Use visual attributes and relationships to classify figures - CogAT Grades 3 Plus

SECTION 1

Why Do We Classify Figures?

Humans have been sorting shapes and patterns for thousands of years. Ancient builders had to tell the difference between a triangle and a rectangle to design roofs and walls. Scientists look at patterns in nature — like the shapes of leaves or the spirals of seashells — to understand the world. Figure classification is the skill of looking at a group of images and figuring out what rule connects them.

On the CogAT Nonverbal Battery, you will see rows of shapes and designs. Your job is to find the hidden pattern. This skill has a long history in both art and science.

~300 BC • Euclid Classifies Shapes

The Greek mathematician Euclid wrote a book called Elements that sorted all shapes by their properties — like number of sides and angles.

1900s • Gestalt Psychology

German psychologists discovered that the brain naturally groups shapes by similarity, closeness, and pattern. This is how you instinctively see a "group" of related figures.

1954 • First CogAT Published

The Cognitive Abilities Test was created to measure reasoning skills, including figure classification — the ability to find rules that connect shapes without using words.

Today • Modern Applications

Figure classification is now used in computer vision, medical imaging, and artificial intelligence. The same skills you practice here are used by real scientists!

The big question is: How do you figure out the hidden rule that connects a group of figures? That is exactly what this lesson will teach you.

SECTION 2

Core Principles of Figure Classification

When you classify figures, you look for visual attributes (the features of each shape) and relationships (how the shapes connect to each other). There are four main types of attributes you should always check.

Shape

Count the sides. Is it a circle, triangle, square, pentagon, or something else? Is it curved or straight-edged?

Size

Compare how big or small each figure is. Are the figures all the same size, or do they get bigger or smaller?

Shading & Color

Is the figure filled in (solid), striped, dotted, or empty (outline only)? Shading is one of the most common attributes tested.

Position & Orientation

Where is the figure placed? Is it rotated, flipped, or tilted? Look at how shapes relate to each other in space.

Number of Parts

Does the figure contain inner shapes, dots, or lines? Count how many elements appear inside or around the main shape.

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KEY TAKEAWAY

Think of figure classification like sorting your closet. You might sort clothes by color, by size, or by type (shirts vs. pants). Figures work the same way — you pick the one rule that all the figures in a group share, and then find the answer choice that follows that same rule.

SECTION 3

Seeing the Pattern: A Visual Guide

The diagram below shows three figures that belong to the same group and five answer choices. Study the top row to find the rule, and then pick the answer choice that matches.

The top row shows three figures that are all triangles (three sides). Even though they have different shading and sizes, the shared rule is their shape. Choice 2 is the only triangle in the answer row.

Notice that the three given figures look different from each other. One is filled in, one is an outline, and one is lightly shaded. But they all share one thing: they are triangles. This is the key idea. The rule is usually about what stays the same, not what changes.

SECTION 4

How to Find the Hidden Rule

There is no single formula for figure classification, but there is a clear process you can follow every time. Think of it as a checklist. You scan each attribute, one at a time, until you find the one that all the given figures share.

The SCAN Method

S — Shape

Do all figures have the same number of sides or the same type of curve? Check this first.

C — Count

Count inner elements: dots, lines, or small shapes inside a larger shape. Is the count the same?

A — Appearance

Look at shading, fill, and color. Are all figures solid? Striped? Empty? Half-filled?

N — kNobs & position

Check rotation, reflection, or placement. Are all arrows pointing the same way? Is a dot always in the top-left corner?

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Pro Tip

Sometimes the rule uses two attributes at once. For example, all the given figures might be "small circles that are shaded." If one attribute alone does not work, try combining two!

After you find the rule using SCAN, go through each answer choice and test it. Only one choice will match the rule. If more than one seems to work, your rule might be too simple — go back and look for a more specific pattern.

SECTION 5

Common Attributes and How to Spot Them

Let's look at the most common visual attributes tested on CogAT figure classification questions. The diagram below shows examples of each attribute side by side so you can train your eye.

This reference chart shows the five main attribute categories: shape, shading, size, orientation, and number of inner elements. The bottom-right corner shows a combined rule example where both shape AND shading must match.

Attribute	What to Look For	Example Rule
Shape	Number of sides, curved vs. straight	All figures are pentagons (5 sides)
Shading	Solid, empty, half-filled, striped	All figures are empty (outline only)
Size	Small, medium, large relative to each other	All figures are the same large size
Orientation	Pointing up, down, left, right, tilted	All arrows point to the right
Inner elements	Dots, lines, or shapes inside the figure	All figures have exactly 2 dots inside

Quick-reference table of common attributes

SECTION 6

Worked Example: Step-by-Step Solution

Imagine you see three figures in the given row: a large solid circle, a large solid square, and a large solid triangle. The answer choices are: (A) small empty circle, (B) large solid hexagon, (C) large empty square, (D) small solid triangle, (E) large striped circle. Let's use the SCAN method.

Finding the Rule with SCAN

1
Step 1 — Check Shape

The given figures are a circle, a square, and a triangle. They are all different shapes. So shape is NOT the shared rule.

Shape varies → not the rule
2
Step 2 — Count Inner Elements

None of the three figures have dots or lines inside. They are all plain, filled-in shapes. There is nothing special to count.

No inner elements → not helpful here
3
Step 3 — Check Appearance (Shading)

All three figures are solid (filled in). This is a match! But let's also check size to see if there is a second part to the rule.

Shading = solid ✓
4
Step 4 — Check Size

All three figures are large. Another match! The rule is: large AND solid.

Size = large ✓
5
Step 5 — Test the Rule Against Answer Choices

We need an answer that is both large AND solid. (A) is small and empty — no. (B) is large and solid — yes! (C) is large but empty — no. (D) is small — no. (E) is large but striped — no.

Answer: (B) large solid hexagon

✦

KEY TAKEAWAY

Using the SCAN method is like being a detective. You check each clue (attribute) one at a time. If one clue doesn't match across all three figures, cross it off and move to the next one. The clue that all three share is your answer key.

SECTION 7

Common Traps and How to Avoid Them

CogAT questions are designed to include tricky answer choices. Here are the most common traps students fall into — and how to dodge them.

Trap	What Happens	How to Avoid It
Partial match	An answer shares ONE attribute but not all. For example, it is the right shape but wrong shading.	Always check every attribute of the rule, not just the first one you notice.
Distractor detail	You focus on a feature that changes between the given figures instead of what stays the same.	Remind yourself: the rule is what is SAME in all three, not what is different.
Overthinking	You invent a complicated rule when the real answer is simple (like "all are circles").	Start with the simplest possible rule. Only add complexity if needed.
Rushing	You pick the first answer that looks similar without fully testing the rule.	Test ALL five answer choices against your rule before selecting one.

Four common traps on figure classification questions

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REMEMBER

Think of traps like wrong turns on a map. If you follow a system (SCAN), you won't accidentally wander down the wrong path. Always verify your rule against all answer choices before locking in your answer.

SECTION 8

Moving to More Complex Figure Classification

As you get more comfortable, the CogAT will throw harder questions at you. These questions use more complex rules — sometimes combining three attributes, or using rules about relationships between figures (like "the inner shape is always different from the outer shape"). Here is how basic questions compare to advanced ones.

Feature	Basic Questions	Advanced Questions
Number of rules	1 rule (e.g., "all triangles")	2–3 rules combined (e.g., "small solid triangles")
Attribute type	Simple: shape or shading only	Abstract: relationships between inner and outer shapes
Distractors	Clearly wrong choices	Multiple partial matches that seem close
Strategy	SCAN through basic attributes	SCAN + look for patterns between elements

Basic vs. Advanced figure classification comparison

Don't worry if advanced questions feel tough at first. The SCAN method still works — you just need to check more attributes and sometimes look at how parts of the figure relate to each other. With practice, you will get faster and more accurate.

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Looking Ahead

On the actual CogAT, figure classification is part of the Nonverbal Battery, which also includes figure analogies and paper folding. The classification skills you learn here — scanning attributes and finding rules — will also help you with those question types!

SECTION 9

Practice Problems

Try these five problems on your own. Read the description of the given figures, find the rule, and pick the correct answer. Check your answers afterward to see how you did.

Question 1: CONCEPTUAL

Three given figures are: a large circle, a medium circle, and a small circle. All three are solid (filled in). Which of these could be the shared rule? (A) All are circles. (B) All are the same size. (C) All are solid.

Show answer

Both (A) and (C) are correct observations! All three are circles, and all three are solid. But (B) is wrong because the sizes are different. On a real CogAT question, you would need to find the answer choice that matches the MOST specific rule. If the answer choices include both circles and solid shapes, pick the one that satisfies BOTH rules (solid circles).

Question 2: BASIC CALCULATION

Given figures: an empty (outline-only) triangle, an empty square, and an empty pentagon. Answer choices: (A) solid triangle, (B) empty hexagon, (C) empty circle with a dot inside, (D) solid pentagon, (E) striped square. Which answer belongs to the group?

Show answer

The rule is that all given figures are empty (outline only). The shapes are all different, so shape is not the rule. (A) is solid — no. (B) is empty — yes! (C) is empty but has a dot inside, adding an inner element the others don't have — no. (D) is solid — no. (E) is striped — no. The answer is (B).

Question 3: INTERMEDIATE

Given figures: a small solid square with 1 dot inside, a small solid triangle with 1 dot inside, and a small solid circle with 1 dot inside. Answer choices: (A) large solid square with 1 dot, (B) small empty triangle with 1 dot, (C) small solid hexagon with 2 dots, (D) small solid diamond with 1 dot, (E) small solid star with no dot. Which answer belongs?

Show answer

Let's SCAN. Shape? All different — not the rule. Size? All small — rule 1. Shading? All solid — rule 2. Inner elements? All have exactly 1 dot — rule 3. Now test: (A) is large, so it fails the size rule. (B) is empty, so it fails the shading rule. (C) has 2 dots, so it fails the inner element rule. (D) is small, solid, and has 1 dot — it matches all three rules! (E) has no dot. The answer is (D).

Question 4: APPLIED

Given figures: a circle with a triangle inside, a square with a circle inside, and a pentagon with a square inside. Notice that in each figure, the inner shape has fewer sides than the outer shape. Answer choices: (A) triangle with a square inside, (B) hexagon with a triangle inside, (C) circle with a circle inside, (D) square with a pentagon inside, (E) triangle with a line inside. Which answer follows the rule?

Show answer

The rule is about a relationship: the inner shape always has fewer sides than the outer shape. (A) A triangle has 3 sides but a square has 4 — the inner shape has MORE sides. Wrong. (B) A hexagon has 6 sides and a triangle has 3 — the inner shape has fewer sides. This matches! (C) Both circles — same number (0 sides). Wrong. (D) The pentagon inside the square has more sides. Wrong. (E) A line is not really a shape with sides in the same way. The answer is (B).

Question 5: CRITICAL THINKING

Given figures: a large empty circle with a small solid square at the top, a large empty square with a small solid circle at the top, and a large empty triangle with a small solid diamond at the top. What TWO rules describe the relationship? Then, which answer fits: (A) a large solid pentagon with a small solid star at the top, (B) a large empty hexagon with a small solid triangle at the top, (C) a small empty circle with a large solid square at the bottom, (D) a large empty diamond with a small empty circle at the top?

Show answer

Rule 1: The outer shape is always large and empty. Rule 2: The inner shape is always small and solid, placed at the top. Also, the inner shape is always different from the outer shape. (A) fails because the outer shape is solid. (C) fails because the sizes and positions are reversed. (D) fails because the inner shape is empty, not solid. (B) has a large empty hexagon (matches Rule 1) and a small solid triangle at the top (matches Rule 2), and the triangle is different from the hexagon. The answer is (B).

SUMMARY

Lesson Summary

Summary

Figure classification on the CogAT Nonverbal Battery asks you to find the hidden rule that connects a group of figures. The five key visual attributes to check are shape, size, shading, orientation, and number of inner elements. Use the SCAN method (Shape, Count, Appearance, kNobs & position) to systematically check each attribute.

The rule is always about what stays the same across all given figures. Watch out for partial matches and distractor details. On harder questions, you may need to find combined rules (two or more attributes) or identify relationships between parts of each figure. With practice, your eye will get faster at spotting these patterns!