## Purpose

## Achievement Criteria

## Explanatory Note 1

*Use mathematical methods to explore problems that relate to life in Aotearoa New Zealand or the Pacific region* involves:

- using a range of mathematical methods that are appropriate to each problem
- communicating mathematical information related to the problem context.

*Use mathematical methods, applying relational thinking, to explore problems that relate to life in Aotearoa New Zealand or the Pacific region* involves at least one of:

- selecting and carrying out a logical sequence of mathematical steps
- connecting different concepts and representations
- forming and using a mathematical model.

AND

- using appropriate mathematical statements to communicate information related to the problem context.

*Use mathematical methods, applying extended abstract thinking, to explore problems that relate to life in Aotearoa New Zealand or the Pacific region* involves at least one of:

- making generalisations or predictions
- explaining assumptions made during the process
- explaining limitations of the answer provided
- devising a strategy to explore or solve a problem.

## Explanatory Note 2

*Aotearoa New Zealand or the Pacific region* means Aotearoa New Zealand or the Pacific region, or a combination of both.

The problems must comprise subject matter which is related to life in Aotearoa New Zealand or the Pacific region.

## Explanatory Note 3

*Mathematical methods* are drawn from number, algebra, geometry, or measurement.

## Explanatory Note 4

*A range of mathematical methods* means three or more methods. These must come from at least two of number, algebra, geometry, or measurement.

## Explanatory Note 5

*A mathematical model* is a way of expressing mathematical information using mathematical language. Examples of mathematical models include:

- equations
- formulae
- graphs.

## Shared Explanatory Note

This Achievement Standard is derived from the Mathematics and Statistics Learning Area at Level 6 of *The New Zealand Curriculum: *Learning Media, Ministry of Education, 2007.

- Kaiako can provide feedback on a student's plan for their exploration.
- Problems that relate to Aotearoa New Zealand or the Pacific region may include the values, beliefs, and customs of the people of Aotearoa New Zealand and the Pacific region, especially Māori and diverse Pacific Islands people.
- Ākonga will have access to appropriate technology and resources.

Students need to be familiar with methods, ie, procedures and reasoning related to the following:

Number:

- more complex rates, ratio, and proportion (including scale diagrams)
- negative and fractional powers
- percentage: increase, decrease, and inverse
- standard form.

Algebra:

- formulae
- graphing
- manipulating and simplifying expressions
- inequations
- quadratic and simple exponential equations
- simultaneous linear equations with two unknowns
- optimal solutions
- relating graphs, tables, equations, and patterns
- relating rate of change to the gradient of a graph
- forming, graphing, or manipulating linear models.

Geometry

- properties of similar shapes
- Pythagoras’ theorem in 3D situations
- trigonometric ratios in right-angled triangles
- transformations (reflection, rotation, translation, and enlargement): their key features and symmetry of patterns.

Measurement

- surface area of prisms, pyramids, cones, and spheres
- volume of composite prisms, pyramids, cones, and spheres
- conversions between more complex metric units such as area, volume, and derived measures, eg, km/h.

## Unpacking the Standard

*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 purpose of this Standard is to enable ākonga to build mathematical literacy allowing them to apply mathematics to 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
- use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned, and reflective citizen.

In this 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.

Ākonga will select and use a range of mathematical skills, and communicate mathematical information appropriate to context.

#### Literacy and Numeracy Requirements

This standard has been tagged for numeracy meaning that it can be used to meet the NCEA Literacy and Numeracy Literacy and Numeracy | Te Reo Matatini me Te Pāngarau requirements until the new unit standards become mandatory.