There’s a brilliant animation of number patterns from Stephen Von Worley. You can find it at http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
Try it straight away. It displays first a single dot, then two, then three in a triangle, four in a square, five in a pentagon. From 6 onwards, the number is likely to be shown as a pattern, so for 8 you get two squares of four.
As you explore, it becomes clear that the displays aren’t any old pattern, but are based logically upon the factors of each number.
I’ve not seen so much excited discussion in my classroom for ages. My Y6 children were transfixed. Words and descriptions tumbled out, ideas and predictions were offered, challenged, revised, replaced.
What would 9 look like? There were two opinions. One was we’d see a hollow triangle, the other was that we’d get a triangle of three small triangles. What delight to find both were correct, and the two suggestions were offering alternative descriptions of the same pattern.
If your pupils are anything like mine, one snag you often find when they’re solving a problem is the failure to build on evidence. Not here. Several times when trying to predict a number they asked to look at a relevant previous one. When thinking about 15 it was “Can we see 5 again?”, and used this to decide that 15 would show a pentagon with each vertex a triangle of three dots.
A week after the first session they were knocking the door down to take things further. Why were some numbers not in a pattern but arranged in a circle and labelled “Prime”? Why did we never get two of these in succession? Which numbers were made up of block of four dots in a square?
I had plenty of frustrations. It moves quite fast and the display changes every second, so we need to stop it each time to look at the pattern, and talk about it and discuss what the next one will look like. The control buttons are quite small, so I often miss. And I dearly wanted to be able to call up a number of my choice. But if we want to see what 243 looks like (and you probably will) we have to start again from the beginning, and what seemed fast now becomes rather slow. There is a faster speed option, which changes three times a second, but even that’s prohibitive when we want to explore larger numbers. My pupils were delighted to learn it would display up to 10 000, less so when we talked about how long it would take. By the way, to reset we have to tell it to count back all the way to 1.
I got round some of these problems by taking snapshots of the display for all the numbers up to 100. I’ve put them into a Powerpoint that gives me greater control, and made subsets with odd numbers, even numbers, and multiples of 3, 4 ,5, and 6. When we got back to the classroom after half-term I was pleased I’d done this; it worked really well and we spent a whole hour working through the first thirty or so counting numbers. Virtually nothing went on to paper, but a thousand diagrams were drawn in the air, and as the session went on – and the numbers and patterns increased – these were often dispensed with, so one person’s mental image was articulated and received and understood by their partner.
Yes, I do wish it offered a few more options, but make no mistake – I’m 100% sold on the animation. It’s brilliant, it’s free, and though I was using it with 10 yearolds it will entrance and stimulate any group of children and adults. If you haven’t tried it already, you should do so at once.