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.

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

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.

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.