Mathematics and Statistics

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.

PRIMARY YEARS 1-6 MATHEMATICS & STATISTICS

Mathematics and statistics is one of the core subjects within the primary years. In a programme delivered by their classroom teacher, students will have daily opportunities to develop their understanding and skills in the following 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.

MIDDLE YEARS 7-10 MATHEMATICS

A course in Mathematics and Statistics is a core part of the learning programme for Y7 to 10. Mathematics and Statistics involves the study of Number and Algebra, Geometry and Measurement and Statistics. Through a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems using language, symbols and texts.

Mathematics and Statistics Year 7/8

Mathematics is taught daily. Units will cover number, measurement, statistics, problem solving, algebra and geometry over a two year programme and may be integrated with other curriculum areas. Students will be given opportunities to explore patterns and relationships in quantities, space, time and data, develop their thinking and problem solving skills and use symbols, graphs and diagrams to communicate.

Mathematics and Statistics Years 9 & 10

Due to the integrated nature of much of the learning for 2016, the key Year 9 Mathematics understandings will be drawn from Number, Measurement, Linear Modelling, Algebra/formula and Statistical modelling areas. Year 10 Mathematics will include the key understandings of Trigonometric design and application, Quadratic modelling and motion, and the extension of Linear Modelling to Statistics and dealing with relationship data.

It is anticipated that students will use real world issues and concerns, often generated within other areas of study, eg. health, social, physical, environmental, sustainable sciences or economics, psychology or technology fields as the basis for their investigations. Students will be using spreadsheets, Desmos graphing and iNZight statistical packages extensively within their work.

SENIOR YEARS 11-13 MATHEMATICS

Year 11 Mathematics

Mathematics A NCEA Level 1

This course is intended for students who require extended lengths of time to achieve at curriculum level 6 and present a sound understanding of basic number and the practical applications of Mathematics. The aim will be to integrate mathematics with each student’s key areas of interest. The mathematics of statistical graphs, statistical literacy and estimating probabilities will be used to demonstrate the requirements for Numeracy within the NCEA qualifications framework. Students will be expected to have a BYOD. The course does not lead to higher level Mathematics.

Mathematics B2 NCEA Level 1

This Mathematics and Statistics course continues and extends the mathematical concepts of number, linear algebra, statistics and probability. Students will be given extended lengths of time to demonstrate their understanding of curriculum level 6 within each of these four areas. Students will be encouraged to use the learning contexts of other areas of study, for example health, physical education, food, metal and wood technology, social sciences and physical sciences to provide the authentic contextual base for their mathematical investigations. This course integrates computer packages within the statistical, linear algebra and probability topics and students will be expected to have a BYOD. This course can lead to NCEA Level 2 Mathematics.

Mathematics B1 NCEA Level 1, 2, 3

This Mathematics and Statistics course is for students who are considering career pathways that require higher level mathematics in both algebra and statistics such as the computing, design technology and environmental, biology, chemistry and physics science fields. Students will need to have a desire to integrate strong algebraic manipulation and equation skills with technology while developing their mathematical understanding. This course requires students to apply these concepts to authentic world problems and to use investigative techniques and write a report on findings. This course covers multiple curriculum levels and students will be expected have a BYOD and the resilience required for higher level Mathematics.

Mathematics C - Algebra NCEA Level 1 , 2, 3

This multi-curriculum level mathematics and statistics course is for students who are looking to build the strong algebraic, equation and modeling skills required within the Engineering, Physics, Architectural Technology and Design fields. The course is fast paced and designed to challenge students to make real world connections and develop their algebraic generalization and reasoning skills at the very top levels. This course is an essential prerequisite for NCEA Level 2 Mathematics with Calculus. Students are expected to have their own BYOD and a graphics calculator for the externally assessed standards.

Year 12 Mathematics

Mathematics for Trade and Industry NCEA Level 2 & 3

This course is intended for students who need to achieve mathematics at Level 2 for entry into tertiary courses e.g. Mechanics, or the Armed forces. This course will include some common areas of study within trigonometry, linear programming, critical path analysis (project management) and statistics and requires a reasonable literacy level for the presentation of statistical reports. The course allows for extended time to complete the learning within these areas, however, it is designed to be flexible and allow the ‘context’ for assessment work to be centered around each students strength within other learning areas. This course covers multiple curriculum levels and students will be expected have a BYOD and the resilience required for higher level mathematics.

Year 12 Mathematics and Statistical Literacy NCEA Level 2 & 3

Students will be given an extended length of time for each of two in-depth statistical investigations. They will be given the opportunity to pursue areas of personal interest, to research, collect data, and develop the statistical literacy and analysis skills required when dealing with measured and experimental data. It is anticipated that students will use real world issues and concerns, often generated within other areas of study, eg. health, social, physical, environmental, sustainable sciences or economics, psychology or technology fields as the basis for their statistical investigations. A deeper understanding of underlying statistical literacy features is essential to enable students to present the level of statistical reporting expected. This course covers multiple curriculum levels and students will be expected to have a BYOD and the resilience required for higher level Mathematics. This course will enable students to study the Statistics and Probability course in Year 13. Some data collection and analysis costs may require personal funding.

Year 12 Mathematics with Calculus NCEA Level 2 & 3

This course is intended for students who have a very strong algebraic foundation in both manipulation and equation skills. This course would suit students who wish to take Mathematics, Chemistry, Physics, Engineering or Design Technology options at Year 13 level or beyond. The course significantly extends the algebra, modeling and graphing concepts from the Year 11 Mathematics C - Algebra course. It includes the introductory differentiation and integration calculus concepts which form the basis for the Year 13 Calculus course. This course covers multiple curriculum levels, is fast paced and requires a depth of algebraic manipulation and the resilience to deal with the constant introduction of new material. Regular time at home to consolidate in-class learning is required for success at the top levels which will be aimed for within this course. Students are expected to have a BYOD and the use of a graphics calculator is expected.

Year 13 Mathematics

Year 13 Calculus NCEA Level 3

This course is recommended for students who are intending to study Engineering, Mathematics, Chemistry, Physics or Computer programming at university or uni-tech level where achievement at curriculum level 8 Calculus is an entry requirement. This course requires a strong algebraic framework and the resilience to deal with the constant introduction of unfamiliar material. The concepts of trigonometry, differentiation and integration are significantly extended and regular time to consolidate in-class learning is required for success at this level. The use of a graphics calculator is expected.

Year 13 Statistics and Probability Distributions NCEA Level 3

In a world that is increasingly data driven the ability to understand and critically evaluate statistical representations and information is important within a wider range of fields. This course is recommended for students who are keen to explore an issue or area of personal interest via data collection and statistical analysis. This course would also benefit students intending to study any Business, Life Sciences or Social Sciences at a tertiary level. Students will be encouraged to begin with the formulation of a statistical hypothesis or problem within a real and authentic area of interest for which the gathering of data will allow further knowledge and understanding in that field. Students will need to be proactive in developing social, physical, economical, scientific, health and well-being issues as the basis for their statistical investigations. Some data collection and analysis costs may require personal funding. Students will be expected to have a BYOD. A variety of probability distribution models and their relevance to the different types of data investigated within the course will also be developed in preparation for the externals.

Year 13 Mathematics NCEA Level 3

Increasingly businesses want data and analysis in relation to their products and clients with improvements in efficiency, production and optimization being key areas of interest. This course would suit students who may wish to pursue career pathways involving Commerce, Management, Science and Computing technology and for university or uni-tech based courses which require a Level 3 Mathematics qualification for entry. This course will include a mixture of calculus, statistical literacy and technology skills. The course will include the advanced differentiation calculus knowledge, linear programming for optimization and also an in-depth investigation into an area of interest via data collection and statistical analysis. A reasonably high level of algebraic confidence is required. Due to the algebra, technology, statistical mix within the course, students are expected to have a BYOD and a graphics calculator will be required for the external.

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