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

fractions in ratio problems

FoundationHigherAll Boards

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

Fastmail

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 in ratio problems

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about fractions in ratio problems. Then check against the key terms: Ratio, Fractions and Ratios. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Ratio, Fractions and Ratios.
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 in ratio problems. 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: A ratio is 5:3. What fraction does the first part represent?

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about fractions in ratio problems.

Lesson 2: Core Concepts: fractions in ratio problems

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on fractions in ratio problems. Check them against the notes below.

Main Content (35 minutes)

Ratio: Compares two or more quantities in order. Written as a:b or a:b:c
Fractions and Ratios: A ratio can be expressed as fractions of the total. In ratio a:b, the first part is a/(a+b) of the total.

Practice (10 minutes)

Q: A ratio is 5:3. What fraction does the first part represent?

Answer: 5/(5+3) = 5/8

Plenary (5 minutes)

Explain Back

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

Lesson 3: Application: fractions in ratio problems

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Ratio, Fractions and Ratios. 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: A ratio is 5:3. What fraction does the first part represent?

Answer: 5/(5+3) = 5/8

Q2: A drink is made from juice and water in ratio 1:4. What fraction is juice?

Answer: 1/(1+4) = 1/5

Q3: £120 is shared in ratio 3:1. How much does the smaller share receive?

Answer: 1/4 × £120 = £30

Q4: In a car park, the ratio of cars to vans is 7:3. What fraction are vans?

Answer: 3/(7+3) = 3/10

Q5: A cake is shared in ratio 2:3:4. What fraction is the largest share?

Answer: 4/(2+3+4) = 4/9

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 in ratio problems

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 business divides its profit between three departments in the ratio 2:3:5. (a) What fraction of the profit does the largest department receive? (b) The smallest department receives £24,000. Find the total profit. (c) The following year, the total profit increases by 20%. The largest department's fraction increases to 6/15. Has the largest department received more money than the previous year? Show working. <div class="

(a) Total parts = 10. Largest = 5/10 = 1/2 of the profit. (b) Smallest = 2/10 = 1/5 of total = £24,000. Total = £24,000 × 5 = £120,000. (c) Previous year: largest = 1/2 × £120,000 = £60,000. New total = £120,000 × 1.2 = £144,000. New largest = 6/15 × £144,000 = 2/5 × £144,000 = £57,600. No — the largest department received less (£57,600 Mark scheme: 1 mark for (a), 2 marks for (b), 3 marks for (c) including comparison and conclusion

Exam Tips: Always find the total number of parts first | Check that your fractions add up to 1 | To find a quantity: multiply the fraction by the total | To find a total: divide the quantity by its fraction | Read carefully - "fraction of" and "fraction more than" are different
Common Errors: Watch Out! 1. Wrong: In ratio 2:3, the first part is 2/3 of the total Correct: Total parts = 5, so the first part is 2/5 of the total 2. Wrong: In ratio 1:4, the second part is 4 times the total Correct: The second part is 4/5 of the total, not 4 times the total 3. Wrong: To find the total from one share in ratio 3:5, just multiply by 5 Correct: If one share is 3/8 of total = £30, then total = £30 × 8/3 = £80
AO3 - Reasoning & Interpretation: Reasoning and Interpretation School X has 180 students and the ratio of boys to girls is 5:4. School Y has 240 students and the ratio of boys to girls is 7:5. (a) Which school has a higher proportion of boys? (b) How many more boys than girls are there in School X? (c) A student says "School Y has more boys than School X because it has more students." Is this necessarily true? Calculate to check. Answers: (a) School X: boys = 5/9 ≈ 55.6%. School Y: boys = 7/12 ≈ 58.3%. School Y has a higher proportion. (b) Boys = 5/9 × 180 = 100, Girls = 4/9 × 180 = 80. Difference = 20 more boys. (c) School Y boys = 7/12 × 240 = 140. School X boys = 100. Yes, School Y does have more boys (140 vs 100), but th
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how fractions in ratio problems connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of fractions in ratio problems
  • Critical: "What are the limitations of the models used in fractions in ratio problems?"

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)