6.1 Figure Matrices: Features and Missing Cells
Key Takeaways
Track shape, count, fill, orientation, and position separately.
Figure Matrices has a missing figure; the public description does not prescribe one grid size.
Use every supported row and column relationship without inventing mandatory ones.
Check the candidate against all predicted features.
Infer the relationship shown by the figures
Riverside describes Figure Matrices as a matrix of figures with one missing figure. Students infer the relationships and choose the figure that completes the matrix. The public description does not establish one fixed grid size for every item. The two-by-two and three-by-three grids below are original teaching illustrations.
The task uses visual relationships. It is not a reading test, but that does not make it culture-free or a pure measure of an unchangeable trait. Familiarity with directions and conventions can affect how comfortably a student approaches a visual exercise. Learn the task, then focus on the actual figures.
Inventory the features before choosing
Separate shape, number, fill, orientation, and position. A circle turning black is a fill change, not a shape change. A triangle moving to the upper-right corner is a position change, even if its orientation stays the same. Multiple features may change at once.
| Feature | What to record | Example distinction |
|---|---|---|
| Shape | Boundary or component type | Circle versus square |
| Number | Count of relevant elements | One dot versus two dots |
| Fill | Outline, solid, or pattern | White interior versus black interior |
| Orientation | Direction relative to the cell | Arrow up versus arrow right |
| Position | Location within the cell | Center versus upper corner |
Track only what the illustration actually shows. A thicker outline may be meaningful in a practice design, or it may simply be a display artifact. A correct explanation should identify the evidence rather than assume every visible variation encodes a rule.
Work a fill-change matrix
In this original grid, the left figure in each row is an outline shape and the right figure is the same shape filled black.
| Left | Right | |
|---|---|---|
| Top | ○ | ● |
| Bottom | □ | ? |
The missing figure is a filled square, ■. The row rule preserves shape while changing fill. The column relation also preserves fill while changing circle to square. A filled circle satisfies the top row but fails the bottom row's shape requirement. An outline square matches shape but fails the fill change.
State the full prediction before inspecting choices: “one square, filled black, with no added components.” This makes a distractor with an extra dot easier to reject.
Work a count matrix
The following three-by-three grid uses counts represented by dots. In each row, the third count is the sum of the first two. Here the columns also follow that relationship.
| First | Second | Third | |
|---|---|---|---|
| Top | ● | ●● | ●●● |
| Middle | ●● | ●●● | ●●●●● |
| Bottom | ●●● | ●●●●● | ? |
The bottom row requires three plus five, or eight dots. The third column independently gives three plus five, also eight. This agreement supports the answer for this illustration. It does not prove that every matrix must use addition or that row and column rules must always be identical.
Counting can be useful even when the dots' positions differ, provided the displayed rule concerns count rather than arrangement. If location is also part of a rule, eight dots in the wrong positions may fail. Preserve all supported features.
Follow orientation separately
Suppose the top row shows an up arrow followed by a right arrow, and the bottom row begins with a left arrow. If the stated rule is rotate ninety degrees clockwise across each row, the missing arrow points up. The same rotation applied to left gives up.
If only one pair of arrows is shown, a reflection or another transformation might also produce the observed result. An independent exercise should supply enough evidence or state the transformation to distinguish such alternatives. Avoid claiming that a single pair proves rotation uniquely.
Use row and column evidence appropriately
Read across rows and down columns to discover possible relationships. A candidate that satisfies one apparent rule but contradicts another clearly supported rule needs reconsideration. Nevertheless, do not impose a row-column commutativity requirement where the figures do not establish it.
A matrix may combine two transformations, one associated with moving right and another with moving down. If those operations affect the same feature, order can matter. The next sections examine transformations and combination rules explicitly.
Diagnose visual mistakes
A missed figure may reflect a feature you did not track, an incorrect transformation, or an answer-choice oversight. Record the actual mismatch: “I preserved fill but selected the wrong shape” is more useful than “bad at spatial reasoning.” One error on an independent exercise does not diagnose a cognitive impairment.
During home practice, redraw a small grid with one feature changed and solve it again. If the original error was count, keep the shapes simple and vary the number. If it was orientation, keep count and fill fixed while rotating an asymmetric figure. This isolates the skill you are practicing.
Check the whole answer
Before selecting, compare shape, count, fill, orientation, and location with your prediction. A near match often preserves most features while changing one. The complete standard Figure Matrices subtest has 22 items in 10 minutes; timing adjustments may be approved. Use that window as context after accurate feature tracking develops, not as a reason to skip the final comparison.
In the displayed fill-change grid, ○ becomes ● and □ becomes what?
○
□
●
■
A row combines counts by addition. Its first two figures contain three and five dots. How many belong in the third?
2
8
15
5
Under a stated ninety-degree clockwise rotation, where does a left-pointing arrow point?
Up
Down
Right
Left
Sections you finish are checked off in the contents.