Simplifying Ratios Adventure

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🧾 Curriculum Alignment

Subject: Mathematics
Key Stage: Upper Key Stage 2
National Curriculum Reference:

• Ratio and Proportion – Year 6
  • 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 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.

This is Lesson 11 of 15 in the unit: “Fractions to Ratios Adventure”
Total duration: 53 minutes
Class size: 30 pupils

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🎯 Learning Objectives

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

• Understand what it means to 'simplify' a ratio.
• Confidently simplify ratios to their lowest terms using common factors.
• Recognise and apply simplified ratios in everyday contexts.
• Use multiplication and division facts to find equivalent ratios.

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🧠 Prior Knowledge

Pupils should already:

• Understand basic fractions and equivalence.
• Know multiplication and division facts up to 12 × 12.
• Have experience with identifying the greatest common factor (GCF).
• Be familiar with ratio notation (e.g. 2:3).

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🗂️ Lesson Structure

⏱️ 0–6 mins | Warm-Up: Ratio Riddles

Activity: Display a series of ‘Ratio Riddles’ on the board. These are mini-puzzles involving equivalent ratios and proportions.

Example Riddle:

“If a toy robot costs £4 for every 2 batteries, how many batteries would I need for 12 robots?”

Purpose: Reactivate thinking on proportional relationships.

Resources: Whiteboard, visual prompts
Facilitation Tip: Cold call or use mini-whiteboards to engage everyone.

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⏱️ 6–15 mins | Direct Instruction

Topic: Simplifying Ratios to Lowest Terms
Delivery Method: Teacher modelling using concrete visual examples and bar models

1. Start with an everyday scenario:

   “Sam is baking cookies with a ratio of 6 parts flour to 3 parts sugar. Can we make this simpler?”

2. Link to simplifying fractions:

   Just like 6/3 = 2/1, the ratio 6:3 simplifies to 2:1.

3. Model step-by-step process:

   • Identify common factors (e.g. GCF of 6 and 3 is 3).
   • Divide both parts of the ratio by the GCF.
   • Write simplified ratio.

4. Visual: Use bar models to show equivalence:

[■■■■■■] : [■■■] = [■■] : [■]

Challenge Thought:

Is 10:15 the same as 2:3? How do we know?

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⏱️ 15–25 mins | Guided Practice

Distribute a short worksheet with scaffolded examples. Example questions:

1. Simplify the ratio 8:4
2. Simplify 14:21
3. Tim runs 12km while Jess runs 9km. What’s the simplified ratio of Tim’s distance to Jess’s?

Partner Work

• Pupils work in pairs using mini-whiteboards.
• Teacher circulates to check understanding, guiding with questioning.

Differentiation:

• Use peer buddies for support.
• Extension problem on back of sheet: Ratio Triangles Puzzle.

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⏱️ 25–38 mins | Main Activity: "Ratio Rescue Mission"

Contextual Problem-Solving Game

Story Hook:

“A team of scientists needs to evacuate an endangered animal species. Supplies must be loaded in a precise ratio for the animals to survive the journey!”

Set-up: Pupils are split into 6 'expedition teams'. Each team gets a mission envelope with a set of 5 challenges. Each challenge requires simplifying a ratio and solving a real-world problem.

Sample Mission Card:

“Your helicopter can only carry food and water in a ratio of 18:24. Simplify it to determine how many crates of each can go.”

Resources: Laminated cards, calculator (optional), reward tokens.

Outcomes:

• Encourage teamwork and logical thinking.
• Pupils race to decode the most 'rescue missions'.

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⏱️ 38–46 mins | Application: Real-Life Ratios

Activity: Bring in familiar UK contexts.
Use examples such as:

• An NEC Arena seating plan (circle and square sections in 5:7 ratio)
• Recipe conversions (e.g. If 2:3 of lemon to sugar serves 5, how many for 10 servings?)

Pupils write and simplify their own real-life ratios from a bank of photos around the room.

Gallery Walk: Teams walk around, try to simplify ratios created by others.

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⏱️ 46–53 mins | Reflect & Review

Plenary Discussion Questions:

• What does 'simplify' really help us with?
• Are some ratios already simplified?
• Is 40:60 and 2:3 the same? Why?

Exit Ticket (on sticky note):

“Write one simplified ratio and a real-life context where it might occur.”

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🧑‍🏫 Teacher Tips

• Use manipulatives if necessary (e.g. Cuisenaire rods or ratio cubes).
• Use explicit thinking aloud strategies during direct instruction.
• Link back to equivalent fractions often for clarity.

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📚 Assessment for Learning (AfL)

• Observation during pair work and Ratio Rescue.
• Quality of explanations during plenary.
• Exit slips to assess conceptual clarity.
• Checklist for mission completion (self/peer-assessed)

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🧰 Resources

• Whiteboard & markers
• Simplifying Ratios Worksheets
• Ratio Rescue Mission Cards
• Mission Envelopes
• Sticky notes
• Photograph bank of real-life ratio examples (laminated images)

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🔁 Homework (Optional)

Create a two-minute video or poster explaining how to simplify a ratio. Use a real-world example from home (e.g. ingredients, favourite sports team stats).

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📌 Notes for TA Support

• Pre-teach keywords: simplify, lowest terms, factor.
• Support small targeted group using physical counters/double number lines.
• Use scaffolded ratio strips for visual learners.

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✨ Stretch & Challenge

For early finishers or higher-attaining pupils:

• Introduce 3-part ratios (e.g. 9:6:3 → simplify to 3:2:1).
• Real-world data handling task: simplify class attendance or home chores ratios!

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📍Next Steps

In Lesson 12: Pupils will build on this by scaling simplified ratios up and down to solve proportional reasoning problems, applying knowledge to map reading and recipes.

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End of Lesson 11 – Fractions to Ratios Adventure