Valentines day is coming

Desmos Valentine

Click on the image and then on the slider!

Desmos Valentine instructions

Why not send your mathematical friends (or anybody else!) a Desmos ValentineThe wonderful team at Desmos have made their brilliant math-o-grams available earlier this year….and watch out for new designs coming soon.

The math-o-grams are really easy to create; why not give it a try? Just select your design, add your message and share!

Mathematical Handwriting


John Kerl – Tips for mathematical handwriting

Is your writing legible? Is that a 5 or an s, a 2 or a z? Included on the Study Tips page see John Kerl’s Tips for mathematical handwriting.

Dr Kevin Lee - A Guide to Writing Mathematics

Dr Kevin Lee – A Guide to Writing Mathematics

Is your writing clear and well structured? Easy to read and follow?
You will find some excellent examples from Dr Kevin Lee in his Guide to Writing Mathematics.

See also Ten Simple Rules for Mathematical Writing from Dimitri Bertsekas.

Algebra Examples & Exercises

These sites are mentioned elsewhere on this site but these all include notes and exercises on Algebra. Answers are included in these resources and of course you can check answers on WolframAlpha.

Note there are resources for older students further down the page.

For younger students (age 11-16) try the Interactive Tutorials from The Centre for Innovation in Mathematics Teaching, (CIMT).
Fundamental Skills   Function Machines   Linear Equations   Basic Factorising
Expansion – Single Brackets  Linear Equations with Brackets
Factorising Expressions 
Substitution into Formulae 1     Substitution into Formulae 2
Linear Equations 1   Linear Equations 2
Coordinates   Plotting Straight Lines   Graphs and Gradients
Laws of Indices   Negative Indices   Fractional Indices
Straight Line Graphs   Linear Equations   Parallel and Perpendicular Lines
Simultaneous Equations   Equations in Context
Equations, Formulae and Identities   Simplifying Expressions   Factorising  Using Formulae
Quadratic Equations: Factorisation  
and by Completing the Square

The following example – note the colours shows how to expand three brackets.
You could check your answers on WolframAlpha and change the query to make up your own examples.
Expand Brackets Colleen Young

The Maths Teacher (age 11-17)
David Smith’s site, The Maths Teacher has an extensive collection of videos to help you study Mathematics. GCSE (age 14-16, though many of these resources would be helpful for younger students also) and A-Level (age 16-18) lessons are available. For each topic not only is a video available but also a transcript and exercises with worked solutions. This makes the site ideal for revision – you have the choice of perhaps just trying the exercises or if you feel you need more help you can watch the video – whatever is right for you.

Trinity school (age 11-16)
Trinity School have very helpful Mathematics resources – many examples for you to try (answers included) including Algebra.
Trinity School Nottingham - numerous questions and answers

Trinity School Nottingham – numerous questions and answers

For older students who have already studied many topics in Algebra, CIMT’s Step Up to A Level Maths includes notes and examples on Basic Algebra, Quadratic Functions and Equations and Inequalities. These exercises could also be used by GCSE students aiming for the highest grades. Another very useful publication is the Algebra Refresher from The Mathcentre which has many questions with the answers provided at the end of the document. Also from the Mathcentre you can view all the topics available – several different resource types such as notes and videos are available for each topic.

Sections 1 (Basic Algebra) & 3 (Equations, Inequalities and Partial Fractions) of the very helpful Helm Workbooks include worked examples and exercises (with answers).

Plymouth University Algebraic Fractions

Plymouth University Support Materials

Plymouth University have some very clear workbooks, try Basic Algebra – Brackets for example or Algebraic Fractions.

For videos try the following sites:

Exam Solutions GCSE Maths     

Exam Solutions A Level Maths (select your exam board from A Level Maths tab)

Hegarty Maths GCSE      A Level  and KS3 for younger students (11-14)

and note The Mathcentre, already mentioned above.


Happy New Year

Math Forum @Drexel 2016 Year Game

Math Forum @Drexel 2016 Year Game

If you want a little something to do then try the Math Forum Year Game. How many numbers from 1 to 100 can you generate using the digits of 2016? Unlike Countdown which uses only the four operations and brackets, additional operations are allowed – see the detailed rules.

And did you know 2016 is an evil number!

Perhaps a good time to remind you of some resolutions I suggested for the New Academic Year:

Firstly – remember the 10 11 Commandments…

or as a poster: 11 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.

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? Do you have the GeoGebra app on your phone?

GeoGebra AppGeoGebra announced the release of their GeoGebra Graphing Calculator earlier this month; currently available for Android, the app will also be available for iPhone and Windows – watch for announcements.

For all the information you need to learn how to use this outstanding app for Mathematics see “What is the GeoGebra Graphing calculator?” and all the Tutorials available.

Having downloaded the app to my phone I can confirm it works really well and i was easily able to follow the instructions given in the links here.

I very quickly created the diagram in the screenshot from my phone below. Using a finger one can drag point D around and note the angle at the circumference. With an account you can also save your files which are standard GeoGebra files.

GeoGebra App

GeoGebra App

Follow GeoGebra on Twitter or Facebook

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 year!

Christmas 2015

Plus 2015 Advent

Plus Advent 2015

So, time to relax and what better way to relax than with a puzzle or two?!

On Nrich you’ll find a collection of advent calendars a Sudoku for each day perhaps? (Solutions are supplied if you want them). Or a tangram? Maybe you want to play a game? (Clearly the year doesn’t matter for an Advent Calendar!)

Plus Magazine also have an Advent Calendar which this year has puzzles and articles designed with your creativity in mind.

For many more games and puzzles, see this collection including a challenging logic puzzle from Coolmath Games – can you set the circuits to light up that Christmas tree?!  If any of you have any little relatives they might enjoy Top Marks’ collection of their favourite Christmas Activities.

Perhaps you could make your Mathematical friends some cards! Why not put a Desmos tree on theDesmos Christmas tree cover?! Note this is simply a collection of lines and circles, as you can see from the syntax it is very easy to restrict x or y values. (For more on getting creative with Desmos, see Graph Art).

Staying with the subject of cards you can practise your coding skills with this Scratch project.
Scratch card

Turn the sound on!

If you are feeling creative you might like these Christmas fonts.

Wishing students everywhere a great Christmas.


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