➕ First Grade Math: Understand Addition
Complete Study Notes & Formulas
📚 What is Addition?
Addition means PUTTING TOGETHER or COMBINING two or more groups to find the TOTAL!
🔤 Addition Vocabulary:
• Addends = The numbers being added
• Sum = The answer/total
• Plus Sign (+) = Symbol for addition
• Equals Sign (=) = Shows the answer
⭐ The Addition Formula
Addend + Addend = Sum
or
Part + Part = Whole
💡 Example:
3 + 5 = 8
• 3 and 5 are the addends
• 8 is the sum
🖼️ Add with Pictures - Sums up to 10
✦ What Does This Mean?
Using pictures or objects to count and add visually!
✦ Steps to Add with Pictures:
Step 1: Count the first group of pictures
This gives you the first addend
Step 2: Count the second group of pictures
This gives you the second addend
Step 3: Count ALL the pictures together
This gives you the sum (total)
✦ Visual Examples:
Example 1: 🍎🍎🍎 + 🍎🍎 = ?
First group: 3 apples
Second group: 2 apples
Total: 5 apples
3 + 2 = 5
Example 2: ⭐⭐⭐⭐ + ⭐⭐⭐⭐⭐⭐ = ?
First group: 4 stars
Second group: 6 stars
Total: 10 stars
4 + 6 = 10
✦ Formula Pattern:
Pictures in Group 1 + Pictures in Group 2 = Total Pictures
✦ All Sums up to 10:
| Group 1 | Group 2 | Addition | Sum |
|---|---|---|---|
| 1 | 1 | 1 + 1 | 2 |
| 2 | 3 | 2 + 3 | 5 |
| 3 | 4 | 3 + 4 | 7 |
| 5 | 5 | 5 + 5 | 10 |
| 4 | 6 | 4 + 6 | 10 |
✏️ Addition Sentences - Sums up to 10
✦ What is an Addition Sentence?
An addition sentence is a mathematical way to write addition using numbers and symbols!
✦ Parts of an Addition Sentence:
3 + 4 = 7
📍 3 = First Addend
➕ + = Plus Sign (means "add")
📍 4 = Second Addend
🟰 = = Equals Sign (means "is the same as")
✅ 7 = Sum (the answer)
✦ How to Write an Addition Sentence:
Step 1: Write the first number (first addend)
Step 2: Write the plus sign (+)
Step 3: Write the second number (second addend)
Step 4: Write the equals sign (=)
Step 5: Write the sum (total)
✦ Complete Addition Sentences (Sums up to 10):
| Addition Sentence | Sum | In Words |
|---|---|---|
| 0 + 1 = 1 | 1 | Zero plus one equals one |
| 1 + 1 = 2 | 2 | One plus one equals two |
| 1 + 2 = 3 | 3 | One plus two equals three |
| 2 + 2 = 4 | 4 | Two plus two equals four |
| 2 + 3 = 5 | 5 | Two plus three equals five |
| 3 + 3 = 6 | 6 | Three plus three equals six |
| 3 + 4 = 7 | 7 | Three plus four equals seven |
| 4 + 4 = 8 | 8 | Four plus four equals eight |
| 4 + 5 = 9 | 9 | Four plus five equals nine |
| 5 + 5 = 10 | 10 | Five plus five equals ten |
✦ Important Rule - Commutative Property:
💡 You can ADD numbers in ANY ORDER and get the same sum!
3 + 5 = 8
5 + 3 = 8
Both equal 8!
📏 Addition Sentences Using Number Lines - Sums up to 10
✦ What is a Number Line?
A number line is a straight line with numbers in order. We can use it to add by "jumping" forward!
✦ Number Line (0 to 10):
0 1 2 3 4 5 6 7 8 9 10
├─┼─┼─┼─┼─┼─┼─┼─┼─┼─┼─┤
✦ How to Add on a Number Line:
Step 1: Find the FIRST addend on the number line
This is your starting point
Step 2: Count FORWARD (jump to the right)
Jump the number of spaces equal to the SECOND addend
Step 3: The number you land on is the SUM!
That's your answer!
✦ Number Line Addition Formula:
Start at First Number → Jump Forward by Second Number → Land on the Sum
✦ Detailed Examples:
Example 1: 3 + 2 = ?
🎯 Start at: 3
➡️ Jump forward: 2 spaces
📍 Land on: 5
3 + 2 = 5 ✓
0 1 2 3 4 5 6 7 8 9 10
↑START
→→
↑LAND HERE (5)
Example 2: 4 + 5 = ?
🎯 Start at: 4
➡️ Jump forward: 5 spaces
📍 Land on: 9
4 + 5 = 9 ✓
0 1 2 3 4 5 6 7 8 9 10
↑START
→→→→→
↑LAND HERE (9)
Example 3: 6 + 4 = ?
🎯 Start at: 6
➡️ Jump forward: 4 spaces
📍 Land on: 10
6 + 4 = 10 ✓
✦ Number Line Tips:
✅ Always start at the FIRST number
✅ Count your jumps carefully
✅ Jump to the RIGHT (forward) for addition
✅ The bigger the second number, the more jumps you make
0️⃣ Adding Zero
✦ The Zero Property of Addition:
🎯 When you add ZERO to any number, the answer is that SAME number!
✦ The "Zero Rule" Formula:
Any Number + 0 = That Same Number
0 + Any Number = That Same Number
✦ Why Does This Work?
💡 Zero means NOTHING or NO items
💡 When you add nothing to something, it stays the same!
💡 Think: You have 5 cookies and add 0 more cookies = You still have 5 cookies!
✦ All Addition Sentences with Zero (0-10):
| Zero First | Result | Zero Last | Result |
|---|---|---|---|
| 0 + 0 | 0 | 0 + 0 | 0 |
| 0 + 1 | 1 | 1 + 0 | 1 |
| 0 + 2 | 2 | 2 + 0 | 2 |
| 0 + 3 | 3 | 3 + 0 | 3 |
| 0 + 4 | 4 | 4 + 0 | 4 |
| 0 + 5 | 5 | 5 + 0 | 5 |
| 0 + 6 | 6 | 6 + 0 | 6 |
| 0 + 7 | 7 | 7 + 0 | 7 |
| 0 + 8 | 8 | 8 + 0 | 8 |
| 0 + 9 | 9 | 9 + 0 | 9 |
| 0 + 10 | 10 | 10 + 0 | 10 |
✦ Visual Example with Pictures:
🌟 Example: 5 + 0 = ?
You have 5 stars: ⭐⭐⭐⭐⭐
You add ZERO more stars: (nothing)
You still have: ⭐⭐⭐⭐⭐ (5 stars)
5 + 0 = 5 ✓
✦ Zero on a Number Line:
When adding zero, you DON'T MOVE on the number line!
Start at 7 → Jump 0 spaces → Stay at 7
7 + 0 = 7
✦ Remember:
⚡ Zero is called the "IDENTITY" for addition
Because adding zero keeps a number's identity (it stays the same)!
📌 Addition Quick Reference
🖼️ Pictures Method:
Count Group 1 + Count Group 2
= Total Objects
✏️ Addition Sentence:
Addend + Addend = Sum
Example: 4 + 3 = 7
📏 Number Line:
Start → Jump Forward
→ Landing Point = Sum
0️⃣ Zero Rule:
Any Number + 0 = Same Number
Example: 8 + 0 = 8
🌟 Important Addition Properties
✅ Commutative Property: Order doesn't matter! (3 + 5 = 5 + 3)
✅ Identity Property: Adding zero keeps the number the same!
✅ Counting On: Start at the bigger number and count forward
✅ Make 10: Look for pairs that make 10 to add faster!
💪 Practice Tips for Success
🎯 Use fingers to count when starting out
🎯 Draw pictures to visualize the problem
🎯 Practice with real objects (toys, snacks, etc.)
🎯 Use a number line until you memorize facts
🎯 Start with smaller numbers and work your way up
🎯 Practice every day - even 5 minutes helps!
🌟 Addition is one of the most important math skills! 🌟
Keep practicing and you'll become an addition expert! 🎉