Where Did Adding and Subtracting Come From?
People have been adding and subtracting for thousands of years! Long ago, before calculators or even pencils, people needed to count things like sheep, fish, and bags of grain. Let's look at how math grew up over time.
All these years of work led us to the cool tricks you will learn today. The big question is: How can we add and subtract numbers up to 100 in fast, smart ways?
The Big Ideas You Need to Know
Before we start adding and subtracting, let's learn four super-important ideas. These are the tools in your math toolbox!
Place Value
Break Apart Numbers
Make a Ten
Addition and Subtraction Are Buddies
See It! Place Value Blocks
Let's look at a picture that shows how place value works. In the diagram below, you can see how the number 47 is made of 4 tens and 7 ones.
See how the tall blue blocks are tens and the small yellow blocks are ones? When we add and subtract, we can work with the tens and ones separately. This makes big problems feel easy!
Smart Strategies for Adding and Subtracting
Here are the best strategies you can use. Think of them like superpowers for your brain!
Strategy 1: Break Apart (Expanded Form)
Split each number into tens and ones. Add the tens together, add the ones together, then put them back together!
Strategy 2: Add Tens, Then Add Ones
Keep one number whole. Then add the tens from the other number. Then add the ones.
Strategy 3: Make a Ten
Sometimes the ones digits add up past ten. You can borrow from one number to make a nice, round ten.
Strategy 4: Use Addition to Subtract
Addition and subtraction are best friends! If you need to subtract, you can count up instead.
The Number Line — Your Jumping Tool
A number line is like a road with numbers on it. You can jump forward to add and jump backward to subtract. Let's see how to use it to solve 54 + 28.
We started at 54. We broke 28 into 20 + 8. First we made a big jump of +20 to get to 74. Then we made a small jump of +8 to land on 82. You can use this same trick for subtraction — just jump backward!
| Strategy | Best For | Example |
|---|---|---|
| Break Apart | Adding two 2-digit numbers | 36 + 42 → 70 + 8 = 78 |
| Add in Parts | Adding tens first, then ones | 27 + 35 → 57 + 5 = 62 |
| Make a Ten | When one number is close to a ten | 48 + 7 → 50 + 5 = 55 |
| Number Line | When you want to see the jumps | 54 + 28 → jump 20, jump 8 = 82 |
| Count Up (Think Addition) | Subtraction problems | 62 − 45 → 45 + ? = 62 → 17 |
Let's Solve One Together!
Let's work through a problem step by step. We will solve 73 − 48 using the break apart strategy.
Which Strategy Should I Pick?
You might wonder: which strategy is the best? The truth is, they are all great! Different problems work better with different strategies. Let's compare them.
| Strategy | Strengths (What's Great) | Watch Out For |
|---|---|---|
| Break Apart | Works with any two numbers. Very organized. | Lots of steps. You need to remember all the parts. |
| Add/Subtract in Parts | Fewer steps. Keep one number whole. | The second step can sometimes be tricky. |
| Make a Ten | Super fast when a number is close to a ten! | Not always helpful if numbers aren't near a ten. |
| Number Line | You can see the jumps. Great for understanding. | Takes a little time to draw. |
| Think Addition | Makes subtraction easier if you know addition facts. | Needs strong addition skills first. |
What Comes Next?
The strategies you are learning now are building blocks for bigger math! Soon you will use these same ideas with even larger numbers. Let's peek at what's ahead.
| What You Do Now (2nd Grade) | What You'll Do Next (3rd Grade and Beyond) |
|---|---|
| Add and subtract within 100 | Add and subtract within 1,000! |
| Break numbers into tens and ones | Break numbers into hundreds, tens, and ones |
| Use the "make a ten" trick | Use "make a hundred" and other rounding tricks |
| Use addition to check subtraction | Use multiplication and division (they're buddies too!) |
Everything you learn today makes tomorrow's math easier. You're building a strong math brain, one step at a time!
Practice Time! 🎉
Try these problems on your own. Take your time, pick a strategy, and check your answers when you're ready!
Let's Remember What We Learned!
You learned that every number has tens and ones, and understanding place value helps you break numbers apart into easier pieces. You discovered several smart strategies: the break apart strategy splits both numbers into tens and ones, the add in parts strategy keeps one number whole while adding or subtracting pieces of the other, and the make a ten trick helps when a number is close to a round number like 10, 20, 30, and so on.
You also learned that a number line lets you see your jumps, and that addition and subtraction are related operations — if you know an addition fact, you know a subtraction fact too! Remember, there is no single "best" strategy. The best strategy is the one that helps you solve the problem quickly and correctly. Keep practicing, and soon you'll be adding and subtracting within 100 like a true math superstar! ⭐