Level 2

Mathematics and Statistics clarifications

Show: Mathematics and Statistics homepage | All Mathematics and Statistics clarifications

91258: Apply sequences and series in solving problems

Updated December 2016. This document has been updated in its entirety to address new issues that have arisen from moderation.

Solving problems

Students need to investigate a situation that can be modelled by sequences and series. It is not appropriate to specify the type of sequence that models the situation.

The problem needs to provide sufficient scope for students to demonstrate and develop their own thinking. If there are parts to the problem, all the parts need to contribute to the solution.

A task with a number of discrete questions based on skills and straightforward calculations is not appropriate for students to demonstrate evidence of the required levels of thinking.

Students need to make their own decisions about what to do and how to solve problems. Where an assessment task has a series of instructions that lead students through a step or a sequence of steps towards the solution, it is likely that the opportunity for students to demonstrate all levels of thinking will be compromised.

Expected evidence for Achieved

For Achieved, the requirements include selecting and using methods. To be used as evidence, a ‘method’ needs to be relevant to the solution of the problem and at the appropriate curriculum level for the standard. The result of a numerical calculation only is insufficient, working is expected and students need to indicate what the calculated answer represents.

A table of values, on its own, for an arithmetic or geometric sequence does not provide sufficient evidence for the standard. Students need to demonstrate knowledge of concepts and terms and communicate using appropriate representations. These aspects are likely to be evidenced by the use of appropriate formulae.

The use of iterative formulae such as tn+1 = tn + d and tn+1 = rtn could provide evidence for the standard.

Expected evidence for Merit

Students are likely to demonstrate relational thinking when forming and using tn and Sn as part of the solution of the overall problem. Students need to clearly indicate what they are calculating and their solutions need to be linked to the context.

Expected evidence for Excellence

Students are likely to demonstrate extended abstract thinking when making a generalisation or considering different options. The response needs to be clearly communicated with correct mathematical statements, and students need to explain any decisions they make in the solution of the problem.

Skip to main page content Accessibility page with list of access keys Home Page Site Map Contact Us newzealand.govt.nz