Non-Verbal Reasoning Practice: 20 Worked Examples for the 11+
· 12 min read
A practical, worked-through guide to the most common 11+ non-verbal reasoning question types — odd-one-out, pattern matrices, shape sequences, reflections, rotations, nets, and analogies — with worked examples and solving methods.
Why non-verbal reasoning matters more than parents expect
Non-verbal reasoning (NVR) is the 11+ subject parents most often underestimate. Because the questions are 'just pictures' — shapes, patterns, sequences — they look simpler than verbal reasoning or mathematics, and they don't require vocabulary or curriculum knowledge. In practice, NVR is one of the strongest discriminators in the 11+ test cohort. The reason is that NVR rewards a specific cognitive habit — looking at a visual pattern systematically and exhaustively, rather than spotting it intuitively — that primary-school maths and English do not develop. Bright children who have not practised NVR can score significantly below their verbal-reasoning level on their first attempt, simply because they have never trained the habit of decomposing a visual rule. The good news is that NVR question types are finite, predictable and highly trainable. Once a child has worked through twenty or thirty examples of each major type with a clear solving method, their scores typically improve faster than in any other 11+ subject. This article walks through the seven question types you will see most often, with worked examples for each.
Type 1 — Odd one out (5 worked examples)
In odd-one-out questions, your child sees five shapes and must identify the one that does not share a property with the other four. The solving method has three steps: first, look for a property all five could share (number of sides, symmetry, shading, rotation); second, check each shape against that property; third, identify the exception. Worked example 1: four shapes have an odd number of sides (3, 5, 7, 9 sided), one has an even number (6). Method: count sides. Worked example 2: four shapes are symmetric horizontally, one is asymmetric. Method: try drawing a horizontal line through each. Worked example 3: four shapes have a black centre dot, one has a white centre dot. Method: scan for the most obvious visual element first. Worked example 4: four shapes contain a triangle, one contains a square. Method: look for the inner shape, not just the outer. Worked example 5: four shapes have curved edges only, one has both curved and straight edges. Method: classify edge types. The general principle: scan systematically rather than guessing. If the first property you check doesn't separate one shape from the rest, move to the next property. Most odd-one-out questions resolve in under thirty seconds with a systematic method, but bog children down for two minutes when they look for the answer 'intuitively'.
Type 2 — Shape sequences (3 worked examples)
Shape sequence questions give your child four or five shapes in a row, with one position missing, and ask them to choose the shape that completes the sequence. The trick is identifying the rule that links each step to the next. Worked example 1: a triangle rotates 90 degrees clockwise at each step. Rule: rotation. Method: track one vertex through the sequence to confirm. Worked example 2: a shape gains one extra side at each step (triangle → square → pentagon → hexagon → ?). Rule: counting. Answer: heptagon. Worked example 3: a black dot moves one position clockwise around a square at each step, while the surrounding shape alternates between square and circle. Rule: compound (two rules running together). Method: split the question — solve the dot rule first, the surrounding shape rule second, then combine. Compound rules are the most common cause of wrong answers in sequence questions; children spot one rule, ignore the second, and pick an answer that satisfies only half the pattern.
Type 3 — Pattern matrices (4 worked examples)
Pattern matrix questions show a three-by-three grid with one cell missing. The child must identify the rule that links the rows and columns, then choose the shape that completes the missing cell. Worked example 1: row 1 has three triangles of increasing size; row 2 has three circles of increasing size; row 3 has two squares plus one missing. Rule: each row contains one shape type, sized small/medium/large. Answer: a large square. Method: identify the row rule first, then verify with the column rule. Worked example 2: each cell contains a number of dots equal to the row number times the column number. Rule: multiplication. Method: count, don't pattern-spot visually. Worked example 3: each cell shares a property with its row and its column (the shape is determined by the row, the shading by the column). Rule: two independent variables. Method: split the variables. Worked example 4: the third cell of each row is the result of combining the first two cells visually (overlaying, subtracting, or rotating). Rule: a transformation across the row. Method: try each transformation on the first row to find the rule, then apply it. Pattern matrices reward methodical work — make notes on the question paper if allowed (some test conventions discourage this; check your region's rules).
Type 4 — Reflections and rotations (3 worked examples)
Reflection and rotation questions ask your child to identify what a shape would look like after being flipped or rotated. They are visual tests of spatial reasoning. Worked example 1: a shape is reflected through a vertical line. Rule: left-right swap. Method: track the position of a distinctive feature (a black dot, an arrow) through the reflection. Worked example 2: a shape is rotated 90 degrees clockwise. Rule: rotation. Method: imagine the top of the shape moving to the right, the right to the bottom. For children who struggle, drawing an arrow on the question paper showing the direction of rotation can help. Worked example 3: a shape is reflected through a diagonal line. Rule: diagonal mirror. Method: this is the trickiest reflection direction; ask your child to mentally fold the page along the diagonal and see what overlaps. Reflections and rotations are the question types where mental-rotation practice (using physical objects, magnetic tiles, jigsaw pieces) outside of paper practice produces the biggest gains. Children with strong spatial play habits in Year 3-4 often find these questions intuitive in Year 5.
Type 5 — Nets, cubes and 3D (2 worked examples)
Net questions show a two-dimensional shape (a 'net') and ask which three-dimensional solid it would fold into, or vice versa. Cube questions are the most common. Worked example 1: a flat cross-shape with six squares is shown, with letters or patterns on each square. The child must identify which assembled cube matches the net. Method: identify which squares end up opposite each other (in a standard cube net, the second and fifth squares in a row of four are opposite; the squares on the 'wings' of the cross are adjacent to the central square). With practice, this becomes a memorised rule rather than mental rotation each time. Worked example 2: an assembled cube with patterns on three visible faces is shown, and the child must identify the missing fourth face from the net. Method: identify the orientation of the cube from the visible faces, then deduce the orientation of the hidden face. Net questions appear less often than pattern matrices but reward dedicated practice — children who have not worked through cube-net examples often guess on these questions and score poorly.
Type 6 — Analogies (3 worked examples)
Visual analogy questions take the form 'A is to B as C is to ?'. The child sees a pair of shapes with a relationship between them, then a third shape and four or five answer options. They must identify the option that has the same relationship to the third shape as B has to A. Worked example 1: A is a small black triangle, B is a large black triangle. Rule: size change. Apply to C (a small white circle): answer is a large white circle. Method: identify the transformation from A to B, then apply it to C. Worked example 2: A is an unshaded square, B is the same square with a black dot inside. Rule: addition of feature. Apply to C (an unshaded hexagon): answer is a hexagon with a black dot inside. Worked example 3: A is an arrow pointing up, B is the same arrow pointing left. Rule: 90-degree anticlockwise rotation. Apply to C (an arrow pointing right): answer is an arrow pointing up. Visual analogies often combine multiple transformations (size change plus rotation, for example) — work through each transformation type one at a time.
How to practise NVR effectively
The single highest-leverage thing you can do for NVR is methodical, untimed practice of each question type until your child can articulate the rule out loud. Once they can say 'this is a 90-degree rotation' or 'this is an addition-of-feature analogy' before picking the answer, they have moved from intuition to method, and their scores will start to climb steeply. After that point, introduce time pressure gradually — first allowing 90 seconds per question, then 60, then 45. The real test pace varies by region but typically allows 30-45 seconds per NVR question. Practise with mixed-type sets in the final two months — the real test alternates types rapidly, and your child needs to switch solving methods without losing momentum. For a wider picture of how NVR sits inside your child's overall 11+ preparation, see our 11+ preparation guide for 2027. For region-specific weighting of NVR — it varies a lot between, say, the Kent Test and the Buckinghamshire Secondary Transfer Test — check our regional pages, starting with the Kent Test guide and the Bucks 11+ guide. If your child has never sat an NVR question, our free diagnostic at grammarprep.uk/onboarding includes a short NVR section that gives a fair starting benchmark.
Common mistakes parents see
Three patterns appear in almost every parent's NVR diagnostic conversation. First, children who score well on simple-type questions but collapse on compound types. The fix: practise compound-type questions explicitly, slowing down to identify each rule separately. Second, children who answer quickly but inconsistently — strong on rotations one week, weak on the same type the next. The fix: this is usually a method gap. Force them to articulate the rule out loud before picking the answer. Once they can name the rule reliably, accuracy stabilises. Third, children who tire visibly on NVR papers, with accuracy dropping in the final third. The fix: NVR is cognitively demanding in a different way to verbal reasoning — eye-tracking and visual concentration matter more. Build stamina with longer practice sessions, and ensure your child takes a real visual break (no screens, look out the window for thirty seconds) between paper sections in mocks. The goal is not for your child to find NVR easy. It is for them to find it methodical.