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 ProgrammingSusan 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.
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.
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.
CheckNathan 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.
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.
My 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.
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.
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.
CheckNathan 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.
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.
My 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.