Ratio, Proportion and Rates of Change

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

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

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.

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.