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.


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!

The Nrich problem ‘Making Maths: Planet Paths‘ challenges students to draw some planet paths using a Spirograph. In case there is no Spirograph to hand they give instructions for making a simple one.


Spirograph – Desmos

Alternatively try an online version. Try Spirograph on the Desmos Graphing calculator.

From comes this very clear and easy to use applet (the moving circle is outside the fixed circle).

Spirograph - Autograph Activity

Spirograph – Autograph Activity by Owen Elton

Owen Elton has written an excellent Spirograph Autograph activity (see Simon’s comment below) and also available on the Autograph player a very impressive 3D Spirograph!

For GeoGebra fans there are various applets available, including this which allows colour changes.


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. There are 30 challenges to try which are all free.

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.

Graph Art

Darth Vader curve

Darth Vader-like curve on WolframAlpha

Did you know you can plot Darth Vader on WolframAlpha?! There are many more fun curves! A dalek perhaps or Batman?!

PacMan on Desmos by Alec Schultz

If those equations are a bit much you could try something simpler  using the Desmos graphing calculator; for example look at Alec Schultz’s PacMan.

Art Elements

Try some Art on Desmos! Select the image, reload page if necessary.

To experiment click here or on the image above to see how this was created and experiment yourself. (In case you see a blank graph screen just reload the page).

Lovely evening by Petr Feidler on Desmos

Desmos have a whole gallery to inspire you! You can of course get very sophisticated. Look at this lovely evening by Petr Feidler! Note the use of inequalities for shading and the slider!


Send a math-o-gram …

Note this was a special for Valentine’s Day. Look out for this next time!

Mathematics, Learning and Technology

…to the one you love – or any of your mathematical friends!

Note that this was a special for Valentine’s Day – look out for this next year!

Desmos valentine

Choose one of the supplied romantically mathematical designs, add a custom message and send it off! Being a Desmos math-o-gram there’s more – using the slider, the hearts on this design will dance! (Click on the image).

Desmos valentine 2

Sending Valentine good wishes to mathematicians everywhere!

….and in case you have not used Desmos before you might find some of the posts on this page useful.

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Lots of lovely puzzles!

set game 231212

There are many excellent puzzle sites freely available, have you seen the excellent Set Game from the New York Times? How many sets can you find? Click ‘How to play’ in the menu on the left for the rules. A new puzzle is set every day.

Other favourite puzzle sites are provided here on Mathematics – Games. Erich Friedman’s Puzzle Palace site for example includes numerous mathematics puzzles.

Another great collection comes from Simon Tatham, I have been enjoying his ‘Untangle’ puzzles; note that it is possible to change the number of nodes – use the Type menu.

You may be familiar with Suduko and Kenken type puzzles, have you seen Rogo?

Wishing students everywhere a very Happy Christmas. Good luck with any examinations you may have early in 2013.

Can you solve this problem?

This has been doing the rounds on the Internet recently.

This problem can be solved by pre-school children in five to ten minutes, by programmers in an hour and by people in higher education ….well, check it yourself!

I’m pleased to say despite my various Maths degrees I solved the problem quickly!
I obviously have the mind of a pre-schooler!
You can find a hint then check the answer here.

I present the problem as posed everywhere – though it looks like a misuse of the = sign!
Only put an equals sign between equal expressions!

Sporkle Mathematics Quizzes

You may have tried the Sporke site with its extensive collection of timed quizzes.
There are several mathematics quizzes available. It is also possible to create your own quizzes, give the link to your friends and see how they do!

Can you give all the missing prime numbers in 2 minutes or less?
Can you square the numbers from 1 to 25 in 2 minutes or square the numbers from 1 to 50 in 4 minutes?!

Can you get the correct answers to 60 simple calculations in 1 minute? A mistake will end the quiz.