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National Curriculum Links

• Mathematics Program of Study, Year 4: Number - Fractions and Decimals

  • Understand and use place value to multiply and divide decimals by 10 and 100
    (Reference: NC maths – Number – decimals, Year 4)

• Statutory Requirements:

  • Use place value, known and derived facts to multiply and divide mentally, including dividing two-digit numbers by 10 and 100
  • Recognise the effect of dividing a number by 10 or 100 on the digits and the decimal point

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Learning Objectives

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

• Mentally divide 1 and 2-digit numbers by 10 and 100 using place value understanding.
• Explain how the digits and decimal point shift when dividing by 10 and 100.
• Apply mental division strategies to different contexts and justify their reasoning.

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Success Criteria

I can:

• Divide whole numbers and decimals by 10 and 100 in my head.
• Describe how the digits move and where the decimal point goes.
• Explain my thinking clearly using correct mathematical language.
• Solve problems involving dividing numbers by 10 and 100 with increasing difficulty.

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Resources

• Whiteboard and marker
• Number cards (1–99)
• Place value grids and arrow cards (to show digit shifts)
• Exercise books and pencils
• Mini-whiteboards for quick AFL
• Visual decimal place value charts

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Lesson Structure (30 minutes)

1. Engaging Introduction (5 minutes)

Activity:
Show the number 84 on the board. Then, write 8.4 and ask:
“What do you notice about the digits and the decimal point? How did we get from 84 to 8.4?”

Discussion:

• Highlight that dividing by 10 moves all digits one place to the right, the decimal moves too.
• Demonstrate dividing by 100 (e.g., 84 ÷ 100 = 0.84) by moving digits two places to the right.

Targeted Questions:

• Why does the decimal point move when dividing by 10 or 100? (Understand)
• If the number is 70, what will 70 ÷ 10 and 70 ÷ 100 be? Explain your answer. (Apply & Explain)
• Could dividing any number by 10 move the decimal point differently? Why or why not? (Analyse)
• How is dividing by 10 different from subtracting 10? (Evaluate)

Note: Use the 'think-pair-share' strategy to encourage all pupils to verbalise reasoning.

AFL Checkpoint #1

• Use mini-whiteboards: Pupils write 84 ÷ 10 and show answers simultaneously. Teacher scans and selects a few to explain their method and reasoning.

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2. Modelling and Guided Practice (8 minutes)

Teacher Modelling:

• Write on the board: 56 ÷ 10 = ?
• Model shifting digits and the decimal point: “56 is 56.0. Dividing by 10 moves each digit one place to the right, so 56 becomes 5.6.”
• Next, 56 ÷ 100 = ?
• Model moving decimal two places: “56.0 moves two places to 0.56.”

Explain:

• “We can see that when dividing by 10, the digits shift right by one place; by 100, shift right by two places.”
• Show linking to place value columns to scaffold understanding (tens to ones, ones to tenths, tenths to hundredths).

Provide an example for pupils to copy:

Question	Answer	Explanation
43 ÷ 10	4.3	Decimal point moves one place right
43 ÷ 100	0.43	Decimal point moves two places right

Targeted Questions:

• What happens to the digit zero when dividing by 10 or 100? (Understand)
• Explain why 50 ÷ 100 is 0.5, not 5. (Apply & Analyse)
• If I say a digit disappears after dividing, is that true? Why? (Evaluate)

AFL Checkpoint #2

• Ask volunteers to come to the board and solve 72 ÷ 10 and 72 ÷ 100, explaining their reasoning to the class.

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3. Independent Practice with Increasing Complexity (10 minutes)

Task Overview:
Pupils complete three sets of questions with increasing complexity levels:

Level 1 (Basic)	Level 2 (Application)	Level 3 (Problem Solving & Reasoning)
Divide 1-digit numbers by 10 and 100 (e.g., 6 ÷ 10, 9 ÷ 100)	Divide 2-digit numbers by 10 and 100 (e.g., 53 ÷ 10, 84 ÷ 100)	Word problems: A car travels 60 miles in 1 hour. How far does it travel in 1/10 of an hour?
Write what happens to the decimal point	Explain why dividing by 10 moves digits one place right	Create own example dividing a number by 10 or 100 and explain the steps and result

Teacher Support

• Circulate to scaffold and support reasoning.
• Challenge pupils who finish early to create and explain their own division by 10 or 100 problem to a partner.

AFL Checkpoint #3

• Select pupils to share their explanations and strategies.
• Use questioning: "How did you decide where the decimal goes? Could you explain your thinking again, differently?"

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4. Plenary (7 minutes)

Summary & Reflection:

• Recap learning objectives and success criteria.
• Each pupil states one thing they understood well and one question they still have (use thumbs up/down for confidence levels).

Engaging Plenary Activity:

• “Decimal Point Detective”: Show a number divided by 10 or 100 with a missing decimal point (e.g., solving: 700 ÷ 100 = ? → 7.00 or 7). Pupils explain where the decimal point should go and why.

Higher Order Question:

• If dividing by 10 moves the decimal one place to the right, what happens when you divide by 1,000? Predict and explain.
• Can you think of a real-life scenario where mental division by 10 or 100 would be helpful?

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Common Misconceptions & Difficulties

• Misplaced decimal point: Pupils sometimes place the decimal point incorrectly after dividing, caused by misunderstanding the place value shift.
• Removing digits instead of shifting: Pupils may think digits “disappear” rather than move to new decimal places.
• Confusion between dividing by 10 and subtraction by 10: Some confuse dividing by 10 with subtracting 10 numerically.
• Difficulty recognising zeros as placeholders: For example, 50 ÷ 100 = 0.5 often confuses pupils who expect a whole number result.
• Misunderstanding the decimal point’s role: They may think the decimal point moves physically rather than understanding it is a position marker.

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Notes on AFL Integration

• Use mini-whiteboards at key stages (post-introduction, post-modelling) for quick checks.
• Employ questioning to assess deeper understanding (Bloom’s taxonomy).
• Use partner talk for peer articulation and reasoning checks.
• Use volunteer explanations to assess verbal understanding post-practice.
• Monitor pupil work during independent activity for errors indicating misconceptions.

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Alignment to White Rose Maths Scheme (Summer Block 1)

• This lesson fits within the White Rose Year 4 Summer Block 1 "Decimals" module, specifically lessons on dividing whole numbers by 10 and 100 using place value.

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Example to Copy Into Books

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Divide 43 by 10 mentally

1. Write 43 as 43.0
2. Move the decimal point one place right → 4.3
3. Final answer = 4.3

Explain: When dividing by 10, digits shift one place right: tens → ones, ones → tenths.

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This structured, engaging lesson plan ensures pupils move beyond rote calculation to a deeper understanding of decimal place value and mental division, aligned carefully with the national curriculum expectations for Year 4.