1. 1 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different contexts.

2. 2 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 2 US:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. Notional Hours Total Notional Hours P&P2FM19 Measuring and using shapes ModulesTopics P&P2FM20 Creating shapes and understanding circumferences and the areas of shapes P&P2FM21 Volumes, contents and percentages TF207.50Working with percentages. TF207.45Identifying basic shapes and measuring angles TF207.46Applying the basic theorems associated with triangles TF207.47Applying the basics of trigonometry. TF207.48Calculating the circumference and area of various shapes. TF207.49Working with volume and contents. 4 8 6 2 30

3. 3 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:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. TF207.45 Identifying basic shapes and measuring angles Understand the concept of angles and how they are measured. Be able to identify all the basic shapes are used in the things that we use in daily life. Understand the concept of interior and exterior angles of a triangle. Be able to use a protractor to measure angles. Be able to draw, measure and name, right angles, acute angles, obtuse angles a circle and a straight line. Be able to draw, measure and identify the various shapes that exist in the workplace and at home.

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: Identify the basic shapes associated with our environment; Demonstrate understanding of the concepts of angles; Use measuring equipment to measure angles; Draw angles and shapes to scale. Notional Hours 4 Assessment Criteria : (The assessor will observe and confirm) The ability to read basic production and process diagrams and measure basic angles and shapes. TF207.45 Identifying basic shapes and measuring angles Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through a study guide on the basics of geometry, studying examples and doing exercises. To ensure that the learners are able to analyse various shapes and angles and relate this analysis to the workplace. Learners study the relevant guide and work through the examples; In a small group learners identify relevant shapes at home and in the workplace and measure and draw these shapes to scale; Learners complete practical exercises, the exercises are submitted for correction and feedback is given with structured group discussion.

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:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. TF207.46 Applying the basic theorems associated with triangles Understand the role of triangles in building shapes. Be able to identify the various types of triangles and explain the basic theorems associated with each type of triangle. Understand the theorem of “Pythagoras” and the meaning of this theorem in practical terms. Be able to calculate lengths using the theorem of “Pythagoras”.

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 the role of triangles in building shapes; Identify the various types of triangles and explain the basic theorems associated with each type; Explain the theorem of Pythagoras in practical terms; Calculate lengths using the theorem of Pythagoras. Notional Hours 4 Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through specific learning workbooks and applying the theory in a practical way. To ensure that the learners can effectively use the theorems associated with triangles to estimate, calculate and manipulate the shapes of triangles and rectangles. Learners study the relevant guide and work through the examples; In a small group learners work through specific problems where they must use the theorems of Pythagoras to determine the lengths of the sides of triangles. The results of the problems are then submitted for correction and discussed in structured feedback sessions. Assessment Criteria : (The assessor will observe and confirm) The ability to read the scales on measuring instruments correctly; The ability to choose the correct instruments for measuring; The ability to draw sketches correctly and interpret diagrams and drawings correctly. TF207.46 Applying the basic theorems associated with triangles

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:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. TF207.47 Applying the basics of trigonometry. Understand the fundamental principles of trigonometry. Be able to apply the concepts of sine, cosine and tangent in calculations to solve practical problems associated with our daily work and private life.. Be able to apply the concepts of sine, cosine and tangent in calculations to solve practical problems associated with our daily work and private life using a basic mathematical calculator.

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 the fundamental principles of trigonometry; Apply the concepts of sine, cosine and tangent in calculations to solve practical problems associated with our daily work and private life; and Apply the concepts of sine, cosine and tangent in calculations to solve practical problems associated with our daily work and private life using a basic mathematical calculator. Notional Hours 8 Assessment Criteria : (The assessor will observe and confirm) The ability to use the basic concepts to explore and transform two dimensional geometric figures constructing rectangular triangles TF207.47 Applying the basics of trigonometry. Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through specific learning workbooks and applying the theory in a practical way. To ensure that the learners can effectively estimate and calculate angles and the length of the sides of triangles using the principles of sine, cosine and tangent. Learners study the relevant guide and work through the examples; In a small group learners estimate and calculate the length of the sides of triangles in the workplace and at home; Learners complete practical exercises, the exercises are submitted for correction and feedback is given with structured group discussion.

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:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. TF207.48 Calculating the circumference and area of various shapes. Understand the basics of the decimal system and the decimal units of measurement. Be able to calculate the circumference of basic figures. Be able to calculate the area of basic figures. Be able to calculate the area of composite rectangular figures. Be able to calculate the circumference and area of rectangular figures, triangles and circles.

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 the basics of the decimal system and the various units of measurement; Calculate the circumference and areas of basic figures including rectangular figures, triangles and circles. Notional Hours 6 Assessment Criteria : (The assessor will observe and confirm).Clear understanding of the various units of measurement and their application in the workplace. TF207.48 Calculating the circumference and area of various shapes. Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through specific learning workbooks and applying the theory in a practical way. To ensure that the learners can effectively recall the various units of measurements as applied in the workplace. Learners study the relevant guide and work through the examples; Learners complete practical exercises, the exercises are submitted for correction and feedback is given with structured group discussion.

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:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. TF207.49 Working with volume and contents. Understand the basics concepts and principles associated with volume. Be able to calculate the volume of a cube. Be able to calculate the volume of a prism. Be able to calculate the volume of a cylinder. Be able to calculate the volume of a cone. Be able to calculate the volume of a right pyramid. Be able to convert volume into content. Be able to apply the calculation of volume and content to physical objects and containers that is used in the daily work and home 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 the basic concepts and principles associated with volume; Estimate and calculate the volume of cubes, prisms, cylinders, cones, pyramids; Calculate the volumes and convert these to content of various vessels used in daily work and private life. Notional Hours 6 Assessment Criteria : (The assessor will observe and confirm) The ability to estimate volumes and contents of vessels used in the workplace within acceptable parameters; An understanding of the basic implications and/or consequences associated with the volumes of raw materials and/or final products within the production system. TF207.49 Working with volume and contents. Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through specific learning workbooks and applying the theory in a practical way. To ensure that the learners can effectively estimate and calculate the volume of various vessels and convert these volumes into contents. Learners study the relevant guide and work through the examples; Learners complete practical exercises, 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:9008Measure, estimate and calculate physical quantities and explore, describe and represent geometrical relationships in two dimensions in different life or workplace contexts. TF207.50 Working with percentages. Understand the concept and practical use of percentage. Be able to calculate percentages in various practical applications. Be able to apply the concept of percentages to the problems of our daily work and personal life.

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 the practical use of percentages; Calculate percentages for various practical applications; Apply the concept of percentages to work and personal situations. Notional Hours 2 Assessment Criteria : (The assessor will observe and confirm) The ability to calculate percentages of production and safety results and draw relevant conclusions from these calculations.. TF207.50 Working with percentages. Assignment Description WHATWHAT WHYWHY HOW An individual exercise of working through specific learning workbooks and applying the theory in a practical way. To ensure that the learners can effectively estimate and calculate percentages and draw relevant conclusions from these calculations that will assist in day to day decision making. Learners study the relevant guide and work through the examples; Learners complete practical exercises, the exercises are submitted for correction and feedback is given with structured group discussion.