Comparing Decimal Values

Age Group

Year 4 (8-9 years old)
Class size: 30 students
Duration: 45 minutes

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National Curriculum References

• Number – decimals (Key Stage 2, Year 4):
  Interpret and write decimal numbers as fractions [for example, 0.71 = (\frac{71}{100})]
  Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
  Compare numbers with the same number of decimal places up to two decimal places

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Learning Objectives

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

• Recognise and understand the place values of decimals up to two decimal places.
• Compare and order decimal numbers with up to 2 decimal places using inequality symbols (<, >, =).
• Justify their reasoning when comparing decimals, using precise mathematical language.

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Success Criteria

Pupils will:

• Identify and explain the place value of digits in decimals to 2 decimal places.
• Compare two or more decimals by examining tenths and hundredths columns.
• Use correct symbols (<, >, =) to compare decimals accurately.
• Explain and justify their comparison using clear reasoning (e.g., “0.54 is greater than 0.47 because 54 hundredths is more than 47 hundredths”).

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Resources

• Whiteboard and visual place value grids for decimals.
• Individual whiteboards for pupils.
• Printed worksheets with increasing difficulty questions.
• Place value charts for decimals (whole, tenths, hundredths).
• Number cards (decimals to 2 d.p.).
• Visual fraction-decimal equivalence alongside place value charts.

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Lesson Structure

1. Introduction (10 minutes)

Engage: Contextual Hook
Ask: "If I have £0.59 and you have £0.95, who has more money?" Display these amounts on the board.

• Discuss what the digits after the decimal point mean in the context of money (pounds and pence).
• Show place value chart emphasising tenths and hundredths places.

Key questions for understanding (Targeted whole-class questioning):

• How do we read the number 0.59 aloud?
• What does the 5 represent in 0.59? What does the 9 represent?
• Can anyone explain why 0.95 is more than 0.59?
• If two decimals have the same tenths digit, what do we compare next?
• Why do we need to look at the hundredths too?
• Is there ever a time when two decimals can look different but have the same value? Give an example.

Bloom’s level focus: Understanding, Applying, Analysing, Explaining.
(Have pupils justify by explaining their reasoning, not just giving answers.)

AfL point:

• Use mini whiteboards to display answers to the question: "Is 0.71 greater than or less than 0.17? Explain your reasoning."
• Teacher circulates to listen to reasoning and gives immediate verbal feedback.

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2. Modelling (10 minutes)

Example to copy into books:

Number	Tenths Place	Hundredths Place	Comparison Explanation	Symbol
0.43	4	3	4 tenths is greater than 3 tenths	0.43 > 0.32
0.70	7	0	Both have 7 tenths; zero hundredths	= 0.70 = 0.70*
0.56	5	6	5 tenths less than 5 tenths? No, examine hundredths	0.56 > 0.54

Note: Explain why 0.70 = 0.7 (trailing zero doesn’t change value)

Teacher thinks aloud, modelling:

• “First, look at the tenths digit... If they are different, that decides which number is greater or smaller. If tenths are the same, look at the hundredths. Remember, 0.70 and 0.7 are the same number because the zero after is just showing hundredths.”
• “Now, write a sentence explaining why 0.43 is greater than 0.32.”

AfL point:

• Ask 3 pupils to read out their explanations aloud; the class votes if explanations are clear or how they could improve them.

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3. Guided Practice (10 minutes)

Task: Compare these decimal pairs and write an explanation for each.

Pair 1: 0.65 & 0.56
Pair 2: 0.40 & 0.4
Pair 3: 0.83 & 0.83
Pair 4: 0.29 & 0.92

• Pupils first write comparison symbols (<, >, =) then a sentence to justify their choice.
• Circulate the classroom supporting and challenging pupils who quickly grasp the concept.

Scaffold for some pupils: Use place value charts to draw digits aligned under tenths and hundredths.

Challenge: Ask advanced pupils to create their own decimal comparisons that are tricky to compare (e.g., 0.49 and 0.5) and explain reasoning.

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4. Independent Work (10 minutes)

Increasing Complexity Task:
A table with decimal numbers, some requiring ordering three or four decimals, including same tenths but different hundredths, and decimals with trailing zeros.

Example questions:

• Order 0.31, 0.35, 0.3 from smallest to largest.
• Which is greatest: 0.70, 0.707, 0.7? Explain why (introduce the understanding of more than 2 decimal places briefly).

Extension Question:
"Two decimals have the same hundredths digit but different tenths digits. How can you quickly decide which is greater without comparing every digit?"

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5. Plenary (5 minutes)

• Recap success criteria.
• Use a quick interactive quiz: Show decimal pairs on screen and ask students to write comparison symbol and explain reasoning aloud or on mini-whiteboards.
• Example: Compare 0.48 and 0.487. Who is greater? Why? (Focus on understanding decimals beyond 2 dp as a stretch).

Plenary Question:
“Why is it important to look at both tenths and hundredths when comparing decimals? What mistakes do you think people make when they don’t do this?”

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Common Misconceptions and Difficulties

• Confusing the digits before and after the decimal point.
• Thinking 0.7 is less than 0.65 because 7 is less than 65.
• Misunderstanding that trailing zeros after decimal do not change value (e.g., 0.5 = 0.50).
• Ignoring hundredths place when tenths differ by a little (e.g., thinking 0.49 > 0.5).
• Mixing up the place value of digits, e.g., reading 0.43 as “forty-three” not “four tenths, three hundredths”.

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Additional Notes

• Ensure all explanations use precise mathematical language (tenths, hundredths, greater than, less than, equal to).
• Encourage pupils to verbalise their reasoning regularly to embed understanding and develop mathematical communication.

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This lesson plan aligns closely with the White Rose Maths scheme’s Year 4 decimals focus and the National Curriculum requirements, incorporating concrete representations, discussion, reasoning, and incremental challenge.