### Mathematics Department

**What is Mathematics and Statistics about?**

Mathematics is the exploration and use of patterns and relationships in quantities, space, and time. Statistics is the exploration and use of patterns and relationships in data. These two disciplines are related but different ways of thinking and of solving problems. Both equip students with effective means for investigating, interpreting, explaining, and making sense of the world in which they live.

Mathematicians and statisticians use symbols, graphs, and diagrams to help them find and communicate patterns and relationships, and they create models to represent both real-life and hypothetical situations. These situations are drawn from a wide range of social, cultural, scientific, technological, health, environmental, and economic contexts.

**Why study Mathematics and Statistics?**

By studying mathematics and statistics, students develop the ability to think creatively, critically, strategically, and logically. They learn to structure and to organise, to carry out procedures flexibly and accurately, to process and communicate information, and to enjoy intellectual challenge.

By learning mathematics and statistics, students develop other important thinking skills. They learn to create models and predict outcomes, to conjecture, to justify and verify, and to seek patterns and generalisations. They learn to estimate with reasonableness, calculate with precision, and understand when results are precise and when they must be interpreted with uncertainty. Mathematics and statistics have a broad range of practical applications in everyday life, in other learning areas, and in workplaces.

**Learning Area Structure:**

The achievement objectives are presented in three strands. It is important that students can see and make sense of the many connections within and across these strands.

__Number and algebra__ – Number involves calculating and estimating, using appropriate mental, written, or machine calculation methods in flexible ways. It also involves knowing when it is appropriate to use estimation and being able to discern whether results are reasonable. Algebra involves generalising and representing the patterns and relationships found in numbers, shapes, and measures.

__Geometry and measurement__** **– Geometry involves recognising and using the properties and symmetries of shapes and describing position and movement. Measurement involves quantifying the attributes of objects, using appropriate units and instruments. It also involves predicting and calculating rates of change.

__Statistics__ involves identifying problems that can be explored by the use of appropriate data, designing investigations, collecting data, exploring and using patterns and relationships in data, solving problems, and communicating findings. Statistics also involves interpreting statistical information, evaluating data-based arguments, and dealing with uncertainty and variation.

# PNBHS Mathematics Department

Level 1 Mathematics

This course covers material up to Level 6 of the National Curriculum, encompassing the three strands – Number & Algebra, Geometry & Measurement and statistics.

Upon completion, students will be fully prepared for their Level 1 NCEA examination.

A predominantly internally assessed alternative course is also available for identified students who struggled with Mathematics in Year 10.

## Level 2 Mathematics

We offer 3 courses at level 2:

- Calculus - Students need to be mathematically able, having good Algebra skills. Are logical thinkers.
- Statistics - Students need to be mathematically confident and have good literacy skills.
- General Mathematics - Students need to have a good work ethic. Solid mathematics and literacy ability an advantage.

## Level 3 Courses

### Statistics (24 Credits)

**Externals**: Probability, Evaluate Statistically Based Reports & Probability Distributions

**Internals**: Design and Conduct an Experiment, Formal Inference & Investigate Bivariate Data Relationships

**Prerequisites : **16 Credits in Level Two Mathematics including both of the Probability and Statistics Standards.

**This course has a high literacy demand. All of the internal Achievement Standards are assessed by a written report.**

### Calculus (24 Credits)

**Externals: **Differentiation, Integration & Complex Numbers

**Internals: **Conics & Trigonometric Relationships

**Prerequisites: **18 Credits in Level Two Mathematics including one of Algebra or Calculus Standards

**This course has a strong dependency on algebraic skills and problem solving. In addition, good reading comprehension is required for problem analysis.**

### Mathematics (20 Credits)

**External: **Probability

**Internals: **Design & Conduct an Experiment, Investigate Time Series Data, Linear Programming, Critical Path Analysis & Simultaneous Equations

**Prerequisites: **14 Credits in Level Two Mathematics or a Level Two NCEA certificate.

**This course has been designed for students who have not met the entry requirements for Calculus but would like to continue with Mathematics rather than a pure Statistics course at Level Three. This course covers the basics of Operational Research.**