# Modelling Variations

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

### Mr Mathematics Blog

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Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

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#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.