Select the Missing Figure That Completes the Matrix - CogAT Grades K 2

SECTION 1

Why Do We Use Picture Puzzles?

People have always loved puzzles! A long time ago, teachers wanted to find out how kids think. They made up special picture puzzles called matrices. A matrix is a grid of pictures that follows a pattern. One picture is missing, and you have to figure out which one goes there. These puzzles do not use any words or numbers. They only use shapes, colors, and sizes.

1936 • First Matrix Puzzles

A man named John Raven made the first set of picture matrix puzzles to test how people think.

1968 • Tests for Kids

Teachers started using picture puzzles to help understand how young children learn and solve problems.

1985 • The CogAT Test

The CogAT test was created. It uses matrix puzzles to see how well kids can find patterns without using words.

Today • You Take the Test!

Kids like you practice these fun puzzles to become great pattern detectives!

So how do you look at a grid of pictures and find the one that is missing? That is exactly what we will learn today!

SECTION 2

The Big Ideas Behind Matrix Puzzles

Before we solve any puzzles, let's learn the big ideas. These are the special rules that every matrix puzzle follows. Once you know them, you will be a pattern detective!

Rows Go Across

A row is a line of pictures that goes from left to right. Each row follows its own pattern.

Columns Go Down

A column is a line of pictures that goes from top to bottom. Columns have patterns too!

Look for Changes

Things can change in a pattern. The shape, color, size, or number of objects might change from one box to the next.

Look for What Stays the Same

Sometimes part of the picture stays the same while another part changes. Pay attention to both!

Check Both Ways

Always check your answer across the row AND down the column to make sure it fits the pattern both ways.

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KEY TAKEAWAY

Think of a matrix like a tic-tac-toe board filled with pictures. Each row and each column tells a little story. Your job is to figure out how the story ends by picking the right missing picture!

SECTION 3

See How a Matrix Works

Let's look at a simple matrix. This is a 3×3 grid. That means it has 3 rows going across and 3 columns going down. Look at the picture below. Can you see the pattern in each row and each column?

Look across each row: the shape stays the same but the number goes up (1, 2, 3). Look down each column: the number stays the same but the shape changes. The missing picture must be 3 yellow triangles!

Did you see it? The row pattern shows the number growing: 1, 2, 3. The column pattern shows the shape changing: circle, square, triangle. When you put both clues together, the missing picture must be 3 triangles!

SECTION 4

How Patterns Work in a Matrix

What Can Change in a Pattern?

In matrix puzzles, things change in special ways. Here are the four most common things that can change. We call these attributes. An attribute is just a fancy word for something you can see about a picture.

Shape

The kind of shape can change. It might go from circle to square to triangle.

Size

Shapes can get bigger or smaller. They might go from small to medium to large.

Color or Shading

The color can change. A shape might go from white to gray to black.

Number

The number of shapes can change. You might see 1, then 2, then 3.

Other Changes to Watch For

✓ Rotation: A shape might turn or spin a little in each box.
✓ Position: A shape might move from the top of the box to the middle to the bottom.
✓ Addition or subtraction: Parts might be added to or taken away from a shape, like a line getting added inside.

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Helpful Hint

Sometimes only one thing changes, like size. Sometimes two things change at once, like size AND color. Always look carefully at everything!

SECTION 5

Different Kinds of Matrix Puzzles

Not all matrix puzzles look the same. Some are small and some are big. Let's look at the different types you might see on a test.

This diagram shows a 2×2 matrix (easy) and a 3×3 matrix (most common). Below the grids, you see the answer choices. You pick the one picture that fits both the row and the column.

Type	Size	How Hard?
2×2 Matrix	4 boxes	Easiest — good for beginners
3×3 Matrix	9 boxes	Most common on the CogAT test
2×2 with two changes	4 boxes	Tricky — two things change at once

Common matrix types on the CogAT

SECTION 6

Let's Solve One Together!

Let's walk through a matrix puzzle step by step. Imagine a 2×2 grid. The top-left box has a small white circle. The top-right box has a big white circle. The bottom-left box has a small white square. The bottom-right box has a question mark. What goes there?

Solving a 2×2 Matrix

1
Step 1 — Look Across Row 1

The first row has a small circle and then a big circle. What changed? The shape stayed the same (both are circles). But the size changed — it got bigger!

Row rule: the shape gets bigger.
2
Step 2 — Look Down Column 1

The first column has a small circle on top and a small square on the bottom. What changed? The size stayed the same (both are small). But the shape changed — circle changed to square!

Column rule: the shape changes from circle to square.
3
Step 3 — Put the Clues Together

The missing picture is in row 2 and column 2. Row 2 starts with a small square, so the row rule says it should get bigger. Column 2 starts with a big circle, so the column rule says it should become a square.

The answer is a big white square!
4
Step 4 — Double Check

Does a big square fit row 2? Yes — small square → big square (size gets bigger ✓). Does a big square fit column 2? Yes — big circle → big square (shape changes, size stays big ✓). It works both ways!

✓ Answer confirmed: big white square.

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REMEMBER THIS TRICK

Always check your answer two ways — across the row and down the column. If it fits both ways, you found the right answer! It's like checking both directions before crossing the street.

SECTION 7

Tips and Common Traps

Some answer choices are tricky! They are put there on purpose to fool you. Let's learn about good tips and common traps so you can avoid mistakes.

Good Tips ✓	Common Traps ✗
Look at rows first, then columns.	Picking the first answer that looks right without checking both ways.
Name what you see: shape, size, color, number.	Forgetting to check one attribute, like color.
Use your finger to point across and down.	Getting confused by answer choices that only match the row but not the column.
If stuck, cross out wrong answers first.	Spending too long on one puzzle — skip and come back!

Tips vs. Traps for Matrix Puzzles

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KEY TAKEAWAY

Think of the wrong answer choices like puzzle pieces that almost fit but not quite. Just like the wrong puzzle piece might have the right color but the wrong shape, a wrong matrix answer might match one direction but not the other. Always check both!

SECTION 8

Getting Ready for Harder Puzzles

As you get better at matrices, the puzzles will get harder. Let's see how easy puzzles compare to harder ones so you know what to expect.

Feature	Easier Puzzles	Harder Puzzles
Grid size	2×2 (4 boxes)	3×3 (9 boxes)
Things that change	Only 1 thing changes	2 or 3 things change at once
Answer choices	Choices look very different	Choices look very similar
Shapes used	Simple shapes (circle, square)	Unusual shapes and designs

How matrix puzzles get harder over time

Don't worry if the puzzles get harder! The same steps always work. Look across, look down, find what changes and what stays the same, and always check your answer both ways.

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Fun Fact

Older kids and even adults solve matrix puzzles too! The same basic idea — finding patterns — is used by scientists and artists every day.

SECTION 9

Practice Problems

Now it's your turn! Try these five problems. They start easy and get harder. Remember to look across rows and down columns.

Question 1: CONCEPTUAL

In a matrix puzzle, which TWO directions do you need to check to find the missing picture?

Show answer

You need to check across the row (left to right) and down the column (top to bottom). The missing picture must follow the pattern in both directions. If you only check one direction, you might pick a wrong answer that seems right.

Question 2: BASIC CALCULATION

Imagine a 2×2 matrix. Top-left: one small star. Top-right: one big star. Bottom-left: one small heart. What goes in the bottom-right?

Show answer

The answer is one big heart. Looking across row 1, the shape stays the same but gets bigger (small star → big star). Looking down column 1, the size stays the same but the shape changes (small star → small heart). So the missing piece must be big (following the row pattern) and a heart (following the column pattern). That gives us one big heart.

Question 3: INTERMEDIATE

Imagine a 2×2 matrix. Top-left: one white circle. Top-right: two white circles. Bottom-left: one black circle. What goes in the bottom-right?

Show answer

The answer is two black circles. Looking across row 1, the color stays the same (white) but the number changes (1 → 2). Looking down column 1, the number stays the same (1) but the color changes (white → black). So the missing piece follows both rules: the number goes to 2 (row rule) and the color becomes black (column rule). Two things changed in this puzzle: number AND color!

Question 4: APPLIED

A 3×3 matrix has this pattern: Row 1 shows a circle getting bigger (small, medium, large). Row 2 shows a square getting bigger. Row 3 shows a triangle getting bigger, but the last box is missing. You have four answer choices: (A) large triangle, (B) small triangle, (C) large circle, (D) medium triangle. Which is correct and why?

Show answer

The answer is (A) large triangle. In each row, the shape stays the same but gets bigger: small, then medium, then large. Row 3 starts with a small triangle, then a medium triangle, so the missing piece must be a large triangle. Choice B is wrong because small is too small. Choice C is wrong because it is a circle, not a triangle. Choice D is wrong because medium is the middle size, but we need the largest size.

Question 5: CRITICAL THINKING

You are solving a 3×3 matrix and you find an answer that works perfectly going across the row, but it does NOT work going down the column. What should you do?

Show answer

You should NOT pick that answer! A correct answer must work in both directions — across the row AND down the column. Go back and look at the other answer choices. One of them will fit both the row pattern and the column pattern. This is a common trap on the test. Some wrong answers are put there on purpose because they match only one direction. Always double-check by looking both ways before you choose.

SUMMARY

What We Learned

Summary

A matrix puzzle is a grid of pictures that follows a pattern. To find the missing figure, you look for what changes and what stays the same. Things that can change include shape, size, color, and number. Always check your answer by looking across the row and down the column.

Remember: be a pattern detective! Name what you see, find the rules, pick the answer that fits both directions, and double-check your work. You've got this!