11+ non-verbal reasoning: patterns, rotations and a clear solving method

11+ non-verbal reasoning uses diagrams and shapes rather than long passages of text. Children may need to identify a pattern, complete a matrix, compare shapes, track a rotation or predict the result of folding. The visual presentation changes, but a reliable approach is to describe what changes and what stays the same.

Non-verbal reasoning is not one fixed national paper. Local authorities and schools choose different test structures. Confirm the current format and use official familiarisation material before deciding which question families deserve the most practice.

The main question families

Shape sequences

A sequence shows figures in order and asks what comes next. More than one attribute may change: shape, shading, number, size, direction or position.

Solving prompt: Compare figure one with figure two, then figure two with figure three. Say the change as a rule. Check whether the same rule explains every transition.

Analogies

A visual analogy applies the change from the first pair to a new figure. The relationship might rotate a shape, add a mark, swap shading or move an element.

Solving prompt: Finish the sentence, “The first shape becomes the second by...” Then apply exactly that operation to the third shape.

Odd one out and classification

Most figures share a property and one does not. Possible rules include symmetry, number of sides, enclosed regions, orientation or the relationship between internal and external marks.

A defensible answer explains the group as well as the exception. “It looks different” is an observation, not yet a rule.

Matrices

A matrix arranges figures in rows and columns with one missing cell. Inspect rows and columns separately. A rule may combine shapes, subtract shared elements, alternate shading or move a symbol by a fixed step.

Solving prompt: Test a proposed row rule on every complete row, then check whether the column pattern supports it. Reject rules that explain only one line.

Rotation and reflection

A rotation turns a figure while preserving its handedness. A reflection flips it, producing a mirror image. Children often confuse the two when a shape is unfamiliar.

Track one asymmetric feature, such as a dot near a corner or a short arm on one side. Imagine that marker travelling with the shape during a rotation. If its left-right relationship reverses, a reflection may be involved.

Folding, nets and spatial reasoning

These tasks ask children to imagine a flat figure folded, unfolded or assembled. Instead of trying to hold the whole object mentally, track one face, edge, hole or mark at a time. Physical paper models can help teach the underlying movement before the child returns to diagrams.

A six-step solving routine

1. Name the family. Is it a sequence, analogy, matrix, classification or folding task?
2. List the attributes. Shape, count, shading, size, direction and position are useful checks.
3. Find what stays constant. A fixed feature narrows the possible rules.
4. Describe each change. Use a precise sentence rather than “it moves”.
5. Test the rule everywhere. A valid rule must explain all completed examples.
6. Eliminate options deliberately. State why each rejected option breaks the rule.

This routine can feel slow at first. Speed should come from recognising and applying reliable checks, not from skipping them.

An original worked example without a diagram

Imagine a sequence of squares. The first contains one dot in the top-left corner. The second contains two dots in the top-right corner. The third contains three dots in the bottom-right corner.

Two attributes change: the number of dots increases by one and the corner moves clockwise. The next figure should therefore contain four dots in the bottom-left corner. An option with four dots in the top-left gets the count right but the position wrong. An option with three dots in the bottom-left gets the position right but the count wrong.

The lesson is to track attributes separately. Many tempting options preserve one part of the rule while breaking another.

Teach rotation and reflection physically

1. Draw an asymmetric arrow or irregular shape on a small card.
2. Add a coloured dot to one corner.
3. Rotate the card a quarter turn and describe where the dot moves.
4. Return to the start, then view the card in a mirror.
5. Compare the marker's relationship to the shape in both cases.

This activity teaches the transformation rather than an answer pattern. Use original shapes or household materials, not copied commercial test content.

How to review errors

• Missed attribute: add a consistent scan for count, shading, direction and position.
• Rotation confused with reflection: track an asymmetric marker.
• Rule fitted one example only: require verification across all complete rows or pairs.
• Mental overload: annotate one element at a time during untimed practice.
• Rushed elimination: state why each remaining option fails.
• Instruction misunderstood: compare the task with an official worked example.

When to use a timer

Begin untimed when a format is new. Move to short timed groups only after the child can explain a reliable method. Review whether time was lost on visual scanning, rule selection, checking or answer transfer. Those causes need different practice.

Full timed papers are useful for rehearsal, but they are poor teaching tools when every unfamiliar question becomes a guess. Trace Learn's paper-test overview explains how fixed papers differ from daily practice, while the free diagnostic pathway covers all four subject areas.

Accessibility and local arrangements

Visual tests can create particular barriers for some children. If a child normally receives adjustments or uses enlarged materials, contact the responsible test authority early. Do not assume that school arrangements will transfer automatically. The authority's published process should explain evidence and deadlines.

A short practice structure

• Teach one transformation with physical or drawn examples.
• Practise a small untimed set from one family.
• Ask the child to explain each rule aloud.
• Mix the new family with two known families.
• Add a brief timed section and review the cause of each error.
• Revisit the same transformation later with different-looking figures.

For language-based reasoning, use the companion 11+ verbal reasoning guide.

Official sources

• GL Assessment free familiarisation materials, including non-verbal reasoning samples and the warning that local tests may differ.
• London Borough of Bexley: current selection-test information.
• Warwickshire County Council: current test sections and format.
• London Borough of Redbridge: current local test guidance and variation warning.