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Maths

Written Subtraction with 3-Digit Numbers

Overview

Students learn the column subtraction method systematically, managing borrowing across columns and developing a strategy for checking answers.

Learning Objective
Students use column subtraction to subtract 3-digit numbers, including examples requiring borrowing (regrouping) from the tens and hundreds columns.

Resources needed

  • Squared paper or mini whiteboards
  • Base-ten blocks (optional)
  • Place value chart

Lesson stages

0 / 7 done
  1. 1 Subtract multiples of 10 and 100 mentally: 350−20, 470−100, 800−300. Students write answers on whiteboards. 'Today we extend this to column subtraction with any 3-digit numbers.'
  2. 2 Model 576−342: ones (6−2=4), tens (7−4=3), hundreds (5−3=2). Answer: 234. Students practise three similar examples, working from right to left.
  3. 3 Model 543−278. Ones: 3−8 — 'I can't do this without going negative!' Exchange one ten for ten ones: tens column goes from 4 to 3, ones go from 3 to 13. Now 13−8=5. Continue: 3−7 in tens... need to borrow again.
  4. 4 Continue 543−278. Tens: 3−7 — borrow from hundreds: hundreds 5→4, tens 3→13. 13−7=6. Hundreds: 4−2=2. Answer: 265. Students verify using addition: 265+278=543 ✓.
  5. 5 Students work through four examples with borrowing, showing all borrowed digits clearly. Teacher circulates. Key prompt: 'Always start in the ones. If you can't subtract, borrow from the next column.'
  6. 6 Emphasise the inverse check: if 724−358=366, verify: 366+358=724. Subtraction and addition are inverses — always check this way. Students check all their work.
  7. 7 A library has 825 books. 367 are borrowed. How many are left? Students set out and solve as column subtraction. 'What does the answer tell us?'

Tap a step to mark it as done.

Variations

  • Extend to 4-digit subtraction
  • Include money contexts (£5.25 − £2.78)
  • Subtract from multiples of 100 (500 − 263 — requires borrowing from a zero)
More information

Use consistent language: 'exchange one ten for ten ones' (not 'borrow'). Annotate each step: 'I cannot take 8 from 3, so I exchange.'

Use base-ten blocks to physically show the exchange. Provide a worked example with annotations for reference. Focus on one level of borrowing before two.

Are borrowed digits crossed out and corrected neatly? Do students always start in the ones column? Do they check their answer by addition?

Work on plain paper with H, T, O columns drawn freehand. Base-ten blocks can be replaced by drawings.

Students may subtract the smaller digit from the larger regardless of position (e.g. doing 8−3 instead of 3−8). Reinforce: in 3−8 we cannot proceed — we must borrow.

Activity details
Primary Medium 35 minutes 5 minutes prep Solo, Pairs Indoor
Topics
Subtraction Written Methods Regrouping Place Value