Identify patterns across rows and columns in a figure matrix - CogAT Grades K 2

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Why Do We Use Picture Puzzles?

People have always loved puzzles! A long time ago, teachers and scientists wanted a way to see how kids think. They wanted to know if kids could find patterns — things that repeat or follow a rule. So they made special picture puzzles called figure matrices. These puzzles use shapes instead of words, so any kid can try them!

Long Ago • People Love Patterns

Even cave people drew patterns on walls! People have always noticed when things repeat.

1936 • First Matrix Puzzles

A man named John Raven made picture puzzles with rows and columns. Kids had to find the missing piece!

1954 • The CogAT Test Begins

Schools started using the CogAT test. It has picture grids to see how well kids find patterns.

Today • Kids Like You Solve Them!

Now millions of kids solve figure matrices. You are learning to do this too!

So here is the big question: How do you look at a grid of pictures and figure out what comes next? That is what we will learn today!

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What Are the Big Ideas?

A figure matrix is a grid of pictures. It has rows (lines that go across, like reading a book) and columns (lines that go up and down, like an elevator). One picture is missing. Your job is to find the rule and pick the right picture!

Look Across the Row

Read each row like a sentence. What changes? What stays the same? The rule in one row works for the other rows too.

Look Down the Column

Now look from top to bottom. Columns have their own pattern. Check if shapes, colors, or sizes change going down.

Watch for Changes

Things can change in many ways: shape, size, color, number, or direction. Look for what is different from one box to the next.

Check Both Ways

The missing picture must follow the row rule AND the column rule. Always check both directions before you pick your answer!

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KEY TAKEAWAY

Think of a figure matrix like a tic-tac-toe board filled with stickers. Each row of stickers follows a rule, and each column follows a rule too. To find the missing sticker, you need to figure out both rules at the same time!

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See It in a Picture!

Let's look at a real figure matrix! In the picture below, you can see a 3×3 grid. Each row and column follows a pattern. The bottom-right box has a question mark — that is the one we need to figure out.

In this matrix, the shape changes going down each column (circle → square → triangle), and the color changes going across each row (blue → purple → pink). So the missing piece is a pink triangle!

See how it works? Going across each row, the color changes but the shape stays the same. Going down each column, the shape changes but the color stays the same. When you find both rules, you know the answer!

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How Does It Work?

There is no hard math here — just detective work! Here are the steps you follow every time you see a figure matrix.

The Detective Steps

Step 1: Look at Row 1 from left to right. What is the same? What is different?
Step 2: Look at Row 2. Does the same rule work here?
Step 3: Now look at Column 1 from top to bottom. What changes?
Step 4: Check Column 2. Same rule going down?
Step 5: Use BOTH rules to pick the missing picture. It must fit the row AND the column!

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Helpful Hint!

When you look at each box, ask yourself: What is the shape? What is the size? What is the color? How many are there? Which way does it face? These are the things that can change in a pattern.

Think about it like getting dressed. Your shirt changes color each day, but your pants might stay the same. Or maybe your hat changes but your shoes do not. In a figure matrix, some things change and some things stay the same. Your job is to figure out which is which!

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What Can Change in a Pattern?

There are five main things that can change in a figure matrix. Let's look at each one so you know what to watch for!

This chart shows the five main types of changes you might see: shape, size, color, number, and direction. Sometimes more than one thing changes at once!

Type of Change	What to Look For	Example
Shape	Circle, square, triangle, star, heart	Circle → Square → Triangle
Size	Small, medium, big	Small → Medium → Big
Color	Light, dark, filled, empty	White → Gray → Black
Number	How many shapes are in each box	1 → 2 → 3
Direction	Which way a shape points or turns	Up → Right → Down

Types of Changes in Figure Matrices

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Let's Solve One Together!

Here is a puzzle. Imagine a 3×3 grid. Row 1 has: one small star, two small stars, three small stars. Row 2 has: one medium star, two medium stars, three medium stars. Row 3 has: one big star, two big stars, and a question mark. Let's find the answer!

Finding the Missing Picture

1
Step 1 — Look Across Row 1

Row 1 has one small star, then two small stars, then three small stars. The number goes up by one each time. The size stays small.

Row rule: number increases (1 → 2 → 3)
2
Step 2 — Check Row 2

Row 2 has one medium star, two medium stars, three medium stars. Same rule! The number goes up by one. The size stays medium.

Row rule confirmed! ✓
3
Step 3 — Look Down Column 1

Column 1 has one small star, one medium star, one big star. The number stays at one, but the size gets bigger each time.

Column rule: size increases (small → medium → big)
4
Step 4 — Check Row 3 So Far

Row 3 has one big star, two big stars, and a question mark. The row rule says the number goes up. So the missing box should have three shapes.

Missing picture needs 3 shapes
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Step 5 — Use Both Rules to Pick the Answer

The row rule says three shapes. The column rule says big size. Put them together and the answer is: three big stars!

Answer: Three big stars ⭐⭐⭐

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REMEMBER THIS!

The answer to a matrix puzzle is like putting together two clues. One clue comes from the row, and one clue comes from the column. It's like baking cookies — you need BOTH the recipe AND the oven. One alone is not enough!

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Smart Tips and Tricky Traps

Some puzzles try to trick you! Here are some smart tips to help you do your best, and some traps to watch out for.

Smart Tips ✅	Tricky Traps ❌
Always check BOTH rows and columns before picking.	Only looking at the row and forgetting the column.
Look for more than one change. Sometimes two things change at once!	Thinking only one thing can change at a time.
Cross out answer choices that break the row rule.	Picking the first answer that looks close without checking.
Use your finger to trace across and down.	Trying to solve it all in your head without looking carefully.

Tips vs. Traps

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DETECTIVE TIP

When you are stuck, try eliminating wrong answers first. If an answer choice does not follow the row rule, cross it out. If it does not follow the column rule, cross it out. The one that's left is your answer!

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Getting Ready for Harder Puzzles

Once you are great at finding patterns in simple grids, you will be ready for harder puzzles! As you grow, the puzzles will have more tricky rules. Let's see what comes next.

What You Learn Now	What Comes Later
One or two things change (shape, color)	Three or more things change at once
Simple shapes like circles and squares	Shapes with lines, dots, and patterns inside
Things get bigger or change color	Things rotate, flip, or overlap
3×3 grids	Larger grids and more complex puzzles

Now vs. Later

Don't worry about the hard stuff yet! If you can find patterns in rows and columns right now, you are building an amazing brain skill that will help you with all kinds of thinking as you get older.

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Try It Yourself!

Now it's your turn! Try these five practice puzzles. Start with the easy ones and work your way up. Think carefully about what changes across each row and down each column.

Question 1: CONCEPTUAL

Imagine a row of three boxes. The first box has a red circle. The second box has a red square. The third box has a red triangle. What is changing in this row, and what stays the same?

Show answer

The shape is changing — it goes from circle to square to triangle. The color stays the same — all three are red. In a figure matrix, you always need to notice both what changes and what does not change.

Question 2: BASIC

A 2×2 grid shows: Top-left is a small blue star. Top-right is a big blue star. Bottom-left is a small green star. Bottom-right is missing. What should go in the missing box?

Show answer

The answer is a big green star. Looking across Row 1, the size changes from small to big. Looking down Column 2, the color changes from blue to green. The missing piece needs to be big (row rule) and green (column rule).

Question 3: INTERMEDIATE

A 3×3 grid has this pattern: Row 1 has 1 circle, 2 circles, 3 circles. Row 2 has 1 square, 2 squares, 3 squares. Row 3 has 1 triangle, 2 triangles, and a question mark. What is missing, and what TWO rules did you use to find it?

Show answer

The answer is 3 triangles. The two rules are: across each row, the number goes up (1 → 2 → 3). Down each column, the shape changes (circle → square → triangle). The missing piece must have 3 shapes (row rule) and they must be triangles (column rule).

Question 4: APPLIED

In a 3×3 matrix: Row 1 has a small white circle, a medium gray circle, and a large black circle. Row 2 has a small white square, a medium gray square, and a large black square. Row 3 has a small white triangle, a medium gray triangle, and a question mark. What goes in the missing spot? Name ALL the things you need to get right.

Show answer

The answer is a large black triangle. You need to get three things right! First, the shape: looking down Column 3, shapes go circle → square → triangle, so it's a triangle. Second, the size: looking across Row 3, size goes small → medium → large, so it's large. Third, the color: looking across the row, color goes white → gray → black, so it's black. Always check all three!

Question 5: CRITICAL THINKING

You see a 3×3 matrix. You check the rows and find that the shape changes. You check the columns and find that the number of shapes changes. But two of the answer choices both seem to follow these rules! What should you do next to pick the right one?

Show answer

When two answers both seem right, you probably missed a rule! Go back and look for a third change you did not see the first time. Check if the size, color, or direction also changes. Sometimes there is a pattern you missed. Look very carefully at each box again. The right answer must match ALL the rules, not just some of them. This is why good detectives always double-check their clues!

SUMMARY

Let's Remember What We Learned!

Summary

A figure matrix is a grid of pictures with one piece missing. To solve it, you look for patterns across rows (left to right) and patterns down columns (top to bottom). The five things that can change are shape, size, color, number, and direction. The missing picture must follow the row rule AND the column rule at the same time.

To be a great pattern detective, always use the five detective steps: check Row 1, check Row 2, check Column 1, check Column 2, and then use both rules to find the answer. If you are stuck, try crossing out wrong answers one at a time. You are now ready to solve figure matrix puzzles like a pro!