Fractions, Decimals & Percentages

Overview

Year group: 7
Duration: 45 minutes
Class size: 1 student
Unit: Mastering Fractions & Percentages (Lesson 5 of 5)
National Curriculum references:

Mathematics Programme of Study – Number – Fractions (Years 7 and 8)
Mathematics Programme of Study – Number – Decimals and Percentages
Key aims: Consolidate and extend understanding of equivalences between fractions, decimals and percentages, and apply to problem solving.

Learning Objectives

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

Convert accurately between fractions, decimals and percentages for a variety of values (NC refs: Years 7 and 8 Number – Fractions and Decimals)
Apply conversions to solve increasingly complex problems including real-life contexts (NC ref: Use common factors to simplify fractions; understand percentage increase/decrease).
Recognise and use equivalence in different forms to inform problem solving and reasoning (NC ref: Express one quantity as a fraction of another, where the fraction is less than 1).
Explain their reasoning clearly when comparing and converting between fractions, decimals and percentages.

Success Criteria

I can confidently convert fractions to decimals and percentages.
I can solve word problems that require mixing fractions, decimals and percentages.
I can justify which form (fraction, decimal, percentage) is most appropriate in context.
I can explain my methods aloud clearly with accurate mathematical language.

Resources Needed

Whiteboard and marker (or notebook and pen)
Fraction, decimal, percentage cards for matching activity (physical or drawn)
Worksheets with integrated problems (mixed word problems, conversion tasks)
Calculator (optional, but encourage mental arithmetic where possible)
Visual aids showing equivalences (e.g., fraction wall, percentage grids)

Lesson Structure

1. Starter / Recap (5 minutes)

Discuss previous lessons briefly: recap key conversions (e.g., ½ = 0.5 = 50%) using quick questioning.
Ask student to convert simple fractions to decimals and percentages orally to warm up.
Use fraction cards vs decimal/percentage cards to match as a memory jog.

National Curriculum Link: Reinforce fluency in number facts (Years 7 & 8 Number)

2. Direct Teaching & Modelling (10 minutes)

Present worked examples converting between fractions, decimals & percentages, including:
- Simple (e.g., ¾, 0.25)
- Complex (e.g., 7/8, recurring decimals like 0.333...)
- Non-exact percentages (e.g., ⅗, which is 60%)
Demonstrate from fractions to decimals using division, then decimals to percentages by multiplying by 100.
Highlight checking methods (e.g., back-conversion to confirm).
Show how to simplify fractions before converting where applicable.

Mathematical Language Focus: numerator, denominator, equivalent, recurring decimal, simplify, multiply, divide.

National Curriculum Link: Use common factors to simplify fractions (Year 7 Number – Fractions).

3. Collaborative Activity / Guided Practice (15 minutes)

Activity: “Fractions, Decimals, Percentages Puzzle”
- Arrange given cards (fraction, decimal, and percentage) into groups that match equivalences.
- For each group, solve a related word problem (e.g., "If ¾ of a test is completed, what percentage is that? How many marks out of 100?")
- Student explains reasoning aloud after each problem.
Provide scaffolded hints for challenging problems: e.g., “Think: what is ⅕ as a decimal?” or “How do you convert 0.6 to a percentage?”
Use real-life contexts such as shopping discounts, part of a journey, or recipes to embed relevance.

National Curriculum Link: Solve problems involving fractions, decimals and percentages (Year 7 Number).

4. Independent Practice & Application (10 minutes)

Work through 3-5 complex, mixed-format problems combining all three concepts.
Example problems:
- "A jacket is on sale for 25% off. The original price is £40. What is the sale price? Express your answer as a decimal and fraction of the original price."
- "Convert 0.375 to a fraction in its simplest form and to a percentage."
- "A student scored 18/24 on a test. Express the score as a decimal and percentage."
Encourage use of a self-checking method (re-conversion) or estimating for plausibility.

National Curriculum Link: Express one quantity as a fraction of another; solve problems involving percentage increase and decrease (Year 7 Number).

5. Plenary / Reflection (5 minutes)

Use a “think aloud” prompt:
- “Explain how you decide to convert a fraction into a decimal or percentage for different problems.”
- “Which form do you find easiest to work with and why?”
Encourage student to summarise the key links between fractions, decimals, and percentages.
Complete an exit-ticket style question: e.g., Convert ⅗ to decimal and percentage and explain your method in one sentence.

National Curriculum Link: Encourages reflection on mathematical methods and develops reasoning skills.

Assessment for Learning

Observe student explanations during activities to assess conceptual understanding and procedural fluency.
Check accuracy and methodology in independent practice problems.
Use exit-ticket response to confirm attainment of conversion and reasoning objectives.
Provide immediate feedback to promote mastery.

Differentiation & Extension

For the one student: Tailor questions dynamically depending on fluency; deepen complexity if confident or support with concrete examples if needed.
Challenge with problems requiring identification of recurring decimals and their fraction forms (e.g., 0.666…).
Extension: Investigate percentage increase/decrease problems linked to real-world data, e.g. population or price changes.

Teacher Notes

Remind student that mastery means not just performing conversions mechanically but understanding why equivalencies hold true.
Foster confidence in explaining answers aloud—this is vital for solidifying knowledge.
Use engaging and relevant examples to cement connections between maths and everyday life.
Highlight that decimals and percentages are often more practical in real-life contexts, but fractions remain valuable for exactness and reasoning.

This final lesson acts as both a comprehensive review and an application challenge, consolidating knowledge of fractions, decimals, and percentages in line with the expectations of the National Curriculum for England for Year 7 students.