Mental Addition Strategies

Overview

Age Group: Years 6 & 7 (10-12 years)
Class Size: 25 students
Duration: 60 minutes
Curriculum Reference:

• National Curriculum for England (Mathematics, Key Stage 2)
• Number – Addition and Subtraction
• Pupils should be taught to:
  • Add and subtract whole numbers mentally, including:
    • Partitioning to break numbers into parts
    • Using number bonds and related facts
    • Employing efficient mental strategies such as compensation and bridging

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Learning Objectives

By the end of the lesson, pupils will be able to:

• Confidently use partitioning to add two-digit and three-digit numbers mentally.
• Understand and apply the mental addition strategies of compensation and bridging.
• Choose and explain the most efficient strategy to solve mental addition problems involving numbers up to 1000.
• Develop flexibility and fluency in mental calculation, supported by reasoning skills.

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Curriculum Links

• Develop fluency in addition and subtraction (NC Year 6 Units – Number: Addition & Subtraction).
• Apply knowledge of number bonds and mental methods to solve calculations mentally.
• Reason mathematically by explaining methods and mental steps clearly.

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Resources

• Whiteboard and markers
• Number cards or digit cards (0-9)
• Worksheets with targeted addition problems
• Mini-whiteboards or paper for individual work
• Visual aids for partitioning, compensation, and bridging (example diagrams)

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Lesson Breakdown

1. Starter / Recap: Partitioning (10 minutes)

Objective: Refresh pupils' understanding of partitioning numbers for mental addition.

• Begin with a quick oral activity: Say a 2-digit number (e.g., 47) and ask pupils to partition it verbally (40 + 7).
• Show a set of addition problems (e.g., 47 + 35). Model partitioning both numbers: (40 + 7) + (30 + 5).
• Ask pupils to solve the addition mentally using partitioning, then share answers.
• Reinforce that partitioning breaks numbers into manageable parts for easier mental addition.

Teaching tip: Use visual aids showing numbers split into tens and ones; this helps kinesthetic and visual learners.

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2. Introduction to Compensation (15 minutes)

Objective: Introduce compensation as adjusting one addend to make mental calculation easier.

• Define compensation: changing one number to a round number, then adjusting the answer.
  • Example: 49 + 36. Change 49 to 50 (+1), so calculate 50 + 36 = 86, then subtract 1 → 85.
• Model several examples with step-by-step ‘think aloud’ demonstrating the benefit.
• Use whiteboards: Pupils try 48 + 37 or 59 + 28 using compensation.
• Discuss how compensating makes adding easier by creating round numbers.

Teaching tip: Emphasise that "balancing" the change makes their calculation accurate – it’s like adding then taking away the same amount.

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3. Introduction to Bridging (15 minutes)

Objective: Teach pupils bridging through multiples of 10 to simplify addition.

• Explain bridging is “jumping” up to the nearest multiple of 10, then adding the remainder.
  • Example: 38 + 46. Bridge 38 up to 40 by adding 2; then add 40 and subtract 2:
    38 + 46 = (38 + 2) + (46 – 2) = 40 + 44 = 84.
• Demonstrate multiple examples on the board.
• Pupils practice bridging in pairs with prompts on mini-whiteboards.
• Highlight bridging’s usefulness for slightly tricky additions where one number is just under a multiple of 10.

Teaching tip: Use a number line for visual learners to see the “bridge” jump clearly.

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4. Consolidation Activity: Strategy Choice and Application (15 minutes)

Objective: Pupils decide which mental strategy to use and explain their thinking.

• Hand out differentiated worksheets:

  • Lower ability: Smaller numbers (two-digit only), guided prompts for which strategy to use.
  • Middle ability: Mixed two- and three-digit numbers, choose own strategy.
  • Higher ability: Larger numbers (up to 3 digits), explain reasoning for chosen strategy in writing.

• Pupils work individually, then share answers and reasoning in small groups.

• Circulate and give feedback — encourage pupils to verbalise their thought process.

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5. Plenary and Assessment (5 minutes)

• Quick fire quiz (oral or on mini-whiteboards) with 3 mental addition problems to be done using either compensation or bridging.

• Example questions:

  1. 67 + 29 (bridging)
  2. 54 + 39 (compensation)
  3. 85 + 16 (choose best strategy)

• Assessment notes: Observe pupils’ use of strategies and reasoning during group discussion and short quiz. Use teacher’s observation notes for informal assessment of understanding and fluency.

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Differentiation Guidance

Group	Support Strategies	Extension Ideas
Lower ability	Use two-digit numbers, guided scaffolding, visual partitioning aids, partner work	Challenge to explain why one strategy is easier than another
Middle ability	Use mixed two- and three-digit numbers, promote choice of strategy	Introduce adding near multiples of 100 using the same strategies
Higher ability	Encourage written explanations of reasoning, larger numbers, and mixed operations	Combine strategies for more complex problems (e.g., compensation + bridging)

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Teaching Tips and Tricks

• Relate strategies to real-life contexts (e.g., shopping, measuring) for engagement.
• Use lots of visual models: number lines, ten-frames, place value charts.
• Encourage pupils to talk through their methods verbally — language supports understanding.
• Praise strategy explanation, not just correct answers: reasoning is key in maths progression.
• Use paired and group work to build confidence and peer learning.

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This lesson plan promotes mental agility and confidence with addition, closely aligning with the National Curriculum statutory aims around fluency, reasoning, and problem-solving. It provides clear, simple steps and supports to allow every child to succeed and progress.