1. 1 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Apply knowledge of statistics and probability to critically interrogate and effectively communicate findings on life- related problems

2. 2 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Apply knowledge of statistics and probability to critically interrogate and effectively communicate findings on life-related problems PF410.53 Collecting, organising and representing data Notional Hours Total Notional Hours PF410.54 Understanding theoretical and experimental probability PF410.55 Using probability and statistical models 20 60 P&P4FM Representing data P&P4FM Probabilities P&P4FM Statistical methods ModulesTopics

3. 3 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 PF410.53 Collecting, organising and representing data 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 two variable scatter plots and lines of best fit Be able to find inconsistencies in collected data and data gathering techniques Be able to calculate measures of centre and spread Be able to use dichotomous, discrete and continuous variables Be able to select random samples in the workplace Be able to formulate questions in surveys to obtain data Be able to examine the correlation between two variables US: 9015 Apply knowledge of statistics and probability to critically interrogate and effectively communicate findings on life-related problems

4. 4 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Topic Specification: TC53 Collecting, organising and representing data 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 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: Are able to collect representative production data to resolve a problem Are able to evaluate and organise collected data Are able to summarise data using graphical and numerical methods Are able to present and support the resolution of a formulated problem. Assignment Description WHATWHAT HOW Notional Hours 4 A group exercise to collect production data and study the relationship between two variables. 1.In a group, decide on two appropriate production variables to be investigated and a representative data collection approach. 2.Collect production data and study the relationship between two variables 3.Calculate mean and variance and draw scatter plots to remove inconsistencies 4.Evaluate and summarise the collected data using numerical and graphical methods 5.Investigate the association between two variables (graphical and numerical) and formulate the relationship between the two variables using lines of best fit and correlation. 6.Draft a report on the group’s findings

5. 5 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 PF410.54 Understanding theoretical and experimental probability 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 compare experimental results with mathematical expectations Be able to use sumulations to compare experimental results with mathematical expectations Be able to determine theoretical and experimental probabilities Be able to distinguish between independent, complementary and mutually exclusive events TOPIC SPECIFICATION US: 9015 Apply knowledge of statistics and probability to critically interrogate and effectively communicate findings on life-related problems

6. 6 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Topic Specification: TC54 Understanding theoretical and experimental probability 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 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: Are able to use the laws governing independent, complementary or mutually exclusive events. Are able to use simulations and probability models to compare theoretical and experimental probabilities Are able to design or choose simulations or experiments to model a probability situation Are able to make predictions based on validated experimental or theoretical probabilities Are able to interpret the results of experiments and simulations correctly Are able to communicate the outcome of experiments and simulations clearly. Assignment Description WHATWHAT HOW Notional Hours 4 An individual exercise to ensure that the learners will be able to use theoretical and experimental probability to study problems and compare with mathematical expectations. 1.Place 8 similar items in a container and number them 1 to 8. Mark any 4 with one colour and the remaining 4 with another colour). Mix, draw one item and record the number. Do this 100 times Repeat the exercise, recording both number and colour. 2.Divide the observations in colour and even or uneven numbers. Determine the probability of obtaining a number between 1 and 8, an even or uneven number, an even number in colour 1,an uneven number in colour 2 3.Compare the outcome of the exercise to mathematical expectations. Define events as independent, complementary or mutually exclusive 4.Present you findings to the group

7. 7 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 PF410.55 Using probability and statistical models 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 make inferences about a population on the basis of a sample selected from it. Be able to evaluate statistically based arguments and make recommendations and describe the use and misuse of statistics in society Be able to manipulate data in different ways to support opposing conclusions. Be able to source and interpret information from a variety of sources including databases Be able to make comparisons between predictions and actual occurrences. US: 9015 Apply knowledge of statistics and probability to critically interrogate and effectively communicate findings on life-related problems

8. 8 Commissioned by PAMSA and German Technical Co-Operation National Certificate in Paper & Pulp Manufacturing NQF Level 4 Topic Specification: TC55 Using probability and statistical models 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: Are able to make inferences about a population on the basis of a sample selected from it. Are able to define and critique assumptions in the collection or generation of data and statistics Are able to correct use data, statistics and probability models Are able to provide valid arguments to support predictions or conculsions Are able to evaluate potential sources of bias or errors in measurement are evaluated. Assignment Description WHATWHAT HOW Notional Hours 4 A group exercise where learners source, interpret information and draw statistically valid conclusions 1.Learners to split into two groups 2.Group 1 identifies a problem to be investigated in the manufacturing pulp and paper. 3.Group 2 collects data, manipulate data, generate statistics from the data and interpret and present conclusions meaningfully to Group 1. 4.Group 1 evaluate the assumptions, potential sampling errors, representation of the data and validity of conclusions and accepts or rejects conclusion via critical evaluation of statistical methods used by Group 2. 5.Group discussion on evaluation of Group 2 and the effect of errors in measurements.