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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Higher content only |
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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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Higher content only |
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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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Higher content only |
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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
Basic foundation content |
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Higher content only |
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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 |