Homeschool Guide: These lesson plans are a guide for parents. Content may contain errors — always cross-reference with official exam board specifications.

fractions & percentages as operators

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: fractions & percentages as operators

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about fractions & percentages as operators. Then check against the key terms: Operator. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Operator.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: fractions & percentages as operators. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Mathematics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: Find 2/3 of £54

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about fractions & percentages as operators.

Lesson 2: Core Concepts: fractions & percentages as operators

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on fractions & percentages as operators. Check them against the notes below.

Main Content (35 minutes)

Operator: In mathematics, "of" means multiply. So "3/4 of 20" means 3/4 × 20, and "25% of 80" means 25% × 80.
TermMeaningExample
1/20.550%
1/40.2525%
3/40.7575%
1/50.220%
2/50.440%
3/50.660%
1/80.12512.5%
1/100.110%

Practice (10 minutes)

Q: Find 2/3 of £54

Answer: 54 ÷ 3 = 18, 18 × 2 = £36

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: fractions & percentages as operators

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Operator. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Q1: Find 2/3 of £54

Answer: 54 ÷ 3 = 18, 18 × 2 = £36

Q2: Find 35% of 240

Answer: 35% = 0.35, 0.35 × 240 = 84

Q3: Increase £180 by 15%

Answer: 115% = 1.15, £180 × 1.15 = £207

Q4: Decrease £250 by 30%

Answer: 70% = 0.7, £250 × 0.7 = £175

Q5: Express 45 as a percentage of 150

Answer: 45/150 × 100 = 30%

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: fractions & percentages as operators

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Extended Answer 6 marks: A house was bought for £180,000. After 3 years its value increased by 12%. It was then sold, and the seller paid 1.5% estate agent fees on the sale price. (a) Find the sale price. (b) Find the estate agent fees. (c) Calculate the actual percentage profit the seller made on the original purchase price after fees are deducted. <div class="

(a) Sale price = £180,000 × 1.12 = £201,600. (b) Fees = 1.5% of £201,600 = £201,600 × 0.015 = £3,024. (c) Profit after fees = £201,600 − £3,024 − £180,000 = £18,576. Percentage profit = 18,576/180,000 × 100 = 10.32%. Mark scheme: 2 marks for (a), 1 mark for (b), 3 marks for (c) including correct profit calculation and percentage

Exam Tips: "Of" always means multiply | Build up from easy percentages: 50%, 10%, 5%, 1% | For percentage change: multiplier = (100 ± %)/100 | Check: percentage should be between 0% and 100% for "part of whole" | Memorise common fraction/percentage equivalents
Common Errors: Watch Out! 1. Wrong: A 20% increase then 20% decrease gets back to the original Correct: 100 × 1.2 × 0.8 = 96 — you end up at 96% of the original 2. Wrong: 3/4 of 60 = 60 ÷ 4 × 3 = 45, but 3/4 of 8 = 8 ÷ 3 × 4 Correct: Always divide by denominator first: 8 ÷ 4 × 3 = 6 3. Wrong: Percentage increase from 40 to 50 is 10% (just subtracting) Correct: Increase = 10. Percentage = 10/40 × 100 = 25% (divide by the ORIGINAL)
AO3 - Reasoning & Interpretation: Reasoning and Interpretation Shop A has a coat for £160 with "1/3 off" in the sale. Shop B has the same coat for £180 with "40% off". (a) Which shop offers the cheaper sale price? (b) How much money would you save by choosing the cheaper option? (c) Shop A then offers an extra 10% off the already discounted price. Does this make Shop A definitely cheaper than Shop B now? Show working to justify your answer. Answers: (a) Shop A: £160 × 2/3 = £106.67. Shop B: £180 × 0.60 = £108. Shop A is cheaper. (b) Save £108 − £106.67 = £1.33. (c) Extra 10% off: £106.67 × 0.90 = £96.00. Shop B is still £108. Yes, Shop A is now definitely cheaper (£96 vs £108).
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how fractions & percentages as operators connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of fractions & percentages as operators
  • Critical: "What are the limitations of the models used in fractions & percentages as operators?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)