# 3.3 Ratio, proportion and rates of change

## R1

Basic foundation content

Higher content only

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

Basic foundation content

Higher content only

use scale factors, scale diagrams and maps

Notes: including geometrical problems.

## R3

Basic foundation content

Higher content only

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

## R4

Basic foundation content

Higher content only

use ratio notation, including reduction to simplest form

## R5

Basic foundation content

Higher content only

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

Basic foundation content

Higher content only

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

## R7

Basic foundation content

Higher content only

understand and use proportion as equality of ratios

## R8

Basic foundation content

Higher content only

relate ratios to fractions and to linear functions

## R9

Basic foundation content

Higher content only

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

Basic foundation content

Higher content only

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

## R11

Basic foundation content

Higher content only

use compound units such as speed, rates of pay, unit pricing

use compound units such as density and pressure

Notes: including making comparisons.

## R12

Basic foundation content

Higher content only

compare lengths, areas and volumes using ratio notation

scale factors

make links to similarity (including trigonometric ratios)

## R13

Basic foundation content

Higher content only

understand that is inversely proportional to is equivalent to is proportional to

interpret equations that describe direct and inverse proportion

construct and interpret equations that describe direct and inverse proportion

## R14

Basic foundation content

Higher content only

interpret the gradient of a straight-line graph as a rate of change

recognise and interpret graphs that illustrate direct and inverse proportion

## R15

Basic foundation content

Higher content only

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

## R16

Basic foundation content