4.1 Shape Sequences, Series & Progressive Matrices

Shape Sequences, Series & Progressive Matrices

Non-Verbal Reasoning (NVR) in the Kent Test (administered by GL Assessment) assesses a child's capacity to analyze visual information, identify geometric rules, and solve abstract logical problems without relying on language or verbal vocabulary. Non-verbal sequence items present series of 2D shapes or 3x3 matrix grids that transform according to precise mathematical and spatial rules. The official familiarisation booklet states that the non-verbal and spatial reasoning tests are divided into subtests, each opening with an untimed practice section worked through with the invigilator and then a timed block of 4 to 5 minutes. Question counts are not published, so the practical consequence is simple: each subtest is short, and a fast, disciplined start matters more than a long think on item one.

To master non-verbal sequences, candidates must abandon unstructured guessing and adopt a disciplined, attribute-by-attribute tracking framework.

---

The SPONGE Method for Multi-Variable Feature Tracking

Complex non-verbal reasoning shapes rarely change by a single rule. Instead, GL Assessment design items combine two, three, or four independent visual variables simultaneously. The SPONGE framework provides a systematic checklist to isolate and track each variable independently.

---

Analyzing Linear Shape Sequences (Series)

Linear sequences display a horizontal row of frames — the official example uses five squares arranged in order — with one square left empty. The gap is not always at the end: it can sit in the middle of the row, in which case you must work the rule forwards from the frames on the left and backwards from the frames on the right and take the answer that satisfies both.

1. Single-Variable vs. Multi-Variable Progressions

• Single-Variable Progression: Only one attribute changes across frames (e.g., a triangle rotates $45^\circ$ clockwise at each step). These appear primarily at the start of the paper.
• Multi-Variable Progression: Two or more attributes change independently according to distinct rules (e.g., polygon sides increase by 1, inner shading alternates, and an outer arrow rotates $90^\circ$ anticlockwise).

2. Common Sequence Patterns

1. Arithmetic Progression: A feature increases or decreases by a fixed numeric increment (e.g., 2 dots, 4 dots, 6 dots, 8 dots).
2. Alternating Series (A-B-A-B Pattern): Frame 1 and Frame 3 follow Rule Set A; Frame 2 and Frame 4 follow Rule Set B.
3. Cumulative Building: Each frame adds one new element to the composite figure until the structure is complete.
4. Pendulum / Oscillation: An element moves back and forth between two positions (e.g., top-left corner $\rightarrow$ bottom-right corner $\rightarrow$ top-left corner).

Worked Example: 5-Frame Multi-Variable Series

• Frame 1: 3-sided shape (triangle), white fill, 1 black dot at top vertex.
• Frame 2: 4-sided shape (square), black fill, 2 black dots at right vertex.
• Frame 3: 5-sided shape (pentagon), striped fill, 3 black dots at bottom vertex.
• Frame 4: 6-sided shape (hexagon), white fill, 4 black dots at left vertex.

Step-by-Step SPONGE Analysis:

1. Shape (Sides): $3 \rightarrow 4 \rightarrow 5 \rightarrow 6 \implies$ Frame 5 must have 7 sides (heptagon).
2. Shading: White $\rightarrow$ Black $\rightarrow$ Striped $\rightarrow$ White $\implies$ Frame 5 must be Black fill.
3. Dot Count: $1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \implies$ Frame 5 must have 5 black dots.
4. Dot Position: Top $\rightarrow$ Right $\rightarrow$ Bottom $\rightarrow$ Left ($90^\circ$ CW rotation around perimeter) $\implies$ Frame 5 dots must be at Top vertex.

---

Mastering 3x3 Progressive Matrices

Progressive matrices display a $3 \times 3$ grid of 9 cells, with the bottom-right cell (Row 3, Column 3) left blank. Candidates must analyze pattern rules across rows (left to right) and down columns (top to bottom).

[ Cell (1,1) ]  [ Cell (1,2) ]  [ Cell (1,3) ]
[ Cell (2,1) ]  [ Cell (2,2) ]  [ Cell (2,3) ]
[ Cell (3,1) ]  [ Cell (3,2) ]  [ ? Target ? ]

Key Grid Rules in GL Assessment Matrices

1. Row-Wise Progression: The rule operates strictly across horizontal rows. Row 1 establishes the rule, Row 2 confirms it, and Row 3 requires its application.
2. Column-Wise Progression: The rule operates vertically down columns.
3. Set Permutation (Distributive Law): Each row (and column) contains the exact same set of 3 attributes, but in permuted order.
   • Example: Every row must contain 1 Circle, 1 Square, and 1 Triangle; 1 Black fill, 1 White fill, and 1 Striped fill.
4. Feature Combination / Overlap (XOR Logic):
   • Addition: Line Segments in Cell 1 + Line Segments in Cell 2 = Cell 3.
   • Subtraction: Line Segments in Cell 1 - Line Segments in Cell 2 = Cell 3.
   • Exclusive OR (XOR): Lines that appear in only one of the first two cells are drawn in Cell 3; lines that appear in both cells cancel out and disappear.

$\text{Cell 3} = (\text{Cell 1} \cup \text{Cell 2}) \setminus (\text{Cell 1} \cap \text{Cell 2})$

---

Exam Execution & Distractor Elimination

Under time pressure, candidates should never attempt to solve all variables mentally before looking at answer options. Use First-Feature Elimination:

1. Pick the Easiest Variable: Identify the variable that is simplest to track (e.g., polygon side count or shading).
2. Formulate the Target State: Determine what that variable must be in the answer (e.g., "Must be a black shape").
3. Eliminate Non-Matching Choices: Cross out all answer choices that violate this single rule. Often, 2 or 3 distractors are eliminated instantly.
4. Track the Second Variable: Focus only on the remaining candidates and evaluate the next variable (e.g., rotation angle) until exactly 1 valid answer remains.