Teaching Subtraction With Borrowing That Actually Works

Borrowing is carrying's tricky cousin. The good news: if a child understands place value, subtraction with borrowing becomes a logical routine instead of a mystery.

Borrowing — known as regrouping in most US classrooms — is what we do when the top digit in a column is smaller than the bottom digit. Rather than getting stuck, we "borrow" a ten from the next column over. Children often find this harder than carrying because it runs in the opposite direction, so it deserves slow, careful teaching.

Begin with subtraction that does NOT need borrowing

Confidence matters. Spend time on problems like 48 − 23 where every top digit is larger than the bottom one. This lets the child master the column routine — ones first, then tens — before adding the complication of borrowing.

Step 1: Show borrowing with real objects

Lay out base-ten blocks for a number like 32 (three tens and two ones). Ask the child to take away 7 ones. There aren't enough! Physically "break" one ten rod into ten ones, so now you have two tens and twelve ones. This is exactly what borrowing means on paper. Doing it with your hands first makes the written steps make sense.

Step 2: Walk through a written example

Take 32 − 7:

1. Look at the ones: 2 − 7. We can't do it, so we borrow.
2. Cross out the 3 tens, make it 2, and add ten to the ones: the 2 becomes 12.
3. Now subtract the ones: 12 − 7 = 5.
4. Subtract the tens: 2 − 0 = 2.
5. The answer is 25.

Narrate each move with place value: "We took one ten from the tens column and gave it to the ones, so now we have twelve ones." Saying it out loud builds the routine.

The hardest case: borrowing across a zero

Problems like 400 − 167 trip up even strong students, because you can't borrow from a zero — it's empty. Teach it as a two-step borrow: the zero "borrows" first from the hundreds, becoming a ten, and then it can lend to the ones. Slow this down and use blocks the first few times. Once a child can handle borrowing across zeros, they have truly mastered the skill.

Common mistakes — and how to fix them

• Subtracting the small from the large no matter the order. For 32 − 7 in the ones column, a child writes 5 by doing 7 − 2. Fix: stress that we must subtract the bottom from the top, and borrow when we can't.
• Forgetting to reduce the column they borrowed from. They add ten to the ones but leave the tens unchanged. Fix: always cross out and rewrite the smaller tens digit.
• Freezing on zeros. Fix: practice borrowing-across-zero problems separately until they feel routine.

Build fluency with mixed practice

Once the steps click, the goal is fluency — getting accurate and reasonably fast. Mix problems that need borrowing with ones that don't, and slowly increase from two-digit to three-digit numbers. A few fresh problems each day, with answer keys to check, is the fastest path. Because each worksheet is randomly generated, your child practices the thinking instead of memorizing a single page.