Ratios and Fractions

Overview

Unit Title: Fractions to Ratios Adventure
Lesson Number: 13 of 15
Lesson Duration: 53 minutes
Class Size: 30 pupils
Key Stage: Key Stage 2
Year Group: Year 6 (Ages 10–11)
Curriculum Area: National Curriculum for Mathematics – Ratio and Proportion

National Curriculum Reference:

• Ratio and Proportion - Year 6:
  ➤ "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 unequal sharing and grouping using knowledge of fractions and multiples."
  ➤ "Use ratio language and link to fraction and multiplication concepts."

Lesson Title

Ratios and Fractions Connection

Learning Objective

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

• Understand and explain the relationship between fractions and ratios.
• Convert simple ratios into equivalent fractions (and vice versa).
• Apply this understanding to solve contextualised ratio/fraction problems.

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Success Criteria

Pupils will:

• Identify a ratio and match it to an equivalent fraction.
• Represent part-to-whole and part-to-part relationships using fractions and ratios interchangeably.
• Solve at least 3 contextual ratio/fraction conversion problems correctly by the end of the lesson.

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Required Resources

• Individual mini whiteboards & pens
• Ratio and Fraction Domino Cards (print-and-play resource)
• Colour-coded counters or linking cubes (30 sets of 2 colours)
• Interactive whiteboard
• Ratio & Fraction Flipbook (for pupil books)
• Visualiser (for live modelling)
• Pupil reflection slips (exit tickets)

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Differentiation & Inclusivity

• Support: Sentence starters and visual ratio models available; TA to support targeted group; Concrete manipulatives available throughout.
• Challenge: Extension tasks involving 3-part ratios; Reasoning questions requiring explanation of equivalence.
• EAL/SEMH: Emphasis on visuals, paired discussion, and accessible vocabulary support.

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Vocabulary Focus

• Fraction
• Ratio
• Equivalent
• Part-to-part
• Part-to-whole
• Simplify
• Whole

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Lesson Breakdown (53 Minutes)

⏱ 0–5 mins – Hook & Recap: "Fraction Detective Game"

Pupil Engagement Task:
Teacher flashes fraction cards quickly on the board (e.g. ½, ¾, ⅔), and pupils must sketch a quick picture or bar model showing the part-to-whole representation on mini whiteboards.

Then: Teacher reveals a ratio and asks, "How is this the same/different from the fraction?"

🗣 Pair discussion: “What makes this ratio look like a fraction—and what doesn’t?”

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⏱ 5–15 mins – Explore: Modelling the Connection

Teacher Input (I Do):
Using the interactive whiteboard and coloured cubes:

• Show "2 red to 3 blue" → Total of 5 cubes
• Ask: “What's the fraction that are red?” (2/5)
• Model converting ratio 2:3 into a fraction of the whole: Red = 2/5, Blue = 3/5
• Then, show another: 1 green to 2 yellow. Ask questions: ➤ What’s the ratio?
  ➤ What's the total?
  ➤ What fraction is green? Yellow?

Visuals used: part-to-part vs part-to-whole diagrams.

Class Discussion with Questions:

• "What’s the total number we’re dividing into fractions?"
• "How can we test if a ratio and fraction are equivalent?"

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⏱ 15–25 mins – Guided Practice (We Do): Ratio & Fraction Match-Up

Paired Activity
Each pair is given a set of domino-style cards (15 total), where half show ratios (e.g. 3:2), and half show fractions (e.g. 3/5). Pupils must match each ratio card to its equivalent fraction card.

• Encourage reasoning aloud: ➤ "If my ratio is 3:2, what’s the total?"
  ➤ "So, 3 out of 5 is…?"

Teacher circulates for formative assessment, posing questions and nudging misconceptions.

📸 Teacher takes photos of clear visual models to showcase via visualiser later!

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⏱ 25–38 mins – Independent Practice (You Do): Solve the Mystery!

Worksheet Task – “The Missing Juice Recipe”
Pupils are given a juice recipe written in ratios:

Apple Juice : Grape Juice = 2:3
Using this, answer 6 scaffolded questions, e.g.:

• What fraction of the recipe is apple juice?
• If we have 500 ml total, how much of each juice do we need?
• If we double all amounts, what happens to the ratio? Why?

Extension:

• Include 3-part ratios, e.g. 1:2:3, and comparisons like "How much larger is the part that’s 3 compared to the part that’s 1?"

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⏱ 38–47 mins – Challenge & Reasoning Deep Dive

Whole Class
Using the visualiser or board, work through one or two of the trickiest questions.

Then: Pose this reasoning task (METACOGNITIVE TWIST):

🧠 “A pupil says ‘If something is in the ratio 4:1, that means 4/1 of it is one part.’
Is this true or false? Prove it.”

• Pupils justify their answer on whiteboards or verbally in pairs.
• Teacher facilitates full-class reasoning discussion.

🗣 Encourage sentence starters:

• "This is incorrect because…"
• "The mistake is due to…"
• "They may have confused…"

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⏱ 47–51 mins – Reflect & Share

Pupil Exit Slip:
Each pupil completes a ‘Ratio & Fraction Reflection’ slip with prompts:

• "One thing I now understand about ratios and fractions is…"
• "I used to think…, but now I know…"
• Draw a model to show a ratio used as a fraction.

👏 Selected pupils share their responses aloud with the class.

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⏱ 51–53 mins – Closing Spark + Teaser for Lesson 14

Teacher asks: 🏆 “Do you think ratios or fractions would be more helpful when splitting 100 sweets between friends? Why?”

📘 Tease: "Next time, we’re designing our own recipes using ratios—and you'll need to make the perfect potion!"

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Assessment Opportunities

• Live questioning during match-up activity and modelling
• Observation during independent problem solving
• Quality of reflection exit slips
• Misconceptions addressed in final reasoning discussion

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Cross-Curricular Opportunities

• Science: Pupils apply ratios/fractions when measuring materials in experiments.
• DT: Ratios principles support scaling recipes and solving volume problems.
• PSHE: Fairness and proportionality in sharing.

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Teacher Reflection Prompts

After lesson, consider:

• Did pupils clearly distinguish between part-to-part and part-to-whole?
• Were they able to justify equivalencies between fractions and ratios?
• Is further consolidation needed before scaling into proportion (Lesson 14)?

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Notes for TA or Support Staff

• Pre-teach fraction vocabulary to target pupils.
• Sit with Group A (Names) during paired tasks to model visualisation of ratios.
• Directly model from concrete to pictorial if gaps emerge.

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WOW Factor Element

🧪 Juice Recipe Mapping + Visual Ratio Dominoes + Real-world reasoning =
A mathematical ‘aha’ moment that bridges two core concepts in a hands-on, age-appropriate and highly visual way.

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End of Lesson 13

📍 Next Up: "Proportion Potions" – Designing ratios that scale up and scale down quantities—perfect for an exciting themed challenge!

Let the adventure continue…