Mātauranga Māori constitutes concepts and principles that are richly detailed, complex, and fundamental to Māoridom. It is important to remember that the practice of these are wider and more varied than their use within the proposed NCEA Achievement Standards and supporting documentation.

We also recognise that the cultures, languages, and identities of the Pacific Islands are diverse, varied, and unique. Therefore the Pacific concepts, contexts, and principles that have been incorporated within NCEA Achievement Standards may have wide-ranging understandings and applications across and within the diversity of Pacific communities. It is not our intention to define what these concepts mean but rather offer some ways that they could be understood and applied within different subjects that kaiako and students alike can explore.

The intent of the Standard

The purpose of this Achievement Standard is to enable ākonga to show they can use mathematics to solve or explore applied problems.

Mathematical literacy means an individual’s capacity to:

• identify and understand the role that mathematics plays in the world
• make well-founded judgements using mathematics when investigating situations
• use, and engage with, mathematics in ways that meet the needs of an individual’s life as a constructive, concerned, and reflective citizen.

In this Achievement Standard, different mathematical problems can be set according to ākonga backgrounds, interests, and pathways, in recognition of the breadth of diversity in Aotearoa New Zealand and the Pacific. Problems do not need to be set exclusively in Aotearoa New Zealand or the Pacific, but it should be clear to ākonga how problems are related to life in these regions.

Ākonga will use a range of mathematical processes and communicate accurate mathematical information appropriate to the context. It is intended that ākonga will have the opportunity to solve or explore a range of problems within a wider contextual setting.

It is intended that ākonga will have the opportunity to explore the context before beginning their independent work. This could include brainstorming in groups or with the whole class, with kaiako support, to gain a greater understanding of the context and the broad areas of mathematics required to complete the activity.

Probability and statistics are excluded from this Standard.

Making reliable judgements

Logical connections link one process to another as part of a problem or problems. Each part of the connection needs to be completed correctly to meet the requirement. Logically connecting three processes meets the requirements for two or more connections. Examples of logical connections include:

• linking Pythagoras' theorem to finding the volume of an object approximated by a cone
• forming two or more linear graphical models and solving points of intersection
• using a quadratic pattern and graph to optimise a solution
• using trigonometric ratios to find the height of a triangular section on the side of a building, finding the whole surface area of a house and roof to be painted, and then calculating how much a tradesperson will need to be paid based on an average painting speed (three connected processes: trigonometric ratios, surface area involving prisms, and more complex rates).

For higher levels of achievement, a minimum of two logical connections is required alongside the requirement to use four or more processes from two or more areas.

Not all problems have a singular or finite solution. For the highest level of achievement, ākonga will further develop (extend) at least one problem or one section from within previously chosen mathematical methods. The considerations they communicate can explore one or more of the following:

• underlying assumptions made throughout the exploration and their mathematical impact on any solution found
• mathematical explanation of limitations of models or solutions
• mathematical generalisations or predictions, including recommendations or best models where appropriate.

When exploring more than one of the above areas, only one example of each is required.

When communicating accurate mathematical information, it is expected that ākonga will show how they reached their answer and indicate what their calculated answer represents. Appropriate use of technology and tools is encouraged with ākonga providing evidence of this usage in their submission. For higher levels of achievement, mathematical conventions should be followed correctly. Solutions should be appropriately rounded and be linked to the context of the problem.

Collecting evidence

Participation in a brainstorm will allow ākonga greater understanding of their investigation but is not required for any level of achievement. Resulting ideas could be included or reflected within their investigation.

When making visual, physical, or audio presentations, ākonga may submit additional evidence of supporting calculations.Sourced data should be appropriate to ākonga and their environment.

Possible contexts

All contexts must be able to relate to life in Aotearoa New Zealand or the Pacific.

Literacy and Numeracy Requirements

This Achievement Standard has been approved for numeracy in the transition period (2024-2027). 

Full information on the co-requisite during the transition period: Standards approved for NCEA Co-requisite during the transition period (2024-2027).