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**Scheme of work: GCSE Higher: Year 10: Term 6: Modelling Variations**

- Use ratio notation, including reduction to simplest form
- Express a multiplicative relationship between two quantities as a ratio
- Understand and use proportion as equality of ratios
- Relate ratios to fractions
- Express the division of a quantity into two parts as a ratio
- Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
- Understand and use proportion as equality of ratios

- Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y;
- Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- Construct and interpret equations that describe direct and inverse proportion.

- The symbol ∝ is used to represent proportional to.
- Direct proportion and varies directly both include y ∝k x, y ∝kx
^{2}and y ∝kx^{3} - Indirect proportion and varies inversely both include y ∝ 1/x
- k is used as the constant of proportionality
- Students need to be able to associate the graphical representations with the various proportions.

- Students often struggle with writing the correct proportional formula from the written description. Writing indirect proportions is particularly difficult for most students.
- Modelling the variation as a formula with the correct value of k is key to accessing this topic.
- When students do write the correct formula they are often unable to correctly manipulate it to calculate unknown values.

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