Ratio and Proportion
KS2MA-Y6-D004
Solving problems involving the relative sizes of two quantities using ratio notation; solving problems involving similar shapes and scale factors; using percentages for comparison; solving problems involving unequal sharing and grouping.
National Curriculum context
Ratio and proportion is introduced explicitly as a named domain for the first time in Year 6, although proportional reasoning has been developed informally throughout the curriculum in contexts such as scaling recipes, comparing measures, and working with fractions and percentages. The formal introduction of ratio notation (a:b) and the language of 'for every' relationships marks a significant conceptual development, bridging the additive thinking that dominates KS1 and lower KS2 towards the multiplicative thinking central to KS3 mathematics. Work on similar shapes and scale factors provides an important geometric application of ratio, connecting proportion to Year 6 geometry content. The study of percentage as a tool for comparison introduces pupils to the idea of a common scale for comparing different quantities, which is extensively used in statistics and financial mathematics. This domain is deliberately brief but conceptually rich, laying foundations for the linear functions, direct proportion, and algebraic ratio work that pupils will encounter in secondary school.
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Concepts
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Clusters
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Prerequisites
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With difficulty levels
Lesson Clusters
Understand and use ratio and proportion to solve problems
practice CuratedOnly one concept in this domain. Ratio and proportion is the new Year 6 domain that bridges to KS3 Ratio, Proportion and Rates of Change.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Ratio and Proportion
Mathematics Worked Example SetPrerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (1)
Ratio and Proportion
process AI DirectMA-Y6-C012
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.
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.
Difficulty levels
Sharing a quantity in a simple ratio using the 'one part' method with concrete or pictorial support.
Example task
Share 20 sweets between Ali and Ben in the ratio 3:2. How many does each person get?
Model response: Total parts: 3 + 2 = 5. One part = 20 ÷ 5 = 4. Ali gets 3 × 4 = 12. Ben gets 2 × 4 = 8.
Solving proportion problems using the unitary method or scale factor, including simple recipes and scaling.
Example task
A recipe for 4 people uses 300g flour. How much flour for 6 people?
Model response: For 1 person: 300 ÷ 4 = 75g. For 6 people: 75 × 6 = 450g.
Solving ratio and proportion problems involving missing values, including percentage contexts, using multiplicative reasoning.
Example task
In a class, the ratio of boys to girls is 3:5. There are 15 girls. How many children are in the class altogether?
Model response: Girls represent 5 parts. 5 parts = 15, so 1 part = 3. Boys = 3 parts = 9. Total: 15 + 9 = 24.
Solving multi-step ratio problems where the ratio must be inferred from context, or where a change in one quantity requires reasoning about the effect on the ratio.
Example task
Purple paint is made by mixing red and blue in the ratio 3:5. Sam has 600 ml of purple paint. He adds 150 ml more red paint. What is the new ratio of red to blue? Give your answer in its simplest form.
Model response: 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.
CPA Stages
concrete
Mixing paint, juice or recipe ingredients in given ratios, physically sharing objects into ratio groups using sorting trays, and using Cuisenaire rods to show proportional relationships
Transition: Child finds the value of one part by dividing by the total number of parts and scales correctly without physical objects
pictorial
Drawing bar models to represent ratios, recording ratio tables showing scaling, and solving proportion problems on paper
Transition: Child solves ratio and proportion problems on paper using bar models or the unitary method, selecting the most efficient approach
abstract
Solving ratio and proportion problems mentally, using the unitary method and scale factors, and distinguishing multiplicative from additive relationships
Transition: Child solves any ratio/proportion problem efficiently and always identifies whether a problem requires multiplicative or additive reasoning
Delivery rationale
Upper primary maths (Y6) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.