Fractions and Decimals

National Curriculum Links

Mathematics — Year 4 (Ages 8-9)

• Number: fractions:
  • Recognise and show, using diagrams, families of common equivalent fractions
  • Add and subtract fractions with the same denominator
  • Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• Number: decimals:
  • Recognise and write decimal equivalents of any number of tenths or hundredths
  • Solve simple measure and money problems involving fractions and decimals to two decimal places

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Learning Objectives

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

• Solve a range of problems involving fractions and decimals to two decimal places with understanding.
• Explain their reasoning when solving fraction and decimal problems.
• Make connections between fractions and their equivalent decimal representations.
• Apply addition and subtraction of fractions with the same denominator in problem contexts.

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Success Criteria

• I can identify fractions and their decimal equivalents.
• I can add and subtract fractions with the same denominator.
• I can solve word problems involving fractions and decimals.
• I explain my reasoning clearly using mathematical vocabulary.
• I check my answers by estimating or using equivalent decimals/fractions.

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Resources

• Whiteboard and markers
• Visual fraction and decimal strips or fraction wall display
• Individual whiteboards and pens for pupils
• Copies of worksheet with progressively challenging problems
• Place value counters (optional)

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Lesson Structure

1. Introduction (10 minutes) — Engaging Starter

Activity:

• Begin by showing a fraction wall/strip (e.g., ½, ¼, ¾, 0.5, 0.25, 0.75) visually represented on screen or board.
• Pose a quick challenge: “Can anyone spot which fractions match the decimals?”
• Use a range of questioning aimed to provoke explanation and reasoning:

Targeted questioning (Bloom’s Taxonomy):

• Remembering: What fraction is represented by 0.5?
• Understanding: How do you know that 0.75 is the same as ¾?
• Applying: Can you write 0.25 as a fraction in its simplest form?
• Analysing: What is the difference between ½ and 0.5 as fractions and decimals?
• Evaluating: Which is easier to use when measuring, fractions or decimals? Why?
• Creating: Can you think of a practical situation where using decimals is better than fractions?

AfL:

• Use “show me” with individual whiteboards for pupils to write fractions or decimals matching the question. Rapidly assess understanding and address misunderstandings immediately.

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2. Modelling and Teaching Input (15 minutes)

Example to copy (into books):

Problem	Method	Answer with Explanation
Sarah ate 1/4 of a cake, and Tom ate 0.25 (decimal) of a cake. Who ate more?	Convert 1/4 into a decimal → 0.25. Both ate the same amount.	Sarah and Tom ate the same amount because 1/4 = 0.25

• Model step-by-step how to convert fractions to decimals and vice versa using tenths/hundredths.
• Demonstrate addition and subtraction of decimals and fractions with the same denominator through word problems.
• Show equivalent fractions and decimals using a fraction wall, linking visual with numeric form.

AfL:

• Ask pupils to explain each step: “Why did I convert the fraction to a decimal here?” and “What would happen if we tried to add 1/4 + 0.3 directly? How can we work this out?”
• Use mini whiteboards for pupils to convert different fractions/decimals you call out, ensuring to pick pupils randomly to respond.

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3. Guided Practice — Increasing Complexity (12 minutes)

Students complete task steps:

Task 1: Simple conversions and comparisons

• Convert fractions (1/2, 3/4, 2/10) to decimals and identify which is larger.

Task 2: Addition and subtraction problems with same denominator fractions and decimals (e.g., 0.4 + 0.3; 3/8 + 1/8).

Task 3: Multi-step word problems involving decimals and fractions:

• Example: "Jane has 0.5 litres of juice. She drinks 1/4 litre. How much juice is left?"

More complex: Pupils create their own problem involving fractions and decimals, swap with a partner to solve and explain reasoning.

AfL:

• Circulate, listen to explanations, and ask probing questions such as “How did you decide which method to use here?”
• Use peer-assessment to check if reasoning is convincing.

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4. Common Misconceptions and Difficulties to Address

• Believing decimals and fractions are always different and not understanding equivalence.
• Adding fractions with different denominators incorrectly (though this is not main focus here, some might attempt it).
• Mistaking the place value of decimals (e.g., thinking 0.5 is less than 0.05).
• Difficulty in converting between fractions and decimals because of lack of confidence with tenths/hundredths.
• Confusing subtraction of decimals as subtraction of whole numbers digit by digit.

Strategies:

• Use visual aids at all stages.
• Reinforce place value language consistently.
• Model careful line-up of decimals when adding/subtracting.
• Emphasise checking by estimation.

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5. Plenary (8 minutes)

Class Discussion:

• Pose a mixed reasoning problem on the board:
  “Anna eats 0.3 of a pizza and Ben eats 1/4 of the same pizza. Who eats more? How do you know?”

• Invite selected pupils to explain step-by-step how they would solve it.

• Reflect on learning: Which part did you find easiest or trickiest today and why? How did you check your answers?

• Use a quick quiz on mini whiteboards – flash 3 questions with fractions and decimals mix requiring explanation, e.g., “Explain why 0.2 and 1/5 are the same or different.”

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Additional Notes

• This lesson follows the White Rose Maths Year 4 schemes for Number: Fractions and Decimals, providing a balance of concrete, pictorial, and abstract learning.
• Encouraging pupils to explain their thinking aligns with progression in mathematical reasoning demanded by the National Curriculum.
• AFL is embedded to support formative assessment and adjust teaching dynamically.

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Summary

This highly interactive, scaffolded lesson develops pupils' abilities to solve fraction and decimal problems through visual models, reasoning questions, and practical application. It emphasises explanation and justification in line with National Curriculum expectations for Year 4 mathematics.