Functions and Graphs
This unit is designed to start by encouraging discussion about functions and graphs using correct mathematical notation and terminology before approaching transformations of functions.
Lesson 1 - The Shell center resource contains many problems along with a mark scheme and examples of pupil answers. The pages for each problem are
The journey - page 12
Camping - page 20
Going to school - page 28
The vending machine - page 38
The hurdles race - page 42
The cassette tape - page 46
Filling a swimming pool - page 52
First start by presenting pupils with one of the problems. Ask them to spend some time solving it in pairs or groups. They can then swap their solution with another group and use the mark scheme that follows the problem to mark their work. Pupils are then learning what to look out for in a good solution.
Then move on to a different problem and this time hand out the model pupil answers provided in the resource along with the problem and the mark scheme and ask pupils to comment on these answers.
Lesson 2 - Use the interpreting activities below to encourage correct notation and mathematical language.
Lesson 3 - Introduce function notation. Use the Functions and Graphs notes.
Lesson 4 - Give pupils access to a computer and let them play with the interactive activity at Waldo Maths. The aim of this should be for pupils to decide for themselves what each of the transformations does to the graph.
Lesson 5 - Use the lesson plan and provided activities in the last resource to explore the relationship between trigonometrical graphs and functional transformations.
Links and Resources
This is a old resource from the Shell Centre, but still a good one. It is a collection of questions based on functions and graphs with a mark scheme and example of pupils answers.
This is a lesson plan and collection of activities to engage pupils in discussion about the link between functions, graphs and tables.
This is a collection of notes and examples, suitable for printing and handing out to pupils. Basic function notation is covered.
This resource provides a lesson plan and activities of a thinking skills nature that explore the realtionship between trigonometric graphs and functional transformations.