**RATIO, PROPORTIONS, RATES OF CHANGE:H**

**1. Change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts**

**2. Use scale factors, scale diagrams and maps**

**3. express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1**

**4. use ratio notation, including reduction to simplest form**

**5. 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;

apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

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**6. Express a multiplicative relationship between two quantities as a ratio or a fraction**

**7. understand and use proportion as equality of ratios**

**8. Relate ratios to fractions and to linear functions**

**9. Percentages.**

- define percentage as ‘number of parts per hundred’
- interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
- express one quantity as a percentage of another
- compare two quantities using percentages
- work with percentages greater than 100%
- solve problems involving percentage change, including percentage increase/decrease and original value problems, and simple interest including in financial mathematics

**10. solve problems involving direct and inverse proportion, including graphical and algebraic representations**

**11. use compound units such as speed, rates of pay, unit pricing, density and pressure**

**12. compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors**

**13. understand that y is inversely proportional to x is equivalent to y=1/x construct and interpret equations that describe direct and inverse proportion **

**14. Interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion**

**15. Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts**

**16. Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.**

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