Addition - Two Digits | Second Grade
What is Two-Digit Addition?
Concept: Two-digit addition means adding numbers from 10 to 99. We use place value (tens and ones) to add these larger numbers!
Two Important Methods:
✓ Without Regrouping: When ones add up to 9 or less
✓ With Regrouping: When ones add up to 10 or more
💡 Tip: Always add ones first, then add tens!
1. Add Multiples of 10
Concept: Multiples of 10 are numbers like 10, 20, 30, 40... When adding these, we only work with the tens place!
Pattern Rule:
Add the tens, keep the zero!
\( 30 + 40 = ? \)
Think: 3 tens + 4 tens = 7 tens
30 + 40 = 70
Examples
10 + 20 = 30
1 ten + 2 tens = 3 tens
20 + 50 = 70
2 tens + 5 tens = 7 tens
40 + 30 = 70
4 tens + 3 tens = 7 tens
50 + 40 = 90
5 tens + 4 tens = 9 tens
💡 Tip: Think of it like adding single digits, then add a zero at the end!
2. Add Two-Digit and One-Digit (Without Regrouping)
Concept: When the ones place doesn't exceed 9, we can add without regrouping (carrying).
📝 Example: 23 + 4 = ?
Vertical Method:
| T | O | |
| 2 | 3 | |
| + | 0 | 4 |
| 2 | 7 |
Step by Step:
Step 1: Add ones
3 + 4 = 7
Step 2: Keep tens
2 tens = 20
Answer: 27
💡 Tip: No regrouping needed when ones add up to 9 or less!
3. Add Two-Digit and One-Digit (With Regrouping)
Concept: When ones add up to 10 or more, we must regroup (carry) 1 ten to the tens place!
Regrouping Rule:
When ones ≥ 10:
Regroup 10 ones as 1 ten
Write the extra ones, carry the ten
📝 Example: 37 + 8 = ?
Vertical Method:
| ¹ | ||
| T | O | |
| 3 | 7 | |
| + | 0 | 8 |
| 4 | 5 |
Step by Step:
Step 1: Add ones
7 + 8 = 15
Step 2: Regroup!
15 = 1 ten + 5 ones
Step 3: Add tens
3 + 1 = 4
Answer: 45
💡 Tip: Remember to add the carried number to the tens column!
4. Add Two Two-Digit Numbers (Without Regrouping)
Concept: Add the ones, then add the tens. No regrouping needed when sums stay within place values!
📝 Example: 42 + 35 = ?
Vertical Method:
| T | O | |
| 4 | 2 | |
| + | 3 | 5 |
| 7 | 7 |
Step by Step:
Step 1: Add ones
2 + 5 = 7
Step 2: Add tens
4 + 3 = 7
Step 3: Combine
70 + 7 = 77
Answer: 77
💡 Tip: Line up the place values - tens under tens, ones under ones!
5. Add Two Two-Digit Numbers (With Regrouping)
Concept: When ones add up to 10 or more, regroup to the tens place. This is the most important two-digit addition skill!
📝 Example: 48 + 27 = ?
Vertical Method:
| ¹ | ||
| T | O | |
| 4 | 8 | |
| + | 2 | 7 |
| 7 | 5 |
Step by Step:
Step 1: Add ones
8 + 7 = 15
Step 2: Regroup!
15 = 1 ten + 5 ones
Step 3: Add tens
4 + 2 + 1 = 7
Answer: 75
💡 Tip: Always write the small "1" above the tens column when you regroup!
6. Addition Input/Output Tables (Up to Two Digits)
Concept: Find the pattern rule, then apply it to find missing outputs or inputs!
📝 Example: Add 15 to each number
| Input | Rule: + 15 | Output |
|---|---|---|
| 12 | 12 + 15 | 27 |
| 24 | 24 + 15 | 39 |
| 30 | 30 + 15 | 45 |
| 43 | 43 + 15 | 58 |
💡 Tip: Look for the pattern - what number is always being added?
7. Ways to Make a Number Using Addition
Concept: Any number can be made by adding different combinations of numbers together!
📝 Example: Different Ways to Make 50
25 + 25 = 50
30 + 20 = 50
40 + 10 = 50
35 + 15 = 50
48 + 2 = 50
45 + 5 = 50
💡 Tip: There are many ways to make any number - be creative!
8. Addition Word Problems (Up to Two Digits)
Concept: Read carefully, find the numbers, look for addition keywords, then solve!
Addition Keywords:
✓ altogether
✓ in total
✓ combined
✓ sum
📖 Example Problem
A farmer has 38 chickens and 27 ducks. How many birds does he have in total?
Solution Steps:
Step 1: Find the numbers (38 and 27)
Step 2: Look for keywords ("in total" = add)
Step 3: Write equation: 38 + 27 = ?
Step 4: Add ones: 8 + 7 = 15 (regroup!)
Step 5: Add tens: 3 + 2 + 1 = 6
Answer: 65 birds
💡 Tip: Draw a picture to help understand the problem!
9. Balance Addition Equations (Up to Two Digits)
Concept: Both sides of an equation must be equal. Find the missing number to balance!
Balance Concept:
\( 25 + 18 = 30 + 13 \)
Left side: 25 + 18 = 43
Right side: 30 + 13 = 43
Both sides equal 43 ✓ BALANCED!
📝 Practice: Find the Missing Number
\( 34 + 28 = 45 + ? \)
Left side: 34 + 28 = 62
Right side must also equal 62
45 + ? = 62
Think: 45 + 17 = 62
Answer: 17
💡 Tip: Solve one side completely, then find what makes the other side equal!
10. Add Three or More Numbers (Up to Two Digits)
Concept: Add multiple two-digit numbers by adding all ones first, then all tens!
📝 Example: 23 + 15 + 32 = ?
Vertical Method:
| ¹ | ||
| T | O | |
| 2 | 3 | |
| 1 | 5 | |
| + | 3 | 2 |
| 7 | 0 |
Step by Step:
Step 1: Add ones
3 + 5 + 2 = 10
Step 2: Regroup!
10 = 1 ten + 0 ones
Step 3: Add tens
2 + 1 + 3 + 1 = 7
Answer: 70
Strategies for Adding Multiple Numbers:
✓ Look for numbers that make 10
✓ Look for multiples of 10
✓ Group easy numbers together
✓ Add from top to bottom carefully
💡 Tip: Be careful with regrouping when adding many numbers!
Important Two-Digit Addition Rules
Place Value Addition
Add ones first, then add tens
\( 24 + 35 \)
Ones: 4 + 5 = 9
Tens: 2 + 3 = 5
Answer: 59
Regrouping Rule
When ones ≥ 10:
Regroup 10 ones as 1 ten
Example: 7 + 8 = 15
15 = 1 ten + 5 ones
Commutative Property
\( a + b = b + a \)
23 + 45 = 45 + 23
Order doesn't matter!
🎯 Tips for Two-Digit Addition Success 🎯
- ✓ Always line up place values - ones under ones, tens under tens
- ✓ Add ones first, then tens - work from right to left
- ✓ Watch for regrouping - when ones add to 10 or more
- ✓ Write small numbers above when you regroup (carry)
- ✓ Check your work by adding in a different order
- ✓ Practice every day to become faster and more accurate!
⭐ You're a Two-Digit Addition Master! ⭐
Outstanding work learning two-digit addition! You now know how to add multiples of 10, add with and without regrouping, use vertical methods, solve word problems, balance equations, and add multiple numbers together. Two-digit addition is a major milestone in math! Understanding place value and regrouping will help you with all future math. Keep practicing these skills - you're building a strong math foundation. You're doing phenomenal work!