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 marvellous teaching and learning resource:
Bridging the gap between GCSE and AS/A Level Mathematics – A Student Guide (scroll right down OCR’s page to the Teacher Guides). Or for a more direct link, use this page. Or this should link straight to the file!

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 valuable 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

Mathematical Miscellany #13

TES Resources
From TES, comes a collection of resources 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 example 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.