Revision Time 2017

That quote from Robert Collier seems so appropriate when it comes to revision. Once again, this academic year I have used the day in, day out approach even more with my students, frequently reviewing earlier work even for short sessions. I am convinced this is important in our teaching and help makes things stick for our students. – Jonathan Hall

Once again we are in the final run up to examinations, so, an annual job I have checked and made many major updates to the series of revision pages. There are two new pages, one is GCSE Questions by topic – I thought it would be useful to collect together resources which allow for revision by examination topic; the other is Chasing the highest grades?

Before mentioning the resources though we should think about how best to use them.

The first page in the series ‘Highlighting is a waste of time’ links to what I believe is a very important report on how students learn effectively; having used testing – even very short ‘self checks’ or ‘mini tests’ as they have come to be known in my classes I am convinced like the authors that this is very effective and we will be using testing in our revision classes, often short with immediate feedback so students can see if they can recall and apply information. When I asked my Year 9 students about good Maths teachers, one said:

A teacher who provides the student with the opportunity to see what they need to revise. Regular tests and quizzes do this.

On Study Strategies, note the very valuable set of resources from The Learning Scientists. See their blog for more information and note the excellent downloadable materials on study strategies including Retrieval Practice. Note the blog on meta-analysis of 217 Retrieval Practice Studies.

So before we worry about amazing revision resources we must consider how we will use them so our students learn effectively. According to research learning strategies with high utility include distributed study sessions (last minute cramming is not effective) and practice testing.

So bearing these learning strategies in mind, many of the resources found on the series of revision pages could be used as mini tests with immediate feedback or several topics mixed up within a lesson and perhaps the trickiest topics revisited several times over the last weeks, even if briefly.

The revision activities can be found on the series of revision pages:

For students, I have added the revision and examination questions to Mathematics for Students.

Resources in the collections allow for a mix it up approach but also provide questions by topic. A huge thank you to the teachers who so willingly share their resources – you are helping students everywhere. Correct attribution has been given wherever possible with the resources. All resources are free.

Wishing your students everywhere success in their examinations.

Examinations, Twitter Lists…

… can be so very useful!

For example, try this list of just the UK Examination Boards Maths teams; you don’t even need to sign up to Twitter, just follow the list for updates and resources from the exam boards.

For some samples from these tweets:

For a more general examinations list which includes more organisations associated with assessment, see this list which includes all the examination boards including WJEC, who I see also have a Question Bank tool which allows teachers of Maths, Computing, Science, Electronics, Business Studies, Food & Nutrition and Physical Education to create a paper at either Entry Level, GCE or GCSE.  I can confirm the Question Bank tool is very easy to use and works brilliantly;  I searched for GCSE Maths filtered by Algebra and Problem and created a paper with mark schemes and examiners’ comments in minutes.

The list also includes Ofqual, the Department for Education and the Chartered Institute of Educational Assessors.

WJEC Algebra problem

WJEC GCSE Algebra problem




Mathematical Miscellany #10

For any of your students studying for STEP direct them to this excellent portal from which has (all free) access to STEP questions and solutions. Create an account, login and you have access to a complete library of resources.

The resources are very clearly presented. For each question you have access to a pdf with the question, Examiners’ Report and both an Official and thanks to Peter Mitchell a fully worked handwritten solution.

Note that you can also download a copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core MathematicsAdvanced Problems in Mathematics is excellent preparation for ANY undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 43 problems. Each problem has been given a title and a rough indication of the mathematical content which means you can pick out questions by topic.

See also, from Cambridge University, their STEP Support Programme and from Nrich, Prepare for University.

These details are also available on Mathematics for Students.

On the subject of challenging questions for older students and with revision on our minds, perhaps a good time to remind everyone of the excellent MadAsMaths site.

MadAsMaths mark scheme example

The AQA Mathematics AS and A Level specifciations have now been accredited. Watch the AQA website for further resources on the new specification. Checking Teaching Resources we see that AQA are developing their route maps; I have always found the GCSE route maps very helpful indeed.

AQA Route Map

Something I have used a great deal with my GCSE teaching for both the current and previous specifications is AQA’s detailed and very clear teaching guidance.

AQA Teaching Guidance

An A Level Teaching Guidance extract is available.

We can also see Command Words which reminds me a little of the Exam Terminology document so useful at GCSE. There seem to be versions of this document in various places, I believe the first time I used it was back in the days when there were more Examination Boards, this may well have come from the then Southern Examining Group!

Under Assessment resources we find Specimen Papers and mark schemes; also an Assessment Guide on using a large data set. On the subject of large data sets, for information on all the Examination Boards and large data sets, read Bruce Hampton’s clear and detailed comparison.

Royal Statistical Society Problem Solving

Eduqas will not be offering AS / A Level Mathematics specifications, but note their Level 3 Statistical Problem Solving Using Software. See also  the International Centre for Statistical Education (ICSE) with Plymouth University and you can follow @IntCSE on Twitter. It may be that some of the resources here will be useful for our teaching of Statistics.

Educas state: “The objective of this qualification is to assist the understanding of the problem-solving cycle of planning, collecting, processing and discussing in meaningful contexts and to use statistical software to process real data sets. It has been specifically designed to be taught in schools and colleges to equip learners aged 16-19 with a broad range of skills empowering them to successfully negotiate statistical problems in Higher Education or the world of work.”

Staying with the subject of Statistics AQA and Edexcel have accredited GCSE specifications; note that coursework is no longer a requirement of GCSE Statistics.

Women In Mathematics

March 8th 2017 is International Women’s Day.
We’ll start with an image I shared this time last year that I think still says it all! Thank you Steve Lomax who shared this wonderful response to the task ‘Describe a mathematician’ from Mansfield Green E-ACT Academy.


Describing a mathematician – Mansfield Green E-ACT Academy

Some useful references on women in Mathematics:

And for some History





Examination Resources

With changes to examinations at both GCSE (UK examination taken at age 16) and A Level (UK examination taken at age 18) all the examination boards are offering help and support for teachers and students. Many excellent resources are available with several published very recently.

For example we have Edexcel’s very helpful resources for teaching new content. For each topic, information, examples and exercises (with answers) are given.





Edexcel – New Content Resources

More helpful Edexcel resources include the Exemplification of the New Sample Assessment Materials and the Topic Tests, note the Show More button which will take you to more resources including for example posters of formulae that students need to know.

From AQA and OCR too we have many excellent resources to support the teaching of the new specifications. Given so many new and useful resources I have separated the UK Assessment pages further and now have pages for AQA, Edexcel and OCR. Whichever board you are using it is well worth while looking at resources from all the boards, the specifications are all based on this content.

I have also been updating (this is a work in progress) the A Level pages, noteable additions to the A Level documentation are Interactive schemes of work from Edexcel and OCR MEI. From MEI – look at this excellent scheme of work for the new specification. Each of the 43 units is based on a topic and includes a commentary of the underlying mathematics, a sample resource, a use of technology, links with other topics, common errors, opportunities for proof and  questions to promote mathematical thinking. The schemes of work is freely available. And from Edexcel for each unit of work you will find Specification References, Prior Knowledge including GCSE Specification References and Key Words. For each sub-unit you will find Objectives, Teaching Points, Opportunities for Reasoning / Problem Solving, Common Misconceptions / Examiner Report Quotes.

MEI Interactive Scheme of Work

MEI Interactive Scheme of Work

Note also the addition of a Use of Technology page.

MEI on Integrating Technology

MEI on Integrating Technology

Mathematical Miscellany #9

Now on the outstanding Diagnostic Quesions site – United Kingdom Mathematics Trust Quizzes – choose a theme or a quiz with random topics. To use the resources will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.” (See this post for Diagnostic Examination Questions).

aqa-ao3From AQA, on their ‘All About Maths‘ site see their Further Guidance and Practice Questions for the AO2 and AO3 requirements of the new 8300 GCSE. The 120 questions in this resource have been selected from legacy specifications which, to quote AQA “exemplify each of the strands of these Assessment Objectives and would therefore be suitable questions for the new GCSE as well.” AQA have arranged the questions in approximate order of difficulty andhave also divided them into those suitable for Foundation tier only, common to both tiers, and those suitable for Higher tier only, as well as by Assessment Objective. To

Remember fAQA 90 Problemsrom AQA we also have the excellent, GCSE Mathsematics: 90 maths problem  solving questions. These problems have been designed for use in supporting the teaching and learning of mathematics. There is a helpful intruductory section for teachers and note also the helpful Classification Tables by Strategy and by Content Area. Em,  has a brilliant PowerPoint with all the questions and answers – see it here.


Staying with problem solving, on TES Resources cchristian’s Multi-Stage Problem Solving is an excellent resource. These problems could make great starter activities.

Also, remember the GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team, @WRMathsHub available on TES Resources.

White Rose Maths Hub problems

The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning now includes Year 7 material (UK age 11-12); an assessment is also available.

scooby-mysteryFrom author Captain Loui a TES resource, BIDMAS – Solve a Scooby Doo Mystery! Note that answers are provided in the author’s description of the resource. The theme is engaging but doesn’t get in the way of doing plenty of Mathematics!  Captain Loui’s resources are all free to use and as you can see have very favourable reviews.

Splat - Steve Wyborney

Splat – Steve Wyborney

A resource that caught my eye recently is Steve Wyborney’s Splat! Definitely a resource I wnt to explore further; you can read Steve’s blog post and download the lessons here.

Thursday 2nd March is World Book Day; we could bring books and Mathematics together with some Statistics (at any time); have a look at this resource from TES, World Book Day Maths Data Investigation where students analyse word length and sentence length in some book extracts. UK readers who remember Statistics coursework, this brings back memories of AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability. Note too the launch of a new website, is an international research-based initiative which sets out to explore various aspects of integrating stories reading and writing in mathematics instruction.

AQA - Read All About It

AQA – Read All About It

The extension task for the TES resource above considers the reading age of a text, you may wish to consider further readability formulae; if you paste some text to this site, Readability Formulas you can easily check statistics for your chosen text and generate a reading age according to the various tests.

WolframAlpha can be used for Words and Linguistics, note the various examples given, including number names.and document length.

Analyze My Writing

Alternatively, try Analyze My Writing. Simply paste in some text for a comprehensive analysis including basic statistics, word and sentence length and readability. It is also possible to create Cloze tests.  You can read more about this resource on Richard Byrne’s always impressive “Free Technology for Teachers”.

It seems appropriate to check some world records on books!

On the subject of books see the free books information and note in particular Colin Foster’s Instant Maths Ideas – lots of ideas you can try in the classroom.

View more posts in the Mathematical Miscellany Category.


Functions – an update


I have updated a post on functions with the excellent PhET simulation, Function Builder

The post includes several excellent resources for teaching functions. See also this further post aimed at older students.

PhET Simulations look excellent, I will be exploring more of these. I have used the Projectiles Simulation with Mechanics A Level students and have posted on this for students on Mathematics for Students. There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for iOS also for Android.

PhET Balancing Act working nicely on my phone!


Learning & Teaching GCSE Mathematics

Following my post, Learning Mathematicsthe following is the slide set used for the Learning & Teaching GCSE Mathematics session at the  excellent Somerset Professional Development Proramme February 2017.

Lots of pages, but if you are interested then the best way to view is via these files:
Learning & Teaching GCSE Mathematics PowerPoint and Learning & Teaching GCSE Mathematics for the pdf file. The pdf version seems much faster to operate if you wish to use all the embedded hyperlinks to the various resources. Note the table of contents which allows for navigation through the various pages.

On Slideshare – you can see the slides – hyperlinks will lead you to all the resources but for slide to slide navgation use the files above.

There have been several updates since this was first published, including:

  • Easier navigation via the Contents page
  • Additional resources, note the oustanding Diagnostic Questions with all its examination questions also the ability to assign your students to one of the streams so they will receive just two questions a day in the run up to the exams. The Insights provided are so valuable. Edexcel have like AQA provided some great Topic Tests. For further very helpful Edexcel Resources see the Edexcel GCSE page.
  • A reminder of some of the many very useful revision resources including this post for students. (Something I will update further over shortly).

Mathsbot – Revision Grid


For Valentine’s Day…Make Linked Möbius Hearts

The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  We even have 9 Maths skills you need to win the Great British Bake Off!

careers-heartsFor Valentine’s Day, have a look at this post from Maths Careers with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked  as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
use-to-create-mobius-heartsNote the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper. See Valentine’s Day for the Desmos details.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white spce at the end – the picture here has been made using strips 10 cells long.

Learning Mathematics


I was delighted to be part of the excellent Somerset Professional Development Progamme February 2017.

I can confirm that Simon Singh was inspirational. His presentation slides are available for teachers to use – all that wonderful Mathematics in both The Simpsons and Futurama. In an earlier post here where Simon Singh spoke on Mathematics Teaching, you will find the link to his presentation.

My own sessions were (1) on all the wonderful resources availabe for Mathematics but with an eye on the learning first and (2) on the new GCSE Mathematics Specifcation.

Firstly, Learning Mathematics – lots of pages, but if you are interested then the best way to view is via these files:
learning-mathematics PowerPoint and learning-mathematics-pdf. The pdf version seems much faster to operate if you wish to use all the embedded hyperlinks to the various resources. Note the table of contents which allows for navigation through the various pages.

My GCSE Mathematics presentation will follow in the next few days.

On Slideshare – you can see the slides – hyperlinks will lead you to all the resources but for slide to slide navgation use the files above.