Building Your Own Number Patterns?

You can use just about anything you find around the house or garden to build your own number patterns: blocks, coins, seashells, gumnuts, toothpicks - whatever you like. You could even use the peas that are served up for dinner, but your parents mightn't be too happy to see you playing with your food.

Here's an example of a pattern built out of blocks:

How many blocks are needed for step 5?

Can you come up with a formula that will tell you how many blocks are needed for each step? Notice that two blocks are added to each step to form the next step. So, the formula might look something like this:

I came up with this formula:
Let's test it out for the steps that are shown:

Step Number	Number of Blocks	Number given by formula
1	1	\(2 \times 1 + 1 - 2 = 1\)
2	3	\(2 \times 2 + 1 - 2 = 3\)
3	5	\(2 \times 3 + 1 - 2 = 5\)
4	7	\(2 \times 4 + 1 - 2 = 7\)

This is looking pretty good!

Another Example

How about this pattern?

Notice that step 2 is obtained from step one by adding 2 blocks to it, step 3 is obtained from step 2 by adding three blocks to it, and step 4 is obtained from step 3 by adding 4 blocks to it. The numbers corresponding to the steps of this pattern are called the triangular numbers because you can arrange them to form triangles. It's not quite so easy to come up with a formula for this pattern, but why not have a try?

A Third Example

The numbers in this pattern also have a special name:

They're called the square numbers because they can be arranged to form squares, just like in the picture above. There's an easy formula for the numbers in this pattern. It's

Conclusion

Number patterns are found all over the place. Why not have a play and see if you can come up with some interesting patterns of your own? Just don't tell mum and dad that I was the one who said it was OK to play with your peas! That can be our little secret.