Look at this illustration of three places around the school. There is a grid of classroom windows, where the first column has one window, the second has two and the third has three. There is a railing fence that goes tall, short, tall, short all the way along. There is a brick wall where each row above the first adds the same number of bricks again.

Each of the three hides a pattern. Which one would be easiest to describe to a friend on the phone, with no picture to help them, so that they could say what comes next?

Here is a pattern from around the school. We will work through two patterns, one that grows and one that repeats, writing a rule for each the way you will write yours today. As we work through each one, listen for how the rule lets you predict a term you cannot see.

Today we work through one full pattern-hunt entry together on the board: the paving slabs outside the door.

First we count the slabs step by step. Then we write the rule three ways: "they keep going", "add one slab each step" and "step n has n slabs". After that we decide which of the three tells a friend the most. Last of all we test the best wording by predicting step 10 before anyone counts that far.

Now you become a pattern hunter around the school. Work on your own, and use the checklist on the screen as the list of what you have to bring back.

Your checklist has four lines. First, find one growing pattern and write down what it is, the counts for the first few terms, and its rule in words. Then find one repeating pattern and write down the unit that repeats and how a friend would know what any railing, tile or brick looks like. After that, write a position rule for at least one of your patterns, in the form term n has ___, and use it to predict a term further along than you counted. The fourth line is the one marked STRETCH, which means it is the harder extra: only start it once the first three are done. For that one, find a pattern that goes up in steps bigger than one and work out a term you cannot see, such as the fifth row of a wall.

For every pattern, count enough terms to be sure before you write the rule.

Underneath, write the rule in words so clearly that a classmate could draw your fifth term without asking you a single question. Then note which pattern you met today was the hardest to put into words, and say why.