Ratios: relationship between two (or more) numbers (with the same unit) indicating how many times the first number contains the second
Rates: A specific type of ratio which measures changes between two numbers (with different units) over a particular period
Gradient: The slope of a line
Linear: Straight line
Direct: Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other
Proportional: In mathematics, two varying quantities are said to be in a relation of proportionality, if they are multiplicatively connected to a constant, that is, when either their ratio or their product yields a constant.
Linear direct proportion: Two quantities that increase or decrease at the same rate/ratio
Inverse proportion: The relationship between two quantities where increasing one variable results in the decrease of the other
Constant of proportionality: A constant variable in an equation which establishes the relationship between the variables y and x
Specific terminology (words and language structures)
Use the word 'per', meaning 'for every' when describing rates
'As the speed increases, the time taken to travel a particular distance decreases', 'The greater the speed, the less time is taken to travel a particular distance', 'The time taken to travel a particular distance is reduced when the speed is increased'.
When solving ratio and rate problems, students should conclude with a statement in words.
When constructing stories and interpreting distance/time graphs, students can use present tense, 'The man travels …', or past tense, 'The man travelled …'.