Exploring Cubic Functions

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Number Rules - OK

Can you produce convincing arguments that a selection of statements about numbers are true?

Take Three from Five

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

Why do this problem?

This problem offers an excellent opportunity for students to gain fluency at describing the graphs of quadratic equations in a variety of ways.

Possible approach

Start by displaying the graphs of one or two quadratic equations and ask students to describe them in as much detail as possible. Expect comments related to maximum / minimum values, roots, axes of symmetry, turning points, intercepts...

Then hand out copies of the worksheets and suggest that students work on the task in pairs.

Key questions

Do any of the graphs satisfy just one of the criteria?

Can any of the criteria be matched to just one of the graphs?

Possible support

Encourage students to consider the Key questions above

Possible extension

Parabolic Patterns challenges students to identify the equations of graphs.