Repeats first: cracking a vertical code

The scariest-looking question on the paper

Some figures down the left, each with a code beside it. One more figure on its own. Five codes to choose from.

Pupils tell us codes are the questions they dread, and it is easy to see why — a page of shapes, a page of letters, and no obvious way in.

So here is the thing worth holding on to for the whole lesson: there are only ever two or three letters to crack, and there is one rule that cracks nearly all of them.

One position at a time

Each letter position describes a different feature. The first letter might be the shape; the second might be the shading. Separate jobs.

So do not try to work out what the whole code means at once. Work out what the first letter means. Then, separately, the second.

The reason is not tidiness. Working memory can juggle only so much, and two unknowns plus four pictures is more than anyone can hold. One unknown is easy.

Cover the second letter with your finger. Solve the position you can see, then move your finger.

The rule that cracks it

Find a letter that repeats. Ask what those figures share that the others do not.

That is the whole thing — and it is worth understanding why it must be true rather than taking it on trust.

A code letter describes a feature. If two figures both got the letter K, then whatever K describes, they have both got it. And if a third figure has no K, then it has not got that feature. So the difference between the K figures and the non-K figures is what K means.

So the first move, every time, before looking at the options at all: run your eye down one letter position hunting for a repeat.

Repeats First, in four steps

1. Take one position at a time — never the whole code at once.
2. Find a letter that repeats in that position, and name what those figures share that the others do not.
3. If nothing repeats, the letter must describe the one feature that is different in every figure.
4. Write each meaning down, then build the new figure's code letter by letter — and check all of them before committing.

Where do pupils lose marks?

Trying to solve the whole code at once, and running out of working memory.

Deciding a letter's meaning from one figure, without a repeat or a contrast to prove it.

Grabbing the first option with the right first letter.

Writing the letters in the wrong order after getting both right.

How can we practise this at home?

The same drill as horizontal codes, and it is better than solving: write codes rather than crack them. Six objects, two letter positions, one for material and one for colour. Hand it over and ask what the code for a seventh object would be.

Then get one wrong on purpose — repeat a letter where the feature is not actually shared — and see whether it gets caught. Spotting a broken code is the same move as proving a rule.