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**Scheme of work: Key Stage 3: Year 8: Term 3: Ratio, Proportion and Rates of Change**

- Work interchangeably with terminating decimals and their corresponding fractions.
- Define percentage as the number of parts per hundred, interpret percentages and percentage changes as a fraction or a decimal
- Interpret fractions and percentages as operators

- If the ratio between two things is the same, they are in direct proportion.
- To divide an amount in a given ratio find the value of one share by finding the total number of shares, then divide the amount by the total number of shares.
- To compare values work out the cost per unit or number of units per pound or penny. This takes the form of 1 : n.
- A common misconception is to write the ratio of 2 : 3 as 2/3. Emphasise the need to consider the total number of shares when writing a ratio as an equivalent fraction or percentage.

- Develop fluency
- Consolidate their numerical and mathematical capability from key stage 2 and extend

their understanding of the number system - Select and use appropriate calculation strategies to solve increasingly complex problems.

- Consolidate their numerical and mathematical capability from key stage 2 and extend
- Reason mathematically
- Extend their understanding of the number system; make connections between number

relationships, and their algebraic and graphical representations - Extend and formalise their knowledge of ratio and proportion in working with measures

and geometry, and in formulating proportional relations algebraically

- Extend their understanding of the number system; make connections between number
- Solve problems
- Develop their mathematical knowledge, in part through solving problems and evaluating

the outcomes, including multi-step problems - Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

- Develop their mathematical knowledge, in part through solving problems and evaluating

- Ratio, proportion and rates of change
- Change freely between related standard units [for example time, length, area, volume/capacity, mass]
- Use scale factors, scale diagrams and maps
- Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
- Use ratio notation, including reduction to simplest form
- Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
- Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
- Relate the language of ratios and the associated calculations to the arithmetic of fractions
- Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- Use compound units such as speed, unit pricing and density to solve problems.

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