16+ Challenge Questions

I have been updating the Advanced Level series of pages (UK 16+) this will remain an important work in prgress as I teach the new Mathematics and Further Mathematics specifications during the next Academic years.

A new page is on challenging questions for this age group. The Oxford Maths Admissions Test multiple choice questions could make ideal starters (or anytime!) questions.

Particular thanks to Dr Jamie Frost, Underground Maths, STEP Maths, UKMT and Dr Trifon Madas.


Dr Frost Maths

To really challenge your students, MAT, STEP and AEA questions provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.

For mark schemes see:


For further sources try UKMT Senior Maths Challenge Questions.

…and also see MadAsMaths with its many papers and solutions increasing in difficulty.

Communicating Educational Research

Ahead of Thursday’s (27th July, 8.30 – 9.00pm)  on communicating educational research I thought I would check and update my Reading series of pages which includes some very useful educational research summaries.

PorterThe various pages on free books have also been checked and updated. With the new A Level Specifcations coming perhaps some of those old textbooks might come in handy and will take older readers on a trip down memory lane – anyone for Porter’s Further Elementary Analysis?!

Several books are available – answers included.

On research, note in particular the pages Research – Learning & Teaching and Research – Mathematics Learning and Teaching.

From Harvard Graduate School of Education, see Communicating Research with readings, tips and strategies for clear expression. There are many good points here for communication generally not just in communicating research.

Harvard Usable KnowledgeSelect ‘Find by topic’ for a menu of Usable Topics’; try Teaching for example for a further menu including the chance to ‘Ask a researcher’. The series, Ask a Researcher, offers evidence-based guidance for the classroom in the areas of literacy, mathematics, and English language learning.

Excellent examples of clear communication are:


Research in 100 Words – Chris Moyse

Research in 100 Words from Chris Moyse who descibes this series as “Simple summaries for busy teachers”. Also from Chris, his favourite research articles in one collection.

Cambridge MathsEasy to digest research on Mathematics education from Cambridge Mathematics, see their Espresso page where in their words, “Each month we bring you an Espresso – a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind. Each Espresso considers one particular issue in mathematics education, and how the latest good-quality research can provide helpful guidance or further reading.”


Games & Other Mathematical Activities

What to do for those last lessons?

Some of these activities would be great for any lessons, not just at the end of term. The complete collection can always be found on the End of term activities page. For readers familar with this collection all links have been checked and there there have been several updates.

You might want something other than a video, though perhaps consider a Numberphile video or I could make an exception for the counting chimps, a video I was introduced to by Alex Bellos at the SSAT conference which he included in his session and shows the astonishing recall of a chimp – compare the human!

Try some UKMT team challenges, their crossnumber puzzles make a great end of term activity. The junior materials can be found here and senior here.


Relays from Chris Smith. These are excellent, note there is a complete set; I used his Valentine relay very successfully this year! Featured in Mathematical Miscellany#2.

JM Quiz & Matchstick PuzzlesFrom JustMaths a great end of year pub quiz. I do like the way this ends with a round on Matchstick puzzles, this will keep our students happily busy! Note the very useful recommendation for Matchstick Puzzles from Dawie van Heerden.

Get your students thinking with some resources from Underground Mathematics. Try Equation Sodukuor perhaps LCM Sudoku.
Equation Sudoku
Another possibility frm Underground Maths, try the Division Game.

UGM Division Game

Let your students get their phones out to play Factris, a new App published in July 2017 developed by Richard Lissaman, of MEI.

Bingo always works really well.


A team game? Try Workers of Zen.

Workers of Zen

(ATM publish books of team games).

I must mention A Little Problem for the Holidays!

Some Mathematical games and puzzles perhaps? There are plenty to choose from.

The Set Game  which is a daily puzzle is set in The New York TimesHow many sets can you find? Click ‘How to play’ in the menu on the left for the rules.

Or try some pencil and paper games such as Sproutsdescribed very clearly here by the Iowa State Math Department.

Countdown - Nrich
Always popular with students is the game of  Countdown. Exellent programs for both games can be downloaded free from Chris Farmer’s CSF software site. For a new challenge why not try Coundown with Fractions from Nrich or another variation – see this Countdown collection.

Make 24
On a similar theme try  Make 24 a game where four numbers in the range of the natural numbers 1 to 9 are chosen randomly; these must be combined to obtain the result 24  –  but you may only use the four basic arithmetical operations and brackets. This online version optionally shows solutions as well as presenting random problems. The program will also show solutions for any given set of four numbers.

Learn the syntax for WolframAlpha, perhaps a chance for students to explore WolframAlpha, using the various slideshows, note the questions on the worksheetNote the last slideshow on a little fun with WolframAlpha!

Explore the Desmos Graphing Calculator (and note the further reference to Desmos below, use Desmos to create some art work!)

For a main activity a Tarsia puzzle provides an engaging activity. I intend to use one to see how many of the formulae needed for the part of the course which my Year 10 students (age 14-15) will be studying next year are already known.

Darth Vader curve

We could of course have some fun with WolframAlpha. Did you know you can plot Darth-Vader?  There are in fact a whole family of Star Wars curves! Or maybe you prefer Dr Who?!

Have you seen Wolfram fun facts? (You can view these on Twitter whether or not you have a Twitter account). Why not try modifying these queries? Note the different cookies you can try in the cookie query shown below. You could perhaps invent similar problems! How many pizzas would it take to fill the moon? OrJupiter?

fun facts

Art Elements

If those WolframAlpha equations are a bit much for younger students they could try something simpler using the Desmos graphing calculator; look at Alec Schultz’s PacMan for example, you could just show your students how to restrict the domain for straight lines, maybe show them the equation of a circle and see what they can produce! See this post on Graph Art on Mathematics for Students.


To generate some more pretty curves why not try Spirograph?! Students could experiment with these online versions to see the various curves that can be generated.

These logic puzzles from John Pratt should keep students happily and usefully occupied. (I have added these to the Puzzles page on Mathematics Games.) Or we could try another Kakuro Puzzlestudents were fascinated by these when introduced to the puzzles by a member of the class. At the end of the year we often ask students to do a presentation to their peers which works well.

Try (or write a new) Sporkle Quiz.

Sporkle: Find the missing primes in two minutes

Still thinking about games, from Nrich these Strategy games are for Primary teachers; but could also be useful for lower secondary.

For more ideas check Jo Morgan’s Resouceaholic.

We could finish with a song or two!

Wishing teachers everywhere a happy holiday (only WolframAlpha would give you the Scrabble score as well as the definition!)

Underground Mathematics – Save & Organise Favourite Resources

A new page in the series of pages on Underground Mathematics …

If you create an account (all free) on Underground Mathematics you can easily save and organise your favourite resources.


Select User from the menu at the top right, then New User to create an account. Note that you also use the User menu to log in.

When you are logged in you can add any resource to your collection by selecting the star to the right of the title. And note this resource Pick a card, which I highly recommend, think about multiple representations for Quadratic Functions. This could be used with younger students too.
Save resource

See also: Tutorials – Saving favourite resources – a video from Underground Maths
To see your resource collection, select ‘Your resource collection from the User menu.
User Menu

You can also use subcollections to help organise your resources. Subcollection1

When you display your resource collection, note the options for each resource, the first of which is the ability to add the resource to a subcollection.

Note the choice to add to one of your existing subcollections or the option to create a new one.

Note that when you display your resource collection you can select a subcollection if you wish:

See for example Building Blocks resources I personally like; I created a subcollection and downloaded as a csv file. The ability to add notes is really useful too.

For reference, this is one of a series of pages on Underground Mathematics. With so many outstanding resources on the site, this is a continuing work in progress.

Mathematics Resources (Age 16+)

As mentioned in my previous post I am continuing to develop the series of A Level pages, for students aged 16-18 which will be a major ongoing project during this Summer and beyond. With a growing collection of resources, I have now split the Resources section into a series of pages and also added a tab to the top level of this blog for I hope easier navigation.

Having just returned from an inspirational MEI Conference I have much to reflect on and will be returning to many ideas from this in future. For now I must highlight MEI’s Problem Solving – Examples and Solutions which has just been published. 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).

MEI Problem Solving

Underground Mathematics, STEM Learning and Nrich have all mapped resources to subject content which makes it simpler to look for good resources for learning which means we can concentrate on teaching well and just how our students will learn. With MEI’s Interactive Scheme of work we have a suggested resource for each unit as well as ideas for using Technology and of course crucially very helpful commentary on learning and teaching. Jonny Griffiths RISPS collection has a very clear resource listing by topic. The list goes on. All the examination boards too have very clear and helpful documentation.

I have also added pages for Vocabulary and Formulae for easy reference.