Maths Library

Vertical Subtraction Algorithm: Year 3 maths

This topic covers the formal vertical algorithm for subtraction with decomposition and exchanging across columns. Pupils practise structured layout, exchanging from tens, hundreds, and thousands, and dealing with interior zeros.

Open in full editor

What this covers

Vertical Subtraction Algorithm is taught in Year 3 (age 8 to 9) as a main teaching focus. It sits in the Number strand.

Worked example

Calculate: 503 - 267 using column subtraction.

  1. Align digits: 3 - 7 requires an exchange. Tens column has 0, so exchange from hundreds: 5 becomes 4, tens becomes 10.
  2. Exchange 1 ten to ones: tens becomes 9, ones becomes 13.
  3. Subtract ones: 13 - 7 = 6; tens: 9 - 6 = 3; hundreds: 4 - 2 = 2. Total is 236.

Answer: 236

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. 2-digit numbers without decomposition
  2. 3-digit numbers with single exchange from tens to ones
  3. 3-digit numbers with exchanges across tens and hundreds
  4. 4-digit numbers with borrowing across interior zeros (e.g., 4005 - 1268)
  5. 5-digit numbers with multiple chained decompositions

Common mistakes

  • Subtracting the top number from the bottom number when top digit is smaller
  • Failing to reduce the lending digit by 1 when decomposing across a zero

Curriculum links

Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M3N02 Add and subtract two- and three-digit numbers using mental and written strategies.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Vertical Subtraction Algorithm

Year 3 maths

Qs
6
Marks
6
NameDateScore / 6
1.
793 − 648 =
[1]
2.
884 − 521 =
[1]
3.
863 − 461 =
[1]
4.
631 − 457 =
[1]
5.
722 − 342 =
[1]
6.
308 − 241 =
[1]

Answer key

  1. 145Subtract column by column, exchanging when the top digit is smaller; 793 − 648 = 145
  2. 363Subtract column by column, exchanging when the top digit is smaller; 884 − 521 = 363
  3. 402Subtract column by column, exchanging when the top digit is smaller; 863 − 461 = 402
  4. 174Subtract column by column, exchanging when the top digit is smaller; 631 − 457 = 174
  5. 380Subtract column by column, exchanging when the top digit is smaller; 722 − 342 = 380
  6. 67Subtract column by column, exchanging when the top digit is smaller; 308 − 241 = 67