A Level Reform

Just some simple updates this week – note some new documents on the A Level Reform page. There are already several very clear resources from MEI who continue to document the new specifications. See their comparison of the specifications from the different Examination Boards which provides a summary of the differences between the current and the 2017 specifications for AS and A level Mathematics and also Considerations for choosing a new specification.

MEI Sample Scheme of Work

MEI Sample Scheme of Work

Something to keep an eye on is MEI’s 2017 A Level Scheme of Work which will be freely available from Spring 2017. The sample units currently available look excellent. Each unit (there will be 43) 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.

Staying with MEI – check the Conference 2016 resources which includes a session on teaching Statistics as part of the new A Level specification and notes from several other sessions on the new A Level specifications.

See also A Level – Draft Specifications.

Introducing Calculus


New on the GCSE specification we have interpretation of the gradient at a point on a curve. I want to introduce this to my very able Year 11 (UK age 15-16) class this week. As this class is also studying for AQA’a Level 2 Further Mathematics Qualification I want to go beyond the GCSE specification. Talking of the Further Maths specification – a wonderful find – thank you Craig Barton  – so many wonderful resources for this specification. Thanks too, to Mark Greenaway, Thomas Whitham Sixth Form College and on YouTube, Raw Maths, Jerry Jam and Riley Maths.

Some resources – I plan on using:

Perhaps after initial explanations with reminders about what they already know about distance time graphs and emphasising that a gradient is a rate of change, a good starting activity, A tangent is … from Underground Mathematics which emphasises rather well that a tangent is a local property of a graph.

I want them to draw some tangents and see how accurate they can be, so I’ll give everyone a good size graph of f(x) = x2 and have them draw tangents at x=0, 1, 2, 3 and 4, something that has worked well with A Level students. We can use Desmos to check our work, Tangents to f(x)=x2 –  Desmos. (For even more @Desmos sophistication – see the end of this post).

Back with Underground Maths again we will use Gradient Match to match functions with their gradient functions. This can be used interactively online. All the reources you need and a solution are provided.

Further Resources
AQA – Bridging the Gap – Pocket 3 is on Graphs and Real Life Contexts; this includes Distance Time Graphs and Velocity Time Graphs.

OCR’s Topic Check In 7.04 Interpreting Graphs     7.04

There are several resources for teaching this topic on AQA’s All About Maths including clear PowerPoints and suggested lesson activities.
(Free for AQA Centres, find out how to register).

Mathematical Miscellany #7

One of my resolutions for Maths teachers, one I think applies to teachers of any subject is a reminder about talking to the students about resolution-study-strategieslearning and study strategies. Read The Learning Scientists blog for more information and note the excellent downloadable materials on study strategies. Since I wrote that post more slides to use in class with your students are now available, including on Retrieval Practice, a subject I have long been interested in and something I have seen as important all through my teaching career. See my own Low Stakes Testing in the Mathematics Classroom.

Follow @AceThatTest on Twitter or on Facebook.

At ResearchEd 2016 I very much enjoyed Oliver Caviglioli’s session on Visual knowledge for better explanation and recall. Oliver is a trainer of Visual Strategies, he collaborated with The Learning Scientists to create the six posters on effective study strategies. Note his free resources for teachers coming soon, Cognitive Science HOW2s.

5-a-dayContinuing on the theme of retrieval practice, a reminder of a favourite resource, something I have used in my first lessons this week with various classes, Corbett Maths 5-a-day. If you scroll down the GCSE 9-1 collection you will see that Mr Corbett is working on the answers too.

Students appreciate the idea of regular reviews throughout the course.

& #math come together here, @cbrownLmath (US) & myself @ColleenYoung (UK) decided we like the idea of a continuing anytime chat. The original idea from Michael Fenton,  see Twitter Chats vs Family Dinners….. (note #slowmathchat – math saves a charcter!)

This coming week we will focus on homework, appropriate for the beginning of the academic year as we establish routines. For some alternative homework ideas, see this page.

On the subject of Twitter, a reminder of just how useful it can be!

Iteration TESAs a member of the TES Maths Panel I have often come across the excellent resources from @Pixi_17. In fact writing the original post on Iterative Techniques (and note the June 16 update with a Further Resources / Questions section) I was able to include a resource of hers on the subject. She has now organised her resources on her own website piximaths.co.uk.

Underground MathematicsCambridge University’s Underground Mathematics is an outstanding resource for teachers of students age 16-19 and I believe will be an important source of ideas for teaching th new Advanced Level specifications.

Iteddy-bear will be regularly featuring favourite resources; here’s a great way to look at circles! The teddy bear! As with all the resources on Underground mathematics much more than just the problem is available; note the printable/ supporting materials for the teddy bear problem.

I can never resist creating a Desmos page!

Further posts on Underground Mathematics.


Teddy Bear Problem – Underground Mathematics on Desmos

More posts in the Mathematical Miscellany category.


This much I know about…my favourite Growth Mindset moment of the Rio Olympics!

On my Reading/Blogs – Learning & Teaching page, you’ll find John Tomsett. His post struck a chord with me – that’s a wonderful video for talking about Growth Mindsets, something I have often mentioned in posts on this blog.


I have been a teacher for 28 years, a Headteacher for 13 years and, at the age of 52, this much I know about…my favourite Growth Mindset moment of the Rio Olympics!

Chris Langridge and Marcus Ellis won Bronze in the Men’s Badminton Doubles in Rio…


…and here is what Langridge said when they won through to the semi-finals…

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Top >10 Mathematics Websites

If you would like a copy of the presentation these versions include navigation from the contents page: Top 10 Mathematics Websites 2016-2017 (PowerPoint) or Top 10 Mathematics Websites 2016-2017  (pdf). Note that hyperlinks seem to work considerably faster on the pdf version.

This and other presentations can all be found in the series of Presentations pages.

Included quite rightly in the section on Questions is Craig Barton’s and Simon Woodhead’s wonderful Diagnostic Questions site. Note Craig’s post on setting up for the new school year including a very clear guide. Check these great collections of Examination questions. This outstanding site just keeps getting better and there are further developments to come.

Top 10

Resolutions for (Maths) Teachers

As the new Academic year approaches in the UK and has already begun elsewhere..
time to review and update ‘Resolutions for (Maths) Teachers’.

Resolutions for Maths Teachers PowerPoint file
or as a pdf Resolutions for Maths Teachers (hyperlinks work in the pdf and can be faster than PowerPoint).

Spaced Practice - Learning ScientistsMy emphasis is naturally on the students’ learning and you will see further emphasis on talking to the students about learning and study strategies; read The Learning Scientists blog for more information and downloadable materials on study strategies. Follow @AceThatTest on Twitter or on Facebook.

Also added to this edition a reminder that we of course need to help our students be great problem solvers. See also the Rich Tasks 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.


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 MathsBot.com 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.

Holiday Time

Looking back over some previous posts, I thought I would put the holiday themed posts together:

Maths in the moviesThis year’s holiday included a visit to the wonderful National Cinema Museum in Turin – see the Mathematics in the Movies post (now with added songs!)

Holidays includes some really interesting links on mathematical buildings, architecture inspired by Mathematics and suggested mathematical tours in London. And did you know you can use WolframAlpha to explore properties of buildings?

Holiday Pictures

cosh x Desmos image

Imaginary Exhibition


I do like to keep my eye open for mathematical pictures (Tetrahedral Numbers on Mathisfun), hence:

Neuwied Schloss cannons Photograph by David Young

Neuwied Schloss cannons. Photograph by David Young

Mathematics in the Movies


Photograph by David Young

At the wonderful National Cinema Museum, Turin – holiday time this week!

Thinking about Maths in the movies led me to this great collection of movie clips featuring Mathematics from Harvard University.

We must of course include Abbot & Costello showing that 7×13=28!

Mathbits.com includes a section on using movie clips in the mathematics classroom. The site suggests several possible movie clips to use and has accompanying worksheets. The Abbott & Costello clip mentioned above is included, the MathsBits worksheet is here.

Donald in MathMagic LandI loved Donald in Mathmagic Land as a child.

For a series of excellent articles see Plus Magazine’s Mathematics in Films.

For a very comprehensive database of mathematics mentioned anywhere is a movie try MMDB – The Mathematical Movie Database from Burkard Polster and Marty Ross.

From Numberphile, Math and Movies (Animation at Pixar) we learn how 3D aminated characters look so smooth.

More from Pixar, see Pixar: The math behind the movies, Tony DeRose on TEDEd; note that this link from TEDEd provides not just the movie but a complete lesson. (See also this article on Pixar’s research on The Verge.)

From SchoolTube, Math in the Movies

If all this inspires you to think about a job in digital animation – see Maths in motion on the excellent Maths Careers site.

I really like the song ‘Math is a wonderful thing’ from School of Rock.

Having got on to songs, here are a few favourites.

These have gone down well with students, particularly the Circle Song!

The Klein Four are a bit beyond school Mathematics, you may appreciate this if you are studying for a Mathematics degree!