Mathematical Miscellany #19

A series of resource updates this week…

Edexcel Codebreaker

Edexcel Worksheets – Codebreaker from @Just_Maths

The Problems and Activites series of pages, still a work in progress in the never-ending quest to make things easier to find, has had several updates, including a new page dedicated to the many excellent teaching resources from the Examination Boards. All the examination boards have excellent teaching resources.

The Problems and Activities Links page is just that, a simple list with brief descriptions. Further detail of resources can be found on the Problems and Activities Resources page. Further resources will be added in the coming weeks.

A new addition to the Examination Board resources is the result of the collaboration between MEI and the Institution of Engineering and Technology (IET); a set of maths resources.  This set of 20 KS4 activities have been created, aiming to:

  • address a range of GCSE Mathematics content
  • promote the development of reasoning and problem solving skills
  • make connections with engineering contexts and/or settings
  • promote student discussion and communication

MEI – IET Project Resources


Updates are regularly made to the 16+ Resources series of pages where you can find excellent teaching resources for this age group.

AQA has recently published a particularly valuable document, a commentary on their specimen papers, in which Dan Rogan, Chair of Examiners, explains how the specimen papers were created and how mark schemes will be applied.

AQA AS example

Note the new and very clear mark schemes which include a typical solution on the right-hand side. These will be very helpful for students. The document all includes information on how the use of calculators will be assessed.

AQA Mark Scheme example

The AQA page on specifications has been updated accordingly.

Venn Activity Craig Barton

Maths Venns – Craig Barton

Checking the tweets from Maths Conference 14, held in Kettering, note that Craig Barton has created a website SSDD Problems – Same Surface, Different Deep Structure maths problems. Read more on the website and you could get involved. Craig has created another new website Maths Venns; I have mentioned his excellent Venn activities before, they now have a dedicated website.


Mathematical Miscellany #18

crashMATHS has some very useful free resources for GCSE and A Level; the site is under development but you will find plenty of useful resources already. Checking for some additional resources on Completing the square for my Year 10 students I came across a GCSE worksheet from crashMaths; this has a good variety of questions including questions to stretch your students aiming at the highest grades. The worksheet solutions are noted as coming soon. For a topic such as completing the square, this is an ideal time to use technology to check our work. Any of Desmos, GeoGebra and WolframAlpha could be used. (Select for Desmos page.)
Completing the Square

crashMATHS AQA styleStaying with crashMATHS, note the A Level Practice Papers and mark schemes, this looks like a very valuable resource. There are several papers and mark schemes available with more coming. Versions are provided for AQA and Edexcel, these use the style of papers we see from the exam boards. Currently, there is nothing for OCR. For Mathematics the content is the same for all the boards and for Further Mathematics we have a prescribed core which must comprise approximately 50% of its content. This common content as we have with GCSE is very useful indeed as we can use resources from all the examination boards.

Continuing with an A Level theme we have a very interesting read, published 25th January 2018, “An evaluation of the item difficulty in AS and A level maths“. This compares the difficulty of items in sample AS and A level maths assessment materials from 2016 and 2017 with the A Level papers from 2015. The overall objective of the exercise was to compare the profile of item difficulty within the SAMs with that of the corresponding 2015 assessments, a question I believe is on the minds of Maths teachers!

SAMS & Legacy A Level comparison

Ofqual: Expected item difficulty Legacy & Reformed Specs



Clearly, we can look at the specimen materials ourselves and make our own judgement on the difficulty but this seems a robust study which used Comparative Judgement. This is a technique where each reviewer reviews many pairs of items and decides each time which item is more difficult to answer.

Items from the sample assessment materials submitted for 4 specifications,  AQA, MEI, OCR and Pearson were used.

The study shows slightly higher levels of expected difficulty for items from the sample assessments relative to the 2015 assessments but the increase in difficulty is small.  The paper states that ‘Such small differences can easily be accommodated by the setting of grade boundaries at awarding. The choice of specifications to teach should be based more on content and style as there is little appreciable difference in difficulty.’

For further reading on Comparative Judgement, look at the work of Daisy Christodoulou.


If you have not yet signed up for the new home of Edexcel’s Maths Emporium then do so! This is such a valuable resource. Latest additions include some great new GCSE maths practice papers. There is a wonderful set of practice papers by topic. Look first at GCSE Mathematics, then choose Cabinet 11 for the current specification. Under Practice Papers you will find the themed set – brilliant!
Emporium Resource

NCETM Secondary Assessment MaterialsTo finish this collection, from NCETM look at their Secondary Assessment materials which have been written to support teachers in making judgements on the degree to which pupils have mastered various components of the KS3 mathematics curriculum. This follows the primary Mastery Materials, which was published in 2015.

See further posts in the Mathematical Miscellany Series.

Mathematical Miscellany #17

Some updates to various pages this week…

In the reading series of pages, Research – Mathematics Learning & Teaching and Research – Learning & Teaching both provide information on research relevant for teachers in the classroom. There are links to many good, easy to read summaries included on both pages.

Recent additions to the Mathematics page includes Working Memory in Mathematics Learning which is an excellent example of the clear and concise communication of research which these Expressos from Cambridge Mathematics provide.

Also added to this page is Improving Mathematics in Key Stages 2 (ages 7-11) and 3 (ages 11-14) From the Education Endowment Foundation. The Guidance Report offers eight practical, evidence-based recommendations—that are relevant to all pupils— but particularly to those struggling with their mathematics. Note the recommendations summary poster.KS2 & 3 Maths Recommendations

On the Research – Learning & Teaching page, note Rosenshine’s Principles of Instruction, such a valuable list of research strategies teachers should know about and I believe well worth asking ourselves if we are incorporating these strategies regularly in our lessons.
Principles of Instruction

The page on free books has been checked and updated recently.

Colin Foster - Instant Maths Ideas

Colin Foster – Instant Maths Ideas

Note Colin Foster’s KS3 Instant Maths Ideas (3 books) which are freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham.

Clumsy Clive

Andy Lutwyche – resources

Included with Spot the mistake we have excellent resources from Andy Lutwyche, look at his excellent Erica’s Errors series and if we check on TES, these free resources also include plenty of errors from Clumsy Clive! I have found these work really well in class.

Finally, on the A Level Statistics page I have included from WJEC, their KS5 resource, Exploring Large Data Sets which includes several data sets and very comprehensive Teacher notes.

WJEC Large Data Set Resources

The notes include many questions to consider and also clear instructions for Excel and GeoGebra.


Mathematical Miscellany #16

A resource miscellany this week, a reminder of where to find excellent teaching resources provided by the examination boards and also from MEI.

MEI, AQA, Edexcel and OCR (also Eduqas, part of WJEC) provide excellent support for teachers. With GCSE and A Level subject content now the same for all the examination boards we have an excellent library of resources to use irrespective of the specification chosen for public examinations.

MEI have produced such a valuable collection for teachers with the latest addition to their work on Problem Solving. See their Problem Solving examples and solutions. As well as all the problems and solutions with very valuable suggestions and commentary, MEI have provided a guide to support teachers with the problem solving content of GCSE (14-16) and A Level (16-18).

At A level MEI’s Interactive Scheme of work includes a resource for each section of the course. See also, MEI on integrating technology into your scheme of work which includes many calculator, Desmos and GeoGebra tasks.

See also MEI Free Reources and a page added to the GeoGebra series on the MEI GeoGebra Institute.



TeachIt Maths



  • GCSE Teacher Support includes new content resources, a worksheet collection for Foundation and Higher, teaching low attainers and formulae posters.

    Edexcel Codebreaker

    Edexcel Worksheets

  • Teaching and Learning Materials includes an extensive collection from baseline tests for younger (KS3, age 11-14) students to demanding GCSE (age 14-16) Problem Solving questions. The Problem Solving questions with full mark schemes are excellent as are the Practice Papers and topic tests.
  • Teaching and Learning Materials – A Level 16+ a wonderful and growing collection
  • Signing up to the wonderful Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you useRegister for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number. In the GCE AS/A Level Mathematics cabinet you will find documents for GCE 2017 including baseline tests and unit tests, also Transiton materials for GCSE to A Level. More will be added to these collections.Edexcel Empoium



Statistics – The large data sets and more for Advanced Level Statistics from AQA, Edexcel, OCR and OCR (MEI) can be found on this page.
GeoGebra Regression

Eduqas is part of WJEC and offers Ofqual reformed qualifications to secondary schools and colleges. Eduqas has many very useful secondary and vocational resources for Mathematics. Note the series of resources for topics new to the GCSE specification.
Educas - Venn Diagrams


Mathematical Miscellany #15

From Colin Foster on Nrich we have Mathematical Etudes where he discusses lovely rich tasks and tedious exercises!

Colin Foster

Colin Foster – Mathematical Etudes

An important read as we begin another school year I feel, the more our students have to think about a task, the more they will learn. I agree with Colin liking the factors task, I have used this approach successfully in class too. In fact we can extend the task and look at finding numbers with varying numbers of factors.

Factors nzmaths

How many Factors – nzmaths

How Many Factors on nzmaths requires students to  find ways to group numbers, which numbers have only two factors and which have only three factors?

For more from Colin Foster his KS3 Instant Maths Ideas (3 books) are freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is an Assistant Professor at the Centre for Research in Mathematics Education in the School of Education at the University of Nottingham.

Colin Foster - Instant Maths Ideas

From PhET Simulations one of my favourites is now available in HTML5 collection: Projectile Motion.

PhET Projectile Motion

I have included a page on PhET simulations in the Tools and Calculators series of pages, part of the Lesson Planning collection.

Educas has many very useful secondary and vocational resources for Maths. Note the series of resources for topics new to the GCSE specification.
Educas - Venn Diagrams

Dr Frost slideI have mentioned Dr Jamie Frost and his plans for the new A Level specifications. Dr Frost has been very busy producing a complete set of resources for Pure Mathematics 1, I do like the fact that Dr Frost has included extension questions for each chapter. These resources reference an Edexcel text but of course the content is common to all qualifications so all the explanations and worked examples for A Level. I have included a page for Dr Frost’s resources as part of the A Level series. Note the collection of extension questions mapped to the new specification.

Dr Frost has some brilliant ‘Just for your interest’ posters; see this for example on e. He has put the complete collection of these together. Follow Dr Frost on Twitter.

For more A Level (UK 16+) resources, Danielle Moosajee has a growing collection of A Level resources on her site PixiMaths, Check her KS5 Teaching Resources Index. The resources include very clear PowerPoints, associated questions and student self-assessments.

A consistently popular post on this blog is one on online whiteboards. All resources / links have been checked and I have removed resources which have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

With UK examination results recently announced I have put links to the results statistics and grade boundaries on the Results 2017 page. Also included are some interesting links from Schools Week, see A-level results 2017: UK subject tables which compare results from 2014-2017. Also from Schools Week, on GCSEs – GCSE Subject Tables and “The 7 most interesting things we have learned”

An important read I feel on such Statistics from Cambridge Mathematics, Examining our own statistical literacy on results day. which makes such important points about the size of the dataset required for it to be explored in context.

And finally, here’s a great read from Shaun Allison on Getting off to the best start with a new class.