It’s Christmas time!

So,Nrich Advent 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 where you will find some of their favourite books and other mathematical toys.

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 the Desmos Christmas treecover?! 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 with a very clear tutorial on how to make a greeting card; not a great work, but I did enjoy playing with Scratch: here’s one I made earlier!  If you are feeling creative you might like these Christmas fonts.

On the subject of coding and Christmas trees you might enjoy  Holiday Lights where you can use coding to light up a holiday tree outside The White House. Holiday Lights comes from Google as part of their Made With Code initiative. Note that Google’s Blockly is being used for the code.

For some rather more advanced coding, there’s a rather nice Christmas tree generator here; select Auto Generate and sit back and admire the tree! Note that for any Scratch project you can ‘look inside’ and see the coding – a good way to learn more syntax.

Christmas Tree Scratch

Scratch project by vidarfw02

Wishing students (and their teachers!) everywhere a very Happy Christmas.


Spirograph by Nathan Friend

Inspirograph by Nathan Friend

As a child my Spirograph was definitely a favourite toy so I was delighted to find this digital version, Inspirograph by Nathan Friend. Try altering the gears so that the fixed and rotating gear are the same size, or make one size a factor of the other, make the two sizes have a common factor, or not! Investigate.

You can change the colours too and create a work of Art!

For some more Spirograph resources including from the awesome Desmos graphing calculator see this post.


Quadratic Inequalities

Quadratic Inequalities

Select image for the Desmos page

To solve a quadratic inequality such as x2-6x+8>0 the best approach is to find the critical values of x which make the value of the function 0 and sketch the graph. Here we can factorise so we see that we require (x-2)(x-4)>0 We are looking for values of x to make x2-6x+8 positive. We see that y is positive when x>4 and when x<2.

Note the link to another Desmos page where you can look at further quadratic functions.

Select link to experiment

Select image to experiment

If you wish to see some worked examples and try some exercises you could check The Maths Teacher – See Algebra AS Level – Inequalities: Linear and Quadratic. Note the choice of video / transcript or go straight to the exercise with worked solutionsYou may find other useful resources here too.

You could of course use WolframAlpha to check the solution to any inequalities and generate as many examples as you want. Simply type in the inequality and plot as well as the he solutions will be returned.

Quadratic Inequality

Select image for query on WolframAlpha




Matrices Resources

A new slideshow on matrices has been added to the WolframAlpha series.

See the spreadsheets by Mike Hadden MatrixDeterimant and MatrixInverse, these enable you to check answers and see working out as well.

If you are looking for notes and examples on Matrices then the following are useful sources and appropriate for Advanced and degree level students.

Notes and examples
Chapter 9 on Matrices and Transformations from the CIMT Further Pure Mathematics A Level material,
Just the Maths,
The Math Centre
and 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.


Code Monkey learn coding

Students of all ages, how are your coding skills? Why not try the challenges on CodeMonkey? This is a great way to learn to code if you have little experience – and still fun if you do have some coding skills already.

Can you help the monkey get all his bananas? Look at this simple example – challenge#8; click on the image to see this solution. Note that you learn about loops in later challenges.

Code Monley Example

Select the image to see the solution

Code Monkey stars
After each challenge is successfully completed, you will receive a number of stars, note the meaning of each. Did you get all the bananas? Did you use what you learned and were you efficient in your coding?

You have the option to return to the challenge return


or share your great code!

You can follow CodeMonkey on Facebook or Twitter.


Research UK university courses with SACU. The site is useful for students of any subject anywhere however as you can take the Spartan Test to help you find the right course; the test is quick and fun to do – select images which best describe you!

You can use the Research Tools (all free to use) to take the Spartan Test, explore subjects, courses, the UK map and Apprenticeships; You can also look at possible careers. The gallery below will give you an idea of the wealth of information available and different ways to explore it. The site is intuitive to use and very well designed.

This slideshow requires JavaScript.

Explore Mathematics

There are many sites where you can explore Mathematics beyond your school syllabus – try some of these:

Maths Careers this site, managed and maintained by the Institute of Mathematics and its Applications has extensive information on careers in Mathematics and applications of Mathematics in everyday life. Note the various tabs such as Science and Engineering at the top of the page and pages for various age groups, see 11-14 for example.

Nrich (note you can search for a topic)

Mudd Math Fun Facts

Amazing Number Facts

Magic Squares

Mathematics in various cultures

A quiz to find a mathematician who shares your interests!

Mathematician of the day


Mathematicians – timeline

Maths is good for you!

Mathematical Moments an extensive collection of pdfs on many different topics in science, nature,technology, and human culture.

Platonic Realms

Mega Mathematics

Famous curves index

Mathematical Images

Fractals video and Play with Fractals!


Plus Magazine

Mathematics News from Science daily

Virtual Mathematics Museum

 For older students:

Mathematical Gems and Understanding Mathematics from Peter Alfeld – University of Utah

The Mathematical Atlas

Famous curves index

Reading list from Cambridge which should interest any student of Mathematics

Mathematics Book Reviews

STEP (university admissions papers)

STEP – Worked examples

Introduction to university Maths from the University of Bath

Lots more questions!

Perhaps you are revising for end of year exams. If you want some basic practice then David Watkins has an extensive collection of spreadsheets so you can try as many questions as you like on many topics at your chosen difficulty level and then check your answers. The spreadsheets can all be found on his Dynamic maths site.

Search Dynamic Maths

Search Dynamic Maths

Start by searching for the topic you want; let’s suppose you want to look at adding and subtracting directed numbers. Select the down arrow in the search box and select the topic you want; here we need integers. You will then see a selection of Dynamic Worksheets which are all Excel files. If you want to add and subtract integers then choose Integers-01 and download it. Once you have your Excel file you can practise as much as you want as you can generate as many questions as you like.

You will need macros enabled.

Dynamic Maths - Integers

Dynamic Maths – Integers

Note that you have several choices, you can show answers when you are ready to check; you can choose the number and type of questions and so on.

For more sites with lots of questions see this post which includes questions for older students too.


Algebraic Fractions

A collection of resources for you to learn and practise algebraic fractions.

For a basic explanation see Mathisfun and note the questions to try at the end of that page.

The University of Hull Mathematics notes seem very clear, in the Algebra section we have clear notes and exercises with answers on Algebraic Fractons. The notes and exercises include adding, subtracting, multiplying and dividing algebraic fractions.

Algebraic manipulation from Just the Maths includes a section (1.5.4) on Algebraic fractions.

The mathcentre has a section on simplifying algebraic fractions. On the subject of algebra generally, the mathcentre has a very useful refresher booklet.

From the Centre for Innovation in Mathematics Teaching see section 10.13 of this chapter on equations for examples and exercises with algebraic fractions. You could check answers to the exercises on Wolfram Alpha. For example :

Select the image top check answer on WolframAlpha

Select the image top check answer on WolframAlpha





By Colleen Young Posted in Algebra