Multiplying by 10

Learning Objectives

• Understand and demonstrate multiplication of 2-digit numbers by 10 using place value and concrete/pictorial representations.
• Use reasoning to explain the effect of multiplying by 10 on a two-digit number.
• Solve problems involving multiplication of 2-digit numbers by 10, applying mathematical language accurately.

National Curriculum Reference (England, Year 4):
Mathematics - Number - Multiplication and Division

• “Recall multiplication and division facts for multiplication tables up to 12 × 12.”
• “Recognise and use factor pairs and commutativity in mental calculations.”
• “Multiply two-digit and three-digit numbers by a one-digit number using formal written layout.”
  (This lesson focuses on the understanding foundation for multiplying by 10, a stepping-stone to formal written methods.)

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Success Criteria

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

• Write multiplication statements showing 2-digit numbers multiplied by 10.
• Explain orally and in writing that multiplying by 10 shifts the digits one place to the left, adding a zero at the end.
• Use place value charts or base-ten blocks drawings to represent multiplication by 10.
• Justify why multiplying by 10 increases the original number tenfold using their own reasoning.
• Solve progressively challenging problems by multiplying 2-digit numbers by 10, including real-life contexts.

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Resources

• White Rose Maths PowerPoint slides (Year 4, Summer Term, Block 1 - Multiplication and Division)
• Base-ten blocks (concrete resources)
• Place value charts printed for pairs
• Whiteboards and pens
• Books and pens for recording work
• Number cards (multiples of 10 and two-digit numbers)

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Lesson Structure (60 minutes)

1. Introduction & Engagement (10 minutes)

Hook:

• Start with a quick mental warm-up: “If I have 24 apples and I multiply that by 1, how many apples do I have? What if I multiply by 0? What happens if I multiply by 10?”
• Using base-ten blocks, demonstrate 24 as 2 tens and 4 ones. Ask students to predict and then observe what happens when you multiply 24 by 10 using blocks (introduce a “place value shift” concept: the 2 tens become 2 hundreds, the 4 ones become 4 tens).

Key Question:
“Why does the number become 240 when multiplying 24 by 10? What is actually happening to each digit?”

Engagement Techniques:

• Use ‘Think-Pair-Share’ to discuss these questions with peers before whole-class feedback.
• Show quick slide animation representing digits moving one place left.

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2. Modelling and Explanation (15 minutes)

• Model carefully on the board:
  Example: 36 × 10
  Write down:

  • Expand 36: (30 + 6) × 10
  • Multiply each part: 30 × 10 + 6 × 10 = 300 + 60 = 360

• Draw place value chart:
  Tens | Ones
  3 | 6
  Multiply by 10 → shift left

• Show an example to copy into books:

36 × 10 = (30 × 10) + (6 × 10)  
          = 300 + 60 = 360

• Use concrete then pictorial representations to solidify understanding.

Targeted Questions (with Bloom’s Taxonomy cognitive levels):

• Remembering: “What happens to the ones digit when multiplying by 10?”
• Understanding: “Can you explain in your own words why multiplying by 10 moves each digit one place value higher?”
• Applying: “If 47 × 10 = 470, what would 47 × 100 be? Explain your thinking.”
• Analysing: “If a number multiplied by 10 ends with zero, what could the original number’s digit in the ones place be and why?”
• Evaluating: “Which is bigger: 65 × 10 or 56 × 10? Why? Can you justify your answer with place value reasoning?”
• Creating: “Can you create your own problem where you multiply a 2-digit number by 10 and explain it to a friend?”

AfL:

• Use mini-whiteboards for pupils to write answers during questioning.
• Listen carefully to explanations, note misconceptions or hesitation.
• Ask individuals to explain the ‘why’ for moving digits to the left, correcting with example or scaffold where needed.

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3. Guided Practice - Gradually Increasing Complexity (20 minutes)

Task 1: Basic Practice (10 mins)

• Worksheet or book task: Multiply these by 10: 21, 54, 89, 70, 42
• Pupils draw place value diagrams or write expanded forms for at least 3 of these.
• Teacher circulates, supports, and poses reasoning questions: “Why does 54 × 10 = 540, not 54?” “What digit changed position?”

Task 2: Applying Skills to Problem Solving (10 mins)

• Word problems contextualised with multiplying by 10:

  • “A packet of 36 sweets is multiplied by 10 for a party. How many sweets are there in total? Explain how you arrived at your answer.”
  • “If you have 58 pencils, and a shop sells them in packs of ten times that number, how many pencils do you get?”

• Encourage pupils to draw place value charts or use expanded forms to support explanation.

• Ask students to read answers aloud and explain, fostering oral maths language development.

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4. Plenary & Reflection (10 minutes)

Activity:

• Use a “Multiplication by 10” quiz race on the whiteboard. Show 2-digit numbers and ask teams to multiply by 10 and justify reasoning aloud with place value explanations.

Flash Discussion:

• “What did you find easy about multiplying by 10?”
• “What was tricky for you and why?”
• “How can understanding place value help us with multiplying by other numbers like 100 or 1000?”

Exit Ticket:

• Pupils write down one thing they learned today and one question they still have.

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Common Misconceptions & Difficulties

• Pupils may think digits get ‘added on’ randomly when multiplied by 10 rather than understanding the place value shift.
• Confusing multiplication by 10 with addition of 10 (e.g., 36 + 10 = 46 instead of 360).
• Not recognising zeros as placeholders, leading to incorrect answers like 36 × 10 = 36.0 or 36 × 10 = 3600.
• Difficulty explaining reasoning using mathematical vocabulary around place value.
• Struggling to generalise the rule beyond simple examples or apply understanding to word problems.

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Notes for Teachers

• Circulate during tasks and encourage pupil talk; explanation is crucial for deep learning.
• Use real objects to embed concrete experience before moving to abstract calculations.
• Scaffold learning by modelling clear representations and expansions before asking pupils to work independently.
• Use questioning to probe thinking beyond surface answers and deepen understanding.
• Refer to White Rose Maths Year 4, Summer Term Block 1, Lesson on "Multiplying 2-digit numbers by 10" to maintain scheme alignment and pacing.

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This lesson plan will empower pupils to confidently multiply two-digit numbers by 10 with a clear conceptual understanding rooted in place value, setting the foundation for multiplication by larger numbers and for formal methods later in Year 4.