….so what is going on with all of these? Can you use Algebra to show why they work?
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…
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.
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.
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.
From Mathiversity – see Online Spirograph where you can create, admire the gallery or read user Chiron’s essay which explains the workings of the Sprigoraph toy in an unusual way.
Mathiversity – Spirograph Gallery
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.
Select the image to see the solution
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
or share your great code!
You can follow CodeMonkey on Facebook or Twitter.
Click on the image and then on the slider!
This year you can even use the Desmos API …
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.
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!
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.
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!
How about some mathematical songs?! (Click the link for a list of song links).
My students like these, particularly the Circle Song!
The Klein Four are a bit beyond school Mathematics you may appreciate this if you are studying a Mathematics degree!
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.