Divide by 10 & 100

Overview

• Age group: Year 4 (age 8-9)
• Class size: 30 pupils
• Duration: 30 minutes
• Subject: Mathematics
• Focus: Using mental methods to divide by 10 and 100, including decimals for middle and high ability pupils
• Curriculum reference: National Curriculum for England, Mathematics - Number: Multiplication and Division
  • Key Stage 2 - Year 4:
    • MA2/1: Recall multiplication and division facts for multiplication tables up to 12 × 12.
    • MA4/3: Use place value, known and derived facts to multiply and divide mentally, including: dividing by 10 and 100, and understanding the effect on the number.
  • White Rose Maths Scheme: Summer Term - Block 2 (Multiplication & Division), Lesson 3: Divide 10 and 100 (including decimals)

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Learning Objectives

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

1. Mentally divide whole numbers by 10 and 100 using place value knowledge.
2. Explain what happens to digits when dividing by 10 and 100 (i.e., digits move one or two places to the right).
3. Apply mental methods to divide decimal numbers by 10 and 100 (middle and high ability pupils).
4. Justify and explain their reasoning when dividing by 10 and 100 through verbalisation and written responses.

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Success Criteria

• I can explain how dividing by 10 and 100 changes the place value of digits.
• I can mentally divide whole numbers by 10 and 100 accurately.
• I can mentally divide numbers with one or two decimal places by 10 and 100 and explain my thinking.
• I can justify my answers and reasoning clearly when working with division by 10 and 100.

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Resources

• Whiteboard and markers
• Place value charts (visual aids)
• Number cards (whole numbers and decimals)
• Mini whiteboards and pens for pupils
• Visual decimals slides/number line

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Lesson Structure

1. Introduction (5 minutes)

Engage & Hook:
Begin with the following prompt: “What do you notice when you divide 50 by 10? What about when you divide 50 by 100? How do the numbers change?”
Display the numbers 50, 5, and 0.5 on the board.

Targeted questions for engagement:

• What is 50 divided by 10? (Wait for answers)
• Why do you think the answer changed from 50 to 5? Where did the zero go?
• What do you expect if you divide 50 by 100? Why?

Encourage pupils to explain their ideas about place value with their partner using the phrase:
“When dividing by 10, the digits move one place to the right because…”

AfL: Listen to pupils’ answers and explanations to gauge understanding of place value before moving forward. Record misconceptions and address them in modelling.

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2. Teaching & Modelling (15 minutes)

Step 1: Whole number division by 10 and 100

• Use a place value chart and demonstrate dividing numbers like 240, 700 by 10 and 100.
• Show clearly that dividing by 10 moves every digit one place to the right; dividing by 100 moves every digit two places to the right.
• Write:

  240 ÷ 10 = 24
  240 ÷ 100 = 2.4
  

• Explain decimal notation that appears when dividing by 100 for whole numbers with zeros at the end.

AfL: Ask pupils to model 360 ÷ 10 on their mini whiteboards and explain their reasoning aloud in pairs. Monitor and give immediate feedback.

Step 2: Introducing decimals (for middle and high ability pupils)

• Work through examples like:

  3.6 ÷ 10 = 0.36
  7.2 ÷ 100 = 0.072
  

• Show how decimals move to the right too and the number gets smaller.
• Use a number line or place value grid to visually demonstrate the effect.

Targeted questioning:

• How does dividing a decimal number by 10 change the digits?
• Can you explain why 3.6 ÷ 10 is 0.36 and not 0.36 multiplied by 10?
• What happens if the digits “run out” on the right side? How do we show this using zeroes?

AfL: Use cold calling to hear from pupils who explain their thinking. Write down ‘common errors’ to address in plenary.

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3. Guided Practice (5 minutes)

• Pupils complete quick questions on mini whiteboards:
  • Divide by 10: 270, 5400, 3.7, 6.5
  • Divide by 100: 1200, 9300, 5.4, 7.23

Targeted whole class questions:

• Can someone explain how they found the answer to 6.5 ÷ 10 mentally?
• Why does the decimal point move? What happens to the value of the number?

AfL: Collect whiteboards from a few pupils for quick assessment — provide immediate feedback and clarifications.

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4. Plenary (5 minutes)

Activity: Thumbs up/down with explanation

• Read different division examples aloud (including some with misconceptions embedded, e.g., 45 ÷ 10 = 4.5 or 45 ÷ 10 = 0.45).
• Pupils show thumbs up if they think correct or thumbs down if incorrect and explain why verbally.

Targeted plenary questions using Bloom’s taxonomy:

• Understanding & Applying: “Explain why dividing by 100 moves the digits two places. Can you visualise this on a decimal place value chart?”
• Analysing: “If 240 ÷ 10 = 24, what mistake was made if someone says 240 ÷ 10 = 2400?”
• Evaluating: “Is dividing by 10 always making the number smaller? Why or why not?”
• Creating: “Can you create your own example of dividing a decimal number by 10 or 100 and explain it to the class?”

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Common Misconceptions & Difficulties

• Pupils may think dividing by 10 makes the number larger instead of smaller.
• Confusing multiplication and division effects on place value (e.g., thinking digits move left when dividing).
• Difficulty understanding decimal shifts, especially when zeros must be added (e.g. 3.6 ÷ 10 = 0.36, not 0.36 × 10).
• Confusing place value positions for decimals (tenths vs hundredths).
• Believing that dividing by 100 simply removes two digits without considering decimal places.

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Notes for Teachers

• Use concrete resources and visuals to reinforce place value.
• Encourage pupils to explain and justify answers regularly to deepen conceptual understanding.
• Check for understanding with well-timed AfL strategies during the lesson and reteach misconceptions instantly.
• Differentiate by providing decimal examples to middle and higher ability pupils while keeping whole number focus for others.

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Alignment with White Rose Scheme

This lesson aligns with White Rose Summer Block 2: Multiplication & Division, lesson on dividing by 10 and 100 (including decimals).

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By following this plan, pupils deepen their understanding of division by 10 and 100 through mental strategies supported by place value reasoning, aligned fully to the English National Curriculum and the White Rose Maths framework.