Dec 042013

Looking around for investigations for our multiplication and division unit I came across a great activity exploring visual patterns, called spirolaterals, in the times table.

Through this inquiry students:

  • practice times tables
  • visually represent patterns in numbers
  • look for patterns
  • make predictions
  • test and refine predictions
  • make generalisations
  • share ideas
  • challenge each other’s ideas

Thanks to Cristina Milos for sharing this activity on Twitter!

IMG_3094Very briefly, the spirolateral is a visual representation of the pattern created through adding the digits of the multiples in a times table.  Initially I had the students draw the patterns by hand.

The patterns produced reminded me of the only tech tool I had available to me as a student teacher in 1991 – the Valiant roamer – based on Logo and guaranteed to impress my tutor.  Ask around and these days you get pointed in the direction of Scratch and Turtle Art. Whilst a handful of students had experience of coding using Scratch, either through personal interest or the school’s after school activity, Turtle Art proved to be preferable due to it’s smaller number of functions (aka distractions).

The first lesson focused on learning how to use the program and the students quickly reproduced what had been painstakingly hand-drawn. 

Here are my observations on the pros and cons of using coding for this activity:


  • created patterns quickly
  • less prone to human error with counting squares
  • errors in the pattern quickly spotted and easy to fix
  • lots of collaboration with helping each other out when trouble-shooting


  • more mistakes made with simple maths – times tables, finding digital root etc
  • fewer aha moments – maybe as they didn’t watch the pattern slowly emerge or more likely that they were too focused on and excited about the programming itself
  • less collaboration on mathematical findings

We returned to the same activity and used their 1-9 times table spirolaterals which were now accurately constructed and neatly organised on their blogs. With a focus on looking on the patterns, rather than learning how to code, students discovered generalisations that we are still trying to explain.

So – next time will I start with coding and not have the students draw out their patterns first? Probably not. However, I am aware of the fact that the novelty of coding influenced the focus and direction of the lesson. This has been a great way to authentically introduce my students to coding and I am currently exploring the endless possibilities for integrating coding into our maths curriculum and beyond. I’d love to hear what you are doing.

  One Response to “Times tables and turtles”

  1. A really great activity. I am surprised you didn’t add “Experience with coding – and all the logical, mathematical thinking that includes – in the “pro’s” list.

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