Lesson 23 Rates of change

# Episode 2

Reasoning Resources: Worksheet 2
Whole class preparation
As in Episode 1, write the function b =a ? on the board and ask for the value of b for different values of a.
Pair work
Mathematics research suggests that it helps to approach rates of change by first tabulating how successive values of the independent variable are changed at a constant rate. If the function is linear, then the differences are constant, whereas if it is of power two, the differences themselves increase at a constant rate. Better understanding of this is likely to be achieved by pupils seeing how the tabulated numbers correspond to visually accessible changes on the graph. Pupils should repeat the process for Episode 1 for the quadratic function on Worksheet 2. They may need more time to present their ideas on the quadratic function. If possible, ask pupils for phrases in natural language which fits the graph such as:'‘the amount of change is itself changing; ‘the increase is increasing steadily’, or even ‘accelerating.'
Whole class sharing and discussion