Y.6 Add ones to two-digit numbers using place value – with regrouping
What is place value?
Place value is the value of a digit based on its position in a number. In a two-digit number, the digit on the left is in the tens place, and the digit on the right is in the ones place.
- In the number 34, the 3 means 3 tens (30), and the 4 means 4 ones (4).
- In the number 57, the 5 means 5 tens (50), and the 7 means 7 ones (7).
- In the number 80, the 8 means 8 tens (80), and the 0 means 0 ones (0).
The tens place is always to the left of the ones place. Think of it as a team: the tens are the big part, and the ones are the small part.
What does regrouping mean in addition?
Regrouping (also called "carrying") is what we do when we add two digits and the sum is 10 or greater. We regroup 10 ones into 1 ten and move it to the tens place.
- 8 ones + 5 ones = 13 ones. 13 ones is the same as 1 ten and 3 ones.
- 9 ones + 7 ones = 16 ones. 16 ones is the same as 1 ten and 6 ones.
- 6 ones + 4 ones = 10 ones. 10 ones is the same as 1 ten and 0 ones.
Regrouping does not change the value of the number. It just shows the same amount in a different way. Ten ones always equal one ten.
Adding ones to a two-digit number without regrouping
Sometimes when we add ones to a two-digit number, the ones digits add up to less than 10. In this case, we do not need to regroup. We simply add the ones and keep the tens the same.
- 42 + 3 = ?
2 ones + 3 ones = 5 ones. 4 tens stay as 4 tens. 42 + 3 = 45. - 61 + 7 = ?
1 one + 7 ones = 8 ones. 6 tens stay as 6 tens. 61 + 7 = 68. - 84 + 2 = ?
4 ones + 2 ones = 6 ones. 8 tens stay as 8 tens. 84 + 2 = 86.
If the ones digits add up to 9 or less, you do not regroup. This is called addition without regrouping.
Adding ones to a two-digit number with regrouping
When the ones digits add up to 10 or more, we must regroup. We take 10 ones and turn them into 1 ten. We add that ten to the tens place. The remaining ones stay in the ones place.
- 27 + 6 = ?
- Step 1: Add the ones. 7 ones + 6 ones = 13 ones.
- Step 2: Regroup 13 ones. 13 ones = 1 ten and 3 ones.
- Step 3: Add the tens. 2 tens + 1 ten = 3 tens.
- Step 4: Combine. 3 tens and 3 ones = 33.
Always start with the ones place. If the ones make 10 or more, you must regroup before you finish the problem.
Using base-ten blocks to understand regrouping
Base-ten blocks help us see regrouping. A rod shows one ten. A cube shows one one. When we have ten cubes, we can trade them for one rod.
- You have 35. That is 3 rods and 5 cubes.
- You add 8 cubes. Now you have 5 cubes + 8 cubes = 13 cubes.
- You group 10 cubes together and trade them for 1 rod.
- Now you have 3 rods + 1 rod = 4 rods, and 3 leftover cubes.
- That is 43.
Base-ten blocks are a great tool. If you do not have real blocks, you can draw a line for a ten and a dot for a one.
Regrouping with a nine in the ones place
Sometimes the ones digit in the two-digit number is 9. Adding any number greater than 0 to 9 will always require regrouping, because 9 + 1 = 10.
- 29 + 5 = ?
9 + 5 = 14. 14 = 1 ten and 4 ones. 2 tens + 1 ten = 3 tens. 29 + 5 = 34. - 49 + 3 = ?
9 + 3 = 12. 12 = 1 ten and 2 ones. 4 tens + 1 ten = 5 tens. 49 + 3 = 52. - 79 + 8 = ?
9 + 8 = 17. 17 = 1 ten and 7 ones. 7 tens + 1 ten = 8 tens. 79 + 8 = 87.
Watch out for 9! It is very close to 10. Any time you add 1 or more to 9, you will make a new ten.
When the sum of the ones is exactly 10
Sometimes the ones digits add up to exactly 10. When this happens, we regroup 10 ones into 1 ten. There are zero ones left over.
- 34 + 6 = ?
4 + 6 = 10. 10 = 1 ten and 0 ones. 3 tens + 1 ten = 4 tens. 34 + 6 = 40. - 52 + 8 = ?
2 + 8 = 10. 10 = 1 ten and 0 ones. 5 tens + 1 ten = 6 tens. 52 + 8 = 60. - 73 + 7 = ?
3 + 7 = 10. 10 = 1 ten and 0 ones. 7 tens + 1 ten = 8 tens. 73 + 7 = 80.
Do not forget to write a zero in the ones place when you regroup exactly 10 ones. The zero is important; it tells us there are no leftover ones.
Regrouping when the tens place changes
Sometimes when we add the regrouped ten, the tens place becomes 10 tens. 10 tens is the same as 1 hundred. This happens when the tens digit is 9 and we add 1 more ten.
- 95 + 9 = ?
5 + 9 = 14. 14 = 1 ten and 4 ones. 9 tens + 1 ten = 10 tens. 10 tens = 1 hundred and 0 tens. 95 + 9 = 104. - 91 + 9 = ?
1 + 9 = 10. 10 = 1 ten and 0 ones. 9 tens + 1 ten = 10 tens = 1 hundred, 0 tens. 91 + 9 = 100. - 88 + 12 is not a ones-only problem, but if we add 8 + 2 = 10, regroup, then 8 tens + 1 ten = 9 tens. No hundred here. (88 + 12 = 100? Wait, check: 8+2=10, regroup. 8 tens + 1 ten = 9 tens. 9 tens + 0 tens? Actually 12 has 1 ten, so we must add that too. This shows why we always line up by place value.)
When you have 9 tens and you add 1 ten, you get 10 tens. That is a hundred! You will see three-digit answers sometimes. That is okay. Numbers can grow!
Writing regrouping problems vertically
When we write an addition problem vertically (up and down), we line up the tens and ones in columns. This helps us see which digits to add. We write the number we are regrouping at the top of the tens column.
Step 1: 6 + 7 = 13. Write 3 in the ones place. Regroup the 1 ten to the tens column.
Step 2: 4 tens + 1 ten = 5 tens. Write 5 in the tens place.
The small "1" you write above the tens place is your regrouped ten. It reminds you to add it when you add the tens.
Common mistakes and how to avoid them
Even careful students make mistakes with regrouping. Knowing what to watch for helps you catch errors.
- Forgetting to regroup: 37 + 5 = 312 (wrong). You cannot put 12 in the ones place. Regroup 12 into 1 ten and 2 ones. Correct answer: 42.
- Adding the regrouped ten to the wrong place: Always add it to the tens place, not the ones place.
- Forgetting to add the regrouped ten: 56 + 9: 6+9=15, regroup 1 ten. 5 tens + 1 ten = 6 tens. Answer: 65, not 55.
- Adding the ones first is good, but forgetting to write the leftover ones: 44 + 8 = 5 tens + 2 ones = 52, not 50.
Always check your work. Ask yourself: Does my answer make sense? If I add a small number to a two-digit number, my answer should be a little bigger, not a lot bigger.
Using mental math for regrouping
Mental math means solving the problem in your head without writing it down. You can use regrouping strategies to add quickly.
- Make a ten first: 28 + 5. Think: 28 + 2 = 30, then 30 + 3 = 33.
- Break apart: 47 + 8. Think: 47 + 10 = 57, then 57 - 2 = 55. (Because 8 is 2 less than 10.)
- Count up: 53 + 9. Start at 53, count: 54, 55, 56, 57, 58, 59, 60, 61, 62. That is 9 more: 62.
Mental math takes practice. Start with small numbers, and soon you will be able to add quickly without paper.
Regrouping in word problems
Word problems tell a story. You must find the numbers and decide what to do. Look for clue words like "in all," "altogether," and "total." These often mean addition.
Maria has 36 stickers. Her friend gives her 7 more stickers. How many stickers does Maria have now?
Step 1: Find the numbers. 36 and 7.
Step 2: Add the ones. 6 + 7 = 13. Regroup: 1 ten and 3 ones.
Step 3: Add the tens. 3 tens + 1 ten = 4 tens.
Step 4: 4 tens and 3 ones = 43 stickers.
Always write your answer as a complete sentence. It helps you check if your answer makes sense in the story.
Practice problems with regrouping
Try these problems on your own. Use base-ten blocks, draw a picture, or write the problem vertically. Remember to regroup when the ones add up to 10 or more.
- 18 + 5 = ?
- 26 + 7 = ?
- 35 + 9 = ?
- 44 + 8 = ?
- 57 + 6 = ?
- 63 + 9 = ?
- 72 + 8 = ?
- 89 + 4 = ?
- 91 + 9 = ?
- 97 + 5 = ?
23, 33, 44, 52, 63, 72, 80, 93, 100, 102
Why regrouping matters
Regrouping is not just a school skill. We use regrouping in real life when we count money, measure ingredients, or add scores in a game. Understanding regrouping helps you work with larger numbers in second grade and beyond.
- You have 47 cents. You find 5 cents in your pocket. Now you have 52 cents.
- You read 28 pages of a book. You read 8 more pages. Now you have read 36 pages.
- You score 65 points in a video game. You earn 9 more points. Now you have 74 points.
Math is everywhere! When you learn regrouping, you are learning a tool you will use for the rest of your life.
Putting it all together
To add ones to a two-digit number with regrouping:
- Look at the ones place. Add the ones digits together.
- If the sum is 9 or less, write it in the ones place. The tens stay the same.
- If the sum is 10 or more, regroup: write the ones digit in the ones place, and add 1 to the tens place.
- Add the tens digits, including the regrouped ten.
- Check your answer. Does it make sense?
- 48 + 7 = ?
- 8 + 7 = 15. 15 = 1 ten and 5 ones.
- 4 tens + 1 ten = 5 tens.
- 5 tens and 5 ones = 55.
You can do this! Regrouping takes practice, but once you learn it, you can add almost any numbers.
Common Core alignment: CCSS.MATH.CONTENT.1.NBT.C.4 – Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.
Notes for teachers
This free lesson is aligned with CCSS.MATH.CONTENT.1.NBT.C.4. Use it for whole-class instruction, small group intervention, independent practice, or homework.
All content is 100% free, student-safe, and designed for classroom and home use. This lesson emphasizes conceptual understanding of place value and regrouping through clear definitions, step-by-step examples, and practical notes. Encourage students to use base-ten blocks and drawings before moving to abstract symbolic methods.