#R1
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
use scale factors, scale diagrams and maps
Notes: including geometrical problems.
#R3
express one quantity as a fraction of another, where the fraction is less than 1 or greater than 1
#R4
use ratio notation, including reduction to simplest form
#R5
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
express a multiplicative relationship between two quantities as a ratio or a fraction
#R7
understand and use proportion as equality of ratios
#R8
relate ratios to fractions and to linear functions
Notes: see also N11, R14
#R9
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
Notes: see also N2, N12
#R10
solve problems involving direct and inverse proportion, including graphical and algebraic representations
#R11
use compound units such as speed, rates of pay, unit pricing
use compound units such as density and pressure
Notes: including making comparisons.
#R12
compare lengths, areas and volumes using ratio notation
scale factors
make links to similarity (including trigonometric ratios)
Notes: see also G19, G20
#R13
understand that \(X\) is inversely proportional to \(Y\) is equivalent to \(X\) is proportional to \(\dfrac{1}{Y}\)
interpret equations that describe direct and inverse proportion
construct and interpret equations that describe direct and inverse proportion
#R14
interpret the gradient of a straight-line graph as a rate of change
recognise and interpret graphs that illustrate direct and inverse proportion
Notes: see also A15, R8
#R15
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
set up, solve and interpret the answers in growth and decay problems, including compound interest
and work with general iterative processes