Look at this row of numbers: 2, 5, 8, 11. Each number in the row is called a term: 2 is the first term, 5 is the second term, and so on. Something is happening as we move from one term to the next. What do you think comes after 11?

A function machine takes a number in, does the same rule every time, and sends a new number out. Watch each machine on screen and see if you can work out its rule. What is each one doing to the number?

Now we explore a hidden-rule machine together on the board. A number goes in, a different number comes out, and the same rule works every time.

Now we try a machine that does two things to each number, just like the 'double then add 1' machine we watched.

Someone puts a number in. Before we reveal the answer, the class works out both steps out loud: first the doubling, then the adding. Then we check the machine agrees with us.

Now we work through these hidden-rule machines together. Each one keeps its rule secret. We probe a few inputs, work out the rule, then check it on the next number.

What we did today

• Every pattern has a rule that takes you from one term to the next.
• Some rules use one step (add 3); some use two steps (double then add 1).
• A good rule works for the whole sequence, not just the last number.

Coming up

Next we will get better at putting a rule into clear words — naming both the action and the amount — so that someone else can use your rule to continue the pattern without any help.