This is a challenging investigation most likely suitable for a small group of confident learners.

Pupils investigate how the length of a spiral increases which is a quadratic sequence. The sequence needs to be split into cases where n is odd and n is even however, unless you use the floor or ceiling function. The introductory video explains these operations and combining the odd/even cases into a single formula using floor/ceiling is the main challenge of this investigation.

Quadratic sequences and or summation of arithmetic sequences.

1. Print off one copy of A3 pupil sheet for each pupil.

2. The basic idea is very simple and pupils should be able to complete table and investigate separate quadratic sequences for odd and even values of $n$.

3. At some point, pupils will need to be told about/watch the introductory video of the ceiling function. This could be done at the start of the investigation or after pupils have completed the first three sections.

Alternatively - if you have already studied functions - you could present 'The ceiling function' question from the function notation > evaluating functions topic menu beforehand/in lesson leading up to this investigation.