Dividing by 10 and 100

National Curriculum Links

Mathematics – Number – Multiplication and Division (Year 4):

• Recall and use multiplication and division facts for multiplication tables up to 12 × 12.
• Recognise and use factor pairs and commutativity in mental calculations.
• Multiply and divide numbers mentally drawing upon known facts.
• Solve problems involving multiplying and dividing by 10 and 100, including using scaling by simple fractions.

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Learning Objectives

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

• Understand and explain what happens to a number when dividing by 10 and by 100.
• Use place value knowledge to divide whole numbers by 10 and 100 accurately.
• Apply division by 10 and 100 in problem-solving contexts.
• Justify their reasoning by explaining the effect of dividing by 10 and 100 on place value.

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Success Criteria

Pupils will:

• Describe division by 10 and 100 as moving digits to the right on a place value chart.
• Correctly divide 2- and 3-digit numbers by 10 and 100 without a calculator.
• Explain why dividing by 10 makes a number 10 times smaller, referring to place value.
• Solve word problems involving division by 10 and 100 using appropriate methods.
• Check their answers by reasoning about the size of the quotient compared to the dividend.

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Resources

• Place value charts (individual and whole-class display)
• Whiteboard and markers
• Mini whiteboards and pens for students
• Printed worksheet with division by 10 and 100 exercises
• Counters or base-10 apparatus (optional for kinaesthetic learners)
• Example problem template for pupil books

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Lesson Structure

1. Introduction (8 minutes)

Engage & Connect

• Start with a quick warm-up: Ask pupils to recall what happens when a number is multiplied by 10. (E.g., 4 × 10 = 40)
• Write examples on the board like 70 ÷ 10 = ? and 400 ÷ 100 = ? to hook interest.
• Show a large place value chart to the class. Write the number 345 on it.
• Ask: "If I divide 345 by 10, what do you think will happen to each digit? Why?"
• Use conceptual questioning to prompt deeper thinking (see below).

Targeted Whole-Class Questioning (based on Bloom’s taxonomy):

• Remembering: What does dividing by 10 mean?
• Understanding: Why does dividing by 10 move the digits on the place value chart?
• Applying: If dividing by 10 moves digits to the right, what would dividing by 100 do?
• Analysing: How does dividing by 10 affect the units digit? What happens to the remainder?
• Evaluating: Is 345 ÷ 10 the same as 345 × 0.1? Why or why not?
• Creating: Can you create your own example and explain what happens when you divide by 10 or 100?

AfL Point: Use mini whiteboards to have pupils respond quickly to “What is 520 ÷ 10?” and “What is 900 ÷ 100?” Show responses on the visualiser or around the room for instant formative assessment.

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2. Teaching & Modelling (15 minutes)

Step 1: Model dividing 345 by 10 using the place value chart.

• Explain: Dividing by 10 shifts every digit one place to the right.
• Show digits moving right: Hundreds → Tens, Tens → Units, Units → Tenths (introduce concept of decimals, but emphasise focus on whole numbers here).
• Write the answer: 34.5.
• Emphasise “We get 34 with 5 tenths left.”

Step 2: Repeat for 345 ÷ 100.

• Shift digits two places to the right.
• Write the answer: 3.45.
• Reinforce that the number is ten times smaller each time.

Example for books:

345 ÷ 10 = 34.5

345 ÷ 100 = 3.45

• Explain when numbers divide exactly (e.g., 320 ÷ 10 = 32) vs. when they result in decimals.

Targeted Questions during modelling:

• How does the value of each digit change as it moves?
• Why do we sometimes get decimal answers?
• Can we divide a number like 37 by 10 in the same way? What would the quotient be?
• What happens to the remainder or leftover when the digits don’t fit neatly?

Common misconceptions to address:

• Pupils may think the digit ‘drops off’ instead of moving right.
• Confusing division by 10 with subtracting 10.
• Ignoring place value shifts and just ‘dropping’ zero.
• Not understanding decimal places or thinking decimals are ‘wrong’.

AfL Point: Ask pupils to explain the process in their own words, either orally or in writing, to check conceptual understanding. Use paired talk: “Explain to your partner what happens to the number when dividing by 10.” Monitor pairs for misconceptions.

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3. Guided Practice (10 minutes)

• Pupils complete targeted questions on mini whiteboards:

  Examples:

  • 470 ÷ 10 = ?
  • 280 ÷ 100 = ?
  • 905 ÷ 10 = ?
  • 630 ÷ 100 = ?

• Include some word problems such as:

  • "A car travelled 540 km in 10 hours. How many km did it travel in 1 hour?"
  • "A pack of 800g sweets is shared equally into 100 smaller packs. How much does each small pack weigh?"

• Encourage pupils to explain their thinking aloud when sharing answers.

AfL Point: Use cold calling to ask pupils to justify answers. Probe reasoning: “Why did you put the digit there?” or “Can you explain how the place value helped you solve this?”

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4. Independent Work (5 minutes)

• Pupils complete a short worksheet in their books with a mixture of direct calculation and simple reasoning questions.

Example Exercise:

1. 650 ÷ 10 = ______
2. 4,200 ÷ 100 = ______
3. Explain in words what happens to the digits when dividing by 10 and 100.
4. True or false? "Dividing 80 by 10 gives us 8 tens." Explain your answer.

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5. Plenary (2 minutes)

• Quick round of “Think, Pair, Share”: Pupils state one thing they learned about dividing by 10 and 100.
• Summarise key points, addressing any misconceptions noted during lesson.
• End with a challenging question: “If dividing by 10 moves digits one place to the right, what would happen if we divided by 1,000?" Invite a few pupils to share ideas.

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Assessment for Learning (AfL) Summary

Stage	AfL Strategy	Purpose
Introduction	Mini whiteboards quick questions	Check prior knowledge and quick recall
Teaching	Paired talk to explain reasoning	Confirm conceptual understanding
Guided Practice	Cold calling + probing explanations	Deepen reasoning and correct misconceptions
Independent	Written explanations in books	Assess individual understanding
Plenary	Oral reflection	Consolidate learning and identify gaps

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Notes for Differentiation

• Support: Use base-10 apparatus and place value charts for kinaesthetic learners.
• Extension: Ask higher achieving pupils to explore division by 1,000 or decimal answers, justifying mathematically.
• Language: Use clear vocabulary: “divide,” “place value,” “digits,” “decimal,” “shift.”

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Alignment with White Rose Maths Scheme

This lesson follows White Rose Year 4 Block 1 Number – Place Value and Block 2 Multiplication and Division, focusing on “Dividing by 10 and 100” using place value understanding and scaling. The use of place value charts and emphasis on reasoning aligns with White Rose mastery approach, promoting deep understanding rather than rote procedures.

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Wow Tip for Teachers:
To make this lesson memorable, try a "Human Place Value Line" activity for kinaesthetic learning: Have 10 pupils hold digit cards and physically step one or two places to the right when dividing by 10 or 100, showing the digit shift live. Students explain what happened to the "number" as the line moves – great for visualising abstract concepts!