Modelling Variations

Modelling Direct Variation

Modelling Inverse Variation

Non Linear Direct Variation

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 ‘is proportional to’.
• Direct proportion and varies directly both include y ∝  x, y ∝ x² and y ∝ x³
• 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.