1. 1 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Measure, estimate and calculate physical quantities and explore, critique and prove geometrical relationships in two and three- dimensional space

2. 2 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 RF411.58Exploring three dimensional geometrical situations Measure, estimate and calculate physical quantities and explore, critique and prove geometrical relationships in two and three- dimensional space RF411.56Measuring, estimating and calculating physical quantities Notional Hours Total Notional Hours RF411.57Exploring two dimensional geometrical situations 15 10 15 40 P&P4FM Measuring, estimating, calculating P&P4FM Two dimensional geometrical situations P&P4FM Three dimensional geometrical situations ModulesTopics

3. 3 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 RF411.56 Measuring, estimating and calculating physical quantities 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 u Pythagoras’ theorem to calculate heights and distances Be able to estimate or measure quantities such as length/distance, area, mass, time, speed acceleration and temperature in ranges from low to high or small to large. Be able to use accurate measuring instruments such as micrometer screws Be able to use basic measuring instruments eg pyrometers Understand Pythagoras’ theorem US: 9016 Measure, estimate and calculate physical quantities and explore, critique and prove geometrical relationships in two and three-dimensional space

4. 4 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Topic Specification: TC56 Measuring, estimating and calculating physical quantities Collect Information Use Multi media Group/Self Study Plant investigation Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Sketch Case studies Analyse/Calculate Develop recommendations Execute, test and evaluate Job assignment Make presentation Complete answer sheet Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to perform accurate measurement, estimation or calculation of quantities Are able correctly read scales on the measuring instruments correctly Are able to choose the appropriate instrument to measure. Are able to measure quantities correctly with a justifiable tolerance Are able to carry out calculations correctly Are able to use symbols and units in accordance with SI conventions Assignment Description WHATWHAT HOW Notional Hours 4 An individual exercise where learners use basic and more accurate measurement apparatus and do basic measurement calculations 1.Each learner to study prepare a list with the appropriate formulae to be used in calculations 2.Each learner obtains an answer sheet and product to measure 3.Measure all agreed parameters such as mass, thickness, surface area using available equipment and write down your answers. 4.Use Pathagoras’s theorem to calculate the length of one side of the product and compare to measured length. 5.Compare variances in measurements and calculation against physical differences between products. 6.Present the average group measurement in the correct units and the range of the measurements. 7.Present your answer sheet to the facilitator for comments

5. 5 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 RF411.57 Exploring two dimensional geometrical situations 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 use the Cartesian co-ordinate system in determining location and describing relationships in two dimensions Be able to use and interpret scale drawings of objects and shapes. Be able to use available technology to represent objects eg software, drawing instruments Be able to use rough sketches to interpret, represent and describe situations US: 9016 Measure, estimate and calculate physical quantities and explore, critique and prove geometrical relationships in two and three-dimensional space

6. 6 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Topic Specification: TC57 Exploring two dimensional geometrical situations Collect Information Use Multi media Group/Self Study Plant investigation Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Sketch Case studies Analyse/Calculate Develop recommendations Execute, test and evaluate Job assignment Make presentation Complete sheet Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Are able to describe shapes based on a systematic analysis of shapes. Are able to correctly assimilate different views Relations of distance and positions between objects are analysed from different views Are able to correctly calculate surface area calculated Are able to use cartesian plane Are able to make rough sketches of a product Are able to use technology to represent an object Are able to correctly interpretscale drawings Assignment Description WHATWHAT HOW Notional Hours 4 A group exercise where learners use, produce and analyse two dimensional geometrical representations 1.Each learner is provided with a answer sheet and the measurements of a single ream of paper. 2.Calculate how many reams will be necessary to cover the warehouse floor. Note answer and calculations on the answer sheet. 3.On a cartesian plane, draw a surface covered with reams, calculate the area and how many reams it contains. 4.Construct a rectangle using the same number of reams. 5.Rotate the surface with 90 degrees. 6.Submit your answer sheets with calculations and drawings for assessment

7. 7 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 RF411.58 Exploring three dimensional geometrical situations 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 top resent 3 dimensional objects by top front and side views. Be able to use available technology to represent objects eg software, drawing instruments Be able to use rough sketches to interpret, represent and describe situations Know how to calculate volumes Measure, estimate and calculate physical quantities and explore, critique and prove geometrical relationships in two and three-dimensional space

8. 8 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Topic Specification: TC58 Exploring three dimensional geometrical situations Collect Information Use Multi media Group/Self Study Plant investigation Media search Interview experts Attend lectures Analyse, plan and make decisions Group Discussions Sketch Case studies Analyse/Calculate Develop recommendations Execute, test and evaluate Job assignment Make presentation Complete documents Draft a report Complete a questionnaire Learning ActivitiesTopic assessment criteria The assessor will observe and confirm that learners: Reflect the property of three dimensional shapes accurately, clearly and completely. Top, side and front views of 3 dimensional objects. Available and appropriate technologies are used in producing views of objects. Quantitative information is used correctly. Assignment Description WHATWHAT HOW Notional Hours 4 An individual and group exercise where learners use, produce and analyse three dimensional geometrical representations 1.Each learner obtains the measurements of a product and calculate the dimensions of a stack of 50 products and present top and side views. 2.Calculate how many such stacks can be loaded in the back of a delivery truck? 3.On graph paper draw a scale model of the factory layout as well as one view of the building from the outside. 4.Draw a map with correct direction and proportions to show directions from your home to the plant. 5.Present your drawings and calculations to the facilitator for assessment.