Why Do We Add Numbers?
People have been adding things together for a very, very long time! A long time ago, before there were schools or books, people still needed to count. If a farmer had 10 apples in one basket and 5 apples in another basket, the farmer needed to know how many apples there were in all. That is adding!
Let's look at how people learned to add over many years.
Adding is one of the most useful things you will ever learn. You use it when you count your toys, share snacks with friends, or figure out how many days until your birthday. Today we will learn how to add a two-digit number (like 34) and a one-digit number (like 5).
Big Ideas to Know
Before we start adding, let's learn four big ideas. These ideas will help you add like a superstar! 🌟
Ones and Tens
Add the Ones First
Making a New Ten
Stay Under 100
Let's See It in Pictures!
Pictures help us understand adding. Let's look at 23 + 5 using blocks. We use long bars for tens and little squares for ones.
Look at the picture! The number 23 has 2 tall blue bars (those are the tens) and 3 small green squares (those are the ones). We are adding 5 more ones (the pink squares). When we put them all together, we still have 2 tens and now we have 8 ones. That gives us 28!
The tens did not change at all. We only changed the ones. That is the secret to this kind of adding!
How It Works — Step by Step
Here is a simple plan you can follow every time you add a two-digit number and a one-digit number.
Let's try 42 + 6.
Now let's try one where the ones add up to more than 9. This is called "making a ten." Let's try 37 + 5.
The Number Line — Jumping Forward!
A number line is like a path with numbers on it. To add, you start at one number and jump forward. Each jump is +1. Let's use it to solve 54 + 3.
See how we started at 54 and made 3 jumps forward? Each jump goes to the next number. After 3 jumps, we landed on 57. So 54 + 3 = 57!
The number line is a great tool. You can draw one on paper or even imagine one in your head. Just start at the bigger number and count forward.
Helpful Addition Chart
Here are some examples of adding a two-digit number and a one-digit number. Can you see the pattern?
| Problem | Tens | Ones | Answer |
|---|---|---|---|
| 21 + 3 | 20 | 1 + 3 = 4 | 24 |
| 35 + 4 | 30 | 5 + 4 = 9 | 39 |
| 52 + 7 | 50 | 2 + 7 = 9 | 59 |
| 46 + 6 | 40 → 50 | 6 + 6 = 12 (new ten!) | 52 |
| 78 + 5 | 70 → 80 | 8 + 5 = 13 (new ten!) | 83 |
Notice: when the ones add up to 10 or more, the tens digit goes up by 1. That is making a new ten!
Let's Solve One Together!
Let's solve 67 + 8 step by step. Follow along!
Tips and Tricks!
Here are some helpful ways to add. Some are fast and some are slow. Pick the one that works best for you!
| Strategy | How It Works | Best For |
|---|---|---|
| Count On | Start at the bigger number and count up. For 45 + 3, say: 46, 47, 48! | Adding small numbers (1, 2, or 3) |
| Break Apart | Split the two-digit number into tens and ones. Add the ones, then put it back. | Any problem — works every time! |
| Make a Ten | Figure out how many to get to the next ten, then add the rest. For 28 + 5: 28 + 2 = 30, then 30 + 3 = 33. | When ones add up past 9 |
| Use Fingers | Start at the big number in your head, then hold up fingers for the small number and count up. | When you're learning — great for checking! |
One common mistake is forgetting to make a new ten when the ones add up to 10 or more. For example, 38 + 4 is NOT 32. The 8 + 4 = 12, which gives you a new ten. So it's 30 + 12 = 42. Always check: did my ones go past 9?
What Comes Next?
You are learning to add a two-digit number and a one-digit number. That is awesome! But math keeps growing. Here is what you will learn soon.
| What You Know Now | What Comes Next |
|---|---|
| Adding a one-digit number (like 34 + 5) | Adding two two-digit numbers (like 34 + 25)! |
| Answers up to 100 | Adding numbers bigger than 100! |
| Making one new ten | Making new tens AND new hundreds! |
| Breaking apart numbers | Using this same idea for subtraction too! |
The great news is that the same big ideas — tens and ones, breaking apart, making new tens — will help you with ALL of these! The things you learn today are like building blocks for everything that comes next. You are getting ready for bigger math, and you are doing great! 🌟
Practice Time! ✏️
Now it's your turn! Try these problems. Think about the steps we learned. Click "Show Answer" when you are ready to check.
What We Learned Today
Today you learned how to add a two-digit number and a one-digit number with answers up to 100! You learned that every two-digit number is made of tens and ones. When you add a one-digit number, you keep the tens the same and add the ones together. If the ones add up to 10 or more, you make a new ten — the tens digit goes up by one, and you keep the leftover ones.
You can use different strategies: counting on for small numbers, breaking apart for any problem, and making a ten when the ones get big. You practiced with pictures, number lines, and step-by-step math. These same ideas will help you add even bigger numbers someday. You are becoming a great mathematician! 🌟