Multiplying by 10 & 100

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National Curriculum Links

• Mathematics Key Stage 2 (Year 4)
• Number - Multiplication and Division
  • Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 10 and 100 (DfE, 2013, NC 2014)
• White Rose Maths Scheme - Summer Term, Block 1
  • Multiply by 10 and 100 using place value understanding and known multiplication facts.

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Learning Objectives

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

• Use known multiplication facts to solve problems involving multiplication by 10 and 100.
• Recognise and explain patterns and place value shifts when multiplying numbers by 10 and 100.
• Apply understanding of multiplication facts to mentally and confidently multiply larger numbers by 10 and 100.

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Success Criteria

I can:

• Recall my multiplication facts quickly and accurately.
• Explain how multiplying by 10 or 100 affects the digits in a number.
• Use my multiplication facts to multiply numbers by 10 and 100 without using a written method.
• Justify my answers by explaining the place value shift that happens in multiplication by 10 and 100.
• Solve problems involving multiplication by 10 and 100 independently and with a partner.

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Resources

• Whiteboard and marker
• Place value charts (on worksheet or projected)
• Mini whiteboards and pens (for AfL)
• Multiplication fact flashcards (x2, x3, x4, x5, x6, x7, x8, x9)
• Example worksheet for children to copy
• Visual aids: arrow cards showing place value shifts
• Timer (for quick mental recall exercises)

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Lesson Structure (60 minutes)

1. Introduction (10 minutes)

Engage and Activate Prior Knowledge:

• Begin with a quick mental multiplication fact recall warm-up using flashcards (e.g., 3x4, 6x7, 9x5).
• Ask pupils to explain the strategy they used to find answers quickly (e.g., doubling, known tables).

Hook: “Magic Shift” Game

• Show the number 4 on the board.
• Ask: “What happens if I multiply 4 by 10? What do you notice?” (Answer 40)
• Show 4 x 100. Ask the same question (Answer 400)
• Introduce the idea of “multiplying by magic shifts the digits to the left.”
• Write 4, 40, and 400, circling the place value digits to highlight the shift.

Questions to deepen thinking:

• Why do you think the zeroes appear when you multiply by 10 or 100?
• If I multiply 37 by 10, where does the 7 go? What about the 3?
• Can everyone explain what’s happening to the place value?

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2. Teaching & Modelling (20 minutes)

Step 1: Using Known Multiplication Facts

• Model multiplying 7 by 10:

  • First remind pupils: What is 7 x 1? (7 – a known fact)
  • Then explain: "Multiplying by 10 is like multiplying by 1, but then moving everything to the left by one place value."

• Draw this on the place value chart: Units → Tens.

• Model 7 x 100: similarly, move two places to the left.

Step 2: Multiplying 2-digit numbers by 10 and 100

• Example: 24 x 10

• Use the known fact 2 x 10 = 20 (confirm with pupils)

• Break 24 into 20 and 4, multiply each by 10:

  • 20 x 10 = 200
  • 4 x 10 = 40
  • Add: 200 + 40 = 240

• Write the calculation and the place value reasoning clearly for children to copy.

Step 3: Use the example below (to copy in books):

Example: 36 x 10

- Break it down: 30 (3 tens) and 6 (units)
- 30 x 10 = 300 (3 hundreds)  
- 6 x 10 = 60 (6 tens)  
- Add them together: 300 + 60 = 360

Targeted whole-class questioning (Bloom’s Taxonomy inspired):

• Remembering: What does 7 x 10 equal? Why?
• Understanding: Can you explain why multiplying by 10 moves the digits one place to the left?
• Applying: If 8 x 10 = 80, what is 8 x 100? Can you explain your reasoning?
• Analysing: What pattern do you see when multiplying by 10 vs. 100?
• Evaluating: Is it easier to multiply 24 x 10 by breaking the number into tens and units or using place value shift? Why?
• Creating: Can you create a real-life problem where you would need to multiply a number by 100? How would you solve it?

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3. Guided Practice (15 minutes)

• Pupils will work with a partner using mini whiteboards to answer questions:

  1. 45 x 10 = ? (Explain your thinking.)
  2. 53 x 100 = ? (Explain your thinking.)
  3. Work out 67 x 10, then 67 x 100.

• Circulate and listen to pupil explanations to assess understanding.

AfL Opportunity #1:

• Use mini whiteboards to check pupils' understanding of place value shifts quickly (write answers & reasoning).
• Ask selected pupils to explain aloud their reasoning to whole class.

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4. Independent Activity (10 minutes)

• Pupils will complete a worksheet with varied questions based on multiplying two-digit numbers by 10 and 100 using known facts and place-value knowledge:
  • E.g., 29 x 10, 41 x 100, 58 x 10, etc.
  • One extension question where pupils justify their method in writing:
    “Explain how you multiplied 36 by 100.”

AfL Opportunity #2:

• Teacher collects a few written responses during activity to review explanations and identify misconceptions.

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5. Common Misconceptions & Addressing Them

• Misconception 1: Pupils think multiplying by 10 means adding zero in any place, not understanding the shift in place value (e.g., thinking 36 x 10 = 3600).

  • Address by modelling place value explicitly and drawing charts to show digit movements.

• Misconception 2: Pupils try to multiply the digits separately without considering place value (e.g., multiplying 3 x 10 and 6 x 10 without combining correctly).

  • Use guided practice emphasising regrouping and addition of partial products.

• Misconception 3: Confusing multiplication by 10 and multiplication by 1 scaled by 10 (e.g., thinking 67 x 10 = 67 + 10).

  • Focus on explanation and reasoning questions to highlight difference.

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6. Plenary (5 minutes)

Exit Ticket Activity: “Explain Your Thinking”

• On a mini whiteboard, pupils write either:

  • A multiplication fact x 10 or x 100, AND
  • A sentence explaining what happens to the digits when multiplying by 10 or 100.

• Ask 3 volunteers to share and justify their explanations.

Recap key learning:

• “What do we need to remember when multiplying by 10 and 100?”
• “How does understanding multiplication facts help with bigger calculations?”

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Additional Teaching Tips

• Use manipulatives (place value counters, arrow cards) to show digit shifts visually, especially for pupils who struggle.
• Pair stronger pupils with others to verbalise their reasoning to increase engagement and peer learning.
• Encourage precise mathematical language: "place value," "shift digits," "multiply," "units, tens, hundreds."

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Summary

This lesson carefully scaffolds multiplication by 10 and 100 through known multiplication facts and place value understanding, following National Curriculum expectations. It blends interactive questioning and carefully targeted AFL to address misconceptions while encouraging deeper reasoning and explanation aligned with Bloom's taxonomy.

By regularly modelling, eliciting explanations, and visually demonstrating, pupils gain confidence and fluency multiplying larger numbers efficiently and with strong conceptual understanding.