# Advanced decision teaching resources: Finding the shortest path

Resources and ideas for mathematics, advanced decision, finding the shortest path, written by teachers to support teaching and learning

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#### Decision Maths Enrichment

3 enrichment task that can be used without any prior knowledge. It was used to show year 10's how maths is used through different decision activities

#### D1/ D2 - Travelling Salesperson game

A Powerpoint game that can be used to help engage students in D1 and D2.Although it is made with the travelling salesperson algorithm in mind, it can also be used for Kruskal's, Prim's on a distance matrix and the nearest neighbour algorithm.

#### Decision 1 - All lessons and resources for all chapters

PowerPoints written so that a teacher can learn from the PowerPoints and teach from them. Students can use the PowerPoints to learn independently too. Many colleagues have used my lessons on Decision 1 without a strong understanding of Decision themselves. Includes all chapters: Algorithms, Networks, Route Inspection, Critical paths, Linear Programming and MatchingsIncludes all worksheets, answers and assessments

#### Mathematics Decision 1 Lessons

This is a set of lessons for Decision Mathematics. The resources include Powerpoints and worksheets. Powerpoint include:Learning objectivesExamples animated at each step to support explanations and independent learningImportant information written in red boxes to scaffold learning.Worksheets include examples on a word document for students to write on.Topics:Spanning TreesLinear ProgrammingDijkstra’s AlgorithmChinese Postman ProblemTravelling Salesman ProblemMatchingSortingAlgorithmsGraph Theory I hope you enjoy these lessons, where they can be used in the following ways:To deliver a course with reduced planning but not reducing quality of the lesson, as this course can be time consuming writing and preparing examples, where this resource can help.As a basis for an observation lesson to save time preparing resources.To give to students for out of lesson learning.To support teachers who are new to this topic, again to reduce planning time.

#### Decision 1 - Chapter 3 - Algorithms on Networks

Everything required to teach chapter 3. Detailed enough to teach(refresh!) the teacher too.

#### Shortest path Algorithm - Dijkstras

Powerpoints that show learners how to complete Dijkstras minimum path algorithm

#### Mathematics Decision 1 Lessons

This is a set of lessons for Decision Mathematics. The resources include Powerpoints and worksheets. Powerpoint include:Learning objectivesExamples animated at each step to support explanations and independent learningImportant information written in red boxes to scaffold learning.Worksheets include examples on a word document for students to write on.Topics:Spanning TreesLinear ProgrammingDijkstra’s AlgorithmChinese Postman ProblemTravelling Salesman ProblemMatchingSortingAlgorithmsGraph Theory I hope you enjoy these lessons, where they can be used in the following ways:To deliver a course with reduced planning but not reducing quality of the lesson, as this course can be time consuming writing and preparing examples, where this resource can help.As a basis for an observation lesson to save time preparing resources.To give to students for out of lesson learning.To support teachers who are new to this topic, again to reduce planning time.

#### Mathematics Decision 1 Lessons

This is a set of lessons for the Decision Mathematics module for A level. The resources include Powerpoints and worksheets. Powerpoint include:Learning objectivesExamples animated at each step to support explanations and independent learningImportant information written in red boxes to scaffold learning.Worksheets include examples on a word document for students to write on.Topics:Spanning TreesLinear ProgrammingDijkstra’s AlgorithmChinese Postman ProblemTravelling Salesman ProblemMatchingSortingAlgorithmsGraph Theory I hope you enjoy these lessons, where they can be used in the following ways:To deliver a course with reduced planning but not reducing quality of the lesson, as this course can be time consuming writing and preparing examples, where this resource can help.As a basis for an observation lesson to save time preparing resources.To give to students for out of lesson learning.To support teachers who are new to this topic, again to reduce planning time.

#### A Level EdExcel Decision Mathematics 1 - Notes and Worked Examples

This is a powerpoint covering all areas of Decision 1 (I realise they are only putting it in further maths from 2017). It contains brief notes by way of an explanation, model answers to questions and a question or two for the students to do; all of the questions come with answers that you can display when ready. The slide show comes with a progress grid (regularly referred to in the presentation) so that students can mark their progress from start to finish and pinpoint any areas that may need extra work with a “red/amber/green” system that they fill in. It’s what I use in my lessons before setting tasks from worksheets or text books to practice.

#### A level applied maths: Decision revison

A great resource for A level students on Decision maths. Specifically for AQA but can be used for all other exam boards as well. Provides quick, easy to understand information for the topics. Has many uses including as flashcards, posters, powerpoint presentation for revision and introduction of decision topics. A great and very helpful resource

#### Dijkstra practice questions + solutions

Discrete 1 - Decision 1 - Dijkstra's Algorithm - Shortest Path - Worksheet with seven questions to be completed on the sheet - solutions included

#### Decision powerpoints AQA + In class questions/notes

Powerpoints on upper,lower bounds, tracing algorithms and Chinese postman ideal for AQA specification.Also attached linear programming powerpoint and in class notes/lessons for whole course

#### Complete Set of Decision 1 Maths Flipcharts with resources

I created a set of flip charts, to aid with teaching of Decision 1 Mathematics, Edexcel. A lot of questions are taken from examsolutions.net. Also attached some other worksheets I created:Bin packing algorithms - cut out activityDefinitions Matching activityD1 Definitions and key points (can't remember where I got this from, or if i made it)

#### Dijkstra's Algorithm

Shortest paths including directed networks

#### Decision 1 Chapter 3 Minimum Spanning Trees

SMART notebook file guiding through Decision 1 Chapter 3 MSTs with notes and examples.Includes: Kruskal, Prim, Prim on a Matrix, Dijkstra

#### Worksheet on Dijkstra's Algorithm

With brief solutions

#### Decisions 1 Dijkstra's Algorithm powerpoint

A presentation introducing dijkstra's algorithm - the shortest path. Graph theory.

#### Decision Maths 1 - Shortest Path Algorithm

Decision Maths 1 - Shortest Path Algorithm A Powerpoint 97-2003 demo of Dijkstra’s algorithm for finding the shortest path in a network. Updated 18/02/10 to correct slight error in path order.

#### AQA Decision 1 Exam Questions by Topic Revision resource

A PowerPoint for students to navigate to revise AQA Decision 1 exam questions by topic.Designed for individual revision, can also be used in the classroom to quickly find an exam question to match the topic being taught/revised.Click to mark scheme and uncover section at a time for checking work before moving on to next part.Our students have used this extensively in the run up to their exams and really enjoy using it.Layout taken from and inspired by supergenau, but altered for AQA. exam board.

#### Dijkstra's Algorithm in Directed Networks

Exercise with brief solutions

#### Decision 1 Edexcel End of Topic Tests

These are 20 mark test sets for each topic within the Decision 1 Edexcel Maths syllabus. Students write their solutions in the boxes provided. Any feedback would be very welcome. Enjoy!Em

#### Traversability and Minimum Spanning Tree

Created from looking at the Islands around Auckland, for the pupils to see where they can sail between, and if it is a Eulerian circuit or path, or neither. Focus given to the context of the question to draw the use of the topic.

#### D1 Mathematics Lesson Mats

Lesson mat worksheets for a half terms worth of D1 lessons for Edexcel specification. Lessons cover, algorithms, graphs and networks, route inspection and matching. The sheets are designed to be printed double sided on 141% enlargement to A3 size. Designed for a further maths class, over five weeks, with additional worksheets and homework where necessary.

#### Decision 1 - Dijkstra's Algorithm (A-Level Maths)

Simple walkthrough example on Dijkstra's Algorithm for Decision 1 (A-Level Maths)Visit www.twitter.com/weteach_mathsor weteachmaths.co.ukFor more resources and schemes of work ready for the new GCSE Maths specification

#### D1 Definitions and Key Points

All the definitions and key points needed for the D1 module, for Alevel Mathematics, which follows the Edexcel Spec.

#### Shortest Paths

A simple introduction to graph theory concepts for KS3 students - what networks and paths are, how to calculate the shortest path, and the relevance of this to Computing. It would also be relevant to older students of networking, and provides a link between algorithm and network (i.e. LAN/WAN) topics. The map and one of the questions in the on-line worksheet are actually adapted from an A level Decision Maths textbook, and questions on the shortest path have also appeared recently on GCSE Maths papers.

#### Dijkstra's Algorithm - video tutorial + exercise

I am creating a website at www.mrhegartymaths.com where I upload videos to help students with their GCSE and A-Level exam revision. My videos are a mixture of exam solutions and topics taught from first principles. I am currently updating as required for the pupils I teach but over time I want to create a comprehensive collection of tutorials on the key GCSE and A-Level topics as well as occasional sets of solutions to exam past papers.

#### Decision Maths 1 - Glossary and Algorithm Summaries

This is a list of all algorithms for the D1 Maths course, along with a quick reminder of they each do and how, along with a full glossary of terms for the Edexcel module.

#### Dijkstra's Exam Questions

Exam questions (and full written solutions) for Dijkstra's algorithm.

#### Demonstration video of Prims algorithm on a matrix

A mini revision video and demonstration of how to use Prims algorithm on a matrix with practice questions. For more videos on other topics see www.mathscasts.co.uk or the YouTube link below.