Modelling Variations

June 3, 2022

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.

Modelling Variations Lessons
Number: Interactive Lessons
Non-Linear Direct Proportion
4 Part Lesson
Non-Linear Direct Proportion
Students learn how to model non-linear direct proportion functions using formulae and graphs.
Number: Interactive Lessons
Modelling Inverse Proportion
4 Part Lesson
Modelling Inverse Proportion
Students learn how to model inverse proportion problems using the constant of variation
Number: Interactive Lessons
Direct Linear Proportion
4 Part Lesson
Direct Linear Proportion
Students learn how to model variables in direct proportion using the constant of proportionality.
Additional Resources
Algebra: Interactive Lessons
Modelling Inverse Variations
Extended Learning
Modelling Inverse Variations
Additional practise learning how to model inverse variations.
Algebra: Interactive Lessons
Modelling Non-Linear Variations
Extended Learning
Modelling Non-Linear Variations
Additional practice modelling direct square, cube and square root variations.
Algebra: Interactive Lessons
Revising Modelling Variations
Revision
Modelling Variations
Revision lesson on modelling variations using formulae for exam students.
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.

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