1 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations

2 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level #Demonstrate an understanding of rational and irrational numbers and number systems within the context TF306.01Understanding rational and irrational numbers TF306.02Understanding fractions and the decimal system TF306.03Doing calculations TF306.04Using numbers expressed as information TF306.05Understanding manipulation of numbers TF306.07Developing spreadsheets TF306.08Using tables and grids TF306.06Working with percentages and fractions Notional Hours Total Notional Hours P&P3FM Doing calculations P&P3FM Converting data P&P3FM Using tools

3 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Know what role irrational numbers play in mathematics Know what role rational numbers play in mathematics Know what calculations can be done with rational and irrational numbers Know what a rational number is Know what an irrational number is TF Understanding rational and irrational numbers Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development Be able to do basic calculations with rational and irrational numbers US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

4 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Understanding rational and irrational numbers Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to demonstrate understanding of what rational and irrational numbers are Are able to demonstrate understanding of what rational and irrational numbers are used for Are able to do basic calculations using rational and irrational numbers Be able to understanding of the application of calculations with rational and irrational numbers to improve workplace stability Assignment Description WHATWHAT HOW Notional Hours 2 Individual and group exercises of practically using basic calculations in informal day to day situations 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

5 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Know the mathematical rules regarding estimations Know what numerators and denominators are Know what a fraction is Know how decimals work TF Understanding fractions and the decimal system Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development Be able to do estimations using basic mathematical rules US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

6 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Understanding fractions and the decimal system Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to demonstrate understanding of how fractions and decimals work Are able to Apply the basic mathematical principles of estimations when working with decimals Are able to Measure and convert to the standard industry units for current, power, pressure, length, mass, temperature and time Assignment Description WHATWHAT HOW Notional Hours 3 Individual and group exercises of practically using basic calculations in informal day to day situations 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

7 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Be able to use a mathematical calculator and demonstrate an understanding of all its functions Be able to do all calculations with a calculator Be able to link decimals to units Be able to correctly +, -, x, / rational and irrational numbers expressed as fractions and decimals without a calculator TF Doing calculations Be able to link fractions to units Be able to correctly +, -, x, / rational and irrational numbers expressed as a unit of weight, volume or measurement without a calculator Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

8 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Understanding fractions and the decimal system Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to link decimals and fractions to units Are able to do basic calculations using rational and irrational numbers expressed as units of weight, volume and measurement Are able to use a basic mathematical calculator to do all these calculations Are able to calculate production throughput, and labour productivity Assignment Description WHATWHAT HOW Notional Hours 2 Individual and group exercises of practically using basic calculations in informal day to day situations 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

9 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Be able to calculate the mean, mode and median Be able to use algebra formulas to convert basic numerical data into usable information Know what mean, mode and median mean and what it is used for Know the differences between data and information Know how equations and inequalities work TF Using numbers expressed as information Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development Know algebra formulas to convert basic numerical data into usable information US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

10 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Using numbers expressed as information Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to demonstrate understanding of the difference between data and information Are able to demonstrate understanding of how equations and inequalities work Are able to calculate mean, mode and median Are able to use basic algebra formulas to convert basic numerical date into usable information Are able to demonstrate understanding of how to turn production information into meaningful data Assignment Description WHATWHAT HOW Notional Hours 2 Individual and group exercises of practically using basic calculations in informal day to day situations 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

11 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Know what factorisation is Understand the distributive law Know what is meant by scientific notation Know what trinomials are TF Understanding manipulation of numbers Know what a binomial is Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

12 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Using numbers expressed as information Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to demonstrate understanding of what scientific notation is Are able to demonstrate understanding of the distributive law Are able to use trinomials and binomials in basic calculations Assignment Description WHATWHAT HOW Notional Hours 2 Individual and group exercises of practically using basic calculations in informal day to day situations 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

13 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Be able to convert decimals and fractions into percentage Be able to convert fractions into decimals and decimals into fractions TF Working with percentages and fractions Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

14 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Working with percentages and fractions Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to convert fractions into decimals and decimals into fractions Are able to convert decimals and fractions into percentages Assignment Description WHATWHAT HOW Notional Hours 3 Individual and group exercises of practically using basic calculations in informal day to day situations 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

15 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Be able to input numbers into a computerised spreadsheet Be able to develop and input formulas to add, subtract, divide, multiply and calculate percentage in tables of a computerised spreadsheet TF Developing spreadsheets Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context

16 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Topic Specification: TF Developing spreadsheets Collect Information Use Multi media Self Study Field visit Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Calculate Case studies Compile lists Complete worksheets Execute, test and evaluate Job assignment Make presentation Multiple choice Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to input numbers into a basic computerised spreadsheet Are able to develop and input formulas into a computerised spreadsheet Assignment Description WHATWHAT HOW Notional Hours 3 Individual exercise to develop computerised spreadsheets using formulae 1.Individually do practical work and private life related exercises provided by the facilitator using the mathematical fundamentals 2.Submit worksheet with exercises to facilitator for comments 3.Jointly work out more complex exercises using the fundamentals and present exercises to the facilitator for assessment 4.Jointly identify the practical application of the mathematical fundamentals and make an appropriate presentation

17 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 3 Be able to use tables and grids to calculate percentages and ratios Be able to convert sets of number information into tables and grids TF Using tables and grids Be able to calculate percentages and ratios Critical Cross-field Outcomes Identify and solve problems Work effectively with others Communicate effectively Organise and manage myself and my activities Collect, analyse, organise and critically evaluate information Use science and technology effectively and critically Demonstrate an understanding of the world as a set of related systems Use mathematics Learner and societal development US: 12442# Demonstrate an understanding of rational and irrational numbers and number systems within the context