How to teach subtraction with regrouping (borrowing)

Subtraction with regrouping, the method many of us learned as 'borrowing', is where a lot of children stall. The written steps look like magic until you tie them back to place value. Teach the meaning first with something children can hold, give the steps a clear order, and the hardest cases (like subtracting across a zero) stop being scary. Here is the sequence that works.

1. Make sure place value is solid first

Regrouping only makes sense if a child truly believes that ten ones make one ten, and ten tens make one hundred. If that is shaky, no amount of explaining the steps will help. Spend a few sessions bundling ten straws into a ten, or trading ten unit blocks for a ten-rod, until the trade is second nature.

This is the single most common reason borrowing feels like magic: the child is following a rule without the place-value idea underneath it. Fix that gap and everything downstream gets easier.

2. Start with subtraction that does NOT need regrouping

Before any borrowing, make sure column subtraction with no trades is automatic, for example 68 minus 25. Line up the ones under the ones and the tens under the tens, subtract each column, and read the answer. This builds the layout habit so the only new idea later is the trade itself.

3. Show the trade with base-ten blocks

Now introduce a problem that forces a trade, such as 52 minus 27. Build 52 with 5 ten-rods and 2 unit blocks. Try to take away 7 ones, and the child sees the problem directly: there are only 2 ones. So trade one ten-rod for 10 ones. Now there are 4 tens and 12 ones, and you can take 7 ones away easily.

Doing the physical trade before writing anything is what makes the written method a record of something the child already understands, rather than a set of steps to memorise.

4. Write it down, step by step

Once the blocks make sense, mirror the exact same moves on paper. Work the ones column first, and only regroup when the top digit is smaller than the bottom one. Here is 52 minus 27 written out:

Ones: 2 is smaller than 7, so regroup. Cross out the 5 tens, make it 4 tens, and turn the 2 ones into 12 ones.
Ones: 12 minus 7 is 5. Write 5 in the ones column.
Tens: 4 minus 2 is 2. Write 2 in the tens column.
Answer: 25. Check it by adding back, 25 plus 27 is 52.

5. Teach the tricky case: subtracting across a zero

The step that trips children up most is a zero in the middle, like 304 minus 158. You cannot borrow a ten from the tens column because it is 0, so you regroup one hundred into ten tens first, then borrow one of those tens for the ones. It is two trades in a row, and it is far clearer with blocks before paper.

Ones: 4 is smaller than 8, and the tens column is 0, so first trade one hundred for ten tens. Now the hundreds are 2 and the tens are 10.
Then trade one of those tens for ten ones: the tens become 9 and the ones become 14.
Ones: 14 minus 8 is 6. Tens: 9 minus 5 is 4. Hundreds: 2 minus 1 is 1.
Answer: 146. Check: 146 plus 158 is 304.

Common mistakes to watch for

Subtracting the smaller digit from the larger one out of habit (doing 7 minus 2 instead of regrouping to do 12 minus 7).
Regrouping but forgetting to reduce the column you borrowed from by one.
Getting stuck on a zero and borrowing from the wrong column.
Not checking the answer by adding it back to the number subtracted.

Free subtraction practice

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