How to Teach Regrouping in Subtraction (Borrowing)

If carrying in addition is where kids first hit a wall, borrowing in subtraction is where many of them give up. The procedure — cross out the tens digit, make it one less, put a 1 next to the ones digit — feels like magic to a child who does not understand place value.

And magic does not transfer. A child who memorizes borrowing without understanding it will fail when the numbers get bigger, when there are zeros involved, or when borrowing across multiple columns.

Here is how to make borrowing make sense.

What borrowing actually means

Consider 42 - 17. The ones column asks: 2 - 7. You cannot take 7 from 2. So you "borrow" — you take 1 ten from the tens column and trade it for 10 ones. Now you have 3 tens and 12 ones. 12 - 7 = 5. 3 - 1 = 2. Answer: 25.

The key: borrowing is just the reverse of carrying. In addition, you trade 10 ones for 1 ten (carrying). In subtraction, you trade 1 ten for 10 ones (borrowing). Same trade, opposite direction.

Key Insight: The word "borrow" is misleading — you are not borrowing anything. You are exchanging. One ten becomes ten ones. The total value does not change. 42 is still 42, whether you think of it as 4 tens and 2 ones or 3 tens and 12 ones.

Prerequisites

Before teaching regrouping in subtraction, your child must:

• Understand place value (what each digit represents)
• Be fluent with regrouping in addition (the forward trade)
• Be able to subtract within 20 without regrouping
• Know that 1 ten = 10 ones (and be able to demonstrate this physically)

Step 1: Physical exchange with base-ten materials

Build 42 with base-ten blocks: 4 ten-sticks and 2 ones.

"We need to subtract 17. Let us start with the ones. We have 2 ones and need to take away 7. Do we have enough ones?"

No. So we trade: break 1 ten-stick into 10 ones.

"Now we have 3 ten-sticks and 12 ones. The total is still 42 — we just rearranged. Now take away 7 ones: 12 - 7 = 5 ones. Take away 1 ten: 3 - 1 = 2 tens. Answer: 25."

The physical trade is essential. The child must see that breaking a ten-stick into 10 individual ones does not change the total value.

Step 2: Record alongside the model

Write the vertical subtraction next to the physical model:

  42
- 17
----

As your child makes the physical trade, record it on paper:

• Cross out the 4, write 3 (we traded 1 ten)
• Cross out the 2, write 12 (we gained 10 ones)
• Now subtract: 12 - 7 = 5, 3 - 1 = 2
• Answer: 25

Every mark on paper corresponds to a physical action. The child sees both simultaneously.

Step 3: Problems with zeros

Borrowing across a zero is the hardest version:

  302
- 147
-----

The ones column needs to borrow, but the tens column is 0 — there is nothing to borrow from. So you must go to the hundreds first.

With blocks:

• 302 = 3 hundreds, 0 tens, 2 ones
• Trade 1 hundred for 10 tens: now 2 hundreds, 10 tens, 2 ones
• Trade 1 ten for 10 ones: now 2 hundreds, 9 tens, 12 ones
• Subtract: 12 - 7 = 5, 9 - 4 = 5, 2 - 1 = 1
• Answer: 155

This double exchange confuses many children. Let them work through it physically until the logic is clear.

The "add up" alternative

For many subtraction problems, counting up is easier than borrowing:

42 - 17: "Start at 17. How far to 42?"

• 17 to 20 = 3
• 20 to 40 = 20
• 40 to 42 = 2
• Total: 3 + 20 + 2 = 25

This mental strategy avoids borrowing entirely and develops number sense. It is particularly useful for comparison problems ("How much more is 42 than 17?").

Both methods are valid. The standard algorithm is important to learn, but the add-up strategy often produces faster, more accurate mental math.

Key Insight: Borrowing is not the only subtraction strategy. "Adding up" from the smaller number to the larger number avoids regrouping entirely and builds flexible number sense. Teach both.

Common borrowing mistakes

Subtracting the smaller digit from the larger (42 - 17 = 35): The child does 7 - 2 = 5 in the ones column instead of borrowing. They are avoiding the hard part. Show them with blocks that you cannot take 7 from 2.

Borrowing when not needed (65 - 23): The child borrows on every problem. Emphasize: "Check first — do you have enough ones? 5 is more than 3, so no trade needed."

Losing track during double borrowing: Problems like 302 - 147 require two trades. Do these slowly with physical models.

Getting the wrong answer after borrowing correctly: They borrow properly but make an arithmetic error. The borrowing concept is fine — they just need subtraction fact practice.

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Borrowing is the reverse of carrying, and it makes complete sense when your child sees the physical exchange. One ten becomes ten ones. The total does not change. Once they understand that single idea, borrowing across any number of columns follows the same logic.

If you want a system that ensures your child truly understands regrouping — not just the crossing-out procedure — before moving to larger numbers, that is how Lumastery works.