Here is a number pattern: 4, 7, 10, 13. Look at it closely. If a friend handed you this pattern with no working, could you say what to do next in a way they would understand?

Hands up: in your own words, what is the rule?

Four number machines, each with its own rule. Look at each machine and the numbers that go in and come out, and see if you can say what the machine does. The last one does two things in a row, so look closely.

Here is the part that matters most: if you add 1 first and then double, you get a different number. Start at 1, add 1 to make 2, then double to make 4, not 3. So the order of the two jobs is part of the rule, not just the jobs themselves.

Today we work on saying the rule out loud. Watch this machine: every number you send in comes out the other side, and the machine always does the same thing.

Today we work through these hidden-rule machines together. For each one, watch a pair go through, say the rule in words, predict the next number, then let the machine check it. If your wording does not predict the right number, that is fine — we just change the wording and try again until it works.

What we learned today

• A good rule in words names the action and the amount, so another person can predict the next term (the next number in the pattern).
• You test a rule by predicting the next number, then refine the wording until it always works.
• Some rules do two jobs in a row, and the order matters.

Coming up

Next we put these rules into a table of values, sending many numbers through the machine at once and recording each input next to its output.