Comparing with Confidence

---

Overview

Unit: Fractions to Ratios Adventure
Lesson Number: 12 of 15
Lesson Title: Comparing Ratios
Year Group: Year 6
Subject: Mathematics
Total Time: 53 minutes
Number of Pupils: 30
Curriculum Link:
Mathematics Programme of Study: Key Stage 2 (Year 6)
National Curriculum Strand: Ratio and Proportion
Statutory Requirement:

“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.”

---

Learning Objectives

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

• Understand the concept of comparing ratios using multiplication and equivalent ratios.
• Identify whether given ratios are equal, greater, or smaller than others.
• Apply knowledge of ratio comparison to solve real-life and problem-based questions.
• Explain their reasoning clearly using mathematical vocabulary.

---

Success Criteria

Pupils will:

• Use multiplication or division to scale ratios.
• Represent ratios visually and understand part-to-part vs. part-to-whole relationships.
• Make accurate judgements when comparing two or more different ratios.
• Communicate answers clearly using terms like “equivalent,” “greater than,” “smaller than,” and “in simplest form.”

---

Resources

• Mini whiteboards and pens
• Large teacher display (IWB or projector)
• Ratio Detective Cards (provided in pack)
• A3 Poster Grids (groups of 5)
• Visual fraction/ratio tiles (plastic or printed)
• Classroom ratio chart (prepared beforehand)
• Stopwatch or timer app

---

Vocabulary

• Ratio
• Equivalent
• Simplest form
• Compare
• Multiply
• Scale factor
• Greater than
• Part-to-part / Part-to-whole

---

Lesson Structure (53 mins)

🔹 1. SETTLER STARTER (5 mins)

Activity: Ratio Scramble
As pupils enter class, they receive a mini whiteboard with a scrambled set of numbers (e.g. 2:6, 1:3, 3:12). Challenge: Match pairs of equivalent ratios.

Ask:

“Who can identify a pair that shows the same relationship?”

Purpose: Recap equivalent ratios in a hands-on, fun way.

---

🔹 2. INTRODUCE NEW LEARNING (8 mins)

Hook: The Great Juice Mix-Up! 🍊
Display two juice recipes:

• Juice A: 2 parts orange to 3 parts water
• Juice B: 4 parts orange to 5 parts water

Ask:

“Which one is stronger? Which has more juice per part?”

Demonstrate using visuals (ratio tiles or bar models projected). Highlight how we compare two ratios by bringing them to a common base using multiplication or division.

Teacher Explanation:

• Recap what a ratio means (link back to fractions of amounts)
• Discuss the importance of equivalent ratios and scaling
• Model how to write both to have a common second term (common denominator-style thinking)

---

🔹 3. GUIDED PRACTICE (10 mins)

Activity: Comparing Mystery Ratios
Project or hand out pre-made comparisons (printed or digital), such as:

1. 3:4 vs 6:8
2. 2:5 vs 4:7
3. 5:6 vs 10:12

Teacher uses IWB to compare the first one as a class, using scaling and bar models. Pupils discuss in pairs and show answers on whiteboards. Use think-pair-share with cold-calling to engage variety of learners.

Encourage mathematical language:

• “I scaled this ratio by…”
• “These are equivalent because…”
• “This ratio is larger because…”

---

🔹 4. MAIN ACTIVITY (20 mins)

Group Challenge: Ratio Detectives 🕵️‍♂️
Pupils split into mixed-ability groups of 5. Each group receives a set of “Ratio Detective Cards” (scenarios involving comparing food recipes, animal weights, map distances, etc.).

Instructions:

• Each card presents a scenario with two or more competing ratios.
• Pupils must work together to compare them and explain their detection methods.
• Pupils record answers on A3 “Investigation Posters,” showing:
  • The compared ratios
  • Working out (on a ratio number line or with scaling)
  • Final judgement (“greater than”, “equal”, “less than”)

Three stations are available for practical reinforcement:

1. Bar Model Maker — Use magnetic strips to model ratios.
2. Juice Lab — Mix water and squash in ratio beakers to compare recipes.
3. Ratio Rollers — Roll dice to create and compare random ratios.

Teaching Support:

• Teacher and TA circulate, probing reasoning and providing guided support.
• Prompt scaffold questions: “Can you scale both to the same second number?” / “What happens if we flip the comparison?”

---

🔹 5. PLENARY (8 mins)

Game: Ratio Rumble (Whole Class)
Split class into two teams. Each round, show a pair of new ratios on screen. One pupil from each team races to compare them first — but must explain their full working aloud.

Example round:

6:10 vs 3:5
Expected reasoning: Scale 3:5 by 2 to make 6:10 — these are equivalent.

Provide strategy praise: celebrate clear explanation, not just speed.

Wrap-up Questions:

• “Why does scaling help us?”
• “How do we know a ratio is greater or smaller?”

---

Assessment for Learning (AfL)

✅ Formative checks through whiteboard responses and group work discussions
✅ Teacher questioning during ratio rotations
✅ A3 Poster outputs for assessment of reasoning and accuracy
✅ Plenary game for oral explanation confidence

---

Differentiation

• Support: Use visual ratio tiles and sentence starters (“I scaled this number by...”)
• Challenge: Introduce 3-part ratios for extension, e.g. 3:5:7 vs 6:10:14
• EAL Pupils: Pre-teach vocabulary using images and fraction equivalents
• SEND: Use tactile manipulatives and smaller group facilitation

---

Homework / Reflection Task

📘 Challenge Booklet Page: “Compare the Cookoff!”
Pupils compare different recipes and justify which is stronger, sweeter, or more concentrated based on given ratios.

---

Teacher Reflection Prompts

• Were pupils able to explain their reasoning clearly and correctly?
• Which strategies were most effective for visualising?
• How did pupils respond to the detective group format?
• Was it clear who needed more scaffolded support for ratio comparison?

---

Next Steps

In Lesson 13, pupils will learn how ratios relate to fractions and scaling quantities, tying recent concepts together as we head toward real-world ratio problem-solving.

---

✅ This lesson experience is designed to combine practical learning with deep conceptual understanding, giving pupils a toolkit to explain and apply ratio comparison with confidence.