# What Is Addition and Subtraction With Regrouping?
Author: Sonakshi Arora
Author URL: https://www.monstermath.app/blog/author/sonakshi-arora
Published: 2026-09-08
Category: Pedagogy
Category URL: https://www.monstermath.app/blog/category/pedagogy
Tags: Place value, addition, creative math strategies, subtraction
Tag URLs: Place value (https://www.monstermath.app/blog/tag/place-value), addition (https://www.monstermath.app/blog/tag/addition), creative math strategies (https://www.monstermath.app/blog/tag/creative-math-strategies), subtraction (https://www.monstermath.app/blog/tag/subtraction)
URL: https://www.monstermath.app/blog/what-is-addition-and-subtraction-with-regrouping

**TL;DR:** _Regrouping means trading between place value columns, ten ones for one ten and back again. In addition you build a ten and carry it left; in subtraction you break a ten open to get ten ones. It's the same trade running in opposite directions, and subtraction is where nearly all the trouble happens._

Regrouping is the word your child's school uses for what you probably learned as carrying and borrowing. It shows up on homework around Grade 2, usually with no explanation attached, and it's the point where a lot of children who were doing fine in math suddenly aren't.

Here's what it actually is, why the subtraction version causes so much more grief than the addition version, and how to teach each one.

## What regrouping actually means

Every digit in a written number stands for a different sized unit. In 28, the 2 doesn't mean two. It means two tens.

Regrouping is trading between those units. Ten ones can be swapped for one ten. One ten can be swapped back into ten ones. Nothing is gained or lost in either direction, exactly like changing a ten-dollar note for ten singles.

That's the whole concept. Addition and subtraction with regrouping are the same trade, run in opposite directions:

- **Addition** builds units up. Ten or more ones get bundled into a ten, and that new ten moves left into the tens column.

- **Subtraction** breaks units down. A ten gets opened up into ten ones so there are enough to take from.


Everything else is bookkeeping. And when a child gets regrouping wrong, it's almost always because the trade itself doesn't feel legitimate to them yet, not because they've forgotten a step.

![What is regrouping in addition and subtraction](https://prod.superblogcdn.com/site_cuid_cm6t228tz007prqzd9vdoqb9s/images/regrouping-in-addition-and-subtraction-final-1788784184777-compressed.webp)

## Regrouping in addition: building a ten

Take 28 + 15.

Add the ones: 8 + 5 = 13. But no column can hold thirteen, because a column only has room for a single digit. So thirteen ones get regrouped into one ten and three ones. The 3 stays in the ones column, the new ten moves across to join the others, and 2 tens (from 28) plus 1 ten (from 15) plus 1 ten (regrouped one) makes 4 tens. Answer: 43.

Here's a sequence that gets a child there.

### 1\. Build both numbers separately

Lay out 28 as two ten-rods and eight ones, then 15 as one rod and five ones, keeping them in two distinct piles. Have your child tell you what each pile is worth before anything moves. This step looks trivial, but it isn't. A child who can't confidently say "that's two tens and eight ones" is not ready for the trade, and pushing on will teach them a procedure they can't reason about. Stay here until both numbers are read fluently.

### 2\. Push the ones together and count the problem

Combine only the loose ones, leaving the rods alone. Your child now has thirteen ones sitting in front of them. Ask what the problem is. Most children spot it themselves: there are too many to write in one column. Letting them notice the difficulty, rather than announcing it, is what makes the next step feel like a solution instead of a rule. Move on when they can articulate why thirteen ones can't just stay as they are.

### 3\. Make the trade physically

Count out ten of those ones, hand them to you, and take back a single ten-rod in exchange. Three ones are left over. Say what happened while it happens: "ten ones traded for one ten, same amount." Then put the new rod with the other rods, which is the part that gives "carrying" its name. Repeat this with a few different numbers before writing anything down, because the trade needs to feel routine before it has to survive being written.

### 4\. Write it beside the blocks, not instead of them

Now do the same problem on paper with the materials still on the table. Write the 3 in the ones column and say "these three are left." Write the small 1 above the tens column and say "and this is the ten we just made, waiting to be added in." Every mark on the page should name something your child physically did seconds earlier. Children who learn the written form first tend to treat the little carried 1 as a decoration and can sometimes forget it, and it's a hard habit to unpick later.

## Regrouping in subtraction: breaking a ten open

Take 36 − 19.

You can't take 9 ones from 6 ones. So one of the three tens gets broken open into ten ones, leaving 2 tens and 16 ones. Now 16 − 9 = 7, and 2 tens − 1 ten = 1 ten. Answer: 17.

The teaching sequence mirrors addition, with one addition at the front. Before subtracting anything, prove the trade is fair in the harder direction: put one ten-rod beside ten loose ones and ask which is worth more. Many children say the loose pile, because it looks like more. Count them together until it's obvious they're equal, and do that on its own for a few sessions.

Then build the larger number, try to remove the ones, get stuck on purpose, and let your child work out that a rod could be broken up. Record each move on paper as it happens.

Subtraction has enough failure modes of its own that we've given it a separate article. If your child is stuck specifically here, our guide to [explaining regrouping in subtraction without confusing your child](https://www.monstermath.app/blog/how-to-explain-regrouping-in-subtraction-to-your-child) covers how to read their wrong answers and work out which part broke.

## Why subtraction causes most of the trouble

If addition regrouping went fine and subtraction fell apart, that's the normal pattern rather than something odd about your child.

When researchers analysed the arithmetic errors of 291 third and fourth graders, [subtraction bugs comprised the bulk of procedural errors](https://pmc.ncbi.nlm.nih.gov/articles/PMC2788949/), with addition errors comparatively uncommon across every group they looked at.

There's a reason for the imbalance. In addition, a child who ignores regrouping produces a visibly silly answer, writing thirteen in a single column. In subtraction, ignoring the trade produces something that looks perfectly reasonable. Faced with 6 − 9, a child flips it to 9 − 6 and writes 3, which looks like a normal answer.

That specific error is the most common one in the research, and it's much more frequent in children who struggle with math: [31% of children with combined math and reading difficulties subtracted the smaller digit from the larger one instead of borrowing, against 9% of children with no learning difficulties](https://pmc.ncbi.nlm.nih.gov/articles/PMC2788949/). The same study found these errors were rarely one-off slips. Children who made a given bug made it on most of the problems where it was possible, which is what a misunderstood rule looks like from the outside.

![Common regrouping mistake in subtraction](https://prod.superblogcdn.com/site_cuid_cm6t228tz007prqzd9vdoqb9s/images/common-mistakes-in-regrouping-1788784384845-compressed.webp)

## Carrying, borrowing, regrouping: why the words changed

You were probably taught carrying and borrowing. Schools now say regrouping. Same math, and the change wasn't arbitrary.

"Borrowing" is the genuinely misleading one. Borrowing implies you give it back, and nothing is ever given back. The ten becomes ten ones permanently. A child who takes the word at face value is reasoning correctly from bad information.

"Carrying" is harmless but empty. It describes moving a mark across the page rather than the trade that produced it.

"Regrouping" is more accurate, and it has its own weakness: it covers both directions at once, so it doesn't tell a child whether they're building a unit or breaking one. Which is why the most useful thing to say at the table isn't any of the three. Say what physically happened. "We traded ten ones for one ten." "We broke a ten into ten ones." Longer, and it leaves nothing for a child to misinterpret.

## If subtraction stays stuck, try counting up instead

Column subtraction with borrowing is one method, not the only one, and for some children it stays hard long after it should have clicked.

Counting up is the alternative. Instead of taking 19 away from 36, start at 19 and work out how far it is to 36. Up one to 20, up sixteen more to 36, so the answer is 17. No borrowing, no broken tens, nothing to track backwards.

It isn't a workaround for weak students. When Dutch researchers studied children in special education solving two-digit subtraction, they found that [students often used counting up spontaneously - even though most had never been taught it](https://link.springer.com/article/10.1007/s10649-011-9351-0)\- and were particularly likely to use it when the numbers were close together, as in 62 − 58. Counting up proved to be a highly successful strategy for these students. They were aged 8 to 12 and were one to four years behind their peers in math.

Worth knowing what it does and doesn't cover. Counting up shines when the two numbers are close together, like 62 − 58, and gets unwieldy when they're far apart, like 62 − 14. Teach it alongside the standard method rather than as a replacement, and let your child choose based on how close the numbers look.

## Before you start: check the foundation

Regrouping sits directly on place value, and if place value is shaky then no amount of practice on the procedure will hold.

A study of 630 Grade 4 students found that [place value understanding made direct, statistically significant contributions to every arithmetic skill the researchers examined](https://www.tandfonline.com/doi/full/10.1080/19477503.2026.2660609), while also noting that place value alone couldn't explain all the differences in children's performance.

The quick check takes thirty seconds. Point at the 6 in 65 and ask what it means. If your child says "six," start with place value rather than with regrouping. Our guide to [teaching place value using household items](https://www.monstermath.app/blog/teach-place-value-to-a-6-year-old-using-household-items) covers how to build it with straws and rubber bands.

## What progress actually looks like

The goal isn't speed, at least not first. It's that your child can explain why the trade is allowed without materials in front of them. A child who can say "I turned one ten into ten ones, and that's the same amount" has the concept, and fluency follows from there.

A child who is quick but can't explain it is holding a memorised sequence. Those hold up fine on a worksheet of similar problems and fall apart the moment something changes, which is usually when a parent finds out the understanding was never there.

So if you only check one thing, don't check whether they got the answer. Ask them why they crossed out the 3.

## FAQs:

### What is regrouping in math?

Regrouping means trading between place value columns: swapping ten ones for one ten, or one ten back into ten ones. In addition you build a ten and carry it into the next column. In subtraction you break a ten open so there are enough ones to subtract from. It's what older textbooks called carrying and borrowing.

### What grade do children learn regrouping?

Most curricula introduce two-digit addition and subtraction with regrouping in Grade 2, around ages 7 to 8, then extend to three-digit numbers in Grade 3. Children who are still developing place value understanding often need longer, which is common rather than a warning sign.

### Is regrouping the same as borrowing and carrying?

Yes, it's the same procedure under a newer name. "Carrying" refers to the addition version and "borrowing" to the subtraction version, while "regrouping" covers both. Borrowing is the least accurate of the three, since nothing is ever given back.

### Why does my child find subtraction with regrouping so much harder than addition?

Because skipping the trade in subtraction produces an answer that looks plausible. A child faced with 6 − 9 will often flip it to 9 − 6, which yields a normal-looking number instead of an obvious error. Research on children's arithmetic errors finds subtraction accounts for the bulk of procedural mistakes, with addition errors much less common.

### Should I teach my child to count up instead of borrowing?

It's worth teaching as an additional method rather than a replacement. Counting up works well when the two numbers are close together, and research with children who were behind in math found they were more successful with it on problems where the numbers were close and a ten had to be crossed. It becomes awkward when the numbers are far apart.

### My child knows the steps but keeps getting regrouping wrong. What's going on?

Usually the trade itself hasn't been accepted as real. Put one ten-rod beside ten loose objects and ask which is worth more. If your child says the loose pile, that's the gap, and no amount of procedural practice will close it. Work on that comparison until "the same" is obvious before returning to written problems.

## References

- Raghubar, K., Cirino, P., Barnes, M., Ewing-Cobbs, L., Fletcher, J., & Fuchs, L. (2009). Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties. _Journal of Learning Disabilities, 42_(4), 356–371. [https://pmc.ncbi.nlm.nih.gov/articles/PMC2788949/](https://pmc.ncbi.nlm.nih.gov/articles/PMC2788949/)

- Peltenburg, M., van den Heuvel-Panhuizen, M., & Robitzsch, A. (2012). Special education students' use of indirect addition in solving subtraction problems up to 100. _Educational Studies in Mathematics, 79_, 351–369. [https://link.springer.com/article/10.1007/s10649-011-9351-0](https://link.springer.com/article/10.1007/s10649-011-9351-0)

- Lenz, K., & Wittmann, G. (2026). Investigating conceptual place value understanding and its interplay with arithmetic skills at the end of primary school. _Investigations in Mathematics Learning_. [https://www.tandfonline.com/doi/full/10.1080/19477503.2026.2660609](https://www.tandfonline.com/doi/full/10.1080/19477503.2026.2660609)


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