**What is regrouping (carrying over) in addition?**

Regrouping is a process that happens when the digits in a single column add up to a number greater than nine. If the numbers in the ones place add up to 10 or more, you place the ones digit from your sum in the ones place of the solution. Then, you carry the tens digit into the tens place.

This works when adding numbers in any place value column. Whenever the sum is greater than 9, place the ones digit in the solution of the column you’re working in, and carry the tens digit into the next highest place value column.

**Here’s why:**

Our number system is a base 10 number system. That means every digit in a number means 10 times more than the same digit in one lower place value. Here’s a visual so you can see what each place value means:

As you can see, 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand, and so on. Each place value can only hold one number, so when a sum goes over 9, you have to regroup.

**How to add three-digit numbers with regrouping (carrying):**

*Note: The steps below are for adding when regrouping is required. If the numbers you’re adding don’t require regrouping, you can head to our triple-digit addition without regrouping page to see step-by-step instructions to follow. *

**Step 1:** Add the numbers in the ones column.

**Step 2:** Place the sum in the solution. (If your sum is greater than 9, place the ones digit in the ones column, and carry the tens digit into the tens column.)

**Step 3:** Add the digits in the tens column (including the digit you carried).

**Step 4:** Place the sum in the solution. (If your sum is greater than 9, place the ones digit in the tens column, and carry the tens digit into the hundreds column.)

**Step 5:** Add the digits in the hundreds column (including the digit you carried).

**Example: Find the solution to 345 + 229.**

**Are there any tips for teaching three-digit addition with regrouping to children?**

- Stay patient: Some children have trouble picking up on the process. You may be tempted to think they’ll never get it, but they will.
- Practice: If the process seems confusing, the best thing to do is practice. With enough repetition, the process will start to sink in.
- Keep it simple: Don’t introduce too many tricks or hacks. Regrouping is a fundamental skill that helps students with number sense. If they can understand the process of regrouping now, then any tricks they learn later will make more sense.

**What are some common mistakes to avoid when adding three-digit numbers with regrouping?**

**Not aligning the numbers properly.** If students don’t line their problems up so the ones are on top of the ones and tens are on top of tens, then it increases the chance that they’ll add the wrong numbers together.
**Not writing the solution in the proper column.** If your student is having trouble keeping their numbers in alignment, you may want to have them use our graph paper. The vertical lines help with the organization of place value.
**Not adding from right to left.** Older students and adults can frequently add from left to right because they can process carrying in their heads. Children who are first learning about regrouping aren’t able to do that. It’s important to insist that they add from right to left, so they can keep things organized and complete the addition problems properly.
**Not carrying the tens.** This can be directly correlated to the mistake above, or it can simply be an oversight. Make sure you’re checking the student’s work regularly to catch and correct any mistakes or carelessness before they become habit.

**Pro tip:** If students understand the process but are frequently making mistakes, have them say the steps they’re taking out loud. Example (using the problem above): “First, I’m going to add 5 and 9. That equals 14. I have to put the 4 in the answer and carry the 1.” Saying things out loud can help with processing and catch mistakes before they’re made.