1. 1 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Demonstrate understanding of rational and irrational numbers and number systems, within the context of relevant calculations.

2. 2 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 US:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.35Understanding what mathematics is and how it is used Notional Hours Total Notional Hours P&P2FM15 Introduction to mathematics ModulesTopics P&P2FM16 Exponents, logarithms and basic algebraic functions P&P2FM17 Factorization, fractions and equations P&P2FM18 Algebraic graphs TF206.36Introducing Algebra TF206.37Using Exponents TF206.38Using Logarithms TF206.39Understanding the four main algebraic calculations TF206.40Understanding what factors are and how they are used TF206.41Understanding fractions and how they are used TF206.42Understanding what equations are and how they are used TF206.43Understanding the concept of algebraic graphs TF206.44Using straight line graphs and hyperbolas 4 2 3 4 3 2 30

3. 3 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 TF206.35 Understanding what mathematics is and how it is used in society 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations Understand what mathematics is and how mathematics is used in life and the workplace. Be able to explain the meaning of the basic mathematical symbols and notations. Know the 1-12 times tables and how these tables are used in mathematics. Be able to list the units of distance, weight and volume. Be able use a basic mathematical calculator to do basic calculations. Be able explain the meaning of the basic terms used in mathematics.

4. 4 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Define mathematics and give examples of how mathematics is used in daily life and workplace; Explain the meaning of the basic mathematical symbols and notations; List the units of distance, weight and volume; Explain the meaning of all the basic terms used in mathematics; Use a basic mathematical calculator to add, subtract, multiply and divide; Demonstrate effective knowledge of the 1 to 12 times tables and explain how these tables are used in mathematics Assignment Description WHATWHAT WHYWHY HOW Individual and group exercises where learners are systematically exposed to the mathematical fundamentals and where they are given ample opportunity to apply these fundamentals in doing workplace and personal life exercises. To ensure that learners develop a clear understanding of the basic terms and structure of mathematics and that they can clearly see the applications in the workplace and develop a desire to continue learning this subject matter. Learners participate in learning sessions to obtain understanding of the principles; Learners individually work through examples and case studies relevant to their personal and work life; Learners identify personal and work related problems where the relevant principles can be applied; The problems is presented to the learning facilitator and agreement is reached on which problems to work on; The problems are individually worked on and jointly discussed during group sessions. Assessment Criteria : (The assessor will observe and confirm) Process & SHEQ The learners knowledge of the mathematical fundamentals and ability to do the basic calculations and explain how these fundamentals are used in maintaining and improving process stability. Notional Hours 4 TF206.35 Understanding mathematical fundamentals

5. 5 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.36 Introducing Algebra Understand what algebra is and why we use algebra in mathematics. Be able to explain the various terms used in algebra and give examples of how these concepts are used in the workplace. Understand the language of algebra.

6. 6 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what algebra is and how it is used in mathematics; Explain the various terms used in algebra and give examples of the use of these concepts in the workplace. Assignment Description WHATWHAT WHYWHY HOW An individual and group exercise where learners study the algebraic concepts and work through examples of the use of these concepts in the workplace. To ensure that learners understands how the basic algebraic concepts are used in mathematics and in real life situations. This topic must lay the foundation for further study of applied mathematics. Learners attend work sessions that explain the structure and function of algebra; Learners work through examples to explain the various concepts; Learners use a pre developed example sheet to identify how the key algebraic concepts are used in the workplace. Assessment Criteria : (The assessor will observe and confirm) Process & SHEQ The ability of the learner to clearly explain the key algebraic concepts and give examples of where these concepts are used to maintain and improve process stability. Notional Hours 4 TF206.36 Introducing Algebra

7. 7 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.37 Using Exponents Understand what an exponent is and why we use exponents. Be able to apply the laws of exponents in a variety of exercises and examples. Understand the laws of exponents.

8. 8 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what an exponent is and why exponents are used in mathematics; Apply the laws of exponents in a variety of exercises and examples. Assignment Description WHATWHAT WHYWHY HOW Individual exercise of studying the various laws and working through exercises and examples. To ensure that the learner has a clear understanding of the application of exponents in mathematics. Learners attend a work session on the subject Learners work through examples and exercises and submit them for correction and feedback. Assessment Criteria : (The assessor will observe and confirm) Process & SHEQ The ability to effectively apply the laws of exponents to do simple calculations based on work related examples. Notional Hours 2 TF206.37 Using exponents

9. 9 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.38 Using Logarithms Understand what logarithms are and how they are used in mathematics. Be able to use the log function on a pocket calculator. Be able to multiply with logarithms. Be able to divide with logarithms. Be able to calculate square root using logarithms. Be able to calculate with logarithms without using a calculator.

10. 10 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what logarithms are and how they are used in mathematics; Use the log function on a pocket calculator; Multiply and divide using logarithms. Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on the concept of logarithms, studying examples and doing exercises of multiplication and division with very big and very small numbers. To ensure that the learners are able to use logarithms in calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where calculations would require one to use logarithms; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion. Assessment Criteria : (The assessor will observe and confirm) The ability to explain the purpose of logarithms in mathematical calculations and use logarithms to multiply and divide. Notional Hours 3 TF206.38 Using Logarithms

11. 11 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.39 Understanding the four main algebraic calculations Understand all the functions and operations of the basic mathematical calculator. Be able to multiply and divide. Know what the four main algebraic functions are. Understand the concept of number lines. Be able to add and subtract. Be able to use brackets in calculations. Be able to do division with more than one term in the numerator. Be able to do long division. Be able to describe how these calculations are used in daily work and personal life.

12. 12 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of all the functions of the basic mathematical calculator; Demonstrate understanding of the four main algebraic functions through effectively doing the various calculations; Describe how the various calculations are used in daily work and personal life. Assessment Criteria : (The assessor will observe and confirm) The ability of the learners to do the various calculations and to relate these calculations to daily work and private life. Notional Hours 4 TF206.39 Understanding the four main algebraic calculations Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on the four major algebraic functions, studying examples and doing exercises. To ensure that the learners are able to do the basic calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where the relevant calculations will be used; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion.

13. 13 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.40 Understanding what factors are and how they are used Understand what factors are and how they are used in mathematics. Be able to resolve equations into common and multiple factors and use these in relevant calculations. Understand what lowest common multiples are and how they are used in mathematics.

14. 14 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what factors are and how they are used in mathematics; Resolve equations into common and multiple factors and use these in relevant calculations; and Indicate how the concept of factors is used in daily workplace and private life. Notional Hours 3 TF206.40 Understanding what factors are and how they are used Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on the four major algebraic functions, studying examples and doing exercises. To ensure that the learners are able to do the basic calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where the relevant calculations will be used; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion. Assessment Criteria : (The assessor will observe and confirm) The ability of the learners to do the various calculations and to relate these calculations to daily work and private life.

15. 15 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.41 Understanding fractions and how they are used Understand what a fraction is and how it is used in mathematics. Be able to simplify fractions. Understand the difference between numerators and denominators. Understand what proper, improper and mixed fractions are. Be able to add and subtract fractions. Be able to multiply and divide fractions. Be able to apply the bracket rule when working with fractions. Be able to multiply and divide algebraic fractions. Be able to multiply and divide algebraic fractions using factorisation. Be able to describe how these calculations are used in daily work and personal life.

16. 16 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what a fraction is and how these are used in mathematics; Simplify, add and subtract fractions; Multiply, divide fractions and use brackets in calculations involving fractions; Use factorisation in the multiplication and division of fractions; and Describe how these calculations is used in daily personal and work life. Notional Hours 3 TF206.41 Understand fractions and how they are used Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on working with fractions, studying examples and doing exercises. To ensure that the learners are able to do the basic calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where the relevant calculations will be used; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion. Assessment Criteria : (The assessor will observe and confirm) The ability of the learners to do the various calculations and to relate these calculations to daily work and private life.

17. 17 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations TF206.42 Understanding what equations are and how they are used Understand what a formula is and how these are used in mathematics. Be able to change the subject of a formula. Understand what an equation is and how it is used in mathematics. Be able to do substitutions in formulas. Be able apply formulas to calculate distance, time and velocity. Be able apply formulas to calculate revolutions. Be able to describe how these calculations are used in daily work and personal life.

18. 18 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what equations are and how they are used in mathematics; Demonstrate understanding of formulas and how these are used in mathematics; Use formulas to calculate distance, time, velocity and revolutions; and Describe how mathematical formulas are used in personal and work life. Notional Hours 3 TF206.42 Understanding what equations are and how they are used Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on working with equations and formulas, studying examples and doing exercises. To ensure that the learners are able to do the basic calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where the relevant calculations will be used; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion. Assessment Criteria : (The assessor will observe and confirm) The ability of the learners to do the various calculations and to relate these calculations to daily work and private life.

19. 19 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations Understand what a graph is and how these graphs are used in daily life. Be able to develop straight line graphs and interpreting the meaning of these graphs. TF206.43 Understanding the concept of algebraic graphs Understand the “Cartesian co- ordinate” system.

20. 20 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of graphs and graphic displays and how they are used in our daily lives; Demonstrate and understanding of the “Cartesian co- ordinate” system; and Develop straight line graphs and interpreting the meaning of these graphs as applied to every day life. Notional Hours 2 TF206.43 Understand the concept of algebraic graphs Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on working with equations and formulas, studying examples and doing exercises. To ensure that the learners are able to do the basic calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where the relevant calculations will be used; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion. Assessment Criteria : (The assessor will observe and confirm) The ability of the learners to do the various calculations and to relate these calculations to daily work and private life. The ability to interpret work and SHEQ related graphs

21. 21 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 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:8982Demonstrate an understanding of rational and irrational numbers and number systems within the context of relevant calculations Understand what a hyperbola is and how these are used in daily life. Be able to develop straight line graphs using data relevant to daily work and personal life. TF206.44 Using straight line graphs and hyperbolas Be able to develop hyperbolas using data relevant to daily work and personal life. Be able to interpret graphs of personal and work related situations and make proposals for positively impacting on the trends reflected in the graphs.

22. 22 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Topic Specification Learning Outcomes On completion of this topic the learner will be able to: Demonstrate understanding of what a hyperbola is and how it is used in daily life; Develop straight line graphs using data from relevant daily work and personal life; Develop hyperbolas using data from relevant daily work and personal life; and Interpret graphs of personal and work related situations and make proposals for positively impacting on the trends reflected in the graphs. Notional Hours 2 TF206.44 Developing straight line graphs and hyperbolas Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on working with equations and formulas, studying examples and doing exercises. To ensure that the learners are able to do the basic calculations and that they can see the use of these calculations in the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify areas within the workplace where the relevant calculations will be used; Learners complete practical exercises where calculations are made, the exercises are submitted for correction and feedback is given with structured group discussion. Assessment Criteria : (The assessor will observe and confirm) The ability of the learners to develop the relevant graphs. The ability to interpret work and SHEQ related graphs.