Select the Number That Continues the Series - CogAT Grades K 2

SECTION 1

Why Do We Look for Patterns?

People have loved patterns for a very long time! A pattern is something that repeats or follows a rule. Long ago, people looked at the stars and saw patterns. They watched the seasons change in a pattern too. Patterns help us know what will happen next.

When we use numbers in a pattern, we call it a number series. A number series is a list of numbers that follow a rule. If you find the rule, you can guess what number comes next!

Long Ago • Patterns in Nature

People noticed patterns everywhere — day and night, seasons, and the shapes of flowers.

Ancient Times • Counting with Patterns

People started counting by 2s, 5s, and 10s. These were some of the first number patterns!

In School • Number Series on Tests

Today, kids learn to find number patterns. Tests like the CogAT ask you to find what comes next in a series.

So the big question is: How do we find the rule in a number series? Let's learn how!

SECTION 2

The Big Ideas About Number Series

Before we start solving number series, let's learn a few big ideas. These ideas will help you every time you see a number pattern.

Find the Rule

Every number series follows a rule. The rule tells you how to get from one number to the next. Look at what changes!

Check Between Neighbors

Look at two numbers that are right next to each other. Ask: did the number go up or down? By how much?

Use the Rule to Predict

Once you know the rule, use it on the last number. That gives you the answer — the next number in the series!

Check Your Answer

Always go back and make sure your answer fits. Try the rule on every pair of numbers to be sure.

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KEY TAKEAWAY

Think of a number series like a set of stepping stones across a pond. Each stone is the same distance apart. If you know the distance between the stones, you know exactly where the next stone will be!

SECTION 3

See the Pattern!

Let's look at a picture that shows how a number series works. In the picture below, you can see the numbers 2, 4, 6, 8 and then a question mark for the next number. Notice how each number goes up by 2!

Each circle shows a number in the series. The arrows show that we add 2 each time. So after 8, the next number is 10.

See how it works? The rule is "add 2." We use the rule on the last number: 8 + 2 = 10. That's the answer!

SECTION 4

How to Find the Rule

Here is a simple way to find the rule in any number series. Think of it like being a detective looking for clues!

Step-by-Step Trick

Step 1: Look at the first two numbers. Ask: did the number go up or go down?
Step 2: Count how much it changed. For example, going from 3 to 5 means it went up by 2.
Step 3: Check the next pair of numbers. Does the same rule work? If yes, you found the rule!
Step 4: Use the rule on the last number to find the missing number.

THE PATTERN RULE

Last Number + Rule = Next Number

For example, if the rule is "add 3" and the last number is 9, then 9 + 3 = 12.

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Helpful Hint!

Sometimes numbers go down instead of up! If you see 10, 8, 6, the rule is "subtract 2." Don't worry — it works the same way!

SECTION 5

Different Kinds of Number Patterns

Not all number patterns are the same! Let's look at the most common types you might see. Knowing these will help you solve number series faster.

This picture shows three kinds of patterns. The adding pattern goes up by 3 each time. The subtracting pattern goes down by 5 each time. The repeating pattern repeats the same numbers over and over.

Pattern Type	What It Does	Example
Adding	Numbers go up by the same amount	2, 4, 6, 8, ?
Subtracting	Numbers go down by the same amount	10, 8, 6, 4, ?
Repeating	The same numbers show up again and again	3, 5, 3, 5, ?

Common Number Pattern Types

SECTION 6

Let's Solve One Together!

Here is a number series: 5, 10, 15, 20, ? Let's find the missing number step by step.

Finding the Next Number

1
Step 1 — Look at the First Two Numbers

The first number is 5 and the second number is 10. Did the number go up or down? It went up!

The numbers are going up.
2
Step 2 — Find How Much It Changed

From 5 to 10, how much did it go up? Let's count: 10 − 5 = 5. It went up by 5.

The change is +5.
3
Step 3 — Check the Rule on Other Pairs

From 10 to 15: that's +5. From 15 to 20: that's +5 too! The rule works every time.

Rule confirmed: add 5 each time.
4
Step 4 — Use the Rule on the Last Number

The last number is 20. We add 5: 20 + 5 = 25.

The answer is 25!

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Great Job!

You found the rule (add 5), checked it, and used it. That's exactly how to solve every number series problem!

SECTION 7

Helpful Tips and Common Mistakes

Even the best pattern detectives can get tripped up! Here are some tips to help you, and some mistakes to watch out for.

✅ Good Tips	❌ Common Mistakes
Always check the rule on every pair, not just the first pair.	Looking at only the first two numbers and guessing.
Use your fingers to count the difference between numbers.	Forgetting to count carefully and being off by 1.
Check if numbers go up or down before you decide the rule.	Adding when you should be subtracting.
Look for repeating patterns if adding and subtracting don't seem to work.	Giving up if the first idea doesn't work. Try another rule!

Tips vs. Mistakes

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KEY TAKEAWAY

Think of finding a number pattern like singing a song. Once you learn the tune (the rule), you know what notes (numbers) come next. If your song sounds wrong, try a different tune!

SECTION 8

Getting Ready for Harder Patterns

You've learned how to find patterns that add, subtract, or repeat. As you grow, you'll learn even trickier patterns! Let's see how what you know now connects to what's ahead.

What You Know Now	What's Coming Later
Add the same number each time (like +2)	Add a different amount each time (like +1, +2, +3)
Simple repeating patterns (like 1, 2, 1, 2)	Longer repeating patterns (like 1, 2, 3, 1, 2, 3)
Small numbers (1 through 20)	Bigger numbers and even patterns with shapes!

Now vs. Later

Don't worry about the harder stuff yet! The steps you learned today — find the rule, check it, and use it — will work for all of these. You're building a strong brain for patterns!

SECTION 9

Practice Problems

Now it's your turn! Try these five problems. Start with the easy ones and work your way up. You can do it!

Question 1: CONCEPTUAL

Look at this number series: 1, 2, 3, 4, __. What number comes next?

Show answer

The answer is 5. Each number goes up by 1. We are just counting! 1, 2, 3, 4 … the next number we say when we count is 5. The rule is "add 1."

Question 2: BASIC CALCULATION

What number comes next? 2, 4, 6, 8, __

Show answer

The answer is 10. Look at the difference between each pair: 4 − 2 = 2, 6 − 4 = 2, 8 − 6 = 2. The rule is "add 2" each time. So 8 + 2 = 10. This is counting by 2s!

Question 3: INTERMEDIATE

Find the missing number: 15, 12, 9, 6, __

Show answer

The answer is 3. This time the numbers are going down! From 15 to 12 is −3. From 12 to 9 is −3. From 9 to 6 is −3. The rule is "subtract 3." So 6 − 3 = 3.

Question 4: APPLIED

A teacher puts stickers on a chart: 3, 5, 3, 5, 3, __. What sticker number comes next?

Show answer

The answer is 5. This is a repeating pattern! The numbers go 3, 5, 3, 5, 3 … The pattern is 3, then 5, over and over. After a 3, the next number is always 5. So the answer is 5.

Question 5: CRITICAL THINKING

What number comes next? 1, 2, 4, 7, 11, __

Show answer

The answer is 16. This one is tricky! The amounts we add are changing: from 1 to 2 is +1, from 2 to 4 is +2, from 4 to 7 is +3, from 7 to 11 is +4. The amount we add goes up by 1 each time! So the next step adds 5: 11 + 5 = 16.

SUMMARY

What You Learned

Summary

A number series is a list of numbers that follow a rule. The rule might be adding the same number each time, subtracting the same number, or repeating a group of numbers. To find the missing number, look at the numbers next to each other, find what changes, check that it works for every pair, and then use the rule on the last number.

Remember the four steps: look at the numbers, find the change, check every pair, and use the rule to find the answer. You are a pattern detective now!