Overview

This 45-minute lesson is designed for Year 3 students and focuses on the commutative property of multiplication. It aligns with the National Curriculum for England for Maths on "Multiplication and division" (Key Stage 2). Students will investigate how multiplication order does not affect the product through interactive, concrete, and pictorial activities, progressing towards a deeper conceptual understanding.

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National Curriculum Links

• Mathematics Programme of Study, Key Stage 2, Year 3

  • Multiplication and Division
    • Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables (3.7a).
    • Write and calculate mathematical statements for multiplication using the multiplication tables they know, including for two-digit numbers times one-digit numbers (3.7b).
    • Understand the commutative property of multiplication, recognising that changing the order in multiplication does not change the product (informally introduced to prepare for formal properties).

• Mathematical Language and Reasoning

  • Use correct terminology such as "commutative", "product", and "factors".
  • Explain reasoning clearly with visual aids and sentence stems.

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Learning Objectives

By the end of the lesson, all students will:

• Describe the commutative property of multiplication in their own words.
• Demonstrate that changing the order of factors does not change the product using physical and pictorial representations.
• Solve multiplication problems applying the commutative property to simplify calculations.

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Resources

• Whiteboard and markers
• Counters or cubes (minimum of 10 sets of 20 for group activities)
• Printed worksheet with multiplication arrays and sentence stems
• Interactive mini-whiteboards and pens (for quick responses)
• Visual aids: multiplication arrays chart, commutative property anchor poster
• Timer for activities
• Sticky notes for exit tickets

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Lesson Structure

1. Starter (5 minutes)

• Engage: Show two simple multiplication calculations on the whiteboard: 3 × 4 and 4 × 3.
• Ask: "Do you think these are the same or different? Why?"
• Quick pair talk (1 min): Students discuss with partners.
• Share answers aloud and write "3 × 4 = 12" and "4 × 3 = 12" to demonstrate equality.
• Introduce the word commutative and explain it means the order doesn’t matter in multiplication.

2. Exploration & Guided Practice (15 minutes)

• Hands-on Activity - Array Building

  • Split class into groups of 3. Each group receives counters and an array grid.
  • Task: Build arrays for 2 × 5 and 5 × 2 using counters and observe the similarities/differences.
  • Students draw arrays on their worksheets, labelling rows and columns.
  • Teacher circulates, prompting questions like:
    • "How many counters in total?"
    • "What happens when we swap the rows and columns?"
  • Groups report back their findings using sentence stems:
    • "When we swap the numbers ______ and ______, the product stays ______."

• Visual Reinforcement

  • Display pre-made arrays on the whiteboard for 3 × 6 and 6 × 3.
  • Students write quick multiplication sentences on mini-whiteboards.

3. Independent Practice (15 minutes)

• Problem-solving worksheet
  • Students complete a worksheet with:
    • Matching multiplication sentences that illustrate the commutative property.
    • Completing arrays and filling missing numbers.
    • Word problems where they identify if statements use the commutative property correctly.
  • Encourage the use of drawings to support answers.

4. Plenary & Assessment (7 minutes)

• Class Discussion: Use exit question to recap –
  "Why does the order of numbers not change the answer in multiplication?"
• Use a ‘Think-Pair-Share’ structure, then invite 3-4 students to share.
• Exit Ticket: On sticky notes, students write a multiplication sentence that shows the commutative property and stick it on the board.
• Teacher quickly reviews for understanding and identifies any misconceptions.

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Differentiation

• Support:

  • Use smaller numbers or known tables (2s, 5s) for building arrays.
  • Provide a sentence starter sheet for verbal and written explanations.

• Challenge:

  • Extension problems with larger numbers or multiplying 2-digit by 1-digit numbers using commutative reasoning.
  • Explain how commutativity helps when estimating.

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Assessment for Learning

• Observations during group tasks to assess conceptual understanding of the commutative property.
• Worksheets reviewed for correct application.
• Exit ticket responses analysed for ability to verbalise and write multiplication statements showing commutativity.

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Reflection and Next Steps

• If most students grasp the concept, next lessons can introduce distributive property and repeated addition connections.
• For students needing reinforcement, revisit this property with visual arrays and include additional practice in multiplication tables.

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Teacher Tips to Wow Your Class

• Use large foam dice or cubes to build arrays dynamically for extra engagement.
• Create “Multiplication Swap” cards where students show pairs like 7 × 3 and 3 × 7, then physically swap to prove equality.
• Encourage students to create short multiplication story problems demonstrating commutativity (e.g., “3 groups of 4 apples” vs. “4 groups of 3 apples”).
• Celebrate “Wow Moments” when students connect new vocabulary with actions, making maths memorable.

This lesson will ignite curiosity about the flexibility of multiplication and prepare students confidently for more complex multiplication concepts later in the unit.