# 3.3 Ratio, proportion and rates of change

## R1

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change freely between related standard units (eg time, length, area, volume/capacity, mass) and compound units (eg speed, rates of pay, prices) in numerical contexts |
compound units (eg density, pressure) in numerical and algebraic contexts |

## R2

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use scale factors, scale diagrams and maps |

**Notes**: including geometrical problems.

## R3

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

## R4

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use ratio notation, including reduction to simplest form |

## R5

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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) |

**Notes**: including better value or best-buy problems.

## R6

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express a multiplicative relationship between two quantities as a ratio or a fraction |

## R7

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understand and use proportion as equality of ratios |

## R8

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relate ratios to fractions and to linear functions |

## R9

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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 |

## R10

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solve problems involving direct and inverse proportion, including graphical and algebraic representations |

## R11

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use compound units such as speed, rates of pay, unit pricing |
use compound units such as density and pressure |

**Notes**: including making comparisons.

## R12

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

## R13

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understand that is inversely proportional to is equivalent to is proportional to |
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interpret equations that describe direct and inverse proportion |
construct and interpret equations that describe direct and inverse proportion |

## R14

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interpret the gradient of a straight-line graph as a rate of change recognise and interpret graphs that illustrate direct and inverse proportion |

## R15

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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 |

**Notes**: see also A15.

## R16

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set up, solve and interpret the answers in growth and decay problems, including compound interest |
and work with general iterative processes |