Why Do We Add and Subtract?
People have been counting and adding things together for a very, very long time — even before there were schools! Long ago, people needed to count their sheep, share food with friends, and trade things at markets. Adding and subtracting helped them do all of that. Let's look at how counting grew up over time.
When you add, you put groups together to find how many in all. When you subtract, you take some away to find how many are left. These are two of the most important things you will ever learn in math!
The Big Ideas
Before we start solving problems, let's learn four super important ideas. These are like the rules of a game — once you know them, everything gets easier!
Adding Means Putting Together
Subtracting Means Taking Away
Order Doesn't Matter for Adding
Adding and Subtracting Are Opposites
The Number Line
A number line is like a road with numbers on it. It helps you see what happens when you add or subtract. When you add, you hop to the right. When you subtract, you hop to the left. Let's look at one!
Look at the number line above! The green hops show adding. We start at 6 and hop 5 times to the right. We land on 11! The red hops show subtracting. We start at 15 and hop 4 times to the left. We land on 11! A number line is a great tool when you need help.
How Adding and Subtracting Work
Let's learn the two big math sentences you will use. Every time you add or subtract, you are writing one of these!
For example, if you have 3 red crayons and 5 blue crayons, you put them together: 3 + 5 = 8 crayons in all. The number 3 and the number 5 are the parts. The number 8 is the whole (also called the sum).
For example, you have 9 grapes. You eat 4 grapes. How many are left? 9 − 4 = 5 grapes left. The 9 is the whole. You took away 4, so 5 is the part that is left (also called the difference).
Making 10 — A Super Trick!
The number 10 is your best friend in math! When you add numbers bigger than 10, try to make a 10 first. For example, to solve 8 + 5, think: "8 needs 2 more to make 10. I can break 5 into 2 and 3. So 8 + 2 = 10, and 10 + 3 = 13!" This trick makes hard problems easy.
Fact Families
A fact family is a group of math facts that use the same three numbers. They are like a family because they all belong together! Knowing fact families helps you add AND subtract faster.
Look at the triangle above. The whole (8) sits at the top. The two parts (3 and 5) sit at the bottom. With just these three numbers, we can write four facts:
| Addition Facts | Subtraction Facts |
|---|---|
| 3 + 5 = 8 | 8 − 3 = 5 |
| 5 + 3 = 8 | 8 − 5 = 3 |
When you know one fact, you can figure out the other three! If you know that 3 + 5 = 8, you also know that 8 − 5 = 3. Fact families are like a secret code that helps you solve problems faster.
Let's Solve One Together
Here is a story problem. Let's solve it step by step!
Helpful Tips and Tricks
There are many ways to add and subtract. Some ways are fast, and some are slower but still helpful when you are learning. Let's compare them!
| Strategy | How It Works | Best For |
|---|---|---|
| Count On | Start at the bigger number. Count up for adding. Example: 7 + 3 → say "7… 8, 9, 10!" | Adding 1, 2, or 3 |
| Count Back | Start at the big number. Count down for subtracting. Example: 10 − 2 → say "10… 9, 8!" | Subtracting 1, 2, or 3 |
| Use Fingers | Hold up fingers to show each number. Count them all up. | Numbers up to 10 |
| Make a 10 | Break a number apart so one part makes 10 with the other number. | Adding to get numbers 11–20 |
| Use Doubles | Know that 4 + 4 = 8, 5 + 5 = 10, etc. Then use "doubles plus 1" for close numbers (4 + 5 = 4 + 4 + 1 = 9). | Numbers that are close together |
What Comes Next?
Right now you are learning to add and subtract with numbers up to 20. That's awesome! But guess what — this is just the beginning. Let's peek at what's coming up as you grow in math.
| What You Learn Now | What You'll Learn Next |
|---|---|
| Add and subtract within 10 really fast | Add and subtract within 100! |
| Use fingers and number lines | Do it in your head without tools |
| Know fact families for small numbers | Know ALL your addition and subtraction facts by heart |
| Solve simple story problems | Solve bigger, trickier story problems with more steps |
Everything you learn today is like building the bottom of a tall tower. The stronger your bottom is, the taller your tower can grow! So keep practicing your facts within 10 until you can answer them as fast as you can say your name.
Practice Problems
Let's try some problems! Start at the top and work your way down. Click "Show Answer" when you are ready to check.
What We Learned
Today you learned that adding means putting groups together to find the sum, and subtracting means taking away to find the difference. You discovered that a number line is a great tool — hop right to add and hop left to subtract. You learned the making 10 trick, which helps you break apart numbers so you can add bigger numbers more easily. You also explored fact families, which show that addition and subtraction are connected — if you know one fact, you can figure out the others!
You practiced strategies like counting on, counting back, using doubles, and making a 10. The most important thing to remember is to keep practicing your facts within 10 until they feel super easy. When those facts become fast and automatic, adding and subtracting all the way up to 20 will feel easy too. You are doing an amazing job! 🌟