# 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.

##### 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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