➕ Addition - Grade 3

What is Addition?

Addition is putting numbers together to find the total or sum!

\(\text{Addend} + \text{Addend} = \text{Sum}\)

In Grade 3, we learn to add numbers up to three digits (up to 999)!

🔢 Add Two Numbers Up to Three Digits

Steps to Add 3-Digit Numbers

Line up the numbers by place value (ones under ones, tens under tens, hundreds under hundreds)
Start from the ONES place (rightmost column)
Add each column from right to left
Regroup (carry) if the sum is 10 or more
Write the final answer

Addition Without Regrouping

Example: \(342 + 125\)

3 4 2
+ 1 2 5
-------

Step 1: Ones: \(2 + 5 = 7\)
Step 2: Tens: \(4 + 2 = 6\)
Step 3: Hundreds: \(3 + 1 = 4\)

Answer: \(342 + 125 = 467\) ✓

Addition With Regrouping (Carrying)

Example: \(385 + 247\)

   ¹ ¹
   3 8 5
+ 2 4 7
-------
   6 3 2

Step 1 - Ones: \(5 + 7 = 12\)
• Write \(2\) in ones place
• Carry \(1\) ten to tens place

Step 2 - Tens: \(1 + 8 + 4 = 13\)
• Write \(3\) in tens place
• Carry \(1\) hundred to hundreds place

Step 3 - Hundreds: \(1 + 3 + 2 = 6\)
• Write \(6\) in hundreds place

Answer: \(385 + 247 = 632\) ✓

Key Formula:

\(\text{Sum} = \text{Addend}_1 + \text{Addend}_2\)

When sum in any column \(\geq 10\),
Regroup: carry \(1\) to the next left column

🔢🔢🔢 Add Three or More Numbers

Steps to Add Multiple Numbers

Stack all numbers vertically (align by place value)
Add the ones column first
Regroup if needed
Continue with tens, then hundreds
Don't forget to add carried numbers!

Example: Adding Three Numbers

Problem: \(234 + 156 + 325\)

   ¹ ¹
   2 3 4
   1 5 6
+ 3 2 5
-------
   7 1 5

Ones: \(4 + 6 + 5 = 15\) → Write \(5\), carry \(1\)
Tens: \(1 + 3 + 5 + 2 = 11\) → Write \(1\), carry \(1\)
Hundreds: \(1 + 2 + 1 + 3 = 7\) → Write \(7\)

Answer: \(234 + 156 + 325 = 715\) ✓

Important Tip:

💡 When adding many numbers, add column by column.
Always check: Did I add all the numbers in the column?
Did I remember to add the carried number?

📊 Addition Input/Output Tables

What is an Input/Output Table?

An input/output table uses a rule to change input numbers into output numbers!

\(\text{Output} = \text{Input} + \text{Rule}\)

Example: Finding the Rule

Input	Output
\(123\)	\(323\)
\(245\)	\(445\)
\(367\)	\(567\)

Finding the Rule:
\(323 - 123 = 200\)
\(445 - 245 = 200\)
\(567 - 367 = 200\)

Rule: Add \(200\)
Formula: \(\text{Output} = \text{Input} + 200\) ✓

⚖️ Balance Addition Equations

What is a Balanced Equation?

A balanced equation means both sides of the equal sign (\(=\)) have the same value!

\(\text{Left Side} = \text{Right Side}\)

Steps to Balance Equations

Find the side without the missing number
Add those numbers to find the total
That total is what the other side must equal
Find the missing number to make it balance

Examples

Example 1: Missing addend on left

Problem: \(? + 234 = 567\)

Step 1: Right side = \(567\)
Step 2: Left side must also equal \(567\)
Step 3: \(? + 234 = 567\)
Step 4: \(? = 567 - 234 = 333\)
Check: \(333 + 234 = 567\) ✓
Answer: \(? = 333\)

Example 2: Missing addend on right

Problem: \(145 + 230 = 275 + ?\)

Step 1: Left side: \(145 + 230 = 375\)
Step 2: Right side must equal \(375\)
Step 3: \(275 + ? = 375\)
Step 4: \(? = 375 - 275 = 100\)
Check: \(145 + 230 = 375\) and \(275 + 100 = 375\) ✓
Answer: \(? = 100\)

Key Formula:

If \(a + b = c\), then:
\(a = c - b\) and \(b = c - a\)

✍️ Complete the Addition Sentence

What Does This Mean?

You need to find the missing number to make the addition sentence true!

Three Types of Missing Numbers

Type 1: Missing First Addend

Problem: \(? + 234 = 567\)

Solution: Subtract the known addend from the sum
\(? = 567 - 234 = 333\) ✓

Type 2: Missing Second Addend

Problem: \(456 + ? = 789\)

Solution: Subtract the known addend from the sum
\(? = 789 - 456 = 333\) ✓

Type 3: Missing Sum

Problem: \(345 + 234 = ?\)

Solution: Add the two numbers
\(? = 345 + 234 = 579\) ✓

Important Formulas:

\(\text{Addend} = \text{Sum} - \text{Other Addend}\)

\(\text{Sum} = \text{Addend}_1 + \text{Addend}_2\)

📈 Addition Patterns Over Increasing Place Values

What Are Addition Patterns?

When you know a simple addition fact, you can use it to solve additions with larger numbers!

If you know \(3 + 4 = 7\),
Then you also know:
\(30 + 40 = 70\)
\(300 + 400 = 700\)

How It Works

Pattern 1: Basic Fact

\(2 + 5 = 7\)

Pattern 2: Tens

\(20 + 50 = 70\)
(Same digits, but one zero added)

Pattern 3: Hundreds

\(200 + 500 = 700\)
(Same digits, but two zeros added)

More Examples

If \(6 + 3 = 9\), then:
• \(60 + 30 = 90\)
• \(600 + 300 = 900\)

If \(7 + 8 = 15\), then:
• \(70 + 80 = 150\)
• \(700 + 800 = 1,500\)

If \(4 + 9 = 13\), then:
• \(40 + 90 = 130\)
• \(400 + 900 = 1,300\)

Key Rule:

The pattern works when BOTH addends
have the same number of zeros!

\(\text{Basic Sum} \times 10^n = \text{Larger Sum}\)
(where \(n\) = number of zeros)

🔍 Addition: Fill in the Missing Digits

What Does This Mean?

Some digits in the addition problem are missing! You need to figure out what they are by using addition rules!

Strategies to Find Missing Digits

Start with the ones column (rightmost)
Use what you know about addition
Look for carried numbers
Work column by column
Check if your answer makes sense

Example Problems

Example 1: Missing Digit in Sum

2 3 5
+ 1 4 2
-------
3 ? 7

Step 1 - Ones: \(5 + 2 = 7\) ✓
Step 2 - Tens: \(3 + 4 = ?\)
\(3 + 4 = 7\), so \(? = 7\)
Step 3 - Hundreds: \(2 + 1 = 3\) ✓

Answer: The missing digit is \(7\) ✓

Example 2: Missing Digit in Addend

4 ? 6
+ 2 3 1
-------
6 8 7

Step 1 - Ones: \(6 + 1 = 7\) ✓
Step 2 - Tens: \(? + 3 = 8\)
What plus \(3\) equals \(8\)? Answer: \(5\)
So \(? = 5\)
Step 3 - Hundreds: \(4 + 2 = 6\) ✓

Answer: The missing digit is \(5\) ✓
Complete number: \(456\)

Example 3: With Regrouping

   ¹
   3 ? 8
+ 2 4 5
-------
   6 2 3

Step 1 - Ones: \(8 + 5 = 13\)
Write \(3\), carry \(1\) ✓

Step 2 - Tens: \(1 + ? + 4 = 12\) (because \(2\) in answer + carry \(1\) to hundreds)
\(1 + ? + 4 = 12\)
\(? + 5 = 12\)
\(? = 7\)

Step 3 - Hundreds: \(1 + 3 + 2 = 6\) ✓

Answer: The missing digit is \(7\) ✓
Complete number: \(378\)

📖 Addition Word Problems

Key Words for Addition

✓ Total - How many in all?
✓ Sum - Add together
✓ Altogether - Combined amount
✓ In all - Total count
✓ Combined - Put together
✓ Plus - Add
✓ More - Additional
✓ Increase - Goes up

Steps to Solve Word Problems

Read the problem carefully (maybe twice!)
Circle or underline the numbers
Look for addition key words
Write the addition sentence
Solve the problem
Check your answer - Does it make sense?
Write the answer with labels (dollars, apples, etc.)

Example Problems

Problem 1: Two Numbers

Emma collected 235 seashells on Monday and 347 seashells on Tuesday. How many seashells did she collect in all?

Step 1: Numbers: \(235\) and \(347\)
Step 2: Key words: "in all" → Addition!
Step 3: Addition sentence: \(235 + 347 = ?\)
Step 4: Solve: \(235 + 347 = 582\)
Answer: Emma collected \(582\) seashells in all. ✓

Problem 2: Three Numbers

A school library has 456 fiction books, 298 non-fiction books, and 167 reference books. What is the total number of books in the library?

Step 1: Numbers: \(456\), \(298\), and \(167\)
Step 2: Key word: "total" → Addition!
Step 3: Addition sentence: \(456 + 298 + 167 = ?\)
Step 4: Solve: \(456 + 298 + 167 = 921\)
Answer: The library has \(921\) books in total. ✓

📝 Important Formulas Summary

Basic Addition Formula:

\(\text{Sum} = \text{Addend}_1 + \text{Addend}_2 + \text{Addend}_3 + ...\)

Finding Missing Addend:

\(\text{Missing Addend} = \text{Sum} - \text{Known Addend}\)

Regrouping Rule:

When column sum \(\geq 10\):
Write the ones digit, carry the tens digit to next column

Balance Equation Rule:

\(\text{Left Side} = \text{Right Side}\)

Place Value Pattern:

If \(a + b = c\), then:
\(10a + 10b = 10c\)
\(100a + 100b = 100c\)

Properties of Addition:

Commutative Property: \(a + b = b + a\)
(Order doesn't matter)

Associative Property: \((a + b) + c = a + (b + c)\)
(Grouping doesn't matter)

Identity Property: \(a + 0 = a\)
(Adding zero doesn't change the number)