National Curriculum Links

Mathematics Programmes of Study (England) - Year 4 Number – Addition and Subtraction

• Add and subtract numbers mentally with increasingly large numbers.
• Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy.

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Learning Objectives

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

• Use efficient mental strategies to add numbers, including partitioning, bridging through 10 or 100, and compensating.
• Explain and justify their choice of mental addition strategy.
• Check their answers for reasonableness using rounding.

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Success Criteria

I can:

• Choose a mental addition method that helps me work out answers quickly.
• Partition numbers to add them mentally.
• Use bridging through 10 or 100 to make addition easier.
• Explain how I did my mental addition and why I chose that method.
• Check my answers using rounding to see if they are sensible.

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Resources

• Whiteboard/Interactive Whiteboard
• Number cards (0-100)
• Place value charts
• Mini whiteboards and pens for each pupil
• Example worksheet with addition questions focusing on mental methods

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Lesson Structure

1. Introduction (10 minutes)

Engagement Activity:

• Begin with a quick mental addition warm-up: “I say a number and then another number, and you have to shout out the answer as fast as you can.” Examples: 23 + 7; 46 + 14; 99 + 1.

Teacher Explanation:

• Explain that mental addition is about using strategies that help us add numbers quickly and accurately in our heads. Write the learning objectives and success criteria on the board.

Targeted Questions:

• “What do you find tricky about adding in your head?” (Remembering challenges)
• “If you had to add 48 + 27 quickly, how might you break the numbers apart to make it easier?” (Encourage partitioning)
• “Can anyone tell me what ‘bridging through 10’ means or why it might help?”

AfL check: Use pupils’ verbal responses to assess prior knowledge of strategies like partitioning or bridging through 10/100.

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2. Modelling (10 minutes)

Demonstration on Board:

• Write an example: 47 + 36
• Show how to partition each number: 40 + 7 and 30 + 6
• Add multiples of ten first: 40 + 30 = 70
• Add units next: 7 + 6 = 13
• Finally, add 70 + 13 = 83
• Label this method as “partitioning.”

Introduce Bridging Through 10:

• Example: 48 + 27
• Explain: 48 + 2 = 50 (bridge to 10)
• Then 50 + 25 = 75
• Emphasise the efficiency of this method.

Modelling Compensating:

• Example: 49 + 36
• Adjust 49 up by 1 to make 50, then subtract 1 from 36 (making 35)
• So, 50 + 35 = 85

Targeted Deep Thinking Questions (Whole Class):

• “Why might someone prefer to use bridging through 10 instead of partitioning?” (Evaluating strategies)
• “If you used compensating for 48 + 27, what would you add and subtract? Show how you worked it out.” (Application and explanation)
• “Can you think of a problem where rounding could help check if your answer is sensible?” (Applying knowledge)

AfL check: Pupils explain reasoning on mini whiteboards. Collect and review for misconceptions.

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3. Guided Practice (15 minutes)

Activity:

• Pupils work on a set of 6 addition questions, mixing numbers that prompt use of the three mental methods modelled. E.g.,

  1. 53 + 29
  2. 67 + 14
  3. 38 + 45
  4. 49 + 26
  5. 72 + 18
  6. 59 + 31

• Pupils write down the method they chose, show their calculation, and explain their reasoning briefly in writing (sentence or phrase).

Teacher Support:

• Circulate to ask probing questions:
  • “Can you explain why you added 7 first in this problem?”
  • “Is there another method you could use here? Why?”

AfL check: Check pupils’ written explanations; provide immediate feedback.

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4. Common Misconceptions / Difficulties

• Adding digits in the same place value without partitioning (e.g., adding 47 + 36 as 4+3 =7, 7+6=13, then 713 instead of 83)
• Forgetting to carry over when units add to more than 10 in mental addition
• Difficulty in understanding why bridging through 10 simplifies addition
• Mixing-up compensating strategy steps (forgetting to subtract after adjusting)
• Over-reliance on written methods rather than mental strategies and inability to explain mental thinking

Strategies to Address:

• Emphasise place value throughout all examples
• Use concrete examples with physical number cards to show bridging
• Model verbal explanations frequently and encourage pupils to verbalise thinking
• Highlight rounding as a tool to check if answers are reasonable

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5. Plenary (10 minutes)

Whole Class Discussion:

• Recap learning objectives and invite pupils to share which mental strategy they found most helpful and why.

Success Criteria Check:

• Pupils tick off from success criteria whether they can use each strategy and explain it.

Higher Order Questioning:

• “If you had 47 + 49, what mental method would you use and why? How does rounding help check your answer here?” (Analysing and applying)
• “Can you create your own addition problem for a friend that is easiest solved using bridging? Explain why.” (Creating and evaluating)

Exit Ticket (on mini whiteboards):

• Write one mental method you used today and explain one benefit it has.

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Example for Pupil Workbook

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Mental Addition using Partitioning
Example: 47 + 36

• Partition: 40 + 7 and 30 + 6
• Add tens: 40 + 30 = 70
• Add units: 7 + 6 = 13
• Add totals: 70 + 13 = 83

Mental Addition using Bridging Through 10
Example: 48 + 27

• Bridge 48 to 50 by adding 2
• Subtract 2 from 27 → 25
• Add: 50 + 25 = 75

Mental Addition using Compensating
Example: 49 + 36

• Change 49 to 50 (+1)
• Change 36 to 35 (-1)
• Add: 50 + 35 = 85

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Alignment with White Rose Maths Scheme

This lesson supports the Year 4 Number - Addition and Subtraction small step 'Add and subtract numbers mentally' and 'Add four-digit numbers using mental strategies' building fluency in mental addition strategies as per White Rose long-term planning.

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Notes for Teachers

• Encourage pupil talk and reasoning to deepen understanding.
• Use mini whiteboards liberally during AfL checks to adapt teaching instantly.
• Remind pupils that mental arithmetic is a skill that improves with practice and explanation.
• Challenge the class with reasoning questions rather than calculation alone to meet mastery demands.

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This plan aims to develop confident mental addition strategies in Year 4 pupils through engaging, conceptually rich approaches, fully aligned with England's National Curriculum and best practice from White Rose Maths.