Multiplying by 1

Overview

This 40-minute lesson is designed for Year 3 students, focusing on the concept of multiplication by 1. The lesson is mapped to the UK National Curriculum for Mathematics, specifically within "Number – Multiplication and Division" at the Lower Key Stage 2 level. By the end of the session, students will understand the principle that any number multiplied by 1 remains the same, develop reasoning behind this property, and apply it in real-world and mathematical contexts.

Learning Objectives

By the end of the lesson, students will:

• Recognise and explain the principle that multiplying a number by 1 leaves the number unchanged.
• Solve problems that involve multiplying by 1.
• Apply the concept through a variety of interactive, creative activities.

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Key Vocabulary

• Multiplication
• Factor
• Product
• Invariant (introducing through simple explanation as "something that doesn’t change")

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Resources Needed

1. Mini whiteboards and markers for each student.
2. A large, clear plastic bag and 1 object for a visual demonstration (e.g., a fruit, pencil).
3. Printed activity sheets (multiplication grids, dot arrays).
4. Rewards (stickers or certificates) for correct participation.

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Timing & Sequence

Introduction (5 minutes)

1. Hook: Begin by placing 1 object (e.g., a pencil or apple) into a transparent bag. Ask:

   • If we have 1 object and “multiply” it by 1 invisible bag, how many objects do we now have?
   • Encourage guesses and use this to hook curiosity.

2. Problem to Ponder: Write on the board:

   • If I have £1 and I “multiply” it by 1 friend, how much do I have altogether?
   • Make it relatable.

3. Present the key rule in child-friendly language: "When you multiply by 1, any number stays the same."

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Whole-Class Main Activity (15 minutes)

1. Guided Concept Activity (5 minutes):

   • Display concrete examples on the board:
     • 4 × 1 = 4
     • 10 × 1 = 10
     • 123 × 1 = 123
   • Illustrate through dot arrays—show the same number of dots being repeated (only once).
   • Break this into "I do, we do" examples to ensure comprehension.

2. Interactive Game – “Pass the Product” (10 minutes):

   • Arrange the students into groups of 8 and give each child a mini whiteboard and marker.
   • Each group receives 1 dice.
   • One child rolls the dice, writes the number down, and multiplies it by 1. The answer is passed to the next student to recheck before passing to the following student (like a relay).
   • First group to correctly finish their answers wins a small prize.

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Partner Work Activity (10 minutes)

1. Creative Problem Solving:

   • Each student is paired with a partner and given a printed worksheet with real-life word problems involving multiplying by 1. Example questions:
     • You have 1 £2 coin. How much money do you have if it’s multiplied by 1?
     • If 1 train passenger buys 1 ticket, how many tickets do they have altogether?
   • Allow pairs to discuss and solve together, with teachers prompting for reasoning and checking.

2. After 5-6 minutes, randomly select a couple of pairs to share their reasoning with the rest of the class.

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Plenary & Reflection (10 minutes)

1. Spot the Trick Question Game:

   • Prepare some “trick” questions on the board where multiplying by 1 isn’t obvious, e.g.,
     • If a battle has 1 knight, and they multiply their weapons by 1 sword each, how many swords in total?
     • 1 football team wins 5 matches. Multiply their wins by 1 referee. How many wins?

2. Discussion: Lead a short discussion guiding students to reflect on why multiplication by 1 works this way. Use terms like identity property of multiplication (in simple language).

3. Exit Activity:

   • Have each student write one number of their choice and multiply it by 1 on their mini-whiteboards.
   • Ask:
     • “What’s your answer?”
     • “Why didn’t it change?”
   • Students hold their boards up; reward creative numbers (e.g., large or decimal values) with stickers.

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Differentiation Strategies

• For Lower-Ability Students: Use concrete objects like counters to physically demonstrate multiplication by 1. Provide more one-on-one support during pair activities.
• For Higher-Ability Students: Challenge these students to write number sentences involving multiplication by 1 and another operation, e.g., (4 × 1) + 6 = ?. Encourage them to explore if the identity property holds true with more complex equations.

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Success Criteria

Students will demonstrate success by:

• Accurately completing “Pass the Product” and partner activities.
• Explaining the invariance of a number when multiplied by 1 in their own words.
• Correctly completing the exit activity with reasoning.

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Assessment

• Observe participation and understanding during the interactive and partner activities.
• Review the students’ written work (e.g., whiteboard answers and worksheets).
• Assess verbal responses during class discussions for confidence and clarity.

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Homework Extension

Ask students to write 3 of their own multiplication-by-1 word problems for a family member or guardian to solve. They should bring these questions back to school for use in the next maths session.

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This dynamic and interactive lesson plan leverages tangible objects, group games, creative partner work, and reflection to instil a deep understanding of multiplication by 1.