Mathematics

Mathematics NCEA Level 1

Mathematics Numeracy - NCEA Level 1

Programme Description : This is a course designed to build mathematical confidence and mathematical thinking to gain the Numeracy requirement for NCEA.

Learning Outcomes/Content:

Complete a number investigation using percentages, GST and currency within a travel, financial, investment, event organisation or vehicle context.

Students will learn how to use the basics of right-angled triangle calculations including Pythagoras and trigonometry. Your calculations could be supported by practical evidence.

Complete a relationship or comparison statistical investigation or choose to do a chance investigation with a range of experimental situations to choose from.

Skills and Capabilities:

Pythagoras and Trigonometry have real world application.

Percentages and financials is something all students should know!

Gain the confidence to justify and/or reason why your method may work, or a solution seems reasonable.

Having the grit to try and try again – not expecting to know how to do something without practicing what the basics are!

Developing a belief in your mathematical ability – you can do Math!

Develop an idea of how to work with data.

Possibly Links to: BCAT’s, Furniture/Carpentry, Engineering, Design and Visual Communication, Art, Photography, Design, Business Studies.

Possibly Leading to: If you are confident you could consider the next Mathematics course.

Assessments: The internal assessments include a number investigation with a financial focus, a practical build with supporting calculations, computer based graphing and a probability/statistical report. Any external examination would be optional.

Contact: Svargo svargo@mbas.ac.nz Carol Boswell. boswellc@mbas.ac.nz

Statistics and Chance Investigations - NCEA Level 1

Programme Description: This is a course with a mix of basic number work, different types of statistics and probability situations and definitely has more of a focus on investigating and writing.

Learning Outcomes/Contexts: This course is recommended for students who are keen to research and look at data on issues we have within the world today. It is about collecting data and/or running an experiment and learning how to then interpret and communicate what you have found. The basic number work could have a financial focus, travel, cars or other personal interests.

Skills and Capabilities:

Make sure you know things to do with percentages, GST, tax and different currencies.

Develop the ability to write statistics and probability reports.

Reading and researching about your chosen topic, and you need a willingness to write.

Use of NZgrapher technology and loads of new statistical words.

Proof reading and respectful critique of others reports.

Ability to question the numbers, critically evaluate what might be missing!

Possible Links: Social Sciences including Tourism, Physical and Environmental Sciences, Health and Nutrition, Psychology.

Possibly leads to: Statistics and Probability Methods, Earth and Space Science and Statistics, Environmental Science.

Assessments: Internal assessments require research and the presentation of what the statistics suggest within either a formal report/ power point/ seminar presentation/ lecture etc. The external assessment is on the basics of the statistics and probability work covered during the year.

Contact: Svargo, svargo@mbas.ac.nz Carol Boswell, boswellc@mbas.ac.nz

Level 1 Statistics.webm

Mathematics - NCEA Level 1

Programme Description : This is a course designed to build mathematical confidence and mathematical thinking in both algebra and statistics topics giving options into further senior courses.

Learning Outcomes /Content:

Students will learn how to use the basics of right-angled triangle calculations including Pythagoras and trigonometry and their application to a range of building and/or design tasks. Complete a number investigation using percentages, GST and currency within a travel, financial, event organisation or vehicle context.

Statistical investigation to see if there is a relationship between two variables.

Either the Chance and data external or Equations/Tables/Graphs external learning will be considered to complete the years learning.

Skills and Capabilities:

Pythagoras and Trigonometry are fundamental to senior mathematics!

Percentages and financials is something all students should know!

Being able to justify and/or reason why your method may work, or a solution seems reasonable.

Having the grit to try and try again – not expecting to know how to do something without practicing what the basics are!

Being prepared to just play with the mathematics – not everything has a ‘real’ focus.

Possibly links to: BCAT’s, Engineering, Business Studies, Tourism, Health and PE.

Possibly leads to : Statistics and Probability Methods or L2 Mathematics course

Assessments: Internal assessments during term 1 and 2, and students will have an external examination.

Contact: Svargo svargo@mbas.ac.nz Carol Boswell, boswellc@mbas.ac.nz

Algebraic Methods - NCEA Level 1, 2 and 3

Programme Description: This Mathematics course is for students who just love “algebra” and are looking to build strong algebraic manipulation, equation and modelling skills! For those keen to do senior Calculus.

Learning Outcomes/Contexts:

The course is designed to challenge students to develop key algebraic manipulation skills that are foundational to all senior calculus and algebra courses. You will develop good reasoning skills so you can justify with confidence why you think an approach might be worth a try. Algebra is the language of our subject – our desire is you get good at it!. You will play lots on Desmos during the learning and assessments will use this technology. Trigonometry is a key topic, as are linear models and quadratic graphs.

Skills and Capabilities:

Loads of new material, that requires mental toughness to stick at it and a preparedness to play and persevere.

Fast paced and the ability to try and try again and try again.

Work collaboratively and communicate your thinking.

Being prepared to share your ideas and justify why you think a way / method might work.

To be able to question and ask for help.

Loads of practice all the time!

Develop logical processes, sequential thinking.

NOT all of the mathematics studied has a ‘practical or everyday’ focus it is sometimes just fun with letters and numbers!

Possibly Links to: Engineering, Physics, Architectural Technology, Art, Photography and Design fields, all Science fields.

Possibly leads to : any senior Mathematics courses.

Assessments: Internal assessments that use Desmos technology and lots of algebra calculations. External examinations – Equations/Tables/Graphs and L2 Algebra.

Contact: Svargo. svargo@mbas.ac.nz

L1 Algebra.mp4

Mathematics NCEA Level 2

Mathematics - NCEA 2

Programme Description: This course is algebra based, all on computer, includes statistics, and is designed to give students the Mathematics required for many tertiary courses and/or the defence forces.

Learning Outcomes /Content:

Students can work on their own or in pairs and will use computer programmes and a mix of graphs to design and document the development of a logo. You should be prepared to present this work to parents/caregivers.

Students will be investigating different financial aspects of budgeting, earning interest, investment options and borrowing money and involves the use of spreadsheets. Your financial intelligence matters.

Thirdly students will be looking at a statistical experiment or comparative investigation. This involves, gathering data, research, computers, statistical graphs, and learning how to write statistical reports.

Skills and Capabilities:

There is a chunk of algebra to begin.

Ability to try and try again, persevere when things don’t work how you think they should!

Lots of new learning on using spreadsheets and all things financial.

Researching, reading and writing which is at the heart of statistics stuff.

Possibly Links to: Design and Visual Communication, Art, Photography, Design, Psychology.

Possibly leads to: Actually not designed to lead to senior courses but maybe Statistics and Probability Distributions and/or Earth and Space Science and Statistics, Environmental Science.

Assessments: All internal assessments – any external assessment would need to be negotiated early in term 3.

Contact: Svargo svargo@mbas.ac.nz Carol Boswell. boswellc@mbas.ac.nz

L2 Mathematics.mp4

Calculus and Algebraic Methods - NCEA Level 2 and 3

Programme Description: A focus on using your new understanding of graphical models to make objects/ designs alongside showing some serious confidence to work with challenging algebraic calculations. Understand rates of change and what forms the basics of senior calculus.

Learning Outcomes/Contexts:

Spend an extended length of time designing and documenting the development of a prototype object/design of your choice using mathematical models. You are encouraged to work collaboratively and have some hard fun using Desmos. You will have to show your calculations with full algebraic working. Then you will present this work to parents/caregivers.

Learn about the set of Complex Numbers – optional but more Algebra!

What is Calculus all about? Rates of change and more new learning!

Skills and Capabilities:

Loads of new material, that requires mental toughness to stick at it and a preparedness to play and persevere.

Fast paced and the ability to try and try again and try again.

Work collaboratively and communicate your thinking.

Being prepared to share your ideas and justify why you think a way / method might work.

To be able to question and ask for help.

Possibly Links to: Physics, Chemistry, Design and Visual Communication, Art, Photography, Design.

Possibly leads to : Calculus L3, Statistics L3,

Assessments: Documentation and presentation of your design and prototype build collaborative task with supporting calculations. External examinations – your choice of Complex Numbers and Calculus or both.

Contact: Carol Boswell. boswellc@mbas.ac.nz

L2 Calc & Algebra.mp4

Statistics and Probability Methods - NCEA Level 2 and 3

Programme Description This course is focussed on developing statistical thinking and statistical literacy through a combination of student investigations and theoretical learning in statistics and probability.

Learning Outcomes/Contexts:

Students will use their time to research, collect data, and develop the statistical literacy and analysis skills required when dealing with measured and experimental data. Students will be encouraged to consider and use real-world/local issues as the basis for their statistical investigations.

Develop an understanding of the Normal Probability Distribution, how we assess risk and work out some tricky probabilities.

Skills and Capabilities:

Finding and reading lots of online articles and other research reports on the issue or topic of each of your investigations to make sure you know what you are reporting on!

Use of NZgrapher technology and how to interpret the different statistical graphs and key statistics.

Develop higher levels of written literacy, statistical literacy and be willing to write lots using formal language.

Referencing of research sources using University recognised APA referencing system.

Proof reading and respectful critique of others reports/statements.

Ability to question the numbers, critically evaluate what might be missing!

Possibly Links to: Social Sciences including Tourism, Physical and Environmental Sciences, Health and Nutrition, Psychology, Industry

Possibly leads to: Tertiary education pathways in subject areas requiring Statistics; Careers in Commerce, Sciences and Industry. L3 Statistics and Probability Distributions.

Assessments: Internal assessments will include practical research and writing of individual statistical reports or presentations that showcase your findings, as well as an external assessment opportunity in probability methods.

Contact Svargo: svargo@mbas.ac.nz

L2 Statistics.mp4

Mathematics NCEA Level 3

Calculus - NCEA Level 3

Programme Description : This course is designed for students who love all things algebra and/or who are intending to study Architecture, Engineering, Chemistry, Physics or Computing at tertiary level.

Learning Outcomes/Contexts:

Build on the basics of trigonometry and the use of trig functions to model situations in the world.

More differentiation rules.

Serious extension of rates of change and working out the rate of change from other rates of change.

But….. in many situations you know the rate at which things change and need to know how it started. So we integrate.

Have some fun designing and working out areas underneath and between curves, aka Integrating.

Skills and Capabilities:

Coping with continuous and fast presentation of new ideas.

Being able to think – ‘what have we done before that might be useful here?’

A resilience to try different algebraic ideas in the solution of a problem.

Working collaboratively, being prepared to reason and /or justify your ideas/ways of finding a solution.

Practising questions and more questions.

Possibly Links to: Statistics – finding a rate of change, Physics, Chemistry.

Possibly leads to : Automatic entry requirements for University Engineering courses, Architecture, Mathematics, Computing, Physics, Chemistry degrees. Gaining UE approved Mathematics as one of your 3 University approved subjects.

Assessment Opportunities: Written/digital internal trig assessment plus 2 big externals.

Contact: Carol Boswell. boswellc@mbas.ac.nz

Level 3 Calculus.mp4

Statistics and Probability - NCEA Level 3

Programme Description: This course is focussed on deepening statistical thinking and statistical literacy through a combination of student investigations and theoretical learning with optional cross-curricular investigations in Biology or other areas of study.

Learning Outcomes/Contexts: This course is recommended for students who are keen to research and look at data on key issues we have within the world today. Data collection in connection with experiments or investigations in Biology, Environmental Sciences, Physical Education, Psychology or other subjects may offer the opportunity to connect their statistics with these other learning areas.

Skills and Capabilities:

Presentation of a formal statistics report or article.

Finding and reading online articles and other research reports of the issue or topic of each investigation.

Use of NZgrapher technology and the interpretation of different statistical graphs and key statistics.

A high level of written literacy, statistical literacy and a willingness to write.

Referencing of research sources appropriately.

Proof reading and respectful critique of others reports.

Ability to question the numbers, critically evaluate what might be missing!

Possibly Links to: Social Sciences including Tourism, Physical and Environmental Sciences, Health and Nutrition, Psychology.

Possibly leads to: Tertiary education pathways in subject areas requiring Statistics; Careers in Commerce, Sciences and Industry. UE approved Mathematics.

Assessments: Internal assessments require research and the presentation of statistical findings within either a formal report/ power point/ seminar presentation/ lecture etc. The external assessment is on probability distributions.

Contact: Svargo. svargo@mbas.ac.nz Carol Boswell, boswellc@mbas.ac.nz

Level 3 Statistics.mp4