What is adding 2-digit and 1-digit numbers with regrouping (Grade 2)?

📚 Adding 2-Digit and 1-Digit Numbers with Regrouping (Grade 2)

Adding two-digit and one-digit numbers with regrouping, also known as carrying over, is a fundamental arithmetic skill taught in second grade. It involves adding numbers where the sum of the digits in the ones place is greater than 9. This requires transferring (regrouping) a group of ten from the ones place to the tens place.

📜 History and Background

The concept of regrouping has been used for centuries, with its roots in ancient numeral systems. As civilizations developed more complex calculation methods, the need for regrouping became apparent. It's a core component of the base-10 number system we use today, allowing for efficient addition and subtraction of multi-digit numbers.

• 🏛️ Ancient civilizations used abaci and other tools that implicitly involved regrouping.
• ✍️ Early written numerals made regrouping explicit by denoting tens, hundreds, and so on.
• ➕ Modern arithmetic notation formalized the process of carrying over, making it easier to teach and learn.

🔑 Key Principles

Understanding place value is crucial for regrouping. Each digit in a number represents a different power of ten (ones, tens, hundreds, etc.). When the sum of the digits in a place value column exceeds 9, we need to regroup by carrying the 'ten' to the next higher place value.

• 🔢 Place Value: Understanding that a '1' in the tens place is worth 10 ones.
• ➕ Addition Facts: Knowing basic addition facts up to 9+9.
• 🤝 Regrouping: Converting 10 ones into 1 ten.
• 📍 Columnar Addition: Arranging numbers vertically to align place values.

📝 Step-by-Step Guide

Here's how to add a two-digit number and a one-digit number with regrouping:

1. Write the numbers vertically: Align the ones and tens places.
2. Add the digits in the ones place: If the sum is greater than 9, proceed to regrouping.
3. Regroup if necessary: If the sum in the ones place is greater than 9, write the ones digit of the sum in the ones place of the answer and carry the tens digit (which is always 1 in this case) to the tens place.
4. Add the digits in the tens place: Add the carried-over digit to the digit in the tens place of the two-digit number.
5. Write the sum in the tens place: This gives you the tens digit of the answer.

➗ Examples

Example 1: 25 + 7

• Write 25 and 7 vertically, aligning the ones places.
• Add the ones: 5 + 7 = 12. Since 12 is greater than 9, regroup.
• Write '2' in the ones place of the answer. Carry over '1' to the tens place.
• Add the tens: 1 (carried over) + 2 = 3. Write '3' in the tens place of the answer.
• The answer is 32.

Example 2: 38 + 4

• Write 38 and 4 vertically, aligning the ones places.
• Add the ones: 8 + 4 = 12. Since 12 is greater than 9, regroup.
• Write '2' in the ones place of the answer. Carry over '1' to the tens place.
• Add the tens: 1 (carried over) + 3 = 4. Write '4' in the tens place of the answer.
• The answer is 42.

Example 3: 56 + 8

• Write 56 and 8 vertically, aligning the ones places.
• Add the ones: 6 + 8 = 14. Since 14 is greater than 9, regroup.
• Write '4' in the ones place of the answer. Carry over '1' to the tens place.
• Add the tens: 1 (carried over) + 5 = 6. Write '6' in the tens place of the answer.
• The answer is 64.

💡 Real-World Examples

• 🍪 A baker has 27 cookies and bakes 6 more. How many cookies does the baker have in total? (27 + 6 = 33)
• 📚 A student reads 19 pages of a book on Monday and 5 pages on Tuesday. How many pages did the student read in total? (19 + 5 = 24)
• ⚽ A soccer team scored 35 goals in the first half of the season and 9 goals in the second half. How many goals did they score in total? (35 + 9 = 44)

✍️ Practice Quiz

1. 18 + 5 = ?
2. 26 + 7 = ?
3. 39 + 2 = ?
4. 47 + 6 = ?
5. 54 + 8 = ?
6. 65 + 9 = ?
7. 73 + 7 = ?

✅ Answers to Practice Quiz

1. 18 + 5 = 23
2. 26 + 7 = 33
3. 39 + 2 = 41
4. 47 + 6 = 53
5. 54 + 8 = 62
6. 65 + 9 = 74
7. 73 + 7 = 80

⭐ Conclusion

Adding two-digit and one-digit numbers with regrouping is a crucial skill for building a strong foundation in arithmetic. By understanding place value and practicing regrouping, second graders can confidently solve addition problems and apply this knowledge to real-world situations.