Linear Programming for GCSE / Core Maths

I have always found it difficult to get across the concepts required to support Linear Programming to my weaker Higher GCSE groups and especially, more recently, my Core Mathematics groups.

There are several issues preventing the less confident mathematicians from doing well in this topic. Firstly, many students are not even confident about plotting simply straight lines such as x = 3, y = 7, x = y etc. Secondly, a lot of them have not fully understood the concept of an inequality. Thirdly, in general these students find it very difficult to convert an English sentences into mathematical statement.

I have put together this 90+ PowerPoint slide set to address these problems.
I have created interesting/funny ways to remember that x = 3 is a vertical line, whilst y = 3 is horizontal. I have included practice on plotting straight lines and shading regions represented by inequalities. I also introduce the idea of a “test point” that will allow stidents to work out which side of the line they require.

I have included practice on solving simultaneous equations using a
Casio fx-991EX CLASSWIZ calcuator, and also by manulally solving the equations. A video of how to use the Casio 991 to solve simultaneous equations in included.

Of course, the idea of an Objective Function covered, together with how to use the feasibility region to locate the required minimum/maximum value.

I focus the students on investigating points close to or at the vertices of the feasibility region. I have stayed away from moving an example objective line through the feasibility region to see which is the last vertex it goes through. This proved a bridge too far for too many of my students!

The slide set includes a lot of worked examples, and practice questions along with their solutions.

I have also uploaded a free preview PowerPoint Slideshow that contains approximately half of the slides.

I hope you find the presentation useful. Please let me know if you find any typos or if you have a suggestion as to how it can be improved.

Regards

Gerard