Multiplying Multiples of 10

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National Curriculum Links

• Mathematics Key Stage 2 – Year 4:
  • Number – multiplication and division:
    • Recall multiplication and division facts for multiplication tables up to 12 × 12
    • Use known multiplication facts to derive other multiplication facts, including multiplying by 10 and 100 (NC programme of study)
  • Multiplication and division:
    • Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit

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Learning Objectives

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

• Use known multiplication facts to multiply multiples of 10 confidently.
• Apply their knowledge of multiplication tables to calculate products involving multiples of 10.
• Explain their reasoning for how they multiply multiples of 10 using known facts.

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Success Criteria

• I can recall my known multiplication facts up to 12 × 12.
• I can use known multiplication facts to multiply numbers like 20, 30, and 40 by other single-digit numbers.
• I can explain how I use a multiplication fact I know to solve a problem with multiples of 10.
• I can check my answers by reasoning about place value and factors.

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Resources Needed

• Whiteboards and pens
• Mini multiplication fact cards (1–12 times table)
• Timer or stopwatch
• Visual place value grids (optional)
• Exercise books

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Lesson Structure: 30 Minutes

1. Introduction & Engagement (7 minutes)

Engagement Activity:

• Start with a quick “Flash Multiplication” game: Show multiplication facts (e.g., 3 × 4, 6 × 7) on the board for 5 seconds each and ask pupils to shout out answers.
• Then present a problem: "If 3 × 4 = 12, what is 30 × 4? How can I work that out quickly without doing the whole multiplication again?"
• Discuss initial ideas and list pupils' responses.

Targeted Questioning:

• “Can someone explain how we might use 3 × 4 = 12 to find 30 × 4?”
• “Why do you think multiplying by 30 is the same or different from multiplying by 3?”
• “How does knowing 3 × 4 help with 30 × 4?”

Purpose: Activate prior knowledge and get children thinking about how to extend known facts to multiples of 10.

Common Misconceptions to Address Early:

• Misunderstanding that 30 × 4 is just ‘30 plus 4’ or ‘30 + 3 × 4’.
• Not appreciating the role of place value (multiplying by 10) in scaling facts.

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2. Modelling and Explanation (8 minutes)

Step 1: Demonstrate Using Known Fact
Write on the board:

• Known fact: 3 × 4 = 12
• To find 30 × 4, multiply 3 × 4 = 12, then multiply the answer by 10 → 12 × 10 = 120

Explain aloud:

• “We used a fact we already knew, then thought about what multiplying by 30 means — it’s like multiplying by 3 and then by 10.”

Prove-It / Reasoning Question:
Display on board:

• “Why does 30 × 4 equal 120? Explain your thinking.”
• Sentence stems for pupils to use:
  • “I know 3 × 4 is ___ so…”
  • “When we multiply by 10, it means we…”
    Use a timer (1 minute) and ask pupils to say their answers out loud with a partner before writing.

AfL Point: Listen carefully during verbal explanations and note misconceptions about place value or steps skipped.

Step 2: Model Another Example

• Known: 7 × 5 = 35
• Calculate 70 × 5 by doing 7 × 5 = 35, then 35 × 10 = 350.
  Explain actively, encouraging pupils to answer questions orally:
• “What do you notice about the ‘0’ in 70?”
• “How does place value help us?”

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3. Guided Practice (8 minutes)

Activity: Pupils work in pairs with mini whiteboards to try these:

• 4 × 6 = ? Find 40 × 6
• 8 × 9 = ? Find 80 × 9
• 5 × 7 = ? Find 50 × 7

Layered Questions:

• “Explain why 40 × 6 is ten times bigger than 4 × 6.”
• “What would happen if we multiplied 4 × 6 and then forgot to multiply by 10? What answer would we get? Why is that incorrect?”
• “Can we multiply 40 × 6 directly without splitting? How might that look?”

AfL:

• Circulate to observe reasoning and conceptual understanding.
• Stop to ask pupils to explain their thinking aloud to check for place value understanding before correcting errors.

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4. Independent Task with Increasing Complexity (5 minutes)

Task: Children complete in exercise books:

1. Start with simple:

   • Known fact: 2 × 7 = 14
   • Find 20 × 7 (show working)

2. Add complexity:

   • 30 × 6 = ?
   • 50 × 8 = ?

3. Apply reasoning in a word problem:

   • “A toy costs £40. If you buy 9 toys, how much will it cost? Explain how you worked this out using multiplication facts you know.”

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5. Plenary (2 minutes)

Whole Class Discussion:

• Ask: “Who can explain how you use a known fact to multiply multiples of 10?”
• One or two volunteers to share their sentence using stems like:
  • “I used ___ times ___ which is ___, then I multiplied by 10 to get ___.”

Reflect on success criteria:

• Check all criteria met by asking yes/no and short explanations for each.

Final Question to Extend Thinking:

• “How is multiplying by 10 different from multiplying by 100? Could we use a similar method?”

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Additional Teacher Notes

Common Misconceptions & Difficulties

• Confusing adding zero to a number with multiplying it by 10 (e.g., thinking 30 × 4 = 30 + 4).
• Forgetting to multiply the product by 10 after doing the base fact (i.e., stopping at 3 × 4 = 12).
• Not seeing 30 as 3 × 10 and thus missing the place value step.

Bloom’s Taxonomy Targeted Questions Examples

• Remembering: What is 7 × 5?
• Understanding: Why do we multiply by 10 when we multiply 70 × 5?
• Applying: Can you use your known facts to find 60 × 8?
• Analysing: What is the difference between multiplying 6 × 4 and 60 × 4?
• Evaluating: Why is it important to think about place value when multiplying multiples of 10?
• Creating: Can you explain another way to work out 40 × 7 without multiplying by 10 separately?

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Alignment with White Rose Maths Scheme

• This lesson fits into the Year 4 "Multiplication and Division" block, specifically focusing on applying known times tables to larger multiples, consolidating understanding of place value in multiplication.
• Use White Rose resources that reinforce multiplication facts and extend to multiplying multiples of 10 by a single digit, promoting reasoning as stressed here.

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Example to Copy into Books

Known Fact	Step 1: Multiply Base Numbers	Step 2: Multiply by 10	Final Answer
3 × 4 = 12	3 × 4 = 12	12 × 10 = 120	30 × 4 = 120

Written explanation to model:
“I know 3 × 4 = 12 from my times tables. Since 30 is 3 multiplied by 10, I multiply 12 by 10 to get 120. So, 30 × 4 equals 120.”

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This plan will maximise engagement, check for deep understanding beyond recall, and scaffold learning for pupils to confidently multiply multiples of 10 using known facts.