Determine the missing number that makes a quantitative relationship true - CogAT Grades K 2

SECTION 1

Why Do We Look for Missing Numbers?

People have been solving puzzles with missing numbers for a very long time! Long ago, people counted things like sheep and apples. Sometimes they knew they had some, but they needed to figure out how many more they needed. That is how the idea of finding a missing number started.

Long Ago • Counting Begins

People first learned to count by using their fingers and small stones.

Ancient Times • Writing Numbers

People in Egypt and other places wrote numbers down to keep track of things they had.

Hundreds of Years Ago • Number Puzzles

Teachers started giving students fun puzzles where a number was hidden, and they had to find it!

Today • CogAT Questions

Now, tests like the CogAT ask you to find missing numbers to see how well you think about math.

So here is the big question: if you see numbers that go together in a special way, can you figure out which number is missing? That is exactly what you will learn today!

SECTION 2

Big Ideas to Know

Before we start finding missing numbers, let's learn some big ideas. These ideas will help you think like a math detective!

A Pattern is a Rule

Numbers can follow a rule, like counting by 2s: 2, 4, 6, 8. The rule is "add 2 each time."

Both Sides Must Match

If you see an equals sign (=), the numbers on the left side must add up to the same amount as the right side.

Use What You Know

Look at the numbers you can see. They give you clues to find the number that is hiding!

Check Your Answer

After you pick a number, put it back in and see if everything works. If it does, you found it!

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KEY TAKEAWAY

Think of it like a seesaw at the playground. Both sides need to have the same weight to stay balanced. If one side has some weight missing, you have to figure out how much to add so the seesaw is level!

SECTION 3

See How It Works

Let's look at a picture! This picture shows a balance scale. One side has blocks and the other side has blocks too. We need to figure out how many blocks are missing so both sides weigh the same.

This balance scale shows 3 + ? on the left side and 7 on the right side. Both sides must be equal, so the missing number is 4.

In this picture, the left side of the scale has 3 and a mystery number. The right side has 7. We need both sides to be the same. We can think: what number do I add to 3 to get 7? The answer is 4 because 3 + 4 = 7!

SECTION 4

How the Math Works

When you see a missing number problem, it usually looks like a number sentence with a blank or a question mark. Here are the kinds of number sentences you might see.

ADDITION WITH A MISSING NUMBER

2 + ? = 5

Ask yourself: what do I add to 2 to make 5? You can count up from 2: three, four, five. That is 3 jumps, so ? = 3.

SUBTRACTION WITH A MISSING NUMBER

8 − ? = 5

Ask yourself: what do I take away from 8 to get 5? Count back from 8: seven, six, five. That is 3 jumps, so ? = 3.

PATTERN WITH A MISSING NUMBER

1, 3, 5, ?, 9

The numbers go up by 2 each time. After 5, add 2 more. So ? = 7.

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REMEMBER

You have three super powers: you can count up, count back, or look for a pattern. Try each one until you find the missing number!

SECTION 5

Different Kinds of Missing Number Problems

Not all missing number problems look the same! Let's look at the different types you might see on the CogAT test. This picture shows you four main types.

This diagram shows four kinds of missing number problems: missing addend, missing result, number pattern, and equal groups.

Type	What It Looks Like	What to Do
Missing Addend	4 + ? = 9	Count up from 4 to 9
Missing Result	6 + 2 = ?	Add 6 and 2 together
Number Pattern	2, 4, ?, 8	Find the rule (add 2)
Equal Groups	3 + 3 = ? + 2	Solve one side, then match

Four types of missing number problems

SECTION 6

Let's Solve One Together!

Here is a problem just like the ones on the CogAT. Let's solve it step by step!

Find the Missing Number: 5 + ? = 8

1
Step 1 — Read the Problem

We see 5 + ? = 8. This means 5 plus some number equals 8. We need to find that number.
2
Step 2 — Count Up

Start at 5 and count up to 8. Say: six, seven, eight. Use your fingers to keep track. How many fingers did you hold up?

You held up 3 fingers!
3
Step 3 — Try the Answer

Put 3 in the blank: 5 + 3 = 8. Is that right? Yes! 5 + 3 is 8.

The missing number is 3. ✓
4
Step 4 — Check It

Let's double check. Count 5 things, then add 3 more: 1, 2, 3, 4, 5 ... 6, 7, 8. We get 8. Both sides match!

Answer: ? = 3

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Helpful Tip

You can also use your fingers, draw circles, or use small toys to help you count. It's okay to use things you can touch and see!

SECTION 7

Strategies That Help

There are many ways to find a missing number. Some ways are faster. Some ways are easier. Let's look at which strategy works best for each kind of problem.

Strategy	When to Use It	Why It's Great
Count Up	When you need to add to reach a bigger number	Easy to do on your fingers!
Count Back	When you need to take away to reach a smaller number	Good for subtraction problems
Draw It	When the numbers are a little bigger	You can see the answer with your eyes
Try Each Choice	When you are given answer choices	You just plug in and check!
Look for a Pattern	When numbers are in a list or row	Find the rule and follow it

Five helpful strategies for missing number problems

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KEY TAKEAWAY

Think of it like a treasure hunt. You have clues (the numbers you can see) and you are looking for treasure (the missing number). Use your clues wisely and check your answer to make sure you found the real treasure!

SECTION 8

How This Skill Grows With You

Finding missing numbers is a skill you will use for a long time! As you get older, the problems get a little harder, but the idea stays the same. Let's see how this skill changes as you grow.

Now (K-2)	Later (Grades 3-5)
Numbers up to 20	Numbers up to 1,000 and beyond
Adding and subtracting	Multiplying and dividing too
Simple patterns like +1 or +2	Trickier patterns like ×2 or +3, −1
One missing number	Sometimes two missing numbers!

How missing number skills grow over time

The great news is that once you learn to find missing numbers now, you are building a strong base. It is like learning to walk before you learn to run. You are getting ready for bigger math adventures!

SECTION 9

Practice Problems

Now it's your turn! Try these five problems. They start easy and get a little harder. Take your time and use the strategies you learned.

Question 1: CONCEPTUAL

Look at this: 2 + ? = 5. What does the question mark stand for?

Show answer

The question mark stands for a number we need to find. It is the missing number that makes the number sentence true. We need to figure out what we add to 2 to get 5. Since 2 + 3 = 5, the question mark stands for 3.

Question 2: BASIC CALCULATION

Find the missing number: 6 + ? = 10

Show answer

Start at 6 and count up to 10. Count: seven, eight, nine, ten. That is 4 counts. So ? = 4. We can check: 6 + 4 = 10. That is correct!

Question 3: INTERMEDIATE

What number is missing in this pattern? 3, 6, ?, 12, 15

Show answer

First, find the rule. From 3 to 6 is adding 3. From 12 to 15 is also adding 3. So the rule is to add 3 each time. After 6, we add 3 and get 9. Let's check: 3, 6, 9, 12, 15. Each number is 3 more than the one before. The missing number is 9.

Question 4: APPLIED

You have 4 red crayons and some blue crayons. You have 9 crayons in all. How many blue crayons do you have? Write it as a number sentence and solve.

Show answer

We write: 4 + ? = 9. We know we have 4 red crayons and all together we have 9. We need to find how many blue crayons there are. Count up from 4 to 9: five, six, seven, eight, nine. That is 5 counts. So you have 5 blue crayons. Check: 4 + 5 = 9. Correct!

Question 5: CRITICAL THINKING

Look at this problem: 3 + 5 = ? + 4. What is the missing number? How do you know?

Show answer

First, solve the left side: 3 + 5 = 8. Now we know the right side must also equal 8. So we need ? + 4 = 8. Count up from 4 to 8: five, six, seven, eight. That is 4 counts. So ? = 4. Check: 3 + 5 = 8, and 4 + 4 = 8. Both sides equal 8, so it works! This kind of problem has two sides that must balance, like a seesaw.

SUMMARY

What You Learned Today

Summary

Today you learned how to find a missing number that makes a math sentence true. You learned that a number sentence with an equals sign means both sides must be the same, like a balanced seesaw. You can find the missing number by counting up, counting back, or looking for a pattern.

You practiced four types of problems: missing addend, missing result, number patterns, and equal groups. Always remember to check your answer by putting it back in and making sure everything matches. You are a great math detective!