How to teach addition with regrouping (carrying), step by step

Quick answer

Regrouping (carrying) happens when a column adds up to 10 or more. Start with base-ten blocks: bundle 10 ones into 1 ten and move it to the tens column. On paper, in 47 + 38, 7 + 8 = 15, so write 5 and carry 1 ten, giving 85. Kids learn this in grades 1–2 and are fluent within 1,000 by the end of 3rd grade.

Regrouping, the step many of us learned as “carrying the one,” is where addition starts depending on place value. Taught as a rule (“write the 1 up there”), it gets forgotten or misapplied. Taught as a trade (10 ones become 1 ten), it makes sense and sticks. Here is how to teach it with blocks first, then on paper.

What regrouping (carrying) actually means

Our number system is built on tens. A place can hold at most 9; once you reach 10, you make a new group and move it one place to the left. That is all regrouping is. In 47 + 38, the ones add up to 7 + 8 = 15. Fifteen ones is 1 ten and 5 ones, so the 5 stays in the ones place and the new ten joins the other tens.

Push the blocks together and you get 7 tens and 15 loose ones. Bundle 10 of those ones into a ten, and you have 8 tens and 5 ones: 85.

When kids learn it

The Common Core State Standards, used by most states, spread regrouping over several years. Your state or school may differ a little.

Before starting, check two things. Does your child know that 47 means 4 tens and 7 ones? And can they add facts within 20, like 7 + 8, without long counting? If either is shaky, spend a few days on place value or on the make ten strategy first.

How to teach regrouping, step by step

You need something that can be bundled into tens: base-ten blocks, straws with rubber bands, or LEGO bricks in stacks of 10. For a place-value mat, draw a line down a sheet of paper and label the sides Tens and Ones.

Step 1: Build both numbers on a place-value mat

Have your child build 47 (4 tens, 7 ones) and 38 (3 tens, 8 ones), each piece in its own column, saying the numbers out loud as tens and ones.

Step 2: Add the ones and trade 10 ones for a ten

Always start with the ones. Push the 7 and 8 ones together and count: 15. Ask, “Do we have enough to make a ten?” Count out 10, bundle them (or swap them for a ten rod), and move that ten to the Tens side. 5 ones are left.

Step 3: Add the tens, including the new one

Now count the tens: 4 + 3 = 7, plus the new one makes 8 tens. 8 tens and 5 ones is 85. Do several problems this way before writing anything down.

Step 4: Write the same steps in columns

Now record exactly what the blocks showed. Line up the numbers so ones are under ones and tens are under tens. Add the ones: 7 + 8 = 15. Write 5 in the ones place and a small 1 above the tens column. That 1 is the bundle you moved. Then add the tens: 1 + 4 + 3 = 8.

147+3885

Step 5: Move on to three-digit numbers

Three-digit addition uses the same trade, sometimes twice. Try 268 + 157:

1. Ones: 8 + 7 = 15. Write 5, carry 1 ten.
2. Tens: 1 + 6 + 5 = 12 tens. That's 1 hundred and 2 tens. Write 2, carry 1 hundred.
3. Hundreds: 1 + 2 + 1 = 4 hundreds.

11268+157425

If the second trade is confusing, build it: 12 ten rods become 1 hundred flat and 2 rods. Ten tens make a hundred, just like ten ones make a ten.

Mental math alternatives

The column method is reliable, but Common Core also asks kids to use strategies based on place value. These mental methods build number sense and are great for checking answers.

• Add tens, then ones. 47 + 38: 40 + 30 = 70, 7 + 8 = 15, and 70 + 15 = 85.
• Make the next ten. 38 + 5: 38 needs 2 to reach 40, so split 5 into 2 and 3. 38 + 2 = 40, then 40 + 3 = 43.
• Jump on a number line. 47 + 38: jump 30 to 77, 3 to reach 80, then 5 more to 85.
• Round and adjust. 47 + 38 is close to 47 + 40 = 87. You added 2 too many, so take them away: 85.

The number line is one of the tools recommended in the U.S. Institute of Education Sciences guide on helping students who struggle with math, so keep using it even after the column method clicks.

Common mistakes (and how to fix them)

• Writing 15 in the ones place. 47 + 38 becomes 715. Each place holds only one digit: 15 ones is 1 ten and 5 ones. Build it with blocks and point to where the ten goes.
• Forgetting the carried 1. 47 + 38 becomes 75. Have your child write the carried 1 in a different color, and say “plus the one I carried” every time.
• Misaligned columns. In 47 + 8, the 8 ends up under the 4, giving 127. Use grid paper or turn lined paper sideways so the lines make columns.
• Carrying when nothing needs carrying. Some children carry a 1 in every problem. Mix in problems like 34 + 25 and ask first: “Will the ones make a new ten?”

Games and everyday practice

• Race to 100. Take turns rolling two dice and collecting that many ones cubes (or pennies). Whenever you have 10 ones, trade them for a ten rod (or a dime). First to 10 tens, which is 100, wins. Every trade is a regrouping.
• Coins. Ten pennies make a dime and ten dimes make a dollar, the same pattern as ones, tens and hundreds. Add two prices like 47¢ and 38¢, then check with real coins.
• Score keeping. Keep a running total for a board game on paper, using column addition.

Practice problems

Most of these need regrouping, but not all. Ask your child to predict which ones will need a trade before they start.

Addition with regrouping (with answers)

1. 26 + 15 = ?
2. 38 + 7 = ?
3. 34 + 25 = ?
4. 59 + 24 = ?
5. 66 + 27 = ?
6. 75 + 19 = ?
7. 148 + 36 = ?
8. 268 + 157 = ?
9. 395 + 128 = ?
10. 456 + 278 = ?
11. 507 + 296 = ?

Show answers

For more practice, print our free addition worksheets. When your child is comfortable carrying, the mirror-image skill is subtraction with regrouping, and the big picture is in our guide on how to teach addition. You can also see where regrouping fits in the year on our 2nd grade and 3rd grade skills pages.

Frequently asked questions

What is regrouping in addition?

Regrouping means trading 10 of one place value for 1 of the next. When the ones add up to 10 or more, 10 ones are bundled into 1 ten and moved to the tens column. When the tens add up to 10 or more, 10 tens become 1 hundred. The total never changes; it is just reorganized.

Is carrying the same as regrouping?

Yes. Carrying is the older name and regrouping is the word most schools use today. Both describe the same step: writing the extra ten (or hundred) above the next column. Many teachers prefer regrouping because it reminds children that they are making a group of ten, not just moving a mysterious 1.

What grade learns addition with regrouping?

Under the Common Core, children start composing a ten with models in 1st grade (1.NBT.C.4), add fluently within 100 in 2nd grade (2.NBT.B.5) and within 1,000 by the end of 3rd grade (3.NBT.A.2). The standard written algorithm is a 4th grade standard (4.NBT.B.4), but many schools teach it in 2nd or 3rd grade. Your state or school may differ.

How do you explain carrying the one to a child?

Use real objects. Build 47 and 38 with blocks or bundles of straws, push the loose ones together and count 15. Ask, “Can we make a ten?” Bundle 10 of them and move the bundle to the tens side. The carried 1 on paper is that bundle: it is worth ten, not one.

Why does my child write 715 for 47 + 38?

Your child added each column correctly (4 + 3 = 7 and 7 + 8 = 15) but wrote the whole 15 in the ones place. Remind them that each place can hold only one digit. Go back to blocks: 15 ones is 1 ten and 5 ones, so the 5 stays and the ten moves to the tens column, giving 85.

Do you add from right to left or left to right?

In the written column method, start on the right with the ones, so you know whether a ten needs to be carried before adding the tens. In mental math, many people go left to right (40 + 30 = 70, then 7 + 8 = 15, then 70 + 15 = 85). Both are correct when done carefully.

Sources

• Common Core State Standards: Grade 1, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 2, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 3, Number & Operations in Base Ten — CCSSI
• Common Core State Standards: Grade 4, Number & Operations in Base Ten — CCSSI
• Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (practice guide) — Institute of Education Sciences, What Works Clearinghouse

Written by The Mathing Team for parents and teachers. Grade expectations follow the Common Core State Standards for Mathematics; your state or school may sequence skills a little differently.