How to Teach Subtraction with Regrouping

Subtraction with regrouping (some adults call it "borrowing") is where many second graders first get stuck in math. The good news is that the difficulty is almost never the subtraction itself. It is place value: the child has not yet seen that one ten can be traded for ten ones. Teach that idea first, and the written method makes sense instead of feeling like a magic trick.

This guide walks through the order that works best with most children, with worked examples you can copy onto a whiteboard.

What your child needs first

Before starting regrouping, check three things. If any of them is shaky, spend a few days there first.

1. Subtraction facts within 20. Every regrouped column becomes a problem like 12 − 7 or 15 − 8. If your child counts on fingers for these, regrouping will feel slow and confusing.
2. Tens and ones. Your child should be able to say that 52 is 5 tens and 2 ones, and build it with blocks or bundles of ten.
3. Column subtraction without regrouping. Problems like 58 − 23, where every top digit is larger, teach the habit of subtracting the ones first and then the tens.

Step 1: Show the trade with real objects

Use base-ten blocks, bundles of ten straws or popsicle sticks held with rubber bands. Build the top number only.

For 52 − 27, build 5 tens and 2 ones. Now ask: "We need to take away 7 ones. Can we take 7 ones from 2?" Your child will say no. Then ask: "What could we do?" Let them suggest it if they can: open one ten and turn it into 10 ones.

Now there are 4 tens and 12 ones. Take away 7 ones (5 left) and 2 tens (2 left). The answer is 2 tens and 5 ones: 25.

Do three or four problems this way before writing anything. The goal is for your child to say in their own words why the trade is fair: one ten and ten ones are the same amount.

Step 2: Write down what the blocks did

Now solve the same problem on paper, saying each step out loud:

• Look at the ones. 2 is less than 7, so we need to trade.
• Cross out the 5 in the tens place and write 4 above it. One ten has moved.
• Write a small 1 in front of the 2, making it 12. Those are the ten new ones.
• Subtract the ones: 12 − 7 = 5.
• Subtract the tens: 4 − 2 = 2.

Keep the blocks on the table for the first few written problems. When your child hesitates, point back to the blocks: "Where did this 4 come from?"

Step 3: Decide when to regroup

Children who have just learned regrouping often start regrouping every problem. Mix in problems that do not need it, and ask the same question before every column: "Is the top digit big enough?"

Many teachers use a short rhyme: "More on top? No need to stop. More on the floor? Go next door." "More on the floor" means the bottom digit is bigger, so you go next door to borrow a ten.

Here are two problems side by side. Only one needs a trade.

Step 4: Check every answer by adding

Subtraction and addition undo each other, so every answer can be checked. For 52 − 27 = 25, add 25 + 27. If you get 52, the answer is right.

This habit catches most careless errors, and it reinforces addition with regrouping at the same time.

Step 5: Move to 3-digit numbers

Three-digit problems use the same idea, one column at a time. Sometimes a trade is needed in both the ones and the tens.

In 432 − 158, the ones need a trade (2 is less than 8), which leaves 2 tens. Then the tens need a trade too (2 is less than 5), so one hundred becomes ten tens.

Go slowly here. Ask your child to finish the ones column completely before looking at the tens.

Step 6: Subtracting across zeros

Problems like 400 − 167 are the hardest kind, because there are no tens to trade from. The trick is to look at 400 as 40 tens. Take one of those tens and turn it into ones: 400 becomes 39 tens and 10 ones. Now every column can be subtracted.

Children who understand the trade with blocks usually handle zeros well. Children who only memorized "cross out and borrow" often get lost here, which is a good sign to go back to Step 1 for a day.

Common mistakes to watch for

Subtracting the smaller digit from the larger one. For 52 − 27, a child writes 35, because 7 − 2 = 5 and 5 − 2 = 3. This is the most common error. Ask: "Which number is on top in the ones column?"

Forgetting to reduce the tens. The child writes 12 − 7 = 5 correctly but then does 5 − 2 = 3 instead of 4 − 2. Crossing out the old digit and writing the new one above it, every time, prevents this.

Regrouping when it is not needed. If a child trades in 68 − 35, they will end up with 18 in the ones column. Go back to the question "Is the top digit big enough?"

Getting lost with zeros. In 400 − 167, a child may subtract the smaller digit in each column and write 367. Build 400 with blocks (4 flats) and do the trade physically.

A simple two-week practice plan

Ten minutes a day is enough. Longer sessions tend to end in tears rather than progress.

Move on when your child gets about 9 out of 10 right on two different days, and can explain one problem to you in their own words. Explaining is a better test than speed.

Frequently asked questions

What grade learns subtraction with regrouping?

Most children in the US learn 2-digit subtraction with regrouping in second grade and 3-digit subtraction, including zeros, in second or third grade.

Should I say "borrowing" or "regrouping"?

Schools usually say regrouping or trading, because nothing is given back. Either word is fine at home, as long as your child knows that one ten becomes ten ones.

My child gets the right answers but cannot explain them. Is that a problem?

It can be later. Children who follow steps without understanding often struggle with zeros and with larger numbers. A few minutes with blocks usually fixes it.