Figure Matrices — Matrix Reasoning Practice for Kids
A figure matrix is a three-by-three grid of small pictures with one panel left blank, usually the bottom-right. 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 Logica's Loom Highlands, each puzzle is a "loom": a 3×3 grid whose rows and columns each follow a rule. Your child reads the pattern, then picks the missing panel from a rack of choices. 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 plus a direct Practice Lab room.
Jump into the rooms.
Free practice in the Lab — six puzzles per room, no login, calm explanations when a guess misses.
One rule at a time — a shape rotates along the row, a size grows, or a mark changes from plain to dotted to striped. The natural first loom for a five- to seven-year-old.
Open Level 1 → Level 2Two crossed rules at once — for example, the shape is fixed by the column while the rotation advances by the row. Genuine grid reasoning.
Open Level 2 → Level 3Three attributes tracked together — rotation by column plus size and mark by row, or "add a mark, then turn" row analogies. The hardest rooms in the Lab.
Open Level 3 →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 rooms climb this exact ladder, from one rule to three, so the practice can start gentle and grow with the child.
Where these puzzles show up
The 3×3 grid is a core nonverbal item type. It appears as CogAT Figure Matrices, as matrix items on the NNAT, and in the NGAT nonverbal section. 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 3×3 grid of pictures 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 rooms give figure matrices practice on a tablet, with a calm explanation after every answer. Start at Level 1, where one rule changes at a time, and move up as the two-rule looms 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.