Figure Matrices — Matrix Reasoning Practice for Kids
A figure matrix is a grid of small pictures with one panel left blank, usually the bottom-right. Tests use different sizes: CogAT's Figure Matrices use a two-by-two grid at the primary levels, and Logica uses two-by-two grids in its first trails and three-by-three grids after that. Something changes across each row and down each column — a shape turns, a mark is added, a size grows — and the child's job is to find the rule and choose the missing piece. They are one of the most common nonverbal reasoning formats, because they test clear thinking with shapes instead of words.
In Loom Highlands, the figure-matrix place in Logica, each puzzle is a grid whose rows and columns each follow a rule: two by two in the first two trails, three by three in the last three. Your child reads the pattern, then picks the missing piece from three choices (five, if a grown-up chooses). A wrong answer brings a calm explanation of the rule, not a red X. It is free, runs on a tablet, saves progress on the device, and never uses a timer. Because the format strips away words and numbers, it shows how a child reasons about relationships — which is why the nonverbal parts of gifted screeners lean on it so heavily.
Browse the skills
Each card opens a parent-readable explanation, with a link to the Logica trail that practices it.
Five trails, from easy to tricky.
Free practice in Logica, the reasoning game in the Practice Lab: six puzzles a trail, no timer, no login, and a calm explanation when a guess misses.
A 2-by-2 grid: one thing changes across, another changes down. At least four choices.
Open trail 1 → Trail 2 · Turns and countsA 2-by-2 grid: a shape turns, changes size or changes number across; its color and its shape or inside change down. At least four choices.
Open trail 2 → Trail 3 · Step by stepA 3-by-3 grid where size, number, turn or inside steps along each row, and each row keeps its own shape or color. At least four choices.
Open trail 3 → Trail 4 · One of eachA 3-by-3 grid where each row has one of each shape, with a second rule for color or size. At least four choices.
Open trail 4 → Trail 5 · Three rules at onceA 3-by-3 grid with three rules together, and the gap can be in any square. At least four choices.
Open trail 5 →Reading a figure matrix: rows and columns
Every grid hides a rule you read in two directions. Look across a row to see what changes from left to right, then look down a column to see what changes from top to bottom. Sometimes one direction carries the whole pattern; often each direction carries its own rule at the same time. Once you can name both rules, the missing panel is the only picture that obeys them.
Because the changes march along in order, this format is also called serial reasoning. And when a single row tells a small story — add a dot, then turn the figure — that row behaves just like an analogy, which is why these are sometimes called matrix analogies. The Loom Highlands trails climb this ladder, from a two-by-two grid with one change across and one change down to a three-by-three grid with three rules at once, so the practice can start gentle and grow with the child.
Where these puzzles show up
Matrix items are a core nonverbal item type. CogAT's Figure Matrices use a 2×2 grid at Levels 5/6 through 9 (Riverside's published test descriptions), and the NNAT and the NGAT nonverbal test also include matrix-style items. Logica starts with 2×2 grids and moves on to 3×3, where a child reads a rule across three rows and three columns. We keep the focus here on the reasoning itself — finding the row rule and the column rule — and leave scores, levels, and district timelines to the guides that cover those.
Common questions
What is a figure matrix?
It is a grid of pictures, often 2×2 or 3×3, with one panel missing. Each row and column follows a rule — a shape turning, a mark being added, a size growing — and the child picks the piece that completes both directions. It is a nonverbal task, so it uses no reading or math.
How do we practice this at home?
The free Loom Highlands trails in Logica give figure matrices practice on a tablet, with a calm explanation after every answer. Start at trail 1, a two-by-two grid where one thing changes across and another changes down, and move up as the bigger grids start to feel readable. Keep it untimed.
Do you have figure matrices worksheets?
The practice here is interactive rather than printable, which is what lets it explain the rule on every miss. If you also want something offline, you can sketch simple grids on paper — draw a short row rule and leave the last box blank for your child to fill.
Want a printable set too?
Get the free Reasonwell sample pack — printable reasoning and test-prep material you can use at the kitchen table.
Download All three Grade 2 workbook samples ↓22 pages · 1.9 MB · No email requiredText versions (screen-reader friendly): NGAT Grade 2 sample, CogAT Level 8 sample and OLSAT Level C sample