Dividing by 100

National Curriculum Links

• Mathematics - Year 4 Number - Decimals
  Pupils should be taught to:

  • Recognise and understand decimal equivalents of any number of tenths or hundredths
  • Recognise that hundredths arise when dividing an object by 100
  • Count up and down in hundredths; recognise that hundredths are 1/100th of a whole

• White Rose Maths Scheme - Year 4, Block 3: Decimals
  Focus: Understanding tenths and hundredths; representing decimals on number lines; recognising decimals as fractions.

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Learning Objectives

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

• Recognise and explain that hundredths arise when dividing by 100.
• Write decimal numbers to two decimal places representing hundredths.
• Demonstrate understanding of hundredths using visual representations and place value.

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Success Criteria

Pupils will:

• Identify and write hundredths as numbers with two decimal places (e.g., 0.01, 0.36).
• Explain what it means to divide a number by 100 verbally and in writing.
• Represent and explain hundredths using pictorial models such as grids or place value charts.
• Justify their answers when solving problems involving hundredths, using mathematical vocabulary.

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Resources

• White Rose Maths Year 4 Decimal Place Value Charts (printed or on whiteboard)
• 100-square grids (printed or projected)
• Base-10 equipment (e.g., place value counters or Dienes blocks)
• Mini whiteboards and pens for quick responses
• Worksheets with guided examples and practice problems

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Lesson Structure (45 minutes)

1. Introduction (10 minutes)

Engaging Starter:

• Begin with a quick mental warm-up: Write the number 1.
• Ask: "What happens to this number if I divide it by 10?" (Expected: 0.1)
• Then ask: "Now, what happens if I divide 1 by 100?" (Expected: 0.01)

Show this using a 100-square grid, shading 1 square out of 100 to represent 1/100.

Targeted Questions (Bloom’s Taxonomy: Understand, Apply):

• Can you explain why dividing by 100 gives you hundredths?
• How is dividing by 100 related to moving the decimal point?
• If I divide 25 by 100, what decimal will I get? Can you explain how you found the answer?

AFL Point: Use mini whiteboards here — ask pupils to write the decimal equivalent of various numbers divided by 100 (e.g., 10 ÷ 100, 75 ÷ 100). Quick show of mini whiteboards for immediate formative assessment.

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2. Modelling and Guided Practice (15 minutes)

Model on the board:

• Write 1 ÷ 100 = 0.01 using place value charts and 100-square grids.
• Show the relationship between fractions and decimals: 1/100 = 0.01
• Model dividing other numbers by 100: e.g., 12 ÷ 100 = 0.12
• Show how the decimal point moves two places to the left when dividing by 100.

Use Visuals:

• Draw a 100-square grid with 12 squares shaded and demonstrate that 12 shaded squares represent 12/100 = 0.12.

AFL Point:

• Ask pupils to come to the board to convert numbers divided by 100 into decimals and explain their reasoning aloud (peer assessment).
• Use questioning to check misconceptions: "Why does the decimal point move two places? What happens if we move it only one place?"

Example to Copy:

Example:  
36 ÷ 100 = 0.36  
Step 1: Write 36 as 36.00 (showing it has two decimal places).  
Step 2: Move the decimal point two places to the left.  
Step 3: The answer is 0.36, which means 36 hundredths.  

Visual: 100-square grid with 36 squares shaded.  

Pupils copy this example into their books.

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3. Independent Activity (10 minutes)

• Pupils complete a worksheet that requires them to:
  • Convert numbers (e.g., 58, 7, 91) divided by 100 into decimals.
  • Represent these as shaded grids.
  • Write an explanation for one of their answers (justifying reasoning).

Targeted Questions:

• How do you know your answer is correct?
• Can you explain what the decimal 0.58 means in terms of hundredths?
• What would happen if you divided by 10 instead of 100?

AFL Point:

• Circulate while pupils work, listen to explanations, and use questioning to identify who understands and who requires support.

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4. Plenary (10 minutes)

• Select a few pupils to share their explanations for converting numbers divided by 100 into decimals.
• Whole class discussion: "Why do we say hundredths arise when dividing by 100?"
• Pose higher-order thinking question: "If dividing by 100 moves the decimal point two places, what might happen if we divide by 1000? How is this pattern helpful?"
• Recap key learning points with a visual demonstration using the place value chart.

Exit Ticket (AFL):

• On mini whiteboards, pupils write down one sentence explaining how dividing by 100 relates to hundredths.
• Collect responses to identify any remaining misconceptions for future lessons.

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Common Misconceptions & Difficulties

• Thinking that dividing by 100 removes two digits rather than moving the decimal point.
• Confusing tenths and hundredths, e.g., writing 0.1 instead of 0.01 for 1/100.
• Misunderstanding the place value and what each digit after the decimal represents.
• Difficulty linking visual grids to decimal notation.

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Teacher Notes and Tips

• Use visual aids consistently as concrete representations strengthen understanding.
• Encourage pupils to vocalise their thinking and reasoning to deepen conceptual understanding.
• Praise detailed explanations and correct use of mathematical vocabulary (hundredths, decimal point, place value).
• Address any misconceptions immediately during AFL checks to prevent acquisition of errors.
• Link the lesson to real-world contexts such as money (e.g., 1p = 0.01 pounds) to enhance engagement.

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This carefully structured lesson plan ensures alignment with the National Curriculum and White Rose Maths, providing engaging, challenging, and formative learning opportunities around recognising that hundredths arise when dividing by 100.