstract thinking (Excellence), across the three methods.
Problem/task instructions involving the keywords "traversable/traversability", "minimum spanning tree"and "shortest path" are inappropriate in assessments. This is because students must select their method, not be given it.
All responses to the tasks (100 Acre Wood Sherwood Forest, The Shire), in this website could be assessed with the criteria below; except that the location of the tasks within the site gives too much indication of the network method to be used.
Solving problems involves drawing a network from a distance table, and demonstrating network methods that are applicable to a given task.
State whether or not the network is traversable (possibly from a specified node)
Find a minimum spanning tree and give its weight
Find the shortest path between specified nodes
Expect TWO of the three methods to be applied.
Answering in context.
Using relational thinking:
Give reasons for why a network is/is not traversable from a specified node and if traversable, give a suitable route
Show use of a suitable method (such as the circuit-delete method) to find a minimum spanning tree
Show use of a suitable method to find shortest paths
Expect TWO of the three methods to be applied with relational thinking.
Use of correct and appropriate mathematical statements.
A problem could be 'modified' with additional conditions or constraints.
Using extended abstract thinking:
Make decisions within a problem related to traversability, with justification
Make decisions within a problem related to a modified minimum spanning tree, with justification
Make decisions related to a modified shortest path problem, with justification
Expect TWO of the three methods to be applied with extended abstract thinking.
New Zealand Curriculum: Achievement Objective M7-5 (Senior Secondary Guide)
TKI (exemplar task and conditions of assessment)
This is a good topic for getting outside and measuring distances between locations in the school. Times between locations are best, and they needn't be too accurate.
Writing on whiteboards and mini-whiteboards seems to help get past that initial barrier of making mistakes. It's also good for working in small groups. However, there's no record of their work without a bit of forethought - get them taking photos as they go.
Some students need lots of practice with the basic skills (Jake's page is great for producing as many worksheets as you could ever need), while some want to crack on with understanding Dijkstra's algorithm. Scope for differentiation is important.
A physical model of a network with lines and sinkers will strike a chord with students inclined to think spatially. Let them play with it, even if it gets tangled. They'll probably enjoy helping you make a new one. Particularly useful for finding a shortest path.
Keen programmers might like to investigate how networks are represented by tables and arrays by computers, and code their own network algorithm.
Using the same colour every day for the network and weights, then another for the degrees, and so on, can help consolidate ideas. "Now we need to put on the blue numbers..."
Students with dyslexia, dysgraphia and/or dyspraxia can struggle with accurately drawing networks, and labelling them correctly. At the most difficult part of this standard, a fully labelled network for Dijkstra's algorithm is information-dense. This clutter can be difficult for some students to cope with.
Some students with perceptual processing disorders (e.g. Irlen Syndrome) prefer to use specific colours, or to minimise the number of colours used in a labelled network.
Some things that may help, depending on the student: