# Ratio, Proportion and Rates of Change

Scheme of work: Key Stage 3: Year 8: Term 3: Ratio, Proportion and Rates of Change

#### Prerequisite Knowledge

• Work interchangeably with terminating decimals and their corresponding fractions.
• Define percentage as the number of parts per hundred, interpret percentages and percentage changes as a fraction or a decimal
• Interpret fractions and percentages as operators

#### Key Concepts

• If the ratio between two things is the same, they are in direct proportion.
• To divide an amount in a given ratio find the value of one share by finding the total number of shares, then divide the amount by the total number of shares.
• To compare values work out the cost per unit or number of units per pound or penny.  This takes the form of 1 : n.
• A common misconception is to write the ratio of 2 : 3 as 2/3.  Emphasise the need to consider the total number of shares when writing a ratio as an equivalent fraction or percentage.

#### Working Mathematically

• Develop fluency
• Consolidate their numerical and mathematical capability from key stage 2 and extend
their understanding of the number system
• Select and use appropriate calculation strategies to solve increasingly complex problems.
• Reason mathematically
• Extend their understanding of the number system; make connections between number
relationships, and their algebraic and graphical representations
• Extend and formalise their knowledge of ratio and proportion in working with measures
and geometry, and in formulating proportional relations algebraically
• Solve problems
• Develop their mathematical knowledge, in part through solving problems and evaluating
the outcomes, including multi-step problems
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

#### Subject Content

• Ratio, proportion and rates of change
• Change freely between related standard units [for example time, length, area, volume/capacity, mass]
• Use scale factors, scale diagrams and maps
• Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
• Use ratio notation, including reduction to simplest form
• Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
• Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
• Relate the language of ratios and the associated calculations to the arithmetic of fractions
• Solve problems involving direct and inverse proportion, including graphical and algebraic representations
• Use compound units such as speed, unit pricing and density to solve problems.

## Ratio, Proportion and Rates of Change Resources

### Mr Mathematics Blog

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

#### T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing