Why not send your mathematical friends (or anybody else!) a Desmos Valentine? The 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!

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.

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.

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.

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

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 Workbooksinclude worked examples and exercises (with answers).

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.

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.

10 – on writing the language of mathematics correctly – see this clear guide to writing Mathematicsfrom Dr Kevin P Leeand 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?

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.

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 Calendarwhich this year has puzzles and articles designed with your creativity in mind.

Perhaps you could make your Mathematical friends some cards! Why not put a Desmos tree on the cover?! Note this is simply a collection of lines and circles, as you can see from the syntaxit 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.

Turn the sound on!

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

The online encyclopedia of integer sequenceswill 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.

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 Aidaims 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!

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

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
Double
Add 4
Halve
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?

For high quality free courses sign up to FutureLearn. Looking 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 Studystrikes 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.

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.

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