We use numbers every day, from counting our toys to checking the time. So far, you've probably worked with smaller numbers. Now, let's explore bigger, four-digit numbers! You see them all the time: in years like 2024, on house addresses, and even in high scores on video games.

Reading and writing these numbers is easy once you know the secret. Let's take the number 3,456. We read it just like it sounds: "Three thousand, four hundred and fifty-six." When you write it in words, you do the same. When you see the words, you just write down the digits. For example, "seven thousand, two hundred and nine" is written as 7,209. Notice we use a zero to hold the tens place because there weren't any!

Every digit in a number has two different values: a face value and a place value. It sounds complicated, but it's quite simple.

The face value is just the digit you see. In the number 5,834, the face value of the 8 is just 8. Easy, right?

Place value is where it gets interesting. This tells you how much a digit is worth based on its position in the number.

Let's look at 5,834 again. The digit 4 is in the ones place, so its place value is 4. The digit 3 is in the tens place, so its place value is 30. The digit 8 is in the hundreds place, so its place value is 800. And the 5 is in the thousands place, making its place value 5,000.

This diagram shows how it works:

Understanding place value helps you see why a number like 91 is much smaller than 190, even though they use similar digits.

Have you ever played a game where you have to split into teams of two? Some groups split perfectly, and some have one person left over. Numbers are the same way! Even numbers can always be split into two equal groups, like 8 which can be two 4s. Odd numbers always have one left over, like 7 which is a 3, another 3, and one extra.

The secret to telling if a number is odd or even is to look only at the digit in the ones place.

If the last digit is 0, 2, 4, 6, or 8, the number is even. So, 1,236 is even.

If the last digit is 1, 3, 5, 7, or 9, the number is odd. That means 9,875 is odd.

It doesn't matter how big the number is. The rule always works.

Math is full of beautiful patterns. Finding them is like being a detective. Number patterns, also called sequences, are lists of numbers that follow a specific rule.

Consider this sequence: 10, 20, 30, 40, ?

What comes next? If you said 50, you're right! The rule is to add 10 each time. What about this one?

55, 50, 45, 40, ?

Here, the numbers are getting smaller. The rule is to subtract 5. The next number would be 35.

Sometimes the pattern is a little trickier. Look at this: 1, 4, 9, 16, ?

This pattern is made of square numbers: $1^2$, $2^2$, $3^2$, $4^2$. The next number is $5^2$, which is 25. Spotting these patterns is a key skill for solving tough problems.

Comparing and ordering numbers helps us understand which values are greater or smaller. We use special symbols for this: > (greater than), < (less than), and = (equal to). Think of the > and < symbols as a hungry alligator's mouth, which always wants to eat the bigger number!

To compare two four-digit numbers, start by looking at the thousands place. The number with the bigger digit in the thousands place is the greater number. For example, in 8,123 and 7,987, we see that 8 is bigger than 7, so 8,123 > 7,987.

What if the thousands digits are the same? Then we move to the hundreds place. Compare 4,567 and 4,812. The thousands digits are both 4. So we look at the hundreds: 5 and 8. Since 8 is bigger than 5, we know that 4,812 > 4,567.

If the hundreds are also the same, you check the tens place, and then the ones place. Ordering a group of numbers from smallest to largest works the same way. You find the smallest number, then the next smallest, and so on.

Ready to test your number sense skills?

Great work. Mastering these ideas about numbers will help you tackle any math challenge that comes your way.