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. It is likely that I will reorganise this as the collection has grown rather, but all links will still work, the main page will simply become a resource index page for easier navigation. The series is 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!

Advanced Level Mathematics

The new UK A Level Mathematics specifications require students to demonstrate overarching knowledge and skills specified as follows:

Overarching Themes:

  • OT1 Mathematical argument, language and proof
  • OT2 Mathematical problem solving
  • OT3 Mathematical modelling

Also required, we have the use of technology and the use of data in statistics.
These links are for pages in the A Level Reform series where information and resources are added and updated regularly. There have been several updates recently and this will be an ongoing project. I am very much looking forward to teaching the new specifications in both Mathematics and Further Mathematics.
A Level Reform Index

Note that all A level specifications are accredited and for Further Maths most specifications are now accredited.

MEI Postcards

MEI’s pstcards illustrate these principles very clearly. Note that solutions are also provided for each postcard with further suggestions. The Large Data Set postcard for example links to the data used. Looking at the Technology and Modelling postcards, we can of course use Technology! I thought I’d have a play with Desmos!
MEI postcard technology

I also had a look at the Modelling problem on Desmos.


Malcolm Swan

Professor Malcolm Swan, a legend in Mathematics Education died in April 2017 at the age of 64. Today, Tuesday 23rd May, the day of his funeral has been designated Malcolm Swan Day. Mathematics Teachers are acknowledging his work by using his materials in as many lessons as possible and tweeting pictures and examples using the hashtag #malcolmswanday.

MEI have dedicated their monthly magazine M4 to Professor Malcolm Swan. The magazine includes articles describing a particular item connected with Malcolm Swan explaining how that item an impact or influence on the writer’s own thinking or development as a practitioner. Note Carol Knight’s classroom resource in the magazine; some excellent ideas. I think I’ll start Year 9 today with the bus stop queue. As you can see Bus Stop Queuefrom MEI, this is taken from the Language of Functions and Graphs which you can download free from STEM Learning. Both the book and masters for copying are available.

I was fortunate to meet and talk to Malcolm Swan at an event for Maths teachers at Greenwich University some years ago. Having discussed a problem he had spoken about, always cautious about making sure it is permissable to store and share resources I asked him if it would be OK to upload his wonderful Improving learning in mathematics: challenges and strategies to my own blog. He said – “of course”. I think this should be compulsory reading for all Maths teachers. It is certainly something I have often referred back to.

My own favourites include the brilliant Standards Unit Resources. This is available from many sources, my go to source is appropriately I think from The University of Nottingham.
Home page

With all my examination classes on Study Leave I don’t have many lessons today but I do have Year 9. After we have started with the Bus Stop Queue which is a good choice having seen one or two misconceptions in a recent school examination I want to do some Algebra. Mostly Algebra has several resources which work very well indeed and I have used many times. Today I think we’ll have a little Number Magic! Note the html resources too, the Number Magic pyramid for example.

More later when Year 9 have tried this.


Bridging the Gap – Student Guide

From OCR, a marvelous teaching and learning resource:
Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide (scroll right down OCR’s page to Teaching and Learning Resources).

I love this resource, the very first example made me smile; I have been teaching for a long time and I think I have been saying this to so many students all that time!

OCR guide eg 1

OCR Student Guide – Bridging the Gap

With sections on Algebra, Trigonometry and graphs including examples, question practice on key topics and suggested reading before starting the A Level this will be so valuble for students.

OCR Student Guide

OCR Student Guide – Bridging the Gap

Thank you OCR for making this available as a Word document, I rather like the look of some of these examples for my excellent GCSE students who are studying both Maths and AQA’s excellent Further Maths Level 2 qualification. I feel an edited version coming on!

The A Level pages have much useful information and I will be developing these further over the coming months. This resource has been added to the A Level Resources page, also to the OCR page.

This is quite simply an outstanding resource for students (and their teachers!). Many exercises are provided and the answers are all at the back. OCR have very helpfully provided the document as a Word document.

OCR Student Guide GCSE to AS & A Level

OCR T&L Resources

Mathematical Miscellany #13

TES Resources
From TES, comes a collection of esources hand-picked by the Tes Maths Panel, organised by topic area and selected for their relevance to the new specifications. This is an extensive collection of quality resources. Checking Probability for exmple we see an excellent selection of free resources, including Venn Diagrams for teaching and learning.
Venn Diagrams TES
This Venn Diagrams post with many resources for teaching this topic has been updated to include the TES collection.

Another update to the Venn Diagrams collection comes from Transum.

Venn Totals Transum


Try Venn Totals 4 different levels of exercises which can all be checked are available. Level 1 – Reading information from a Venn diagram containing two intersecting sets. Level 2 – Reading information from a Venn diagram containing three intersecting sets. Level 3 – Adding information to a Venn diagram containing three intersecting sets. Level 4 – Adding information to a Venn diagram containing three intersecting sets with some problem solving required. There are also exam style questions, to see the worked solutions a subscription is required.

I have written on Transum before, with its very clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning the site is very easy to navigate. The resources are very clear and attractively presented, they display well for demonstration in class as well as being very good for self study for students.
Look at this series on Transformations for example:
Level 5 is on transformations and matrices, very useful for older students studying Level 2 or A Level Further Maths.

This GCSE Exam Preparation resource from JustMaths made me smile, a lovely mix of humour and some very useful reminders.

Mel’s inspiration came from Edexcel’s Maths Emporium Guides to Life: GCSE Mathematics Examinations. Brilliant!
Edexcel GCSE Maths Guide to Life

On the subject of student advice, one of my Year 11 students asked me to confirm for her which transformations are examined at GCSE, a slight change here from the old spec hence her question. I answered her question with a post on Mathematics for Students as I thought it would be useful for others. Transformations of graphs includes Desmos pages for reflections and translations as required at GCSE (see GCSE content on Algebra:

13.sketch translations and reflections of a given function.

The post also includes a couple of examples on finding the equation of the transformed graph.

Another query was just a quick reminder on the required constructions.
bisect angle Math Open Ref

A reminder from Mathematical Miscellany #12, I am very much looking forward to trying Jamie Frost’s wonderful homework site with my Year 9 group.

And finally another reminder because I think it is such an important resource – just in case you missed the news that Underground Maths are helping teachers everywhere who are preparing for the new A Level. Many brilliant resources suggestions are clearly mapped to the subject content for the new A Level.





Underground Maths: Prepare for the new A Level

This will be so helpful for our preparation for the new A Level, I particularly like the Resource suggestions.

For each content statement, Underground Maths have suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.

These of course are suggestions. There are so many outstanding resources on Underground Maths. In our department, like many others I am sure we will be exploring the resources and bookmarking our own favourites.

I have a series of pages on Underground Mathematics. This is a work in progress and I will be adding more content over the coming weeks. Some of my many favourites are on these pages…

Follow Underground Mathematics on Twitter or Facebook.
Note there is also a closed Facebook Group for teachers. We’d love to hear which Underground Maths resources you’ve been using, share your thoughts, ask questions or show your students work for discussion.

Mathematical Miscellany #12

On his outstanding website full of very high quality resources, drfrostmaths.com, Jamie Frost has now launched his new Homework Site.

Completely free this does a lot! Practise questions on National Curriculum and enrichment topics, choosing questions by topic and by diffculty, perhaps choose UKMT Maths Challenge questions as these are in the extensive database too. Students can practise independently and earn points and trophies. Teachers can set and monitor work using the powerful Data Analytic Feature. I will certainly be trying this with my students and easily uploaded my Year 9 class which took moments.

Something I alway do is add myself to my classes so I can get the student view, Colleen Student is a very busy student – she’s in a lot of classes! Jamie Frost has this as an easy feature already provided; you can be Demo McDemoFace (love the name!) in any class.

So here’s Demo McDemoFace practising her Algebra!


What a sophisticated way to choose questions, not just the subject but the difficulty as well and additional skills to include or exclude.

So I can confirm that it is very easy to use as a student, Demo McDemoFace did a bit of Algebra and earned a trophy!

The interface for entering solutions is intuitive and very easy to use,


Explore this site and sign up your students. Thank you Dr Frost from teachers everywhere! This looks superb. More to follow on this.

MEI have published this video (18 minutes) to introduce features of the new MEI AS/A level Maths specs, explaining the decisions made and how they support good teaching, learning and assessment. MEI’s YouTube Channel includes this and other helpful videos. This is helpful in its discussion of the new requirements for Statistics

On the subject of new A Level Specifications I am working on the series of pages on  A Level Reform. There have been several updates recently, a work in progress, there is much to do here and I am very much looking forward to working with the new specification. Using for example Desmos is something I do all the time anyway so I am delighted that the new specifications require the Use of Technology. Quite right too to assess the Use of Data in Statistics and the use of large data sets. MEI discuss their use of Data in the video above.

For schools who use AQA’s excellent Level 2 Further Mathematics Qualification, news from AQA states that this qualification has been extended and will be available for all students in 2019. AQA’s intention is “to redevelop it for first assessment in 2020 to ensure that it still fulfils its stated purpose of filling the gap between GCSE Maths and further studies in Maths at Level 3.”

My Year 11s this year have been studying both AQA’s GCSE 9-1 course and the Level 2 Further Maths; these have made a wonderful complementary pair. Many of the Further Mathematics questions have provided additional practice for the standard GCSE course. The extension will allow us some breathing space to keep working on the new GCSE course and take on the new A level specifications.

And finally..
This has been doing the rounds recently and illustrates beautifully that caution is required in our statistical analysis! Be a little wary of summary statistics! From AUTODESK Research, “Same Stats, Different Graphs… Note that you can download a detailed paper by Justin Matejka and George Fitzmaurice of Autodesk Research.