Ratio and Proportion

Status: Mandatory

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Concepts

This study delivers 1 primary concept and 0 secondary concepts.

Primary concept: Ratio and Proportion (MA-Y6-C012)

Type: Process | Teaching weight: 3/6

Mastery of ratio and proportion means pupils can express the relationship between two quantities using ratio notation (a:b), scale up and down using a multiplier, solve problems involving sharing in a given ratio, and use percentages and fractions as tools for expressing proportional relationships. A fully secure pupil understands the difference between additive comparison (A has 3 more than B) and multiplicative comparison (A has 3 times as many as B) and can identify which type of reasoning is required by a problem.

Teaching guidance: Begin with practical activities: making paint colours from different proportions of red and yellow, mixing squash with water, dividing a class into boys and girls in a given ratio. The 'unitary method' — finding the value of one part and scaling — should be taught alongside the 'scale factor' method. Bar models are particularly effective for ratio problems as they make the proportional structure visible. Connect to percentage increase and decrease as applications of proportion. Similar shapes provide a geometric context in which scale factors arise naturally. Key vocabulary: ratio, proportion, scale factor, unitary method, parts, share, for every, in the ratio, percentage, similar Common misconceptions: Pupils frequently apply additive rather than multiplicative reasoning in proportion problems (e.g., if a recipe for 4 serves uses 200 g flour and 150 g butter, pupils subtract to get 50 g 'difference' and add 50 g for each extra serving rather than using the ratio 4:3). In sharing problems, pupils sometimes give each person the stated number of parts rather than computing the value of each part. The bar model is the most effective tool for preventing both misconceptions.

Differentiation

Model response (Entry): Total parts: 3 + 2 = 5. One part = 20 ÷ 5 = 4. Ali gets 3 × 4 = 12. Ben gets 2 × 4 = 8.

Model response (Developing): For 1 person: 300 ÷ 4 = 75g. For 6 people: 75 × 6 = 450g.

Model response (Expected): Girls represent 5 parts. 5 parts = 15, so 1 part = 3. Boys = 3 parts = 9. Total: 15 + 9 = 24.

Model response (Greater Depth): Original: 3 + 5 = 8 parts. One part = 600 ÷ 8 = 75 ml. Red = 3 × 75 = 225 ml. Blue = 5 × 75 = 375 ml. After adding red: 225 + 150 = 375 ml red. Blue stays at 375 ml. New ratio = 375:375 = 1:1.

Representation stages (CPA)

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Thinking lens: Scale, Proportion and Quantity (primary)

Key question: How big, how many, or how much — and how does that change how we think about it? Why this lens fits: Ratio and proportion are the formal language of multiplicative comparison — this cluster teaches pupils to express and use relative quantities directly, bridging all prior fraction and multiplicative work to KS3 Ratio, Proportion and Rates of Change. Question stems for KS2:

How many times bigger is this than that?

What fraction of the whole is this part?

Which unit of measurement fits best here? Why?

If we doubled the amount, what would change?

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Session structure: Worked Example Set + Practical Application

This study uses 2 vehicle templates:

Worked Example Set (main structure)

A mastery-oriented mathematics sequence moving through the concrete-pictorial-abstract progression with activation and reasoning extension phases. Begins by activating prior knowledge, introduces new concepts with physical manipulatives, transitions to pictorial representations, develops abstract fluency, applies in context, and extends through reasoning challenges.

activation → concrete → pictorial → abstract → application → reasoning_extension Assessment: Graduated practice set moving from guided examples to independent application, with reasoning task requiring explanation of method and justification of answers. Teacher note: Use the WORKED EXAMPLE SET template: activate prior knowledge and address common misconceptions. Guide pupils through the concrete-pictorial-abstract progression, modelling each step with clear mathematical language. Provide varied practice that builds fluency, then extend with reasoning problems that require pupils to explain, justify, or spot errors. Use bar models and diagrams to build conceptual understanding. KS2 question stems:

What do you already know that could help you here?

Can you draw a bar model or diagram to represent this problem?

Where has this gone wrong, and how would you correct it?

Can you explain why this method works, not just how?

Practical Application

A hands-on sequence where pupils apply knowledge and skills to solve a practical problem or create a functional outcome. Begins with a real-world context, builds skills through rehearsal, guides design or planning, supports making or problem-solving, and concludes with evaluation against success criteria.

context → skill_rehearsal → design → make_or_solve → evaluate Assessment: Practical outcome (solution, product, program) evaluated against defined success criteria, with written or verbal explanation of the process and decisions made. Teacher note: Use the PRACTICAL APPLICATION template: set a real-world context or problem that requires pupils to apply knowledge and skills. Rehearse the key skills needed through guided practice. Support pupils in designing their approach, carrying out the practical task, and evaluating their outcome. Encourage them to explain what worked well and what they would improve. KS2 question stems:

What skills will you need to solve this problem?

What is your plan, and why did you choose this approach?

How well did your solution work?

What would you change if you did it again?

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Mathematical reasoning skills (KS2)

These disciplinary skills should be woven through teaching, not taught in isolation:

Checking and verifying results — Use inverse operations, estimation or an alternative method to check whether a result is reasonable, and adjust working when an answer does not make sense in context.

Problem solving with unfamiliar and complex structures — Formulate and solve problems that require choosing from a wide range of mathematical knowledge, devising strategies for problems with no immediately obvious method, and persevering through multi-stage solutions in unfamiliar contexts.

Mathematical proof — Understand and apply the concept of mathematical proof, distinguishing between evidence, conjecture and proof, constructing simple proofs by exhaustion or direct argument, and recognising why a finite number of examples cannot prove a universal statement.

Critical evaluation and error analysis — Critically evaluate the validity of mathematical arguments and solutions presented by others, identifying errors in reasoning or calculation, explaining why a result is or is not correct, and constructing counter-examples to disprove false claims.

Algebraic reasoning and generalisation — Express generalisations symbolically using algebraic notation, reason about the properties of unknown quantities, and use algebra to prove or disprove conjectures about numbers and geometric relationships.

Estimation, checking and reasonableness — Use rounding, inverse operations and known facts to estimate answers before calculating, check the reasonableness of results in context, and identify errors in worked examples by comparing expected and actual outcomes.

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Vocabulary word mat

Prior knowledge (retrieval plan)

Pupils should already know the following from earlier units:

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Assessment alignment (KS2)

KS2 test framework content domain codes assessed by this study:

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Scaffolding and inclusion (Y6)

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Knowledge organiser

Core facts (expected standard):

Ratio and Proportion: Solving ratio and proportion problems involving missing values, including percentage contexts, using multiplicative reasoning.

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Graph context

Node type: MathsTopicSuggestion | Study ID: MTS-Y6-004 Concept IDs:

MA-Y6-C012: Ratio and Proportion (primary)

Cypher query:

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Generated from the UK Curriculum Knowledge Graph — zero LLM generation.