Column Addition Mastery

Overview

This 40-minute lesson introduces Year 3 pupils to column addition involving exchanges in the tens column. The lesson aligns with the National Curriculum for England, Year 3 Mathematics programme of study: number – addition and subtraction, focusing on using formal written methods for addition of numbers up to three digits.

National Curriculum Links

• Year 3 Mathematics – Number: Addition and Subtraction
  Pupils should be taught to:
  • Add numbers mentally, including: a three-digit number and ones; a three-digit number and tens; a three-digit number and hundreds.
  • Add numbers with up to three digits, using formal written methods of columnar addition.

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Learning Objectives

By the end of the lesson, pupils will:

• Understand how to add two 2- or 3-digit numbers using column addition with exchanging (carrying) in the tens column.
• Be able to represent their addition in columns systematically, correctly placing units, tens, and hundreds.
• Explain the process of ‘exchanging’ or ‘carrying’ when the sum of a column exceeds 9, specifically focusing on tens.
• Develop fluency and confidence through guided and independent practice.

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Resources Needed

• Whiteboard and markers
• Base-10 materials (Dienes) or place value counters
• Individual whiteboards and pens for pupils
• Prepared addition problems that require exchanging in the tens column
• Visual place value chart displayed clearly in the classroom
• “I do, We do, You do” flashcards for signalling phase transitions

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Lesson Structure

1. Introduction and Starter – 5 minutes

Objective: Activate prior knowledge of place value and addition.

• Begin by reviewing place value (units, tens, and hundreds) using base-10 materials or place value counters projected or physically presented.
• Ask targeted questions to assess and refresh pupils’ understanding, for example:
  • "If I have 14, how many tens and ones are there?"
  • "What happens when we add 7 ones and 5 ones?" (Lead to highlighting exchange when sum >9.)
• Introduce the concept of column addition, emphasising the importance of lining up digits by place value.

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2. Modelling: I Do – 10 minutes

Objective: Demonstrate column addition with exchanging in tens.

• Write a problem on the board involving numbers that require exchanging in the tens column (e.g., 46 + 27).
• Using a place value chart and base-10 materials, illustrate the addition step-by-step:
  • Add the ones column: 6 + 7 = 13. Explain that 13 is more than 9, so you must exchange 10 ones for 1 ten. Show physically exchanging base-10 pieces or annotate the place value chart.
  • Place 3 in the ones column and carry 1 to the tens column (writing a small ‘1’ above the tens column).
  • Add the tens column: 4 + 2 + 1 (the carried over) = 7.
  • Write the answer (73).
• Talk aloud throughout, modelling mathematical language: "We add… we get more than 9, so we exchange… then add the tens including our exchange."
• Use think-aloud questioning to model reasoning:
  • "Why do I carry 1 here?"
  • "What does this small ‘1’ mean above the next column?"

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3. Guided Practice: We Do – 12 minutes

Objective: Practice column addition together with teacher support.

• Present a second example on the board (e.g., 58 + 36).
• Invite pupils to suggest each step before doing it on the board: "What do we add first?" "What do we get?" "Do we need to carry?"
• Use pupil whiteboards where pairs can write the problem and show their working.
• Circulate, listen to discussions, and ask probing questions:
  • "How did you decide what to carry?"
  • "Can you explain why the tens column changed after carrying?"
• After completing the problem, ask several follow-up questions:
  • “What do you find tricky about exchanging?”
  • “What would happen if we didn’t carry the extra ten?”

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4. Independent Practice: You Do – 10 minutes

Objective: Pupils complete column addition problems independently.

• Distribute a worksheet or pose 3-4 increasingly challenging column addition problems requiring exchanging in the tens column (e.g. 67 + 45, 85 + 29, 74 + 38).
• Pupils work individually on their whiteboards or books.
• Teacher circulates, offering prompts or re-explaining exchanging if necessary.
• Encourage pupils to verbalise their reasoning aloud to a partner or the teacher.

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5. Plenary and Assessment – 3 minutes

Objective: Consolidate learning and assess understanding.

• Use mini-whiteboards for a quick quiz: write two short column additions that require exchanging (e.g., 54 + 28), ask pupils to show their answers simultaneously.

• Ask a few pupils to explain their working to the class or to you individually, focusing on their understanding of exchanging.

• Summarise key learning points:

  • “When the ones add to more than 9, what do we do?”
  • “Why is it important to carry correctly?”

• Note any pupils who struggled for targeted follow-up or intervention.

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Teacher’s Tips for Differentiation and Extension

• For less confident learners: Use more concrete manipulatives throughout; limit numbers to two digits before gradually increasing.
• For rapid graspers: Challenge them with three-digit numbers requiring exchange both in the tens and hundreds columns and reason about why the place value system works.
• Ask extension questions such as, “If this sum of the ones column was 19, what would you do?” to deepen conceptual understanding.

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Success Criteria

• Pupils correctly line digits up according to place value.
• Pupils accurately add the ones column and carry over when sum >9.
• Pupils add the tens column including any carried value.
• Pupils explain the process of exchanging confidently using precise mathematical vocabulary.

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Educational Value

This lesson scaffolds new conceptual understanding by combining concrete resources, visual representation, and gradual release of responsibility (I do, we do, you do). This promotes deep comprehension and prepares pupils for more complex addition involving hundreds and beyond, solidifying a key aspect of the formal written methods expected at Year 3 within the National Curriculum.