Challenge Your Mathematics Students …

To achieve the highest grades at GCSE (taken in the UK by students age 15-16) students will need to be good problem solvers which include being able to make and use connections between different parts of Mathematics. There are many suggested resources in the Problem Solving Presentation.

For older students (16+) I have included Underground Mathematics. I have also used Undeground Mathematics resources with my very able GCSE students; see for example Introducing Calculus. There are many Underground Mathematics Resource Types. One of the types I have written on before is the Review Questions which in the words of the Underground Maths Team:

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Checking the Review Question type in this category we see that O/AO-level questions are included.

I see several questions here that will provide appropriate challenge for my GCSE students.
For example:


Can we fully factorise x4+4y4?
Starts with a Show that….
And then we factorise and will need to recall the difference of two squares.
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.

Can we simplify these algebraic fractions?
Review algebraic fractions, simplifcation including the difference of two squares and quadratic equations. We could of course also talk about functions (including domain and range as these students are also studyling AQA’s Level 2 Further Mathematics)

Can we simplify these simultaneous equations of degree 1 and 2?
Solve simultaneous equations, we’ll need simplification of algebraic fractions again and we can talk about the graphical solution of equations. We will also need to factorise a quadratic, 3y2−y−80 with a coefficient which is not 1 for the square term. We have all decided we are fans of the Box Method!

You can also search on the Line and the Station to narrow your search; you can also save and categorise your favourites by creating a (free) account.


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!



Bloomin’ Mathematics

An important update this week. Looking at my blog Statistics, my post Bloomin’ Mathematics is one of those enduring posts that has had very regular visits with thousands of views each year since I first wrote it in 2011. I thought definitely time to check it and update it. Even if you are not bloomin-googleconvinced by Bloom’s Taxonomy we are all convinced of the need to question our students in a way that challenges them makes them think hard – more than just simple recall type questions.

Getting our questioning right is an essential part of what we do so I have added further sources of questions to the original post to create this updated one.

Note the addition for older students, 16(ish!) and above of the brilliant Underground Mathematics. An introductory post is here and you can view all posts in the category Underground Mathematics.

Watch this space for more!

Underground Mathematics Champions

Underground Mathematics Champions


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 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

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 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.