Addition Basics

For Elementary Students

What is Addition?

Addition means putting numbers together to find out how many you have in total.

Think about it like this: If you have 3 apples and someone gives you 2 more apples, you now have 5 apples total. That's addition!

Example: 3 + 2 = 5

We read this as "3 plus 2 equals 5."

Addition Words to Know

When we add:

• The numbers we're adding are called addends (the parts)
• The answer is called the sum (the total)

Example: In 4 + 5 = 9

• 4 and 5 are the addends
• 9 is the sum

Using a Number Line

A number line is like a ruler with numbers. It helps you count!

To add 4 + 3:

Step 1: Start at 4

Step 2: Jump forward 3 spaces

start
  ↓
0 ─── 1 ─── 2 ─── 3 ─── 4 ─── 5 ─── 6 ─── 7 ─── 8
                        →   →   →
                                    ↑
                                  land here!

You land on 7, so 4 + 3 = 7.

Adding with Your Fingers

Your fingers are great counting tools!

Example: 5 + 3 = ?

• Hold up 5 fingers
• Count up 3 more: 6, 7, 8
• Answer: 8

Adding Zero

Zero means "nothing." When you add zero, the number stays the same!

• 5 + 0 = 5 (you start with 5, add nothing, still have 5)
• 0 + 8 = 8
• 0 + 0 = 0

Order Doesn't Matter!

You can add numbers in any order and get the same answer.

• 3 + 7 = 10
• 7 + 3 = 10

Same answer! This makes addition easier because you can start with the bigger number.

Adding Three Numbers

Add two first, then add the third!

Example: 2 + 5 + 3 = ?

Step 1: 2 + 5 = 7 Step 2: 7 + 3 = 10

Answer: 10

For Junior High Students

Addition Properties

Commutative Property: Order doesn't matter

• 2 + 9 = 9 + 2
• Both equal 11

Associative Property: Grouping doesn't matter

• (2 + 3) + 4 = 2 + (3 + 4)
• 5 + 4 = 2 + 7
• Both equal 9

Identity Property: Adding zero doesn't change the number

• 12 + 0 = 12
• Zero is the "identity" for addition

Adding Larger Numbers (Column Addition)

When adding bigger numbers, line them up by place value and add from right to left.

Example: 34 + 25

  34
+ 25
----

Step 1: Add the ones place

• 4 + 5 = 9 → write 9

Step 2: Add the tens place

• 3 + 2 = 5 → write 5

  34
+ 25
----
  59

Answer: 59

Carrying (Regrouping)

When a column adds up to 10 or more, you need to carry (or regroup).

Example: 47 + 36

  ¹47
+ 36
----

Step 1: Ones place

• 7 + 6 = 13
• Write the 3, carry the 1 (that's 10) to the tens column

Step 2: Tens place

• 4 + 3 = 7, plus the carried 1 = 8

  ¹47
+ 36
----
  83

Answer: 83

More Carrying Examples

Example: 158 + 267

  ¹¹158
+ 267
-----

Ones: 8 + 7 = 15 → write 5, carry 1

Tens: 5 + 6 + 1 = 12 → write 2, carry 1

Hundreds: 1 + 2 + 1 = 4 → write 4

Answer: 425

Adding Multiple Numbers

Example: 23 + 15 + 42

  23
  15
+ 42
----

Ones: 3 + 5 + 2 = 10 → write 0, carry 1

Tens: 2 + 1 + 4 + 1 = 8

Answer: 80

Mental Math Strategies

Make 10: Break numbers to make tens

Example: 8 + 5 = ?

• Think: "8 + 2 = 10, and I still have 3 more"
• 10 + 3 = 13

Doubles: Remember your doubles (same number twice)

• 5 + 5 = 10
• 6 + 6 = 12
• 7 + 7 = 14

Near doubles: Use doubles to help

Example: 7 + 8 = ?

• Think: "7 + 7 = 14, and 8 is one more than 7"
• 14 + 1 = 15

Estimating Sums

Round numbers to make a quick estimate.

Example: 48 + 32 = ?

Estimate:

• Round 48 to 50
• Round 32 to 30
• 50 + 30 = 80

Exact answer: 48 + 32 = 80 (in this case, the estimate was exact!)

Real-Life Uses

Shopping: "Shirt costs $15, pants cost $28. Total?"

• $15 + $28 = $43

Distance: "Walked 2 miles Monday, 3 miles Tuesday. Total?"

• 2 + 3 = 5 miles

Scoring: "Got 85 on test 1, 92 on test 2. Total points?"

• 85 + 92 = 177 points

Checking Your Work

Use subtraction to check addition!

If 34 + 25 = 59, then:

• 59 - 25 = 34 ✓
• 59 - 34 = 25 ✓

Both work, so 59 is correct!

Practice