A grid of shapes (usually 3×3 or 2×2) where you must find the missing shape based on patterns in rows and columns.

1. Look across each ROW for patterns  2. Look down each COLUMN for patterns  3. Find what the missing cell must be to complete BOTH patterns

The correct answer must satisfy the pattern in its row AND the pattern in its column.

Why must you check BOTH rows and columns?

1. Each cell has same shape but different shading  2. Shapes rotate  3. Number of elements increases  4. All three shapes are identical  5. Shapes progress (triangle→square→pentagon)

What patterns might you see across a ROW?

Pattern: +1 dot across the row. 4 + 1 = 5

If Row 1 shows: 1 dot, 2 dots, 3 dots, and Row 3 shows: 3 dots, 4 dots, ?, how many dots are in the missing cell?

1. Size increases going down  2. Shading changes  3. Shape rotates  4. Elements are added  5. Same shape repeated

What patterns might you see down a COLUMN?

Column 3 shows: small circle, medium circle, ?. What size is the missing shape?

The missing shape must have: the feature from its row pattern AND the feature from its column pattern.

How do you combine row and column patterns?

Look for a pattern that works for BOTH, or check if each controls a different feature (row controls shape, column controls shading).

What if row and column patterns seem to conflict?

Combine elements from cells 1 and 2 to make cell 3 in each row.

What is an "addition" pattern in matrices?

Cell 3 shows what's different between cells 1 and 2 (what's in one but not the other).

What is a "subtraction" pattern in matrices?

Addition combines elements from cells 1 and 2

In an addition matrix: Cell 1 has ○, Cell 2 has △. What does Cell 3 have?

The shape might rotate a fixed amount (e.g., 45°) from cell to cell across the row.

If a shape rotates 90° clockwise between each cell in a row, and it starts pointing UP, where does it point in the 3rd cell?

1. Each row has unshaded, half-shaded, fully shaded  2. Shading increases left to right  3. Each column has same shading  4. Shading rotates around the shape

What shading patterns appear in matrices?

Pattern: shading increases. Empty → Half → Full

Row has: empty shape, half-shaded shape, ?. What comes next?

1. Each row has different shapes (circle, square, triangle)  2. Each column has same shape  3. Shapes change by adding sides  4. All cells have same shape type

If column 3 has circle, circle, ?, what shape goes in the missing cell?

1. Size increases across rows  2. Size increases down columns  3. Each row has small, medium, large  4. Size alternates

When cells contain multiple items (dots, lines, shapes). Count them to find numerical patterns.

When should you count elements in a matrix?

If each row totals 6 dots, and the third row has 2 dots and 2 dots, how many dots are in the missing cell?

Each row sums to 9 lines. Row 3 has: 4 lines, 3 lines, ?. How many lines in the missing cell?

Sometimes! Some matrices have patterns along diagonals (top-left to bottom-right, or top-right to bottom-left).

Do you need to check diagonals in matrices?

2×2 matrices have fewer cells, so patterns must be identified with less information. Often one cell is missing.

How are 2×2 matrices different from 3×3?

1. Opposite corners are similar  2. Top row differs from bottom row in one way  3. Left column differs from right column  4. Rotation between adjacent cells

1. Look at Row 1 to find the row pattern  2. Look at Column 1 to find the column pattern  3. Verify patterns in other rows/columns  4. Apply both patterns to find the answer

What's the best order to analyze a 3×3 matrix?

Try each answer option: place it in the missing cell and check if it completes valid patterns for its row AND column.

What if you can't find the pattern in a matrix?

1. Only checking rows OR columns (check both!)  2. Assuming the pattern is simple  3. Not verifying your answer fits all patterns  4. Rushing without checking all cells

What common mistakes should you avoid in matrices?

Put your answer in the missing cell. Check: Does the row pattern work? Does the column pattern work? If yes to both, it's correct.

Check more carefully: one probably breaks a subtle pattern. Check all features: shape, size, shading, rotation, and number of elements.

Master grid-based pattern problems with rows and columns

Matrices

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