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Information mostly for teachers; NZQA information and useful links for generating resources
Information mostly for teachers; NZQA information and useful links for generating resources
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.
Exercise.pdfPlease feel free to use this site however you wish, with the provisos that:
- downloaded PDF files are unmodified, and retain the link to this site;
- none of these resources are re-used as part of a site that requires a subscription or fee;
- no task or practice assessment can be used as or modified to become actual assessments; and
- if you find errors in any of the content, you email to let me know!
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:
- cover Hamiltonian paths and Travelling Salesman problems - these are not listed in the standard as methods to be assessed;
- mistake "visit every town" instructions in tasks for traversability problems - traversability means travel every edge;
- place the skill 'draw a network diagram from a distance table' anywhere other than near the start;
- use difficult and spurious contexts, such as doors between rooms in a building - distance between rooms is a questionable thing to define;
- leave traversability until last (as it's the most accessible of the three methods assessed);
- only cover the 'find all paths' method for finding a shortest path;
- include 'hard' exercises and tasks set outside the scope of the standard, with weird ideas like longest Hamiltonian circuit;
- have too much emphasis on the awful 'method of trees' for finding a shortest path (I find that if students can do this, they can do Dijkstra's algorithm too).
You may also want to read this about free sharing of resources.
External Links
External Links
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.
Achievement Criteria breakdown
Achievement Criteria breakdown
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.
Achieved
Achieved
Solving problems involves drawing a network from a distance table, and demonstrating network methods that are applicable to a given task.
Traversability
Traversability
State whether or not the network is traversable (possibly from a specified node)
Minimum Spanning Tree
Minimum Spanning Tree
Find a minimum spanning tree and give its weight
Shortest Path
Shortest Path
Find the shortest path between specified nodes
Expect TWO of the three methods to be applied.
Achieved with Merit
Achieved with Merit
Answering in context.
Using relational thinking:
Traversability
Traversability
Give reasons for why a network is/is not traversable from a specified node and if traversable, give a suitable route
Minimum Spanning Tree
Minimum Spanning Tree
Show use of a suitable method (such as the circuit-delete method) to find a minimum spanning tree
Shortest Path
Shortest Path
Show use of a suitable method to find shortest paths
Expect TWO of the three methods to be applied with relational thinking.
Achieved with Excellence
Achieved with Excellence
Use of correct and appropriate mathematical statements.
A problem could be 'modified' with additional conditions or constraints.
Using extended abstract thinking:
Traversability
Traversability
Make decisions within a problem related to traversability, with justification
Minimum Spanning Tree
Minimum Spanning Tree
Make decisions within a problem related to a modified minimum spanning tree, with justification
Shortest Path
Shortest Path
Make decisions related to a modified shortest path problem, with justification
Expect TWO of the three methods to be applied with extended abstract thinking.
NZQA, Ministry of Education, and other 'official' stuff
NZQA, Ministry of Education, and other 'official' stuff
New Zealand Curriculum: Achievement Objective M7-5 (Senior Secondary Guide)
TKI (exemplar task and conditions of assessment)
Learning styles
Learning styles
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..."
Learning difficulties and support
Learning difficulties and support
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:
- larger copies of the node diagram
- strategies for checking information is transferred from distance table to node diagram correctly
- using a ruler to make all edges straight - and assessing so that this is possible (no long loopy roads)
- "confining" the name of each node within its circle to minimise clutter (compare the node names on the Exercise sheet to the wordy node names in the 100 Acre Wood task)
- including one or two edges in the node diagram to help get them going
- keeping instructions and contexts as straightforward as possible
- having students practice instructing/working with their reader-writer in completing a network diagram
- allowing students to complete the assessment by annotating an electronic file.
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