11+ Non-Verbal Reasoning: Shape Series and Sequences

Note: shape series questions are inherently visual. The worked examples below describe the shapes and transformations in words as a stand-in for the diagrams the published article will need — these require real graphics before going live, matching the diagram treatment used in the NVR overview article.

Shape series questions show a row of shapes that change step by step and ask your child to work out what comes next, or what is missing partway through. The underlying skill is the same as matrix reasoning and analogies: spot the rule, apply it. The difference is that the rule plays out across a whole sequence. That gives more evidence to confirm it from, but it also means the rate of change can shift partway through, not just once.

What this question family covers

• Rotation series: a shape rotates by a consistent amount at each step
• Reflection series: a shape alternates between its normal and mirrored form, or flips at each step
• Progressive series: a shape or pattern grows, shrinks, gains elements, or loses elements steadily across the sequence

Worked example 1: Simple rotation series

Description: a row of four squares, each containing an arrow. Step 1: arrow points up. Step 2: arrow points right. Step 3: arrow points down. Step 4 is missing.

Work out the rotation amount and direction between each consecutive step, then confirm it is consistent before applying it again.

• Step 1 to 2: arrow rotates 90 degrees clockwise (up to right)
• Step 2 to 3: arrow rotates 90 degrees clockwise again (right to down)

The rule is "rotate 90 degrees clockwise each step," confirmed across two transitions. Applying it once more from step 3 (pointing down):

Answer: the arrow points left.

Worked example 1b: A series with an increasing rate of change

Description: a row of four squares, each containing a line of dots. Step 1: 1 dot. Step 2: 3 dots. Step 3: 6 dots. Step 4 is missing.

Check the difference between each step, not just the value. The rate of change might itself be changing.

• Step 1 to 2: +2 dots
• Step 2 to 3: +3 dots

The gap increases by 1 each time, so the next gap should be +4.

Answer: 10 dots (6 + 4).

This is the same "check whether the rate of change is itself changing" habit covered in the VR codes and sequences article, and it transfers directly to shape and dot-count series.

The mistakes we see most often

1. Checking only one pair of steps instead of confirming the rule across the whole sequence. A rotation that looks right between steps 1 and 2 still needs to hold between steps 2 and 3 before it is safe to apply again.
2. Assuming a constant rate of change when it is actually accelerating or decelerating, as in worked example 1b. This is one of the most common sources of wrong answers on this topic.
3. Losing track of rotation direction (clockwise versus anticlockwise) partway through a longer sequence, especially under time pressure.
4. Confusing a reflection with a rotation. For simple, symmetric shapes these can look very similar. Building the habit using shapes with clear asymmetric detail, like an arrow, makes the distinction easier to spot reliably.
5. Treating "what comes next" and "what is missing in the middle" as the same task. A missing-middle question needs the rule confirmed from both sides of the gap, not extrapolated from one end only.

A practice strategy parents can use at home

Use a physical object, a pencil, a phone, a toy, and have your child rotate it step by step while describing each rotation out loud ("that's 90 degrees clockwise"). Handling a real object builds an intuitive sense of rotation amount and direction that transfers directly to the flat, printed version in the exam.

For rate-of-change series like worked example 1b, try writing the gaps between each step underneath the sequence before answering. Separating "the sequence" from "the gaps between the sequence" makes an accelerating pattern much easier to spot.