Decision Mathematics – Teaching Resources

Linear Programming Grapher

Trying to make things easy to find, I have added two new pages to the Further Mathematics series. This series can be found on the A Level (16+) Tab.

AQAEdexcelOCR AMEI (OCR B)
GraphsDecision Mathematics 1Mathematical PreliminariesAlgorithms
NetworksAlgorithms and Graph TheoryGraphs and NetworksNetworks
Network FlowsAlgorithms on GraphsAlgorithmsNetworks and graphs
Linear ProgrammingCritical Path AnalysisNetwork AlgorithmsNetwork Flows
Critical Path AnalysisLinear ProgrammingDecision Making in Project ManagementCritical path analysis
Game theory for zero-sum gamesDecision Mathematics 2Graphical Linear ProgrammingSolving network problems using technology
Binary OperationsTransportation ProblemsThe Simplex AlgorithmLinear Programming
Allocation (assignment) problems Game TheoryThe Simplex Algorithm
Flows in networks
Dynamic Programming
Game Theory
Recurrence relations
Decision Analysis
Decision Mathematics Subject Content
Teaching Resources – GeoGebra Resource from the OR Society

Decision Mathematics

The A Level course material from CIMT includes chapters on Discrete Mathematics. I have always found these a useful source of examples, several of which I have successfully used in class.

Each chapter includes very clear worked examples and exercises. Answers are included.


MathedUp – Mohammed Ladak

On Mohammed Ladak’s ‘MathedUp’ see his A Level Further Maths Takeaway, a wonderful source of exam questions by topic with mark schemes including very useful legacy AQA questions on Decision Maths.

MathedUp Challenges

OCR A and OCR B resources include their excellent Check In Tests, full worked solutions are provided. 10 varied questions are provided in each test covering AS and A Level and full worked solutions are provided.

OCRA – Linear Programming Check In Test

AQA Topic Test Map extract – A Level Further Maths

A set of really useful Topic Tests are available for both Maths and Further Maths A Levels from AQA. I like the index provided by the mapping documents, one for Maths and one for Further Maths. For each test there is a clear statement of what is assessed in the test which comprises two sections. The questions in section A test basics of the topic and those in section B require a bit more thinking. Mark schemes are provided for all tests.
(How to get access to AQA’s free portal – All About Maths).


Transum Mathematics – Linear Programming

Susan Whitehouse – Discrete resources

From Susan Whitehouse you will find will find a whole collection of Discrete resources as part of her resource collection. I do like her Multiple Choice resource with solutions in her Discrete / Revision and Tests section.


A page in the Further Mathematics series has several resources for Linear Programming. Note the excellent resources on Finite Mathematics from Stefan Waner and Steven R. Costenoble. There is a great deal to explore on this site, look at the tabs at the top, we see that Topic Summaries are available.

Linear Programming Grapher

From Pearson, these GeoGebra resources are designed to be used in conjunction with exercises from Edexcel’s Decision Mathematics textbooks.

The Pearson Edexcel A Level Further Mathematics specification includes two Decision Mathematics Options, Decision Mathematics 1 and Decision Mathematics 2. The specification starts on page 38 of the specification document and usefully includes glossaries for each paper.


Edexcel – Mathematics in Context

Preparing solutions I often use colour and highlighting in my explanations where I think this helps clarity. The following slideshow demonstrates the solution to a question on Dijkstra’s algorithm for finding shortest paths in network. I have changed colour once a new vertex has been chosen.

In case the Powerpoint is useful I have uploaded it here also: Dijkstra’s Algorithm – Colleen Young


A further source of resources can be found by looking at Core Maths qualifications. Looking at AQA’s Certificate Level 3 Mathematical Studies, we see from the specification that one of the optional papers is on Critical Path and Risk Analysis and I see Linear Programming on Pearson Edexcel’s Mathematics in Context (Level 3 Core Maths) qualification. See for example Edexcel’s practice questions. On STEM Learning check the Nuffield Mathematics resources where resources are recommended for each qualifications. amsp have a useful set of links to resources for Core Mathematics.


OR Society Resources

The Operational Research Society has a section on Teaching Resources, including some OR games which can be found on TES. A good excuse to play with some Lego perhaps!

…and a rather good GeoGebra resource to illustrate the optimum solution. I like the way you can drag the objective function.


To finish on a light note, teachers of Decision Mathematics will be familiar with sorting algorithms which put elements in a list in order. A bubble sort is a sorting algorithm that works by working through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until no further swaps are necessary, the elements are then all in order having ‘bubbled’ to their correct positions.

Check Nathan Yau’s Flowing Data blog where he has embedded this video created by Sapientia University in Romania showing a bubble sort illustrated by a Hungarian folk dance.

For further dancing of sorting algorithms see this YouTube channel.

Teaching sorting algorithms will never be quite the same again! If you look at the comments on Nathan’s blog some users have spotted errors but it certainly illustrates the comparison of adjacent pairs very well indeed.

And a little Dancing with Desmos!

Colourful Mathematics

DijkstraMy Year 12 students have just completed a Decision Mathematics mock examination. Preparing solutions to questions causing the most problems made me realise how often I use colour and highlighting in my explanations where I think this helps clarity. The following slideshow demonstrates the solution to a question on Dijkstra’s algorithm for finding shortest paths in network. I have changed colour once a new vertex has been chosen.

In case the Powerpoint is useful I have uploaded it here also: Dijkstra’s Algorithm – Colleen Young

See also Colour in Mathematics a presentation with examples showing how colour can help to make explanations clearer. I have many examples I have used for students of all ages, particularly in Algebra.

Dancing the Bubble Sort

Teachers of Decision Mathematics will be familiar with sorting algorithms which put elements in a list in order. A bubble sort is a sorting algorithm that works by working through the list to be sorted, comparing each pair of adjacent items and swapping them if they are in the wrong order. The pass through the list is repeated until no further swaps are necessary, the elements are then all in order having ‘bubbled’ to their correct positions.

Check Nathan Yau’s Flowing Data blog where he has embedded this video created by Sapientia University in Romania showing a bubble sort illustrated by a Hungarian folk dance.

For further dancing of sorting algorithms see this YouTube channel.

Teaching sorting algorithms will never be quite the same again! If you look at the comments on Nathan’s blog some users have spotted errors but it certainly illustrates the comparison of adjacent pairs very well indeed.

And a little Dancing with Desmos!

Decision Maths Tools

There are a variety of free tools available, for example this Graph Creator from the Illuminations site includes the facility to explore Hamiltonian cycles.

For the Simplex method this tool is very easy to use. Selecting Example then Solve shows how to use the applet.

A Linear Programming Grapher is available from the same site.
Alternatively use the excellent Desmos graphing calculator which shows inequalities very clearly.

This applet allows you to enter a network and then find the shortest path using Dijkstra’s Algorithm.
Firstly click to draw the nodes, once all the nodes are in place use the drop down menu on the left to draw the arcs.
The documentation at the top desctribes each function.

To see some Kruskal examples try ‘Step Solve’ on this applet and similarly for Prim.

On a lighter note – some Decision Maths Dancing!