Two rules at once: series questions

What the question is really asking

Five squares in order, one missing, five options.

The series is built from a rule applied by the same amount every step. Find the rule and the missing square stops being a guess — it becomes a calculation.

And here is the difference between a Year 4 question and an 11+ one: one rule is a Year 4 question. Two rules at once is the standard 11+ question.

The S.T.E.P. method

S — Spot it. Compare two squares that are side by side. T — Track it. Confirm the change repeats by the same amount. E — Every part. Look for the second rule. There usually is one. P — Predict it. Decide the answer before reading a, b, c, d, e — then check it against the square on each side of the gap.

The E is where the marks are won and lost.

The six rules

Position — round the corners, round the edge, or one place along. Shading — a repeating cycle, usually of three. Rotation — a quarter turn or an eighth of a turn each time. Size — growing or shrinking by the same step. Number — one more, or one fewer, each time. Sides — the shape gains or loses a side.

Almost every series question in the test is one or two of these. That is a short enough list to hold in your head, which is the point of having it.

When two rules run at once

Deal with them one at a time. Never both together.

1. Work out rule one and write down what it gives you.
2. Ignore it completely. Work out rule two.
3. Put the two answers together, and find the option that matches both.

Options that satisfy only one of the two rules are the commonest trap on the paper — and there are often two of them, one built from each half of the rule, so a child who half-solves has a very tempting answer waiting.

Where do pupils lose marks?

Solving only the first rule.

Off by one. The gap is the fourth square, so the rule gets carried on from the fifth instead of from the third. Anchor on the square immediately before the gap and move exactly one step.

Direction slips. Clockwise and anticlockwise look the same when you are rushing. Trace the path with a finger across three squares before deciding.

Working left to right when the gap is first. If the gap opens the series, find the rule from the squares you can see and run it backwards one step. The rule still holds.

How can we practise this at home?

Build them rather than buy them. Four boxes, a dot moving round the corners, and a shading cycle of three underneath it — that is a genuine two-rule question and it takes a minute to draw.

The habit worth insisting on is saying both rules aloud before choosing. A child who says "the dot moves clockwise" has solved half of it. A child who says "the dot moves clockwise and the shading goes black, grey, white" has solved it.