Adding with Regrouping

Overview

This 30-minute lesson is designed for Year 4 students (ages 8-9) to develop a clear understanding of addition with regrouping using the CPA (Concrete, Pictorial, Abstract) approach. The lesson aligns with the National Curriculum for England: Key Stage 2 Mathematics Programme of Study, specifically focusing on addition and subtraction (Number - Addition and Subtraction, Year 4).

National Curriculum Reference:

• Mathematics – Number – Addition and Subtraction
  • Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate.
• Mathematics – Number – Number and Place Value
  • Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones).

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Learning Objectives

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

• Understand and explain the concept of regrouping (carrying) when adding two-digit and three-digit numbers.
• Use concrete materials to physically regroup ones and tens.
• Represent addition problems pictorially with place value charts and base-10 blocks.
• Solve arithmetic addition problems involving regrouping using the formal columnar method accurately.
• Demonstrate confidence in addition with regrouping through independent work.

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Resources

• Base-10 blocks (ones, tens, hundreds) – physical manipulatives
• Place value charts (laminated or whiteboard versions)
• Mini whiteboards and pens for students
• Prepared arithmetic questions on worksheet (in columnar format and word problems)
• Visual aids/posters illustrating steps of regrouping
• Timer or stopwatch
• Visualiser or interactive whiteboard for modelling

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Lesson Structure

1. Starter Activity (5 minutes)

Objective: Activate prior knowledge on place value and simple addition without regrouping.

• Recap place value using a quick flash activity: Teacher shows numbers, and students shout out digit values.
• Mental arithmetic warm-up: Add two 2-digit numbers without regrouping (e.g., 24 + 35).
• Emphasise the role of ones and tens before moving to regrouping.

2. Concrete Stage (7 minutes)

Objective: Introduce regrouping physically using manipulatives.

• Present an addition problem requiring regrouping (e.g., 48 + 36).
• Pupils use base-10 blocks to represent each addend separately on their place value charts.
• Demonstrate adding ones first: combine ones blocks and exchange ten ones for one ten block.
• Add tens blocks, including the newly regrouped ten.
• Encourage pupils to verbalise the regrouping process explicitly: “10 ones become 1 ten”.

3. Pictorial Stage (7 minutes)

Objective: Translate concrete understanding into drawings and place value charts.

• Show the same addition problem represented with pictorial place value charts (drawn tens and ones).
• Model how to record the exchange of ten ones for one ten on the diagram.
• Pupils draw their own diagrams for a new addition problem requiring regrouping (e.g., 57 + 29).
• Check and praise accurate depiction of regrouping.

4. Abstract Stage (7 minutes)

Objective: Transition to formal columnar addition with regrouping.

• Model the column addition method on the whiteboard using the same problem (e.g., 57 + 29).
• Emphasise writing numbers in columns correctly and carrying digits above the next column.
• Use stepwise verbalisation: “Add the ones first, it’s more than 10, so we write 6 and carry 1 to the tens.”
• Pupils complete 3 similar columnar addition questions independently on mini whiteboards (e.g., 64 + 28, 73 + 19, 82 + 49).

5. Plenary – Assessment and Reflection (4 minutes)

Objective: Consolidate learning, check understanding, and encourage self-reflection.

• Random selection of pupils to explain the regrouping process using a number they solved.
• Quick quiz with show of hands or thumbs up/down: “Do you understand how to carry numbers in addition?”
• Final question on worksheet: Solve 85 + 37 using column addition with regrouping. Collect for formative assessment.
• Exit prompt: On a mini whiteboard, write one thing you found easy and one thing you found tricky about regrouping.

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Differentiation

• Support: Provide additional base-10 blocks for tactile learning. Work alongside the pupil during pictorial tasks.
• Challenge: Introduce three-digit addition with regrouping or two-step word problems involving regrouping. Encourage use of mental strategies once confident.

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Assessment Opportunities

• Observation during concrete and pictorial activities to check conceptual understanding.
• Review mini whiteboard answers for immediate feedback during abstract stage.
• Mark final independent worksheet adding with regrouping to assess procedural fluency.

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Cross-Curricular Links

• English: Use of precise mathematical language (ones, tens, carry, regroup).
• PSHE: Encourage sharing and explaining ideas in a clear manner during partner work.

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Notes for Teachers

• Emphasise the CPA approach fully; do not rush abstract calculations.
• Use positive reinforcement as students verbalise regrouping steps.
• Encourage students who grasp the concept quickly to peer tutor others.
• Consider using a visualiser to show clear examples of manipulatives and drawings to all students.
• Engage students with questions throughout to keep lesson interactive.

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This structured approach will support Year 4 pupils to gain confidence and fluency in addition with regrouping, meeting the expectations of the National Curriculum for key arithmetic skills.