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**Higher GCSE: Year 10: Term 6: Modelling Variations**

Students learn to set up and use formulae to model direct and indirect variations. Later, as learning progresses, students illustrate these models using graphs.

This unit takes place in Year 10 Term 6 and follows on from Ratio and Proportion.

- 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 ‘is proportional to’.
- Direct proportion and varies directly both include y ∝ x, y ∝ x
^{2}and y ∝ x^{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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