How People Learned to Count and Add
People have been adding things together for thousands of years! Long before calculators or phones, kids and grown-ups had to add using their brains. Let's look at how people learned to add over time.
When you can add and subtract quickly in your head, you become a math superstar. You don't need to stop and count on your fingers every time. That's what this lesson will teach you!
Four Big Mental Strategies
A mental strategy is a trick you use in your brain to figure out an answer fast. Here are the four best strategies for adding and subtracting within 20.
Make a Ten
Doubles & Near Doubles
Count On / Count Back
Think Addition for Subtraction
See It With Pictures: Make a Ten
Let's see how the "Make a Ten" strategy works with a picture. We'll solve 8 + 5 step by step.
See how we moved 2 orange dots over to fill up the first ten-frame? Now we have a nice, easy 10 plus 3 leftover. That gives us 13! This is the "Make a Ten" strategy.
How the Strategies Work With Numbers
Let's write out what happens in each strategy using numbers. Don't worry — these are easy patterns to follow!
Each strategy breaks a hard problem into easy steps. The more you practice, the faster these will become — until you just know the answer without any steps at all!
The Addition Facts Table
By the end of 2nd grade, you should know from memory all the sums of two one-digit numbers. That means numbers from 0 through 9. Here is the complete addition table. Can you spot any patterns?
Did you notice? The pink numbers going diagonally are the doubles (0+0, 1+1, 2+2, and so on). The yellow numbers are sums bigger than 9. Also, look: 3 + 5 and 5 + 3 both equal 8! You can add numbers in any order and get the same answer. That's a rule called the commutative property — it means you can swap the numbers around.
The smallest sum of two one-digit numbers is 0 (when you add 0 + 0). The biggest is 18 (when you add 9 + 9). So all your sums will be somewhere between 0 and 18!
Worked Example: Solving 7 + 6
Let's solve 7 + 6 using two different strategies so you can see how they both get the same answer.
Both strategies give us 13! You can use whichever one feels easier to you.
Which Strategy Should I Use?
Different strategies work best for different problems. Here's a helpful chart that shows when to use each one.
| Strategy | Best For | Example |
|---|---|---|
| Make a Ten | When one number is close to 10 (like 8 or 9) | 9 + 7 → 10 + 6 = 16 |
| Doubles | When both numbers are the same | 8 + 8 = 16 |
| Near Doubles | When numbers are 1 apart | 6 + 7 → 6+6+1 = 13 |
| Count On | Adding 1, 2, or 3 | 8 + 2 → 9, 10! |
| Think Addition | Subtraction problems | 13 − 7 → 7+?=13 → 6 |
At first, you'll think about which strategy to pick. But after lots of practice, you'll just know the answer right away — like how you know your own name without thinking about it!
What Comes Next?
Once you know all your addition and subtraction facts within 20, you're ready for bigger numbers! Here's how what you learn now helps you later.
| What You Learn Now | What Comes in 3rd Grade |
|---|---|
| 7 + 8 = 15 | 70 + 80 = 150 (same fact, bigger numbers!) |
| Doubles like 6 + 6 = 12 | Multiplication: 6 × 2 = 12 (doubling IS multiplying by 2) |
| 14 − 9 = 5 | 140 − 90 = 50 (same thinking, just add a zero) |
| Make a Ten strategy | Adding 3-digit numbers by making hundreds |
See the pattern? The strategies you learn in 2nd grade are the building blocks for all the math you'll do in 3rd grade, 4th grade, and beyond. If you know that 7 + 8 = 15, then you can figure out that 70 + 80 = 150 and even 700 + 800 = 1,500 someday. That's pretty cool!
Practice Problems
Now it's your turn! Try these five problems. Use any strategy you like. Click "Show Answer" when you're ready to check.
Let's Review!
In this lesson, you learned four powerful mental strategies for adding and subtracting within 20: Make a Ten, Doubles and Near Doubles, Count On / Count Back, and Think Addition for Subtraction. Each strategy is like a shortcut that helps you solve problems faster. You also saw the complete addition facts table for all one-digit numbers, where sums range from 0 all the way to 18.
The big goal is to know all these sums from memory by the end of 2nd grade — just like you know the words to a song by heart. Remember: you can add numbers in any order (commutative property), which means there are fewer facts to memorize than you might think! These facts are the building blocks for all the bigger math you'll learn later. Keep practicing, and you'll be a math superstar! ⭐