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.

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.


Mathematical Miscellany #8

Tidy UpIt’s Half Term this week and a time I always find useful for a tidy up!
Checked and updated posts include:


Happy Birthday Nrich! To celebrate Nrich’s 20th Birthday they have been digging in the archives and freshening up some old problems. This is still one of the best websites around and one I have been using for a long time! See also their Hidden Treasures. and the Teacher Birthday Feature.

The 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!

Note the Poster Competition closing in January 2017 for UK students age 11 to 18. The entries will be judges in three categories Years 7 and 8, Years 9, 10 and 11 and Years 12 and 13.

celebration-of-mindFor some brilliant Puzzles and Games resources – see celebration of mind and more resources here.

Find out more about Celebration of Mind.

More posts in the Mathematical Miscellany category.

Mathematical Miscellany #7

Questions Questions..

I have been busy checking and updating various pages on this blog, taking into account popular resources.

Mr Barton Maths
Craig Barton has been working hard redesigning his wesite, Mr Barton Maths. You will find a treasure trove here for teachers and students. Note in particular Craig’s Maths Topic Index Page.

For each topic, you will find information on all the GCSE specifications, a whole variety of resources, questions and more. The pages are very easy to navigate. Note the inclusion of Diagnostic Questions for each topic, a resource which is going from strength to strength this now has over 20,000 Multiple Choice Questions. Multiple Choice Questions when well written like this can be an excellent way of addressing student misconceptions.

logoNote these free CPD Events from Underground Mathematics including a webinar at the beginning of November.

For more on Underground Mathematics, an introductory post is here and you can view all posts in the category Underground Mathematics.

Suppose you are interested in Quadratics and want to stretch your students – you’ll find an extensive collection here, As always, for each resource, you will find so much more than just the question and solutions but for example all the printable materials you need and suggestions for teaching with the resource.

If you create an account you can easily save and organise your favourite resources. This list of favourites can be downloaded as a csv file.
For some of my recent favourites see this Excel file cy-ugmaths-favourites or as a pdf: cy-ugmaths-favourites Note the handy Excel =hyperlink(cell) command for turning the text to a hyperlink).

The favourites facility is sophisticated – you can create sub collections also.

Note Scary Sum – what a lovely problem!



Mathematical Miscellany #6

Another compilation this week, this time of updates to this and some companion blogs.


A consistently popular page on this site has been Rich Tasks – this has now been split into two separate pages, one for age 11-16 and the other for age 16+. The 16+ page has been updated with considerably more detail. With the UK new A Level specifications having a greater emphasis on problem solving and more challenging questions, activities such as those here should be a natural part of our regular teaching.

Do explore the brilliant Underground Mathematics site as well as Jonny Griffiths’ various sites. Further resources are provided in the presentation at the end of the page.

Carom MathsWith a new academic year approaching for UK students or just started for students elsewhere, I have updated Transition Time on Mathematics for Students. This is a collection of resources and activities aimed at students changing stages in their studies – perhaps starting more advanced studies at school or heading off to university.
The illustration here is from Jonny Griffiths’ Carom Maths, a collection of forty mathematics activities bridging the gap between A Level and University. Check the List of Activities, for Inequalities for example, illustrated here, choose Carom 1-2: Inequalities. This will lead you to a complete PowerPoint with information and questions on Inequalities.

J Hall Maths ToolsIn last week’s Mathematical Miscellany #5 I included Jonathan Hall’s site with its many excellent Tools for Maths Teachers. With some great starters and a bank of GCSE questions with solutions more detail has been added to this post on Mathematics – Starters and Plenaries. The Collections page on the same site has also been updated and checked. As the name implies these are sites with a fantastic supply of starters.

Mathematical Miscellany #5

Twitter can be useful for alerting one to resources / news, note the first two items.

Problem Solving – an open access (free) book which looks at research on Mathematical Problem Solving.
Problem Solving

Note this page for a large collection of free Mathematics books.

Tools for Maths Teachers J HallJonathan Hall has many excellent Tools for Maths Teachers. Here you will find various tools including Starters and also a bank of GCSE questions. Note that you can show solutions for the GCSE questions – there is a link at the bottom of the page for each question.
JHall site

The page on Apps has recently been updated, there are fuller descriptions of the various apps and note the addition of Summaze2 from MEI and Sigma. A wonderful example of a free app – Maths to make you think, visually attractive and no irritating adverts trying to make you buy the premium edition!

Sumaze Integral

In Mathematical Miscellany 4, I mentioned the excellent Linar Equations Calculator; for an excellent way to illustrate the balance method of solving linear equations, try this manipulative on Mathisfun, this is very simple to use and does not require the user to log in.
Mathisfun Algebra Balance

tickUK Results 2016 – a new page has been created which I will update as A Level & GCSE results / news comes in. As I do each year, I will provide links to the results statistics and grade boundaries for the various examination boards.

Note my Twitter Examinations list. Check this for announcements / news. (You do not have to be a Twitter subscriber to use the list.)

Whilst this is Mathematical Miscellany #5 I have been writing these compilation posts for quite some time. They were at one time ‘Thoughts this week…”. Previous posts are all filed under the category (note the Category menu on the right) Mathematical Miscellany.

Mathematical Miscellany #4

A compilation post this week…
(More collections of mathematical goodies.)

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

AQA Problem Solving Questions

AQA 90 ProblemsFrom AQA comes an outstanding resource, ‘Problem Solving Questions‘.
The Teacher’s Guide includes indices by topic and also by strategy.
AQA Problems – updated version.

Em   has a brilliant PowerPoint with all the questions and answers – see it here.


Linear Equation CalculatorThe Subtangent resources from Duncan Keith are available from the National Stem Centre (the original site is no longer available). This is a great collection including various worksheets, starters, investigations and revision activities. Some files are also available on Mathisfun. A personal favourite of mine has always been the linear equation calculator.

And finally, 28th June is a Perfect Day to enjoy some Mathematics!
28 is also a happy number!
It’s also National Tau Day! Pi is wrong…..
This video provides a short version of the Tau Manifesto (14 minutes)

Mathematical Miscellany #3

Exam PowerPoint @westiesworkshop

Mr Westwater – TES Resources

With revision still in mind, for some excellent PowerPoint resources with A Level questions and mark schemes by topic try Mr Westwater’s resources on TES. (Twitter @westiesworkshop). Though Edexcel questions these are clearly useful for other examination boards also. There are six of these PowerPoint files available:
Core 1   Core 2
Statistics 1  Mechanics 1
Core 3
    Core 4

Diagnostic Questions

Diagnostic Questions

Craig Barton’s and Simon Woodhead’s Diagnostic questions site includes some excellent question collections for revision; as well as GCSE questions, there are quizzes for AQA’s excellent Level 2 Further Mathematics specification and for Core 1 at Advanced Level. Questions from the Oxford University Mathematics Admissions Test are also available.


From AQA this set of revision tests and mark schemes is very useful and from Oxford University Press a lovely set of free revision resources is available. Under Mathematics Revision Guides, choose the ZIP file Worksheets. Note that these are headed New GCSE – this is the old new specification, not the new new specification! These are clearly perfect for UK students taking exams this year but still excellent for future years.

AQA Revision Algebra

For many more revision resources note the Revision Activities series of pages.

GCSE Problem Solving: Steve Blades’ site has many excellent resources; on the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book.

For more Problem Solving Resources, see Problem Solving and Problem Solving 16-19.

Alec McEachran’s Furbles – a large data set!

Alec McEachran’s Furbles – a large data set!

Statistics – thinking about large data sets which we will need to for the new A Level specification – for an amusing large data set, how about the Furbles?! The images generated here are from the original 2003 version which is still available on Alec McEachran’s Talk to students about summarising this data, perhaps ask for their impressions as to which colour is the most or least common. Data can be presented as a bar chart or a pie chart and you can choose to categorise in various ways. It is also possible to vary the number of Furbles, the maximum and minimum number of eyes and sides. The illustration here show the largest data set possible.

Alec McEachran’s Furbles

Alec McEachran’s Furbles

Visual Patterns

Visual Patterns – Fawn Nguyen

From Fawn Nguyen comes the brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who’ve used visual patterns in their classrooms.



Mathematical Miscellany #2

Click on the image and move that slider!

Last week in Mathematical Miscellany #1 I included a reminder that Valentines Day is approaching – save your money and send a Desmos math-o-gram!

This morning I was reminded once more of the value of a quick peek at Twitter (it’s a bit like a lucky dip!) when I came across Chris Smiths’ tweet on his lovely Valentine relay race which you can download with his other relays from TES Resources.

Valentine Relay - Chris Smith

Valentine Relay – Chris Smith

Dot to dot
I read an article from Science Alert stating that Australian researchers have discovered that school children fare better at solving maths problems when they trace their fingers over practice examples, outperforming students who simply read the questions without touching them.

Polar dot to dot

Polar curves – join up the dots (in the correct order!)

Well that’s certainly easy to try and in fact reminded me of my love of dot to dot as a child. Some years ago I created some polar curves for my students. So Year 13 can try these this week, they can work out the correct order to join the dots themselves and trace out those curves! (Join the dots 4 curves for the file in case anyone wants it). These were created with Colderado University’s Mathematical Visualization Toolkit note you can download the application if Java causes you problems trying to use the application online).

Dotty Desmos

Desmos – join the dots

You can easily create some graphs in dots on Desmos – see Desmos dot to dot. Here’s a dotty version of f(x) =x3.

On the subject of polar curves, with Year 13 last week we strayed from the simpler curves to rather more sophisticated ideas; they suggested all sorts of curves we could try – great fun and way off the specification; but then I think they understand the specification content better barbecue we go beyond it where appropriate. Thinking about their suggestions I have something I think they will like this coming week, look at r=acos(kcosθ)!


Note the use of the slider which enables students to see how the curve is traced out as the angle increases. For more such polar resources – see Polar Graphs on Mathematics for Students).
(Polar curves – always remind me of a childhood favourite toy – Spirograph).

Thinking about sophisticated curves lead me to this rather nice publication : Fifty Famous Curves from the Department of Mathematics, Computer Science, and Statistics Bloomsburg University.

Problems & Activities
The Problems and Activities page has been updated with several new entries – so many wonderful free high quality resources – a massive thank you to the teachers who willingly share their work.

Rich Questionsquestions, a popular page has been updated with the addition of the Multiple Choice Questions collection.



Mathematical Miscellany #1

Just over three years ago I started writing compilation posts, a kind of newsletter style – a mix of mathematical goodies. I was inspired by Doug Belshaw’s Thoughts This Week – now Thought Shrapnel. It’s been on my blog to do list to revisit this idea again; how appropriate that Doug’s Thought Shrapnel today includes newsletters he enjoys. I was very happily distracted by some of these great compilation posts this morning and particularly struck by a post from Doug’s first suggestion Austin Kleon – important for any blogger, What to leave out and what to leave in. Some great quotes there including Elmore Leonard’s:

“Try to leave out all the parts readers skip.”

(Wondering which bits you are all skipping here!)

So I decided it was time for a new title for posts of this kind – hence ‘Mathematical Miscellany’. Previous compilation posts can be found under the category (note the drop down menu on the right for categories) Mathematical Miscellany.

In class
With my Year 10 GCSE class I used some ideas from a site I often use: Mudd Math Fun Facts. Squares Ending in 5 and Multiplication by 11 both made excellent starters, we looked at proofs as well as enjoying the mental Maths tricks! You will find more lightening arithmetic suggestions on the site.

OCR Check In TestsOCR have published some very useful new resources; I have written before on their Check in tests. New tests for Foundation and Higher have been added. The Higher resources include Triangle mensuration, Language of functions and Algebraic expressions; these really are excellent resources and I will definitely be using all of them.

The GCSE New Content pages are updated regularly, note all the further resources at the end of that page, including from the wonderful Just Maths, GCSE questions by topic.

Published this month we have the KS2 Mathematics 2016 teacher assessment exemplification, and also the KS1 version. Clearly teachers of secondary age children need to know what students are covering in Primary school. These documents have been added to the GCSE New Content page.

If you read just one blog post this week – from 2014, but Tom Sherrington’s 10 Silver Arrows: Ideas to penetrate the armour of ingrained practice is as valid now as it was then. I think these ideas are important for any teacher to reflect on – I’m pleased to see 6, a subject I have often written on (see Mini Tests).

Tests are good.

…and finally
It’s coming up to that time of year again, I see Valentines cards in the shops, save your money and send your loved ones (or anybody!) a math-o-gram!

Click on the image and move that slider!

Click on the image and move that slider!

In what happily seems to have become an annual tradition Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!
Desmos Valentine instructions

Geeky people you could even use the Desmos API …

Valentine’s Day seems an appropriate time to express love for Desmos!

Elsewhere – express your feelings for WolframAlpha!

I Love YOU

Transum Valentine Puzzle
and here’s a logic starter from Transum for Valentine’s Day!