I discovered the art of Spirolaterals a few weeks ago when on a mission to find some more exciting ways of exploring times tables. I was fascinated and immediately gave it a go.
I quickly discovered that learning the art of Spirolaterals supports the learning of how to find digital roots, which comes in very useful when teaching divisibility tricks.
It is also a fantastic activity for developing reasoning skills. Once you have created the Spirolaterals, it opens up discussion and brings about questions such as:
- Which ones are the same/similar?
- Why might this be?
- Which is the odd one out?
- Did anything surprise you?
- Which pattern do you like the best?
- Why?
If you’re reading this post, the chances are you’d like to learn how to create these fascinating mathematical works of art! Here’s how:
Choose your times table you’d like to represent.
Write the times table out (I’ll use 5x as an example):
Next you have to find the digital roots of each number. To do this, you add the digits together until you are left with a one-digit number.
As you can see, the sequence starts repeating again after the 9.
N.B the digital root of 65 is 2 because 6+5=11 and 1+1=2.
Once you have the sequence (shown in red) you are ready to create your spirolateral. Simply get some squared paper (smaller squares are best) and draw lines of the lengths in the sequence, making sure you always go in the same direction. I always tend to go clockwise.
This is where it repeats:
Continue until it links back upn again with the starting point (shown by the red dot).
It will end up looking like this:
My pupils were fascinated when we had completed them all why the 4 and 5x table made the same pattern. We then investigated the digital roots of each one and made some incredible discoveries! Let me know what you find out!
