Checking with Inverse

National Curriculum Reference

This lesson links to the following Programme of Study for Mathematics, Key Stage 2 (Year 4):

• Number – Addition and Subtraction: Use inverse operations to check answers to calculations, and solve missing number problems.
• Key objective: Pupils should be able to use inverse operations to check calculations (DfE 2013, National Curriculum in England).

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Lesson Overview

Duration: 60 minutes
Class Size: 1 student
Subject: Mathematics
Year: 4 / Age 8-9
Focus: Checking answers using inverse calculations (addition-subtraction, multiplication-division)
Teaching style considerations: Functional Skills approach - practical, clear, step-by-step, supporting conceptual understanding

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Learning Objectives (WALT)

WALT: Use the inverse operation to check answers and solve missing number problems confidently.

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Success Criteria

By the end of this lesson, the student will be able to:

• Explain what the inverse operation is for addition, subtraction, multiplication, and division.
• Use inverse operations to check the accuracy of given calculations.
• Apply inverse calculations to solve simple missing number problems.
• Identify and correct errors in their work using inverse checking.

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Resources

• Whiteboard and marker
• Printed worksheets with calculations and missing number problems
• Number cards (0-20) for hands-on activities
• Visual aids showing inverse operation pairs
• Dry-wipe mini boards and pens for quick working out
• Access to a simple calculator (optional for checking)

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Lesson Structure

1. Starter Activity (10 minutes)

Aim: Refresh the idea of inverse operations and prior knowledge.

• Begin with quick fire oral questions: What is 8 + 5? What is the inverse of addition?
• Use number cards to demonstrate: “If I add 5 to 8, to check the answer, I can do...”
• Introduce simple paired operations: addition-subtraction, multiplication-division.
• Show visually the inverse pairs with examples on the whiteboard.

Teacher tip: Encourage the student to verbalise reasoning aloud to check conceptual understanding.

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2. Main Teaching / Guided Practice (20 minutes)

Aim: Model the checking process using inverse operations.

• Write a question on the board, e.g., 34 + 29 = 63. Ask: “How can we check this?”
• Demonstrate subtraction 63 – 29 = 34 as the inverse to check addition.
• Emphasise the two-step process: Calculate → Check with inverse.
• Repeat for multiplication-division: e.g., 7 × 6 = 42 → check with 42 ÷ 6 = 7.
• Provide the student with prepared questions to try on their mini board, encouraging spoken reasoning.
• Introduce missing number problems using inverse operations, e.g., _ + 15 = 47, find _.

Differentiation:

• For support: Use smaller numbers and physical counters or number lines.
• For challenge: Use larger numbers or problems involving two-step calculations (e.g., 48 ÷ _ = 6; find missing number).

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3. Independent / Practice Activity (15 minutes)

Aim: Apply learning independently with teacher monitoring and targeted feedback.

• Give the student a worksheet with mixed problems including:
  • Calculations to check using inverses.
  • Missing number problems requiring inverse operations.
  • Deliberate ‘wrong’ calculations to identify and correct by inverse checking.
• Encourage use of mini whiteboards for showing working.
• Use questioning to encourage explanation of methods and checks.

Extension for advanced learner:

• Introduce inverse operations with fractions or decimals (if appropriate).
• Solve multi-step problems needing multiple inverse checks.

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4. Plenary / Review (10 minutes)

Aim: Consolidate learning and reflect on strategies.

• Discuss: Why is checking with inverse calculations useful?
• Encourage the student to explain the steps to check an answer confidently.
• Ask the student to create their own calculation, solve it, and then demonstrate the checking process using inverse.
• Provide positive feedback and note any areas needing further support in planning next steps.

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Differentiation Strategies

• Use concrete manipulatives (counters, number cards) for conceptual support.
• Provide sentence starters to scaffold explanations ("I know this is correct because…").
• Adjust number size and complexity according to learner’s ability.
• Offer visual aids for learners who benefit from visual supports.
• Simplify steps or provide more worked examples if needed.

Extension Activities / Homework

• Create a "Math Detective" worksheet: The student is given “mistake riddles” where calculations don’t add up—tasked with finding the error using inverse checking.
• Challenge to write their own inverse check problems to quiz someone else (family, friend).
• Explore inverse checking in everyday contexts, e.g., checking change when shopping, recording their findings in a short journal entry.

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Assessment & Feedback

• Informal assessment through observation of working methods and explanations during activities.
• Mark worksheet for accuracy; note if inverse checking steps were explicitly used.
• Use plenary discussions to assess deeper understanding of purpose and method.
• Provide constructive feedback targeting accuracy and explanation clarity.

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Reflection points for teacher

• How well did the student grasp the concept of inverse as a checking method?
• Did the student explain their reasoning aloud? Support verbalisation more next session if needed.
• Was differentiation sufficient to keep engagement and reduce frustration?
• Plan follow-up incorporating real-life problem-solving applying inverse calculations.

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This detailed, interactive lesson plan follows the National Curriculum requirements, focusing on embedding understanding of inverse operations to check answers, with functional and conceptual skill development suitable for Year 4 learners and aligned with entry level Maths skills development.