Tips for Teachers by Craig Barton

Two-digit subtraction with exchange

Subtract 2-Digit Numbers with Exchange

Subtract a 2-Digit Number from a 2-Digit Number Requiring Exchange in the 1s

Atoms of Knowledge

(F) Place value in 2-digit numbers – A 2-digit number is made up of tens and ones (e.g., 63 = 6 tens and 3 ones)
(C) When borrowing is needed – Knowing when we need to exchange from the tens place
✗45 – 23. How do I know? Because 5 ones is greater than 3 ones, so we can subtract directly without borrowing.
✓52 – 27. How do I know? Because 2 ones is less than 7 ones, so we need to borrow from the tens.
✓81 – 36. How do I know? Because 1 one is less than 6 ones, so we need to borrow from the tens.
✓73 – 58. How do I know? Because 3 ones is less than 8 ones, so we need to borrow from the tens.
✗67 – 32. How do I know? Because 7 ones is greater than 2 ones, so we can subtract directly without borrowing.
(F) The exchange – 1 ten = 10 ones (so when we borrow, we trade 1 ten for 10 ones)
(R) Subtracting single-digit numbers – Being able to subtract numbers like 13 – 5 or 12 – 7
Example: Calculate \(13 – 5\)
Steps:
Step 1: Start with 13
Step 2: Subtract 5 from 13
Step 3: \(13 – 5 = 8\)
Commentary: We need to be confident with single-digit subtraction because after borrowing, we’ll often need to subtract numbers like 13 – 7 or 12 – 6.
(T) Decomposing a 2-digit number when borrowing – Breaking down a number to exchange 1 ten for 10 ones
Example: Decompose 63 when we need to borrow
Steps:
Step 1: Start with 63 = 6 tens and 3 ones
Step 2: Borrow 1 ten from the tens place: 6 tens becomes 5 tens
Step 3: Add the borrowed ten (which equals 10 ones) to the ones place: 3 ones becomes 13 ones
Step 4: Now we have 63 = 5 tens and 13 ones
Commentary: This transformation is the key to subtraction with exchange. We’re not changing the value of the number (63 is still 63), we’re just regrouping it to make subtraction possible.

I Do (Teacher Demonstrates)

Example 1: \(63 – 45\)

Calculate: \(63 – 45 = ?\)

Example 2: \(63 – 46\)

Calculate: \(63 – 46 = ?\)

We Do (Guided Practice)

Practice Problem

Calculate: \(52 – 27\)

You Do (Independent Practice)

Complete all 10 questions. Click “Show Solution” to check your work.

1. \(74 – 28\)
2. \(51 – 36\)
3. \(82 – 47\)
4. \(65 – 29\)
5. \(93 – 58\)
6. \(40 – 23\)
7. \(71 – 54\)
8. \(86 – 39\)
9. \(54 – 27\)
10. \(97 – 68\)

Challenge

These questions will challenge your understanding. Click “Show Solution” to see the working and explanation.

1. Factual recall

What does it mean to “exchange” or “borrow” when subtracting 2-digit numbers?
2. Carry out a routine procedure

Calculate: \(72 – 38\)
3. Classify some mathematical object

Look at these subtraction problems. By solving them, identify which one is the odd one out:

a) \(54 – 28\)
b) \(67 – 43\)
c) \(81 – 35\)
d) \(72 – 49\)
4. Interpret situation or answer

Emma had 53 stickers. She gave 27 stickers to her friend. How many stickers does Emma have left? Show your working using the borrowing method.
5. Proof, show, justify

A student says: “When I borrow 1 ten, I’m making the number smaller.” Is this statement correct? Justify your answer using the example \(61 – 34\).
6. Extend a concept

Calculate \(100 – 37\) using the borrowing method. (Hint: Think about 100 as having tens and ones)
7. Construct example/instance

Create a 2-digit subtraction problem that meets ALL of these conditions:
• Requires borrowing from the tens place
• The minuend (first number) has a 0 in the ones place
• The answer is less than 20

Write your problem and solve it.
8. Criticize a fallacy

A student attempts to solve \(64 – 28\) and shows this working:

“Since 4 is less than 8, I borrow from the 6.
6 becomes 5, and 4 becomes 14.
14 – 8 = 6 in the ones place.
5 – 2 = 3 in the tens place.
So the answer is 36.”

Find and correct any errors in this working.