Can you find the next few terms of this sequence?

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, ….

The online encyclopedia of integer sequences will identify a sequence you enter. Simply type in your sequence and choose Search. Note that you can list, graph or even listen to the sequence! There are more pages available, try Puzzles for some unusual sequences.

Alternatively – put the first few terms of your sequence into WolframAlpha.
This will return a great deal of information; scroll down the page for the possible closed form for the nth term of the sequence; 2(2n+1) in the example here (4n+2). Note the various sequence queries you can try.

WolframAlpha - sequences

WolframAlpha – sequences

WolframAlpha recognises the first sequence above by name 

Answer questions & help a charity



Freerice is owned by and supports the World Food Programme. For every correct answer 10 grains of rice are donated through the World Food Programme. Users can answer questions in several categories including two on Maths, one on multiplication and one on basic Maths. It is possible to play at various levels, so choosing level 10 for example means that questions on fractions and directed numbers will be included. Students can sign up (under 14s need parents permission) or login easily with their Facebook account to track their totals and join and create groups.

Well Good Water Aid

Well Good Water Aid aims to raise funds for wells to supply water to the developing world. Well Good has questions just on Number as shown in the image here. A good way for younger students to practise their skills with Negative Numbers!

Magic (actually Algebra) Tricks

….so what is going on with all of these? Can you use Algebra to show why they work?

Regifting Robin

Regifting Robin

We could start with a little mind reading – try Regifting Robin (turn the sound on).
Can you work out what is going on?

Think of a number…
Add 3
Add 4
Take away the number you first thought of

Try with several different starting numbers.

Think of a small positive number

1. Square it.
2. Add the result to your original number.
3. Divide by your original number.
4. Add 17.
5. Subtract your original number.
6. Divide by 6.

Try with several different starting numbers.

Multiply any two digit number by 11.
What do you notice?
Can you prove this result?

Solutions soon if you are puzzled.


Today, November 2nd 2015 marks George Boole’s 200th birthday.

So an appropriate day to look at logic!

For some useful Logic notes, have a look at these published on
Supplementary Chapters to Accompany Finite Mathematics by Stefan Waner & Steven R Costenoble

See also Logic notes from the Centre for Innovation in Mathematics Teaching

Note this Finite Mathematics & Applied Calculus website has extensive resources for students.

and you can use WolframAlpha for some logic queries:

Free Courses With FutureLearn

For high quality free courses sign up to FutureLearnLooking at what is coming up for example, we have from The University of Leicester a course on Real World Calculus: How Maths Drives Formula One and Launches Angry Birds. The course starts on 9th November for three weeks and requires about 2 hours a week. The course is entirely free; certificates of participation are available to buy (£34 plus delivery for this course) if you would like proof of your learning.

This particular course is one of the FutureLearn Choices series which offer a chance for students to see what studying a subject at university will be like. Several of these courses would also be useful for students already studying at university.

The Preparing for University course (started 28th September so you can join and have a look) includes a video on what lecturers value in their students; I’d say that is what teachers at school value in their students too.

From The University of Reading, A Beginner’s Guide to Writing in English for University Study strikes me as a useful course for Sixth Form students many of whom take a Level 3 Extended Project qualification as well as students studying in Further Education.

Once you have signed up to a course you can use it at any time, looking at my own profile I realised I had signed up to a course back in 2013 and happily all the materials are there for me to return to at any time I like.

Future Learn Course Categories

FutureLearn Course Categories

There are many courses to choose from, take a look at all the course categories here. Checking Science, Maths and Technology, I see from The University of Bristol Cracking Mechanics: Further Maths for Engineers  and from UNSW Australia – Maths for Humans: Linear, Quadratic & Inverse Relations.

Another interesting category for students is Teaching and Studying. I mentioned the Extended Project above, under this category I discovered a course on just that. Already under way, from The University of Southampton is Developing Your Research Project.

You can find out more about FutureLearn here.

I personally like the flexibility of online courses – I can access them for as long as I want whenever I want. I also like the fact that the courses include quizzes to check learning

Numbers Large & Small

Try You’re Getting Old. Enter your date of birth and generate some large numbers (even if you are quite young!)

You're Getting Old

You’re Getting Old

To practise writing numbers in Standard Form, try some of the calculators here.

Other sites of interest:

Scale of the universe. 

Magnifying the Universe

Secret Worlds: The Universe Within

You can find lots of data with very large numbers using Gapminder

From TED see the best stats you’ve ever seen with Hans Rosling using Gapminder.

Desmos Apps

This slideshow requires JavaScript.

The best graphing calculator around is free and available on Android, get it on Google play here and is also available for Apple devices – iOS apps.

Desmos on Android has had a major upgrade and you can now access your account with all your saved graphs and also create new graphs. Press the three lines in the top left corner to sign in, sync up, and take all of your graphs on the go.
Android App

Tons of examples

Tons of examples

Also included in this update:

* implicit inequalities
* draggable table columns
* a ton of new example graphs
* bugfixes and performance improvements
Maths students everywhere get this app! It’s great for younger students as it is easy to use for learning about graphs but has the sophisticated features that older students need.
From simple linear graphs to polar or parametric curves – Desmos does it all!

There are several examples in the slideshows here to show you the syntax you need on Desmos if you are unfamiliar with it and a series of pages giving you more information.

Mathematics – Transition Time

Notes from Mr Barton

As we start a new academic year, it will be a time of change for many students. Perhaps you have completed GCSEs or equivalent qualifications (UK age 15-16) and are about to start on your A Levels or perhaps you have completed those and are about to start studying Mathematics at university.

To be in a position to begin your new courses well you should be thoroughly familiar with the essentials of the work you have studied to date. At whichever level you are studying your Algebra should be at a standard where you can manipulate expressions with ease.

Some resources to help you prepare and will be useful reference material for you during your course…

Make sure you have some useful apps on your phone if you don’t have them already. Mathscard app from Loughborough university is free and a handy reference guide of mathematical facts and formulae. Every student should have the Desmos app (free) and you could also get the  WolframAlpha app (low cost).

Sign up to Brilliant and follow them on Facebook so Maths problems appear in your stream and hopefully distract you from trivia!

For students going on to A Level then these GCSE revision resources will be useful. The takeaways are really useful and Mohammed Ladak has picked out Transition Takeaways specifically chosen to help with A Level Maths preparation.

You could also look at Step Up to A Level Maths from The Centre of Innovation in Mathematics Teaching which helpfully lists skills you should be confident with and provides resources to support your study of these skills.

As you study your A level course you may find some of the material in the section below useful.

If you are preparing for university, then make sure your A Level knowledge is secure – perhaps check the Algebra Refresher from The Mathcentre which has many questions and the answers are at the end of the document. The The Mathcentre has an extensive collection of helpful resources for students of Mathematics.

Calculus workbook from Plymouth University

Calculus workbook from Plymouth University

For older students AJ Hobson’s Just the Maths (individual pdfs hosted by UEA) (or a complete pdf from the Math Centre:   AJ Hobson’s ‘Just the Maths’is very useful as is the excellent Math Centre site which includes extensive resources. The quick reference leaflets which are available on numerous topics are very clearly written and succinct, see these for example on the Product Rule and the Quotient Rule. There are also teach yourself booklets, revision booklets, videos and diagnostic tests. See also these very clear notes with exercises from Plymouth University. There are many free courses available from The Open University and MIT .

The HELM Project. If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include clear worked examples. You can see on the list that a very small number of titles are ‘not ready yet’; for the sake of completeness the complete set is hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.

See this Evernote shared notebook: Mathematics notes for many more useful links. Several universities have created very helpful Mathematics support which they have made available to all students. (You do not need an Evernote account to view the notebook).

If you are studying or about to study at university then have a look at Kevin Houston’s ‘How not to get a good mathematics degree‘ and ‘How to get a good mathematics degree‘. He also has provided a pdf file you can download: 10 Ways to Think Like a Mathematician. Kevin Houston works at the University of Leeds in the UK.

From Professor Stephen Chew of Samford university, this series of 5 videos looks at how to get the most out of studying (any subject, not just maths). Part 1 includes ‘beliefs that make you stupid’!
How to get the most out of studying (Part 1),  Part 2,  Part 3 Part 4Part 5

The Open University has several helpful publications for students of Mathematics. Many of these resources would be helpful for students still at school.

From John Kerl – see these excellent tips for mathematical handwriting.

For older students Peter Alfeld wrote this guide on Understanding Mathematics for his students at Utah University.

And finally – check the 11 Commandments of Mathematics!

Wishing Mathematics students everywhere – whatever stage you are at a very successful year.

New Academic Year Resolutions

New Academic Year


Happy New Academic Year  (using geoGreeting) (Click on the image).

Many of you will still be enjoying your holidays but holidays are perhaps a good time to make some resolutions for the next academic year.

Firstly, remember the ten eleven commandments!

To elaborate a little more on some of these:

5 – looking it up – there are several excellent resources online for you to look up definitions or find extra examples. Never rely on just one source if you are finding a topic tricky, it can be helpful to see explanations written by different authors.

6 – To learn Mathematics you need to do Mathematics. You can never do enough examples! There are plenty of questions here (with answers included). Have you looked at the problems on Brilliant? New problems are published regularly and are suitable for younger school students all the way through to university students. Or perhaps you might like to try some of the trickier problems from the challenges set by the University of Mississippi. (These problems from the Problem of the Week category are open to people of any age).

9 – if you want to practise your arithmetic you could play some games! If you enjoy Maths games there are many excellent free resources available.

10 – on writing the language of mathematics correctly – see  this clear guide to writing Mathematics from Dr Kevin P Lee and from John Kerl some excellent tips for mathematical handwriting, many of these tips these apply to students of all ages – do you distinguish carefully between a 1 and a 7 for example? Perhaps it is hard to tell whether you have written a 2 or a z or perhaps your 5s look a bit like a letter s?

Have a look at Peter Alfeld’s  guide to Understanding Mathematics which he wrote for his students at Utah University.

Are you familiar with all the excellent (free) resources online to help your studies? Have you tried the brilliant Desmos graphing calculator for example, or used WolframAlpha to check your work?

Some more thoughts for you.

If you are trying to get organised generally then some of the resources on this page might be useful. I recommend Evernote highly (it’s free).

Wishing you all a very happy and productive new academic year!