Addition Basics

Addition is the act of combining groups together to find a total. When you put 3 apples and 4 apples in a basket, you add them to get 7 apples. Let's learn powerful strategies to add quickly and accurately.

What Addition Means

Addition answers the question: "How many in all?" We use the + symbol to show addition and the = symbol to show the result.

3 + 4 = 7

We call 3 and 4 the addends and 7 the sum.

Strategy 1: Counting On

Start with the bigger number and count up by the smaller number. This is faster than counting everything from the beginning.

Counting On: 8 + 3

Start at 8 (the bigger number). Count up 3 more:

8 ... 9, 10, 11

So 8 + 3 = 11.

Strategy 2: Making Ten

The number 10 is special in our number system. If one addend is close to 10, you can break the other number apart to make a ten first.

Making Ten: 7 + 5

7 needs 3 more to make 10.
Break 5 into 3 + 2.
Now add: 7 + 3 = 10, then 10 + 2 = 12.

7 + 5 = 7 + 3 + 2 = 10 + 2 = 12

Strategy 3: Doubles and Near Doubles

Doubles are easy to memorize: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18.

For near doubles, use a double you know and adjust by one.

Near Doubles: 6 + 7

You know that 6 + 6 = 12. Since 7 is one more than 6:

6 + 7 = 6 + 6 + 1 = 12 + 1 = 13

Adding Bigger Numbers

For two-digit numbers, add the tens first, then the ones.

Adding 34 + 25

Add the tens: 30 + 20 = 50.
Add the ones: 4 + 5 = 9.
Combine: 50 + 9 = 59.

The Order Does Not Matter!

In addition, you can switch the order of the addends and get the same answer. This is called the commutative property: 3 + 5 = 5 + 3 = 8. Use this to your advantage -- always start counting from the bigger number!

Common Mistake

When adding two-digit numbers, students sometimes forget to carry. For example, 28 + 15: the ones column gives 8 + 5 = 13, which is 1 ten and 3 ones. Write the 3 in the ones place and carry the 1 to the tens column. 2 + 1 + 1 = 4 tens. The answer is 43.

Practice Problems

1. Use counting on: 9 + 4 = ?

Show Solution

Start at 9, count 4 more: 10, 11, 12, 13. The answer is 13.

2. Use making ten: 8 + 6 = ?

Show Solution

8 needs 2 to make 10. Break 6 into 2 + 4. So 8 + 2 = 10, then 10 + 4 = 14.

3. Use near doubles: 7 + 8 = ?

Show Solution

7 + 7 = 14, and 8 is one more than 7, so 7 + 8 = 14 + 1 = 15.

4. Add: 45 + 32 = ?

Show Solution

Tens: 40 + 30 = 70. Ones: 5 + 2 = 7. Total: 70 + 7 = 77.

5. Add: 67 + 28 = ?

Show Solution

Ones: 7 + 8 = 15 (write 5, carry 1). Tens: 6 + 2 + 1 = 9. The answer is 95.

Summary: Addition combines groups to find a total. Key strategies include counting on, making ten, and using doubles. The order of addends does not change the sum. For larger numbers, add by place value and remember to carry when the ones column goes past 9.