Ratio, Proportion and Rates of Change

Students learn how to use ratio notation to solve problems ranging from interpreting the scale of a map to calculating a speed, distance or time.

This unit takes place in Term 3 of Year 8 and follows on from multiplying and dividing with fractions.

Ratio, Proportion and Rates of Change Lessons


Prerequisite Knowledge
  • Work interchangeably with terminating decimals and their corresponding fractions.
  • Define percentage as ‘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.


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