Subtraction Techniques

Overview

In this lesson (Lesson 3 of 20), students strengthen mental subtraction by using place value partitioning and the inverse relationship between addition and subtraction. They learn to choose efficient strategies, then apply them to two- and three-digit numbers without a calculator.

Learning intentions

Students will:

• subtract two- and three-digit numbers by partitioning into place value parts and regrouping if needed
• use addition facts to support subtraction (addition and subtraction as inverse operations)
• explain their thinking using part-part-whole diagrams or written equations

Success criteria

Students can:

• partition both numbers and record subtraction by parts (tens, ones, and hundreds where needed)
• regroup when required and still arrive at the correct answer
• justify an answer by linking it to related addition facts or using “count back”/“find what makes…”
• choose a strategy (partitioning or related facts) that is efficient for the given numbers

Curriculum links

• Number: VC2M3N04 — add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup to assist calculations without a calculator
• Algebra: VC2M3A01 — recognise and explain the connection between addition and subtraction as inverse operations; apply to partition numbers and find unknown values in number sentences
• Algebra: VC2M3A02 — extend addition and subtraction facts to 20 and use them for efficient mental strategies with larger numbers

Lesson structure (60 minutes)

1. 0–5 min · Retrieval warm-up

• Teacher displays quick equations (e.g., 14 + 6 =?, 20 − 7 =?, 18 + 2 =?), including some that connect directly to subtraction facts.
• Students answer on mini-whiteboards and share one strategy (e.g., “I used a near fact” or “I counted on/back from a landmark”).

2. 5–15 min · Direct teach: partition subtraction

• Teacher models: 485 − 236 using place value partitioning.
• Action: “Partition the numbers first: 485 = 400 + 80 + 5 and 236 = 200 + 30 + 6. Subtract ones, tens, then hundreds, and regroup if the ones are too small.”
• Students watch a part-part-whole diagram, then complete a similar example together: 372 − 158 (teacher draws the framework; students contribute each part).

3. 15–25 min · Worked example with regrouping

• Teacher chooses a problem that requires regrouping (mental regroup, not paper algorithms), e.g. 402 − 168.
• Teacher prompts: “When ones/tens won’t subtract, what can we regroup from the next place value?” (e.g., make 2 ones into 12 ones by taking 1 ten).
• Students record the strategy steps using place value headings (Hundreds / Tens / Ones) and finish the calculation independently, then check by estimation (about 400 − 170 ≈ 230).

4. 25–40 min · Guided practice: inverse operations

• Teacher introduces a “make it true” structure:
• __ + 47 = 93 (students find the missing number, then connect it back to subtraction: 93 − 47 = __)
• Then mirrors the inverse: 93 − 47 = __ and students explain why it matches.
• Students work in pairs on 6 cards (mix of two- and three-digit versions). Each card requires:
• one subtraction equation
• one related addition fact explanation (“If 47 more makes 93, then subtracting 47 leaves what was added.”)

5. 40–52 min · Independent practice: choose the best strategy

• Teacher gives a short worksheet with three sections:
• A: Partition and subtract without regrouping (e.g., 523 − 241 where ones/tens work cleanly)
• B: Partition and subtract with regrouping (e.g., 610 − 389)
• C: Mental subtraction using near facts (e.g., 250 − 198 by adjusting from 200)
• Students choose a method for each question and must show at least one part-part-whole or place value step.

6. 52–57 min · Whole-class discussion

• Teacher selects 2–3 student strategies (one correct/efficient, one with a common error).
• Students discuss: “Which strategy was most efficient and why?” focusing on regrouping choices and inverse reasoning.

7. 57–60 min · Exit ticket

• Students complete two problems:
• 1) 536 − 248
• 2) __ + 36 = 74
• Students circle whether they used partitioning, inverse facts, or count-back.

Resources

• Mini-whiteboards and markers
• Part-part-whole diagram templates (ones/tens/hundreds)
• Place value cards (H, T, O) or base-ten blocks (optional)
• Student worksheet (3 sections: A/B/C)
• Set of “inverse operation” card prompts for pair work
• Teacher slide/board examples for worked modelling
• Exit ticket slips

Assessment

• Formative checks during warm-up: observe strategy language and accuracy on mini-whiteboards
• Guided practice: listen for inverse explanations (“addition undoes subtraction” / “subtraction undoes addition”) and correct partitioning/regrouping
• Exit ticket: confirm students can subtract accurately and provide an inverse connection for the unknown-value task

Differentiation

• Support:
• Provide sentence starters: “I partitioned…”, “I regrouped because…”, “It’s the inverse because…”
• Offer a structured graphic organiser with boxes for hundreds/tens/ones for regrouping steps
• Reduce the number of practice questions while keeping the same strategy target
• Extension:
• Include a challenge prompt on the worksheet: “Solve using two different strategies and compare: partitioning vs near facts/inverse facts.”
• English language support:
• Pre-teach key phrases: “partition”, “regroup”, “ones/tens/hundreds”, “inverse”
• Allow responses using diagrams and oral explanations first, then written notation
• SEN adjustments:
• Use colour-coding for place value (hundreds/tens/ones) and allow base-ten blocks for regrouping before removing them
• Provide a worked example checklist students can tick as they complete steps

Extension (optional)

Not included for this lesson.