Patterns of cubes - the first in the sequence

Looking at patterns and how they grow is something we've done lots before. But this time in Year 4 we took particular time over something different: what exactly the first step should be.

Look at this pattern here, a pattern of "C" shapes:

We had a long discussion about that first single cube. Did it really belong in the sequence? Some thought yes, some no. We didn't really come to a definite conclusion, but the good thing was that we were able to explain our reasoning one way or the other.

For instance with this pattern of "H"s:

The two girls were more than happy to explain their thinking:

Click on picture to see video

How about these other sequences? Do you think the first one is right? 

You can see more of this Year 4's mathematics learning on the Y4 blog.

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: