Resources
All exercises and tasks (with the task resources) are collected together on this page and downloadable as PDF files.
Embedded Files
Exercises
Exercises
Use this sheet to practice the methods:
- Draw each network, including the weight of each edge (Intro)
- State whether the network is traversable from two nodes, traversable from any node, or not traversable. (Tours)
- Find a minimum spanning tree (Trees)
- Find a shortest path from A to Z (Routes)
There is also a further set of exercises to practice Dijkstra's algorithm (4X).
Exercise.pdfExercise 4x.pdfMilestones
Milestones
Milestones A, B and C are short tests of understanding of each of the key network methods.
Teachers could print them (4 to a page) as mini-tests or exit cards.
Milestone A.pdfMilestone B.pdfMilestone C.pdf100 Acre Wood
100 Acre Wood
Three tasks relate to a map of the 100 Acre Wood where Christopher Robin plays with his friends, including Winnie-the-Pooh and Tigger. It is the setting of Winnie-the-Pooh and The House at Pooh Corner by A. A. Milne. The map is by E. H. Shepard.
Task 1
Task 1
Use the distance table (Resource B) and node diagram (Resource C) to draw the network, including distances.
Task 2
Task 2
Tigger wants to bounce along all the tracks to check there are no Woozles, ending at Pooh's house. He would like to know if he has to go along any tracks more than once. Find a route that checks all tracks which requires as little walking as possible.
Task 3
Task 3
Task 3: Christopher Robin decides that some tracks need to be patrolled daily to be kept clear of Woozles. The shortest total length of track should be patrolled, with all locations should be accessible from his house.
Find an optimal list of tracks to be patrolled, and suggest how four friends (Christopher Robin, Kanga, Owl and Rabbit) could best patrol these tracks.
Task 4
Task 4
Pooh wants to visit Christopher Robin for lunch. He also wants to stop by Rabbit's house when returning, on the off chance that he is offered a second lunch. Plan his trip, there and back.
100acre-resource.pdfSherwood Forest
Sherwood Forest
Three tasks relate to the Sherwood Forest and its surrounding towns. Home to Robin Hood, the Sheriff of Nottingham, and Robin Hood's band of Merry Men, Sherwood Forest is part of English folklore from the Middle Ages.
Sherwood Forest was a roughly triangular forested area between Workshop at its northern limit, Mansfield in the west, and Nottingham in the south. Only parts of the forest remain today.
The map is a 2017 road map of the region.
Task 1
Task 1
Use the distance table (Resource B) and node diagram (Resource C) to draw the network, including distances.
Task 2
Task 2
The Sheriff of Nottingham wants to start in Nottingham and set out to patrol as many of the roads as possible, looking for Robin Hood's men. He does not want to patrol any road twice (it scares the peasants). Prepare a route for the Sheriff to take, giving reasons for your choice.
Task 3
Task 3
The Prior of Newstead Abbey (near Mansfield) is an important landowner, who wants to keep roads between markets safe for his tenants. Recommend a web of roads that should be kept safe, and tell him how much longer this web would need to be if the three roads through Sherwood Forest are not included (those roads shown in the diagram).
Task 4
Task 4
Robin Hood is camped in Derby, and needs to meet Maid Marion halfway between Wakefield and Pontefract. What is the best way for him to get there?
sherwood.pdfThe Shire
The Shire
Three tasks are set in a region of Middle Earth called The Shire, in the fictional world of J R R Tolkien's The Hobbit and The Lord of the Rings trilogy.
The map is Tom Maringer's 1991 'Official Postal Map of The Shire and nearby districts'.
Task 1
Task 1
Use the distance table (Resource B) and node diagram (Resource C) to draw the network, including distances.
Task 2
Task 2
Gandalf wishes to be seen across The Shire, and will travel every one of the roads between the notable towns (marked with black circles). Plan an efficient route, which takes every road at least once, starting in Waymoot.
Task 3
Task 3
Peregrin decides to widen some of the roads of The Shire, to improve commerce across the region. He wants to widen some the roads linking the towns (marked with black circles) and also the town of Bree. Firstly, recommend the shortest system of roads that should be widened. Secondly, suggest (with reasons) which two roads might be widened next.
Task 4
Task 4
Sam is at Weathertop, and needs to get to the Grey Havens. He expects that the shortest route will cross the Brandywine Bridge.
What is the shortest route that he can take, and how much longer would it take if he wanted to avoid crossing the Brandywine Bridge?
shire.pdfPractice Assessment (Dr Seuss)
Practice Assessment (Dr Seuss)
This is a practice assessment for students to attempt in their own time. The context is the fictional world of Dr Seuss.
One final skill that needs practicing is deciding which of the three methods is being asked for within a task. When there are three tasks, it would be reasonable to assume that traversability, minimum spanning tree and shortest path will all be in there somewhere.
practice.pdfJust want everything in one folder, including the answers? All of the PDF files are here on Google Drive.
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