Ratios in Action

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📚 Curriculum Details

Curriculum Framework:
UK National Curriculum – Mathematics
Key Stage: KS2
Year: 6
Strand: Ratio and Proportion
Programme of Study Link:
Pupils should be taught to:

• solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
• solve problems involving the calculation of percentages – for example, of measures, and such as 15% of 360 – and the use of percentages for comparison
• solve problems involving similar shapes where the scale factor is known or can be found
• solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

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📍 Lesson Overview

Lesson Number: 14 of 15
Unit Title: Fractions to Ratios Adventure
Lesson Title: Real-Life Applications of Ratios and Percentages
Lesson Duration: 53 minutes
Class Size: 30 pupils
Learning Context: Building on prior work with fractions, ratios, and percentages, pupils apply their knowledge to interpret and solve real-world problems, providing a meaningful context to abstract mathematical ideas.

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✨ Learning Objectives

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

• Identify and solve real-life problems using ratios and percentages
• Apply ratio reasoning in budgeting, recipe scaling, and scale models
• Communicate mathematical workings clearly and confidently in small groups
• Demonstrate an understanding of proportionate reasoning in realistic contexts

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🔍 Success Criteria

• I can read a real-life problem and identify where to use a ratio or percentage.
• I can use multiplication and division facts to solve ratio problems.
• I can calculate percentages of amounts accurately.
• I can explain my reasoning and check that my answer makes sense in context.

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🧠 Prior Knowledge

Pupils should already be familiar with:

• Converting between fractions, decimals, and percentages
• Basic percentage calculations (e.g., 10%, 25%, 50%)
• Writing and simplifying ratios
• Using ratio language (e.g., "for every 1 of this, there are 3 of that")

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🛠️ Resources Required

• Mini-whiteboards and pens
• Pre-prepared 'Scenario Cards' (see below)
• Printed Budgeting Worksheets, Recipe Cards, and Scale Model Task Sheets
• Calculators (optional, teacher discretion)
• Rulers, coloured pencils, and glue sticks (for modelling task)
• Real object examples to support tasks – e.g., food packaging, toy models, paper recipe cuttings

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⏰ Lesson Breakdown

⏱️ 0–4 mins: Warm-Up — Percentage Quick Fire

Objective: Quick recall of key percentage equivalences.

• Teacher reads aloud percentage questions (e.g., “What’s 25% of 200?”)
• Pupils write answers on mini-whiteboards and show them
• Emphasis on mental strategies and quick calculations

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⏱️ 5–10 mins: Hook — "Where We See It"

Objective: Spark curiosity by connecting maths to real life.

• Pose the question: “Where do we see ratios and percentages in the real world?”
• Think-Pair-Share structure:
  • 1 min to think silently
  • 2 mins to discuss with partner
  • 2 mins class discussion — teacher scribes responses on board (e.g., discounts, recipes, sharing packs, map scales)

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⏱ 11–15 mins: Teaching Input — Mini Modelling

Objective: Demonstrate how to unpack a real-life ratio problem.

Example Scenario: You have £100 to plan a pizza party for 5 people. You want to use £60 of your budget for food, £20 for drinks, and save 20% for decorations. Is that possible?

• Teacher models how to:
  • Find 20% of £100
  • Allocate funds using ratio reasoning (3:1:1 split)
  • Check totals
  • Discuss alternative logical strategies
• Pupils take notes or record steps in maths journals

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⏱ 16–34 mins: Grouped Project Tasks — Real-Life Rotations

Objective: Experience solving real-world problems in engaging contexts.

Pupils rotate through three mini-stations. Each station lasts 6 mins, with an additional 2 min movement/reset time between each.

Station 1: Budgeting Challenge (Ratio Focus)
Task: Plan a school disco with a £150 budget. Allocate spending using a 3:2:1 ratio for food, entertainment, and prizes.
Outcome: Pupils work in pairs on a budgeting worksheet. Must show workings and justify choices.

Station 2: Recipe Rescue (Scaling Focus)
Task: Adjust ingredients for a recipe that serves 4 to serve 10.
Outcome: Pupils use ratio scaling and calculate adjusted quantities. Bonus challenge: find the total cost if flour is priced at 75p per 500g.

Station 3: Build a Bedroom (Scale Model Focus)
Task: Design a simple floor plan for a bedroom using a 1:20 scale.
Outcome: Pupils read requirements and create scale model layouts using rulers/paper templates. Must make logical furniture decisions based on space.

Each station has a visual aid, task cards, support prompt cards for pupils needing scaffolding, and extension prompts for early finishers (e.g., flip the task – what if the ratio changes?)

Grouping: 3 groups of 10 students, with teacher and TA floating to support.

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⏱ 35–44 mins: Class Reflection – Mathematician’s Market

Objective: Support metacognitive reflection and discussion.

Each group picks one task to briefly “sell” to the class — what they did, how they solved it, and what maths was involved. Use sentence starters like:

• "At our station, we worked with…"
• "We calculated percentages to…"
• "We learnt that using ratios helps when…"

Teacher records vocabulary on a working wall or flip chart (‘ratio’, ‘scale’, ‘unitary method’, etc.)

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⏱ 45–50 mins: Independent Task / Challenge Question

Objective: Consolidate understanding through a reasoning-rich task.

Task:
“You’ve planned a birthday party for 8 guests. You’ve used a budget of £80, split in a 5:3 ratio between food and decorations. You now have 3 more guests—how does this affect your plan?”

Pupils work independently in books showing all steps. Differentiation: challenge students to recalculate full budget; support students with simplified version featuring fewer guests or steps.

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⏱ 51–53 mins: Plenary — Exit Tickets

Each pupil completes an exit ticket:

• One thing I learned about ratios or percentages is…
• One place I use this in real life is…
• A question I still have is…

Collect exit tickets to inform future planning and final lesson revision.

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🧱 Support & Differentiation

• Support: Prompt cards, guided examples at each station, concrete materials for scale visualisation
• Challenge: Open-ended “what if” tasks, requiring multi-step reasoning and justification
• Vocabulary Focus: reinforce language of ratio, proportion, and percentage with word walls, verbal prompts, and sentence stems

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📊 Assessment for Learning (AfL)

• Observational assessments during rotations
• Pupil dialogue during ‘Mathematician’s Market’
• Work completed in books and recorded on station sheets
• Exit tickets for reflective assessment

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🧠 Extension Opportunities

• Plan an event in full using only a fixed budget and real supermarket/online product listings
• Create a scale model of their dream bedroom or classroom
• Investigate sales and discounts from leaflets—What’s the best deal?

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🪜 Follow-Up for Lesson 15

In the final unit lesson, pupils will synthesise their learning across all 15 lessons with a 'Ratios and Fractions Festival' project which includes cross-curriculum links to DT and Art.

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🎯 Teacher Takeaway

This lesson blends mathematical rigour with creative application. By embedding ratios and percentages into budgeting, food, and design tasks, students see purpose and relevance. Consider making displays of pupil-made scale models and ratio recipes to celebrate learning!

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This lesson supports the development of reasoning and fluency – as highlighted in the DfE's mathematics guidance – and is fully aligned with mastery approaches to Key Stage 2 teaching.