Learning & Teaching A Level (Post 16) Mathematics

IndexI have made several updates to every page in the A Level series of pages recently. The A Level Resources page has had many new additions. I am currently reorganising this as the collection has grown rather and I wish to add more resources and commentary, but all links will still work, the main page will simply become a resource index page for easier navigation. The series is very much a work in progress, I will continue to develop these as I teach both A Level Maths and Further Maths next year.

All three examination boards are developing really helpful resources to support teachers in delivering the new specifications. For A Level Mathematics, like GCSE we now have common content which means that it is well worth exploring resources from all the examination boards, something I have been doing for the new GCSE specification.

For some images to ilustrate these resources, see the Slides here. A summary slide has been included to aid navigation. You can view the slides on slideshare but as slide to slide links do not work on slideshare you may wish to download the PowerPoint file or the pdf version for easier navigation.

For Maths Conference 10 delegates, these are the slides used in my presentation on 24th June 2017. I have added a small number of slides which I hope aid navigation and help you find A Level resources on this blog. It was lovely to meet and talk to so many enthusiastic and dedicated teachers. Please do not hesitate to get in touch using the comment facility here or drop me an email.


A Level – Free MEI samples

Looking at the samples for MEI’s Integral resources we see several outstanding resources for the new specification; these should give you some good ideas on high quality teaching resources. Note also the free resources for teaching the 2017 specifications where you will find a lovely collection. These can be used with MEI’s with MEI’s scheme of work which can be used with any of the 2017 A level specifications.

You can sample resources here for AS Mathematics. These samples are for four topics including Problem Solving. The level 1 exercise may well give you ideas for Higher abaility GCSE students.

MEI Sample Problems Level 1 Exercise

Note that schools and colleges can register with the Further Maths Support Network which has many benefits including a free single-user teacher access account to extensive online resources to support the teaching and learning of Further Mathematics, and also enrichment materials for A level and GCSE mathematics students; access to all the Large Data Set materials will be available free. You can find the correct form here, Note that the form makes the terms and conditions very clear: the resources can be used to support teaching and learning within your mathematics department, including displaying resources to students and distributing hard copies of formative assessments to students. They cannot however be made available to students by any other means, a VLE for example.

MEI Exponential FunctionsLooking at Integral Maths on Twitter, (you do not need a Twitter account to access this link) we see that for subscribers to Integral, Summary Sheets for the new A Level Specification will be provided. Summaries like this used at intervals throughout a linear course will provide very useful reviews of previous learning for students. A very useful free sample is provided on Exponentials and Logarithms. Looking at this document, we see a 5 page very clear summary of what students need to know. I do like this explanation, it is exactly what I find useful to say to students: “What power do I need to raise the base to….?”

MEI Exponential Functions 2

For a further taste of these summaries, see these extracts from Graphs and Transformations and Coordinate Geometry.
Graphs & Transformations

Coordiante Geometry

SumazeAlso from MEI, some free apps including a free resource to help your students make the Transition to post GCSE work, try Bridge It!, a quiz game. Note that Bridge It! will only run on devices with a Flash player. This version is best played on a laptop or desktop computer using a mouse or finger pad. Sumaze! and Sumaze! 2, puzzle games are available on IoS and Android. And watch this space as more free apps are on the way!
Bridge It



Mathematical Miscellany #14

Years 7 and 8 (UK ages 11-12 and 12-13) Summer Assessments

WR 7 & 8 Assesments

From the White Rose Maths Hub, (@WRMathsHub on Twitter) Year 7 and 8 Summer assessments.  I have mentioned the White Rose team before, recall their excellent Problem Solving resource.White Rose Maths Hub problems

The GCSE Problem Solving Questions of the Day – Compilation  available free on TES Resources. The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided.

GeoBoard Activities
Answering a question from a reader on unique triangles on a 4×4 GeoBoard, I have updated GeoBoard Activities to include the solution to this and also added several new activities, including the use of GeoGebra.
GeoGebra GeoBoardGeoGebra isometric dot paper

Staying with the subject of GeoGebra, I discovered some very nice resources by Tom Carpenter,  I do like his Line Graph worksheet which demonstrate how to draw a line graph and/or how to interpret a line graph.
Line Graph, Tom Carpenter
As I mentioned in last week’s post on GeoGebra, even if you are not familiar with GeoGebra, there are so many resources already available ready to use.

I have mentioned the excellent PhET simulations before. This on Least Squares Regression provides a very easy to use demonstration. Try and find the line of best fit then see how closely your line matches the actual line.
PhET Residuals
On this subject you can also very easily use GeoGebra, Desmos, or WolframAlpha for regression, full details with examples are provided here.
GeoGebra Regression

See more posts in the Mathematical Miscellany series. Collections of mathematical goodies!



GeoGebra is astonishingly powerful and seems to keep just getting better. It works brilliantly on my phone and my tablet as well as on a desktop. I will be using it a great deal more in future with all the students I teach.

Time for some new pages on GeoGebra, this collection will grow, but I wanted to bookmark the tutorials and note also how to very simply use the Data Analysis tools. Sophisticated analysis is possible of course but in moments one can copy data from a spreadsheet application to GeoGebra’s spreadsheet view and see some charts.

GeoGebraThese Tutorials are an excellent place to start learning how to use GeoGebra. GeoGebra works not only on desktops but on phones and tablets as well.

The Manual is comprehensive and note the Quick Start tutorials which are very clear. You will also find manuals and much helpful documentation on the same page. The great thing about GeoGebra is that so much has already been written you can probably find what you need already online!

You can also use GeoGebra’s YouTube channel to watch demonstrations.

GeoGeoGebra is not just for Geometry, as mentioned above note how good it is for Statistics too, copy in those large data sets and get analysing! (GeoGebra Data Analysis as a pdf file or  PowerPoint: GeoGebra Data Analysis.)

The slides show the Classic application first which perhaps experienced users are most familiar with, followed by the newer Maths Calculators interface. If you are new to GeoGebra I would recommend using the Calculators which of course have the same functionality and more and will give consistency across the various platforms.
GeoGebra classic & Maths Calculators

So much is already written for GeoGebra you can use material already written. For example thinking try MEI’s very helpful advice on the Use of Technology, also on Integrating Technology into schemes of work for older students (UK A Level  age16-18). Note that tasks are also given by type of software including GeoGebra.
MEI Tasks AS

Another source where you will find GeoGebra used to help students understand and explore Mathematics is Underground Maths where many tasks have associated GeoGebra resources. An Underground Mathematics search on GeoGebra reveals the extent to which it has been made use of!

Note also some excellent examples from the ATM Conference 2017.

See also Use of Technology and Statistics in the A Level series of pages.

I would like to thank MEI for an inspirational (and free) conference recently. So many good sessions including the use of GeoGebra for statistical analysis.  A highlight had to be looking at the GeoGebra 3D graphics view with our 3D glasses!