Make a pattern

There is a wonderful site called http://visualpatterns.org/ where you can view all sorts of visual patterns that people have submitted. The idea is to work out the next in the series, and then to see how each step is created so that you could predict the 43rd one.

In Year 5G we tried out some of the simpler ones, like this one, submitted by Nic Doran:

How many Lego pieces are in step 43?

We'd already been looking at some sequences, like:


but it was time to create our own:



Here are some of our patterns:

We then set about understanding the pattern mathematically:

• How does the pattern grow?
• What number does it grow by each time?
• What number is there in each step of the pattern?
• Can you write this with algebra?
• Can you work out what the 43rd step in the series would be?

We began to answer some of these questions:

The next day we documented our patterns on squared and isometric paper, and tried to understand the mathematics involved. Here's an example on the whiteboard: