Apply the same relationship to complete a number analogy - CogAT Grades K 2

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Why Do We Use Number Analogies?

People have loved finding patterns for a very long time! Long ago, people noticed that numbers follow rules. For example, when you count by twos, you say 2, 4, 6, 8. That is a pattern! Finding patterns helps us solve problems and think in smart ways.

A number analogy is like a number puzzle. It shows you a rule with one pair of numbers. Then you use that same rule to find a missing number. Let's see how people started using these puzzles!

Long Ago • People Count Things

Early people counted animals, food, and objects. They noticed numbers go in order: 1, 2, 3, 4, 5!

In School • Kids Learn Patterns

Children started learning to spot patterns like adding 1, adding 2, or doubling a number.

Puzzles • Number Analogies Are Born

Teachers made fun puzzles where kids find the rule between two numbers and use it to solve a new pair.

Today • Tests Use Number Analogies

Now, tests like the CogAT use number analogies to see how well you can think about number patterns!

So here is the big question: if you see a rule that changes one number into another, can you use that same rule to change a different number? That is what number analogies are all about!

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What Are Number Analogies?

A number analogy looks like this: 2 goes to 4 the same way 3 goes to ?. Your job is to find the rule and fill in the missing number!

Find the Rule

Look at the first pair of numbers. Ask: what happened? Did the number get bigger? Smaller? By how much?

Name the Rule

Say the rule out loud! For example: "I added 2" or "I took away 1" or "I doubled it."

Use the Same Rule

Now do the exact same thing to the new number. If you added 2 before, add 2 again!

Check Your Answer

Make sure your answer follows the same pattern. Does it make sense? Great job!

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KEY TAKEAWAY

Think of a number analogy like a recipe. If you make cookies by adding chocolate chips, you add chocolate chips every time you bake. The rule stays the same! In a number analogy, the rule stays the same for both pairs of numbers.

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See the Pattern!

Let's look at a picture that shows how a number analogy works. In this picture, you will see two pairs of numbers and the rule that connects them.

Pair 1 shows 2 → 5 (we added 3). Pair 2 uses the same rule: 6 + 3 = 9. The answer is 9!

Look at the picture above. In Pair 1, the number 2 turns into 5. How? We added 3! Now in Pair 2, we start with 6. We use the same rule and add 3 again. So 6 + 3 = 9. The missing number is 9!

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How Do We Find the Rule?

There are a few common rules you might see in number analogies. Let's learn about them!

Adding a Number

Sometimes the rule is to add a number. If 3 goes to 5, we added 2. So if 7 goes to ?, we add 2 and get 9!

ADDING RULE

3 + 2 = 5, so 7 + 2 = 9

We found that 2 was added. We do the same thing to the new number.

Taking Away a Number

Sometimes the rule is to take away (subtract) a number. If 8 goes to 6, we took away 2. So if 5 goes to ?, we take away 2 and get 3!

SUBTRACTING RULE

8 − 2 = 6, so 5 − 2 = 3

We found that 2 was taken away. We subtract 2 from the new number too.

Doubling a Number

Sometimes the rule is to double the number (add it to itself). If 3 goes to 6, we doubled it! So if 4 goes to ?, we double it and get 8!

DOUBLING RULE

3 + 3 = 6, so 4 + 4 = 8

Doubling means adding a number to itself. The number gets twice as big!

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Different Kinds of Number Rules

Let's look at a chart that shows all the different rules you might see. Each row shows a different kind of rule and an example.

This chart shows three common rules: adding, subtracting, and doubling. Each one has an example that shows how the rule works with a new pair.

Here is a helpful trick. If the second number is bigger than the first, the rule is probably adding. If the second number is smaller, the rule is probably subtracting. And if the second number is exactly twice the first, the rule is doubling!

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Let's Solve One Together!

Let's try this number analogy step by step: 4 goes to 7, so 5 goes to ?. Follow along!

Solving: 4 → 7, so 5 → ?

1
Step 1 — Look at Pair 1

Our first pair is 4 and 7. The first number is 4. The second number is 7. The number got bigger!
2
Step 2 — Find the Rule

How much bigger did it get? Let's count up from 4: 5, 6, 7. That is 3 more! The rule is add 3.

Rule: add 3
3
Step 3 — Use the Same Rule on Pair 2

Now we start with 5. We use the same rule and add 3. So we count up from 5: 6, 7, 8.

5 + 3 = 8
4
Step 4 — Check Our Answer

Let's check: 4 + 3 = 7 ✓ and 5 + 3 = 8 ✓. Both pairs follow the same rule. Our answer is 8!

? = 8 ✓

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Helpful Tips and Common Mistakes

Sometimes number analogies can be tricky. Here are some tips to help you and some mistakes to watch out for!

Good Habits ✓	Common Mistakes ✗
Always find the rule FIRST by looking at Pair 1.	Guessing without finding the rule.
Check if the number got bigger or smaller.	Adding when you should subtract.
Count carefully on your fingers if needed.	Counting too fast and making a mistake.
Check your answer by making sure both pairs follow the same rule.	Forgetting to check your work.

Tips for solving number analogies correctly

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REMEMBER THIS!

Think of it like wearing matching socks. Both socks have to be the same color! In a number analogy, both pairs have to follow the same rule. If Pair 1 adds 2, then Pair 2 must add 2 too!

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Getting Ready for Harder Puzzles

As you get better at number analogies, the puzzles might get a little harder. Here is what you know now and what you will learn next!

What You Know Now	What's Coming Next
Add a small number (like +1, +2, +3)	Add bigger numbers (like +5, +10)
Subtract a small number (like −1, −2)	Subtract bigger numbers
Double a number (×2)	Multiply by 3 or more
One rule at a time	Puzzles with pictures and numbers together

Your learning path for number analogies

Don't worry about the harder puzzles right now. If you can find the rule and use it again, you are doing great! Each new puzzle will make your brain even stronger.

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Practice Problems

Now it's your turn! Try these five number analogy puzzles. Remember: find the rule in Pair 1, then use the same rule to solve Pair 2.

Question 1: CONCEPTUAL

2 goes to 3, so 5 goes to ?. What is the missing number?

Show answer

The answer is 6. Look at Pair 1: 2 goes to 3. The number went up by 1. So the rule is add 1. Now use the same rule: 5 + 1 = 6!

Question 2: BASIC CALCULATION

3 goes to 6, so 4 goes to ?. What is the missing number?

Show answer

7. In Pair 1, 3 goes to 6. We count: 4, 5, 6. That's 3 more! The rule is add 3. Now we do the same: 4 + 3 = 7. The missing number is 7.

Question 3: INTERMEDIATE

8 goes to 6, so 5 goes to ?. What is the missing number?

Show answer

3. In Pair 1, 8 goes to 6. The number got smaller! We count back from 8: 7, 6. That is 2 less. The rule is subtract 2. Now we do the same: 5 − 2 = 3. The missing number is 3.

Question 4: APPLIED

2 goes to 4, so 5 goes to ?. Think carefully — is the rule adding 2, or is the rule doubling?

Show answer

This one is tricky! 2 goes to 4 could mean add 2 (2 + 2 = 4) OR double (2 × 2 = 4). On the CogAT, you look at the answer choices to decide. If the choices include 7, the rule is add 2 (5 + 2 = 7). If the choices include 10, the rule is doubling (5 + 5 = 10). Both could be right — the answer choices help you decide!

Question 5: CRITICAL THINKING

10 goes to 5, so 8 goes to ?. What is the missing number, and how did you figure out the rule?

Show answer

The answer is 3. In Pair 1, 10 goes to 5. The number got smaller by 5 (10 − 5 = 5). The rule is subtract 5. Now we use the same rule: 8 − 5 = 3. We know it's right because both pairs follow the subtract 5 rule. Great thinking!

SUMMARY

What We Learned

Summary

A number analogy is a puzzle where you find the rule between two numbers and then use that same rule to find a missing number. The rule might be adding, subtracting, or doubling.

To solve a number analogy, follow these steps: first, look at Pair 1 and find the rule. Then, apply that same rule to the new number. Finally, check your answer to make sure it works. You are a number detective!