Modelling Variations

March 13, 2023

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

Prerequisite Knowledge

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

Success Criteria

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.

Key Concepts

The symbol ∝ is used to represent proportional to.
Direct proportion and varies directly both include y ∝k x, y ∝kx² and y ∝kx³
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.

Common Misconceptions

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.

Modelling Variations Resources

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