Comparing Two-Digit Numbers

Section 1

Why Do We Compare Numbers?

People have been comparing amounts for a very, very long time! Even before anyone wrote numbers down, people needed to know things like: "Do I have more apples or fewer apples than my friend?" Comparing is one of the first things humans ever did with numbers.

Long, Long Ago

Early people compared groups of things by lining them up. They matched one apple to one apple to see who had more!

Thousands of Years Ago

People invented numbers so they could count and compare without lining things up. Now they could say "I have 23 and you have 17!"

About 400 Years Ago

A math teacher named Thomas Harriot invented the symbols > (greater than) and < so people could write comparisons quickly.

Today

We still use those same symbols! You will learn them today. We also use the = sign when two numbers are the same.

So here is the big question this lesson will answer: When you see two two-digit numbers, how do you figure out which one is bigger? The secret is inside the tens and ones places!

Section 2

The Big Ideas

Before we compare, we need to remember what a two-digit number is made of. Every two-digit number (like 10, 25, or 73) has two parts: tens and ones. Let's learn the big ideas!

Tens Come First

The left digit tells you how many groups of ten. A group of ten is worth a lot! Always look at the tens first when you compare.

Ones Come Second

The right digit tells you how many ones are left over. You only need to check the ones if the tens are the same.

Three Special Symbols

We use > for "greater than," < for "less than," and = for "equal to."

The Mouth Opens Wide

The > and < symbols are like a hungry mouth. The open side always points at the bigger number!

✦ Key Takeaway

Think of tens and ones like dollars and pennies. If you have 4 dollars and your friend has 3 dollars, you have more money — even if your friend has more pennies! The dollars (tens) matter more. You only count the pennies (ones) when you both have the same dollars.

Section 3

Picture It: Tens and Ones Blocks

Let's look at two numbers using tens rods (tall blue bars) and ones cubes (small yellow squares). This picture shows us 34 and 28. Which one is bigger?

Visual comparison of 34 and 28 using tens rods and ones cubes.

See how 34 has 3 tall blue rods (3 tens = 30) and 28 only has 2 tall blue rods (2 tens = 20)? Even though 28 has more little yellow cubes (8 ones), it doesn't matter. The tens are more important! Three tens beats two tens, so 34 is greater than 28.

Section 4

How to Compare: Step by Step

Here are the easy steps to compare any two two-digit numbers. Follow these in order and you will always get it right!

Step 1

Look at the TENS digit first.

The tens digit is on the left side of the number.

Step 2

If the tens are different → you have your answer!

The number with MORE tens is the BIGGER number.

Step 3

If the tens are the SAME → look at the ONES.

The number with MORE ones is the BIGGER number.

Step 4

If tens AND ones are the same → they are equal!

Use the = sign. The numbers are the same!

That's it! Just four steps. Always start with tens. Only check the ones if the tens match. Let's learn about the three symbols we use to write our answer.

Section 5

Meet the Three Symbols

We use three special math symbols to show how two numbers compare. Let's get to know each one!

The three comparison symbols: greater than, less than, and equal to, each with an example and an alligator mouth illustration.

Here is a fun trick to remember > and <: Think of them as a hungry alligator's mouth. The alligator always wants to eat the bigger number! So its mouth opens toward the bigger side.

Symbol	Name	What It Means	Example
>	Greater than	The first number is bigger	72 > 45
<	Less than	The first number is smaller	31 < 56
=	Equal to	Both numbers are the same	88 = 88

✦ Key Takeaway

The > and < symbols are like an alligator's mouth. The alligator is very hungry, so it always opens its mouth toward the bigger number to gobble it up! If both numbers are the same, the alligator isn't hungry — we use = instead.

Section 6

Worked Example: Comparing 47 and 43

Let's walk through a full problem together! We want to compare 47 and 43.

Comparing 47 and 43

Step 1 — Look at the TensThe number 47 has 4 in the tens place. The number 43 also has 4 in the tens place. Both numbers have 4 tens. That means they both have 40 in them. The tens are the same!

Step 2 — The Tens Match, So Look at the OnesSince both tens digits are 4, we move to the ones place. 47 has 7 ones. 43 has 3 ones.

Step 3 — Compare the Ones7 ones is more than 3 ones. So 47 is bigger than 43!

Step 4 — Write the AnswerWe write it like this: 47 > 43. Read it out loud:

"47 is greater than 43." The alligator opens its mouth toward 47 because 47 is the bigger number! 🐊

Section 7

Tips, Tricks, and Common Mistakes

Comparing numbers is fun once you get the hang of it! Here are some tips and mistakes to watch out for.

✅ Do This	❌ Don't Do This
Always check the tens first.	Don't just look at which digit is bigger anywhere in the number.
Only check the ones when the tens are the same.	Don't compare 29 and 31 by saying "9 is bigger than 1, so 29 wins!" (It doesn't — 3 tens beats 2 tens!)
Remember: the open side of > or < faces the bigger number.	Don't mix up which way the symbol points.
Use = when both numbers are exactly the same.	Don't use > or < when both numbers are equal.
Say it out loud to check: "Is 56 greater than 52? Yes!"	Don't rush — take your time with each step.

✦ Key Takeaway

The biggest mistake kids make is looking at the ones when the tens are different. Remember: tens are like big buckets of ten things. One extra bucket of ten is always worth more than a few extra single ones. Think of it like a race — the tens are in the lead car. Only when both lead cars tie do you check the second car (the ones)!

Section 8

What Comes Next?

Great job learning to compare two-digit numbers! Once you master this, here is what you'll learn next as you grow in math.

What You Know Now	What You'll Learn Next
Comparing two-digit numbers (10–99)	Comparing three-digit numbers (100–999) using hundreds, tens, and ones!
Using >, <, and = with two numbers	Putting numbers in order from smallest to biggest (and biggest to smallest!)
Knowing tens are worth more than ones	Learning about hundreds — they're worth even more than tens!

The amazing thing is that the same steps you learned today work for bigger numbers too. You always start with the biggest place value and work your way right. Today it's tens and ones. Soon it will be hundreds, tens, and ones. The idea is the same — you're already building a superpower!

Section 9

Practice Problems

Now it's your turn! Try these five problems. Think about the steps, then click "Show Answer" to check.

PROBLEM 1 — WHAT DOES IT MEAN?

What does the symbol > mean? Can you say it in your own words?

PROBLEM 2 — PICK THE SYMBOL

Compare these two numbers. Which symbol goes in the box? 63 ☐ 58

PROBLEM 3 — SAME TENS!

Compare these two numbers. The tens are the same — what do you do? 75 ☐ 79

PROBLEM 4 — REAL LIFE!

Maya has 36 stickers. Leo has 42 stickers. Who has more stickers? Write a number sentence using >, <, or =.

PROBLEM 5 — THINK HARD!

Fill in a digit to make this true: 5☐ > 54 What numbers could go in the box? Can you find all of them?

Summary

Let's Review!

Every two-digit number is made of tens and ones. When you compare two numbers, always start with the tens digit (the one on the left). If one number has more tens, it is the bigger number — no matter what the ones say! Only when the tens are the same do you move on to compare the ones digit.

We write our answers using three symbols: > means greater than (the first number is bigger), < means less than (the first number is smaller), and = means equal to (both numbers are the same). Remember the hungry alligator trick — the alligator's open mouth always faces the bigger number! You now have all the tools to compare any two two-digit numbers. Keep practicing and you'll get faster and faster! 🎉