National Curriculum Links

Mathematics Programme of Study – Year 4:

• Recognise and write decimal equivalents to 1/4, 1/2, 3/4, and tenths and hundredths (Number - Decimals).
• Count in multiples of 6, 7, 25, and 1000 (Number - Number and Place Value).
• Understand and use place value for decimals (Number - Decimals).

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Learning Objectives

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

• Recognise decimal equivalents of tenths and hundredths.
• Write decimal numbers for given fractions with denominators of 10 and 100.
• Explain the relationship between fractions, decimals and the place value of tenths and hundredths.
• Use and interpret decimal numbers in various contexts.

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Success Criteria

• I can identify decimals that represent tenths and hundredths.
• I can write fractions as decimals up to two decimal places.
• I can explain why, for example, 3/10 is 0.3 and not 0.03.
• I can solve problems involving decimals and place value for tenths and hundredths.

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Resources

• Place value charts (including columns for tenths and hundredths)
• Fraction and decimal cards
• Whiteboard and markers
• 30 individual mini whiteboards and pens
• Worksheet with a gradual increase of difficulty
• Visual aids (e.g., decimal grids, hundred squares)

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Lesson Structure (45 minutes)

1. Introduction (10 minutes) – Hook & Engage

Activity:
Start with a simple visual – a hundred square coloured to show fractions like 1/10 and 1/100, alongside their decimal form.
Ask the class: "What do you notice about the number of shaded squares?"
Then link this to decimals on the board.

Targeted questioning to deepen thinking:

• "Why do we write 0.1 for one tenth and not 1.0?"
• "What does the digit in the tenths place actually represent?"
• "How is 3/10 similar to and different from 30/100 both as fractions and decimals?"
• "If 0.3 is the same as 3/10, what decimal would 7/10 be and why?"

AFL Point:
Use mini whiteboards for pupils to sketch a fraction and decimal pair (e.g. 4/10 and 0.4). This allows you to quickly assess who understands the place of digits in decimals.

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2. Modelling & Teacher Explanation (10 minutes)

• Model writing fractions 1/10, 3/10, 7/10 as decimals (0.1, 0.3, 0.7) on the board, referencing place value columns (tenths).
• Then show fractions like 4/100 and 57/100 as 0.04 and 0.57, using place value columns (hundredths).
• Use a place value chart to demonstrate how the place affects the decimal number value.
• Incorporate a visual of a decimal grid highlighting tenths and hundredths sections to represent above fractions.

Example for pupils to copy:

Fraction: 3/10 = Decimal: 0.3  
Fraction: 57/100 = Decimal: 0.57  
Explanation: The digit 3 is in the tenths place, meaning 3 parts out of 10. The digits 5 and 7 in 0.57 represent 5 tenths and 7 hundredths.

AFL Point:
Ask "Show me on your mini whiteboard 6/10 as a decimal." Scan the room to assess quick understanding.

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3. Guided Practice – Gradually Increasing Complexity (15 minutes)

Task Structure:

1. Write simple tenths fractions as decimals (3/10, 8/10).
2. Write hundredths fractions with zeros (40/100, 9/100) as decimals (0.40, 0.09).
3. Write fractions with nonzero tenths and hundredths (57/100, 23/100).
4. Identify decimals from word problems (e.g., "If a ribbon is 7/10 metre long, what is this in decimals?")
5. Challenge: Compare decimals and fractions to explain which is bigger/smaller and justify.

Questioning to encourage reasoning:

• "How do you know that 0.07 is the same as 7/100 and not 7/10?"
• "Explain why 0.5 is bigger than 0.47 using place value."
• "If you have 0.4 and 0.04, which is larger, and why?"
• "Can you write a fraction for 0.36? Explain how you know."

AFL Points:

• Circulate while pupils work and listen to explanations.
• Select random pupils to explain their reasoning out loud.
• Use mini whiteboards to quickly check answers to simple decimal conversion questions.

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4. Common Misconceptions & Difficulties (Interwoven during task)

• Misreading tenths and hundredths places and mixing up 0.3 and 0.03.
• Believing a higher decimal digit always means a larger number without checking the place value (confusing 0.7 and 0.07).
• Writing decimals with too many digits or missing zeroes (writing 0.5 as .5 without zero).
• Confusion between tenths and hundredths fractions (e.g., calling 3/10 as 0.03).

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5. Plenary – Consolidation & Reflection (10 minutes)

Whole Class Discussion:

• Invite pupils to explain a decimal equivalent of a fraction they saw today.
• Pose higher order questions to promote evaluation:
  • "Why do decimal fractions help us write numbers more quickly than words?"
  • "How would you explain decimals to a younger pupil who only knows fractions?"
  • "Can you think of a real-life situation where knowing decimals would be useful?"

Exit Ticket – AFL:
On mini whiteboards, ask pupils to write the decimal equivalent of a fraction you say aloud (e.g., 6/10, 45/100).
Collect and scan for understanding or need for reteaching next lesson.

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Differentiation

• Support: Use concrete resources (fraction bars and decimal grids) for pupils who find place value abstract.
• Challenge: Pupils can attempt converting decimals to fractions and finding decimal equivalents for mixed numbers (e.g. 1 3/10).

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Alignment with White Rose Mathematics Scheme

This lesson specifically matches Year 4 Block 3 (Decimals) from White Rose Maths which aims to consolidate understanding of decimal place value, tenths, and hundredths, linking fractions to decimals with emphasis on fluency and reasoning.

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Summary

This 45-minute lesson targets Year 4 pupils’ understanding of decimal equivalents to tenths and hundredths in line with the National Curriculum. It uses engaging visuals, questioning techniques derived from Bloom’s taxonomy to promote deep reasoning, incorporates formative Assessment for Learning tools, and gradually builds complexity to solidify comprehension. Pupils gain clear conceptual links between fractions and decimals, their place value, and practical use.