Understanding Hundredths

National Curriculum Links

• Mathematics: Number - Fractions (Year 4)
  • Recognise and use thousandths and relate them to tenths, hundredths, and decimal equivalents. (Year 4 Programme of Study)
  • Pupils should be taught to understand the place value of digits in decimals with up to three decimal places.
• White Rose Maths Scheme - Summer Term, Week 1: Decimals (Recognising and Writing Decimals to Two Decimal Places)

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Learning Objectives

By the end of this lesson, pupils will:

• Understand that hundredths arise from dividing a unit into 100 equal parts.
• Identify hundredths visually and numerically.
• Accurately write decimal numbers to two decimal places representing hundredths.
• Explain their reasoning about the size and value of hundredths using appropriate mathematical language.

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Success Criteria

Pupils can:

• Recognise that 1 hundredth is one part out of 100 equal parts.
• Represent hundredths using visual representations (grids, hundred squares).
• Write decimals correctly to two decimal places to show hundredths (e.g., 0.01, 0.45).
• Compare and order decimal numbers by reasoning about their place value, justifying their answers.

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Resources

• Hundred square grids (large classroom display and individual copies)
• Whiteboard and digital projector (for visual modelling)
• Place value counters or place value charts
• Books for pupils
• Visual decimal slides (showing fractions, decimals and division connections)

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Lesson Structure (45 Minutes)

1. Engaging Introduction (10 minutes)

Goal: Spark curiosity about the concept of hundredths through visual and real-world context.

• Present the class with a large 10x10 hundred square grid projected on the board. Colour one square and explain it represents 1 out of 100 parts — ask:
  • “What fraction does this coloured square represent?”
  • “How can we write this fraction as a decimal?”
• Think-Pair-Share: Pupils discuss with a partner how to divide a whole into 100 equal parts in real life (e.g., money - £1 divided into 100 pence).
• Reveal a real-world example: "Imagine a chocolate bar cut into 100 tiny pieces." Ask:
  • “If I eat one piece, what fraction and decimal part of the chocolate bar have I eaten?”
• Introduce the idea that hundredths come from dividing by 100. Show 1 ÷ 100 and explain the link to 0.01.

Engagement question:

• “Can you explain why dividing by 100 is so important when we think about decimals?” (AFL to listen for correct use of vocabulary like ‘tenths’, ‘hundredths’, ‘equal parts’)

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2. Modelling and Guided Practice (15 minutes)

Whole-class interactive modelling:

• Draw a 10x10 grid on the board. Shade 23 squares. Write as a fraction and decimal: 23/100 and 0.23.
• Write the division equation: 23 ÷ 100 = 0.23. Explain that every square represents 1 hundredth.
• Show how the decimal places correspond to places in the grid (tenths vertically, hundredths horizontally).

Copy example into books:

  1. Ten by ten grid represents 100 equal parts.
  2. Shaded squares = 23.
  3. Fraction form: 23/100.
  4. Decimal form: 0.23 (2 tenths and 3 hundredths).
  5. Division: 23 ÷ 100 = 0.23.

AF L – Check pupils’ books for correct copying and understanding of decimal notation. Ask a few pupils to explain aloud their working process and reasoning.

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3. Targeted Whole Class Questions (10 minutes)

Use Bloom’s Taxonomy to deepen understanding and to encourage explanation and justification.

Question	Bloom’s Level	Purpose	Example Prompts
What does the digit ‘3’ represent in 0.23?	Understanding	Check place value knowledge	“Why is the 3 not in the tenths place?”
How could you explain to a friend why 0.23 is the same as 23/100?	Applying	Encourage verbalisation and peer teaching.	“What language would you use to describe hundredths?”
If I divide 45 by 100, what decimal will I get? How do you know?	Applying/Analysing	Promote calculation and reasoning skills	“What strategy can you use to find the answer?”
Can you compare 0.23 and 0.32? Which is greater? Explain how you know.	Analysing/Evaluating	Develop reasoning skills	“What does the position of the digits tell you?”
If I shaded 57 squares in my grid, what fraction and decimal would that show? How would you explain this to me step-by-step?	Synthesising	Combine knowledge of fraction, decimal, and division	“Why do we divide by 100 in this situation?”

AF L – Use mini whiteboards to have pupils write down their answers to questions 3 and 4. Immediate feedback to correct misconceptions live.

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4. Independent or Paired Activity (7 minutes)

• Give pupils individual or paired 10x10 grids with shaded squares representing various numbers (e.g., 14, 53, 78).
• Pupils write the fraction and decimal equivalent in their books.
• Teacher circulates to check understanding and provide scaffolding.

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5. Common Misconceptions and Difficulties

• Pupils confusing hundredths with tenths (e.g., thinking 0.23 means 23 tenths).
• Misunderstanding place value, especially mixing the meaning of digits, e.g., thinking ‘3’ in 0.23 represents three hundredths but writing 0.32 instead.
• Difficulty linking division by 100 to decimal placement.
• Students interpreting the decimal as a whole number rather than part of a whole.

Strategy to address: Use visual aids continuously; frequent questioning to force explanation; relate to money and real-world examples to anchor understanding.

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6. Plenary (3 minutes)

• Use a rapid-fire quiz: Show different decimal numbers (e.g., 0.02, 0.1, 0.45, 0.67) and ask pupils to quickly write the fraction out of 100.
• Ask one or two children to explain how they know what the number represents in terms of hundredths.
• Recap key learning points: “What does dividing by 100 do?”, “How do we show hundredths in decimals?”, “Why is 0.30 not the same as 0.3?”

Final AFL: Quick thumbs up/down for confidence in understanding. Can also use exit tickets: “Write a sentence explaining what a hundredth is.”

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Summary

This carefully scaffolded lesson supports Year 4 pupils to fully grasp that hundredths arise from dividing by 100, using multiple representations aligned with the National Curriculum and White Rose Maths expectations. Through rich visuals, carefully structured questioning requiring explanation and justification, and clear modelled examples, pupils gain a deep, conceptual understanding of hundredths and their decimal notation. The plan integrates formative assessment (AfL) throughout to address misconceptions early and maintain engagement.