## Purpose

## Achievement Criteria

## Explanatory Note 1

*Demonstrate mathematical reasoning* involves:

- using mathematical methods
- using mathematical concepts and terms
- communicating using appropriate representations.

*Demonstrate mathematical reasoning with relational thinking *involves:

- carrying out an appropriate sequence of steps
- using appropriate mathematical statements.

*Demonstrate mathematical reasoning with extended abstract thinking *involves at least one of:

- developing a clear chain of logical reasoning
- forming a generalisation or providing a proof
- extending mathematical methods to investigate or solve a problem.

## Explanatory Note 2

*Mathematical methods* mean methods from number, algebra, measurement, or geometry and space.

## Explanatory Note 3

*A sequence *consists of two or more mathematical methods within a single problem.

## Shared Explanatory Note

Refer to the NCEA glossary for Māori, Pacific, and further subject-specific terms and concepts.

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.

## External Assessment Specifications

The External Assessment Specifications are published by NZQA and can be found on their website using this link:

## NZQA Mathematics and Statistics

## 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.*

*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 develop the capabilities required to use mathematics to demonstrate reasoning and assess the truth of mathematical statements.

Ākonga will reason mathematically using skills from the following topics: Number, algebra, measurement, or geometry and space. This Achievement Standard will focus on mathematical concepts, not on how mathematics applies to real-life contexts.

**Making reliable judgements**

Evidence submitted for this Achievement Standard must demonstrate mathematical reasoning – answers only are insufficient.

Ākonga achieving at higher levels are likely to engage in problems requiring several methods to reach a solution. They should identify and provide evidence of each chosen method, which may not require statements. They should also ensure that all working shown follows mathematical conventions correctly.

At the highest levels of achievement, ākonga will apply a range of methods to problems without direction. The methods required may not be immediately identifiable, and ākonga should expect to approach the problem from more than one perspective.

**Collecting evidence**

Throughout a year’s study, ākonga should become familiar with a wide range of mathematical methods. There should be opportunities to apply these methods in unfamiliar tasks or problems that require the application of skills from across the methods listed.

Evidence for this Achievement Standard will be collected through a range of problems. Each problem could draw from more than one of the four topics. Ākonga should therefore be confident in identifying several useful skills that may be required in finding a solution to a problem.

As new concepts or skills are taught, kaiako may wish to have ākonga engage in wānanga to relate these to mathematical methods that have been covered previously. Identifying where skills can be linked together will build capability and confidence in identifying and applying methods.

**Possible contexts**

Problems will be set in mathematical contexts.

**The intent of the Standard**

The purpose of this Achievement Standard is to enable ākonga to develop the capabilities required to use mathematics to demonstrate reasoning and assess the truth of mathematical statements.

Ākonga will reason mathematically using skills from the following topics: Number, algebra, measurement, or geometry and space. This Achievement Standard will focus on mathematical concepts, not on how mathematics applies to real-life contexts.

**Making reliable judgements**

Evidence submitted for this Achievement Standard must demonstrate mathematical reasoning – answers only are insufficient.

Ākonga achieving at higher levels are likely to engage in problems requiring several methods to reach a solution. They should identify and provide evidence of each chosen method, which may not require statements. They should also ensure that all working shown follows mathematical conventions correctly.

At the highest levels of achievement, ākonga will apply a range of methods to problems without direction. The methods required may not be immediately identifiable, and ākonga should expect to approach the problem from more than one perspective.

**Collecting evidence**

Throughout a year’s study, ākonga should become familiar with a wide range of mathematical methods. There should be opportunities to apply these methods in unfamiliar tasks or problems that require the application of skills from across the methods listed.

Evidence for this Achievement Standard will be collected through a range of problems. Each problem could draw from more than one of the four topics. Ākonga should therefore be confident in identifying several useful skills that may be required in finding a solution to a problem.

As new concepts or skills are taught, kaiako may wish to have ākonga engage in wānanga to relate these to mathematical methods that have been covered previously. Identifying where skills can be linked together will build capability and confidence in identifying and applying methods.

**Possible contexts**

Problems will be set in mathematical contexts.

### Literacy and Numeracy Requirements

This Achievement Standard has been approved for numeracy in 2024 and 2025.

Full information on the co-requisite for 2024 and 2025: Standards approved for NCEA co-requisite for 2024 and 2025.

### Literacy and Numeracy Requirements

This Achievement Standard has been approved for numeracy in 2024 and 2025.

Full information on the co-requisite for 2024 and 2025: Standards approved for NCEA co-requisite for 2024 and 2025.