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GETC-ABET Level 4 ~ @ NQF Level 1 1 | P a g e

General Education and Training Certificate

Adult Basic Education and Training

NQF Level 1

EXAMINATIONS AND ASSESSMENT GUIDELINES

MATHEMATICAL LITERACY L4

CODE: MLMS4

2013 - 2015

Examinations and Assessment Guidelines: MLMS4

TABLE OF CONTENTS

1. Introduction 3

2. The GETC-ABET Level 4 Qualification 4

3. Unit Standards for MLMS4 Learning Area 7

4. LTSM in PALCs 18

5. Weighting of the Specific Outcomes and Assessment Criteria 18

6. Core Knowledge Areas 18

7. Taxonomies used in scaffolding questions 22

8. Site-Based Assessment (Formative) 23

8.1 Structure of SBA Tasks 23

8.2 Exemplar SBA Tasks 24

9. External Assessment (Summative) 49

9.1 Structure of a question paper 49

9.2 Exemplar question paper 49

10. Promoting the Principles of quality assessment practices 62

1. INTRODUCTIONGETC-ABET Level 4 ~ @ NQF Level 1 2 | P a g e


This document aims to be an Examinations and Assessment Guidelines in its orientation. It should be seen against the background of the review of the General Education and Training Certificate (GETC): Adult Basic Education and Training (ABET) qualification and the re-registration of some of its constituent Unit Standards. Against this background, it must be seen to replace any other guideline document that has preceded it. What it does not do, however, is signal a radical shift from formal national assessment processes that have been managed by the Department of Higher Education and Training (DHET). It attempts to consolidate such assessment practices. It formalises them into a useful reference document for mainly examiners and moderators of ABET assessment. At the same time it is a useful guide to educators, in order to prepare their learners for assessment.

The MLMS4 Examinations and Assessment Guidelines document is based on the GETC-ABET interim qualification with the SAQA ID number 71751. The guidelines should be viewed as developmental in nature aimed at enhancing the quality of the implementation of assessment for the interim qualification. The other users of this document shall be the Public Adult Learning Centres (PALCs) management teams, departmental officials, policy analysts, learning area coordinators or advisers and any interested stakeholder in adult education.Furthermore, the guidelines document is intended to assist the Learning Area Facilitator in preparing the learner for the examination as well as the site-based assessment. It should be treated as resource material that seeks to indicate the unit standards for the MLMS4 learning area and how to unpack them for assessment. It also indicates the possible content knowledge (as mentioned in the unit standards) to be assessed. It will provide clarity on how specific outcomes and assessment criteria are weighted. The possible teaching and learning support materials relevant to the learning area are also highlighted.

While our aim is not to be prescriptive on curriculum, it is our hope that this document will offer educators more guidance in their own teaching and assessment practice. The document creates a uniform framework for examinations and formative assessments, in order to avoid a variety of different approaches to examinations. It must be pointed out that while the guidelines are based on the Unit Standards, it should not be read without the accompanying unit standards, or replace the unit standards as a guideline to teaching.

The document also contain the GETC - ABET qualification which among others reflects on the rules of combination, core components and the academic learning areas. The structure of an examination question paper, the taxonomies used in scaffolding of questions, an exemplar question paper and marking memorandum together with exemplar site-based assessment tasks are outlined.

This examinations and assessment guidelines document provides guidance on how to use available resources to achieve the specified unit standards of the learning area. The national Policy on the Conduct, Administration and Management of the GETC - ABET Level 4 examinations and assessment has a bearing on this document.

All users are encouraged to alert the Department of Higher Education and Training of any unrealistic suggestions that might hinder quality implementation of the assessment for the interim GETC – ABET Level 4 qualification. It must be noted that these guidelines are by no means exhaustive in its suggestions of possible assessment activities. Suggestions to improve the implementation of assessment in the MLMS4 learning area will be greatly appreciated.

2. THE GETC-ABET LEVEL 4 QUALIFICATION



The General Education and Training Certificate (GETC) in Adult Basic Education and Training (ABET) with ID No. 71751 will provide adult learners with fundamental basics of general education learning. It replaces SAQA qualification ID No. 24153. The table below provides a synoptic view of the qualification.

SAQA QUAL ID QUALIFICATION TITLE

71751 General Education and Training Certificate: Adult Basic Education and Training

ORIGINATOR REGISTERING PROVIDER

Task Team - Adult Basic Education and Training

QUALITY ASSURING ETQA

-

QUALIFICATION TYPE FIELD SUBFIELDNational Certificate Field 05 - Education, Training and

Development Adult Learning

ABET BAND MINIMUM CREDITS NQF LEVEL QUAL CLASS

ABET Level 4 120 Level 1 Regular-Unit Standards Based

REGISTRATION STATUS SAQA DECISION NUMBER REGISTRATION START DATE

REGISTRATION END DATE

Registered SAQA 1179/08 2008-11-26 2011-11-26

LAST DATE FOR ENROLMENT LAST DATE FOR ACHIEVEMENT

2012-11-26 2015-11-26

The purpose of the Qualification is to equip learners with foundational learning by acquiring knowledge, skills and values in specified Learning Areas. In addition, it also allows learners to choose Elective Unit Standards which relate to occupational type learning relevant to their area of interest or specialisation. In particular, the purpose of the qualification aims to:

Give recognition to learners who achieve and meet the necessary requirements and competencies as specified in the Exit Level Outcomes and Associated Assessment Criteria.

Provide a solid foundation of general education learning which will help prepare learners and enable them to access Further Education and Training learning and qualifications, particularly occupational workplace-based or vocational qualifications.

Promote lifelong learning to enable learners to continue with further learning. Prepare learners to function better in society and the workplace.

Rationale:

Adult Basic Education is identified as a critical priority in South Africa and plays a vital role in equipping adult learners with the necessary knowledge, skills and values in order to be functional in society and as a person by contributing to the workforce, community and economy. This GETC: ABET qualification provides learners with foundational learning through the acquisition of knowledge and skills needed for social and economic development and the promotion of justice and equality. It also seeks to promote and instill learners with a culture of life-long learning needed for future learning. It also enables learners to acquire the necessary competencies in order to access further education and training, career development and employment opportunities.

The achievement of the GETC: ABET qualification allow learners the following learning pathways:

To choose a vocational route through completion of the National Certificate (Vocational) Qualifications at Levels 2, 3 and 4 which contain vocational specialisations.

To access academic learning at NQF Level 2 and above. To access Occupational specific qualifications at NQF Level 2, which consist of knowledge, skills and workplace experience and learning.



The qualification aims to equip learners to:

Develop and apply relevant skills, knowledge and attitudes in the chosen Learning Areas. Function better in and contribute to the world of work. Be sensitive and reflective of issues relating to diversity, inclusivity, cultural values, human rights,

gender, development and change. Develop an appreciation for lifelong learning. Function better as a citizen in South Africa and contribute to cultural, social, environmental and

economic development. Make informed judgments about critical ethical issues. Develop study skills to be able to access further learning.

It is assumed that learners have literacy and numeracy skills in order to cope with the complexity of learning in this qualification.

Recognition of Prior Learning:

The structure of this Qualification makes Recognition of Prior Learning (RPL) possible through the assessment of individual Unit Standards. The learner and assessor should jointly decide on methods to determine prior learning and competence in the knowledge, skills, and values implicit in the Qualification and the associated Unit Standards. RPL will be done by means of an integrated assessment which includes formal, informal and non-formal learning and work experience. This Recognition of Prior Learning may allow for accelerated access to further learning at this or higher Levels on the NQF; gaining of credits for Unit Standards in this Qualification; and obtaining this Qualification in whole or in part. All RPL is subject to quality assurance by the relevant ETQA or an ETQA that has a Memorandum of Understanding with the relevant ETQA.

It is recommended that learners have achieved the following in order to access this qualification: Communication at ABET Level 3 or equivalent and Mathematical Literacy at ABET Level 3 or equivalent.

The GETC-ABET qualification comprises the Fundamental, Core and Elective components in its rules of combination. Learners are expected to offer a minimum of 5 Learning Areas. The 2 fundamental Learning Areas and the 1 Core Learning Area are compulsory offerings. Learners may choose 2 or more Learning Areas from the Elective component.

Learners are expected to meet the following requirements to be awarded a GETC-ABET qualification:

RULES OF COMBINATION FOR THE GETC-ABET QUALIFICATION: 120 CREDITS

FUNDAMENTALS COMPONENT: COMPULSORY 39 OR 37 CREDITS

1. One Official Language: 23 Credits2. Mathematical Literacy: 16 Credits OR3. Mathematics and Mathematical Sciences: 14 Credits NOT BOTH

CORE COMPONENT: COMPULSORY 32 CREDITS

1. Life Orientation: 32 Credits

ELECTIVES COMPONENT: OPTIONAL 49 OR 51 CREDITS

Academic Learning Areas:

1. Human and Social Sciences: 23 Credits2. Natural Sciences: 15 Credits3. Economic and Management Sciences: 21 Credits4. Arts and Culture: 17 Credits 5. Technology: 11 Credits



6. One Additional Official Language (Excluding the language chosen as a Fundamental): 23 Credits

Vocational Learning Areas:

7. Applied Agriculture and Agricultural Technology: 20 Credits8. Ancillary Health Care: 45 Credits9. Small, Medium and Micro Enterprises: 17 Credits10. Travel and Tourism: 38 Credits11. Information Communication Technology: 23 Credits12. Early Childhood Development: 26 Credits13. Wholesale and Retail: 30 Credits

OPTION 1( 5 Learning Areas)

OPTION 2( 6 Learning Areas)

OPTION 3( 7 or more Learning Areas)

TWO Fundamentals ONE Core and TWO Electives

TWO FundamentalsONE Core andTHREE Electives

TWO Fundamentals ONE Core and FOUR Electives

If you choose mathematics and mathematical sciences in the fundamentals component then you must have a minimum total of 51 credits in the electives component.

Critical Cross-field Outcomes (CCFO):

UNIT STANDARD CCFO IDENTIFYING Identify and solve problems in which responses display that responsible decisions using critical and creative thinking have been made.

UNIT STANDARD CCFO WORKING Work effectively with others as a member of a team, group, organisation and community.

UNIT STANDARD CCFO ORGANISING Organise and manage oneself and one`s activities responsibly and effectively.

UNIT STANDARD CCFO COLLECTING Collect, analyse, organise and critically evaluate information.

UNIT STANDARD CCFO COMMUNICATING Communicate effectively using visual, mathematical and/or language skills in the modes of oral and/or written presentation.

UNIT STANDARD CCFO SCIENCE Use science and technology effectively and critically, showing responsibility towards the environments and health of others.

UNIT STANDARD CCFO DEMONSTRATING Demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation.

3. UNIT STANDARDS FOR MLMS4 LEARNING AREA

The following Critical Cross-Field Outcomes (CCFO) underpin the entire Unit Standards:

CRITICAL CROSS-FIELD OUTCOMES (CCFO): GETC-ABET Level 4 ~ @ NQF Level 1 6 | P a g e


UNIT STANDARD CCFO IDENTIFYING Identify and solve problems and make decisions using critical and creative thinking.

UNIT STANDARD CCFO WORKING Work effectively with others as members of a team, group, organisation and community.

UNIT STANDARD CCFO ORGANISING Organise and manage themselves and their activities responsibly and effectively.

UNIT STANDARD CCFO COLLECTING Collect, analyse, organise and critically evaluate information.

UNIT STANDARD CCFO COMMUNICATING Communicate effectively using visual, symbolic and/or language skills in various modes.

UNIT STANDARD CCFO SCIENCE Use science and technology effectively and critically showing responsibility towards the environment and the health of other.

UNIT STANDARD CCFO DEMONSTRATING Demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.

UNIT STANDARD CCFO CONTRIBUTING Contribute to the full personal development of the learner and the social and economic development of the society at large, by making individuals aware of the importance of: Reflecting on and exploring a variety of strategies to learn more effectively; Participating as responsible citizens in the life of local, national and global communities; Being culturally and aesthetically sensitive across a range of social contexts; Exploring education and career opportunities; Developing entrepreneurial opportunities.

The MLMS4 Learning Area comprises 4 unit standards:

SAQA US ID US TITLE CREDITS119373 Describe and represent objects in terms of shape, space and measurement 5119364 Evaluate and solve data handling and probability problems within given

contexts5

119362 Work with numbers, operations with numbers and relationships between numbers

4

7450 Work with measurement in a variety of contexts 2Total 16

SAQA US ID US TITLE CREDITS119373 Describe and represent objects in terms of shape, space and measurement 5

PURPOSE OF THE UNIT STANDARD

People credited with this unit standard are able to: Describe and interpret the environment geometrically Use scales to interpret maps and to draw simple maps to scale Draw different views of objects in real life situations Solve measurement problems in the contexts of perimeter, areas and volumes by the selection and use of

appropriate formulae



LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING

It is assumed that learners undertaking the learning of this unit standard have prior knowledge and skills for reading and writing, working with numbers, operations with numbers and relationships between numbers at ABET level 3. UNIT STANDARD RANGE N/A



SPECIFIC OUTCOMES AND ASSESSMENT CRITERIA FOR US ID 119373:

SPECIFIC OUTCOME 1 Recognize, identify, name, compare, sort and visualise geometric figures and solids, including cultural forms and products.

OUTCOME RANGE Includes regular and irregular shapes and polyhedra, spheres, cylinders, shapes of and decorations on cultural products such as drums, pots, mats, buildings, necklaces and architecture.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Basic geometric shapes are identified correctly.

ASSESSMENT CRITERION 2 Basic transformations are identified correctly.

ASSESSMENT CRITERION RANGE Translations, reflections and rotations.

SPECIFIC OUTCOME 2 Analyse properties of geometric figures and solids.

OUTCOME RANGE Include triangles, quadrilaterals, regular and irregular polygons and polyhedra.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Geometric shapes are drawn and models of solids are constructed in order to investigate and compare their properties.

ASSESSMENT CRITERION 2 Geometry of straight lines and triangles are used to solve problems and justify relationships in geometric figures.

ASSESSMENT CRITERION 3 Transformations, congruence and similarity are used to investigate, describe and justify properties of geometric figures and solids.

ASSESSMENT CRITERION 4 The theorem of Pythagoras is used to solve problems involving missing lengths in known geometric figures and solids.

ASSESSMENT CRITERION RANGE Include triangles, quadrilaterals, regular and irregular polygons and polyhedra.

SPECIFIC OUTCOME 3 Use scales to interpret maps and draw simple maps to scale.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1

Scales are used correctly to find distance and length.

ASSESSMENT CRITERION 2 Maps are drawn as accurately as the context requires.

SPECIFIC OUTCOME 4 Solve problems in a range of measurements contexts.

OUTCOME RANGE Include polygons, circles, triangular and rectangular based prisms and cylinders.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Appropriate formulae are selected and used correctly.

ASSESSMENT CRITERION 2 Solutions are given with appropriate SI units.

ASSESSMENT CRITERION 3 Perimeters of polygons and circles are calculated correctly from given dimensions.

ASSESSMENT CRITERION 4 Areas of triangles, rectangles and circles are calculated correctly from given dimensions.

ASSESSMENT CRITERION 5 Areas of polygons are calculated by decomposition into triangles and rectangles.

ASSESSMENT CRITERION 6 Volumes of triangular and rectangular prisms and cylinders are calculated correctly.

SPECIFIC OUTCOME 5 Draw different views of objects in real-life situations. ASSESSMENT CRITERIA

ASSESSMENT CRITERION 1 Views from different viewing sites are given which are consistent with the shape of the object from that view.

ASSESSMENT CRITERION 2 Scales are used correctly.



UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS

Providers of this Unit Standard must be accredited by the relevant Education and Training quality Authority (ETQA) before they can offer training against this unit standard.

Moderation will be overseen by the relevant ETQA according to moderation guidelines in the relevant qualification and the agreed ETQA procedures.

UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE N/A

UNIT STANDARD DEVELOPMENTAL OUTCOME N/A

UNIT STANDARD LINKAGES N/A

SAQA US ID US TITLE CREDITS119364 Evaluate and solve data handling and probability problems within given

contexts5


People credited with this unit standard are able to: Collect data to answer questions related to human rights, social, economic, cultural, environmental and political

matters Summarise data into tables and summary statistics Display data in diagrams Critically analyse data in tables and diagrams in order to draw conclusions and make predictions Interpret and determine chance variation


It is assumed that learners undertaking the learning of this unit standard have prior knowledge and skill of reading and writing, working with numbers, operations with numbers and relationships between numbers and understanding of data handling and probability at ABET level 3.

UNIT STANDARD RANGE

N/A




SPECIFIC OUTCOME 1 Collect data to answer questions.

OUTCOME RANGE Data collection sheets; questionnaires; experiments; interviews Questions include: human rights, social, economic, cultural, environmental and political matters.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Appropriate sources of data (peers, family, newspapers, books, magazines, Internet) are identified.

ASSESSMENT CRITERION 2 A distinction between populations and samples is made.

ASSESSMENT CRITERION 3 The data that is collected (alone and/or as a member of a group or team) is appropriate to answer questions related to the investigation.

ASSESSMENT CRITERION 4 Data collection sheets are designed and used to collect data.

ASSESSMENT CRITERION 5 Questionnaires are designed and used to collect data.

ASSESSMENT CRITERION 6 Experiments involving random number generators, coins, spinners, dice and cards are designed and used to collect data.

ASSESSMENT CRITERION 7 Interviews are used to collect data.

SPECIFIC OUTCOME 2 Summarise data into tables and summary statistics.

OUTCOME RANGE Tally tables; frequency tables; two-way tables; stem-and-leaf diagrams; broken line-diagrams; mode (most frequently occurring score); median (middle number or number between two middle numbers of a data set arranged in size order); mean (sum of all the scores divided by number of scores); range (difference between largest and smallest scores)

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Data is organised and recorded in tally tables.

ASSESSMENT CRITERION 2 Data is organised and recorded in frequency tables.

ASSESSMENT CRITERION 3 Data is organised and recorded in two-way tables.

ASSESSMENT CRITERION 4 Data is organised and recorded in stem-and-leaf diagrams.

ASSESSMENT CRITERION 5 The mode is used as a measure of central tendency to summarise ungrouped data.

ASSESSMENT CRITERION 6 The median is used as a measure of central tendency to summarise ungrouped data.

ASSESSMENT CRITERION 7 The mean is used as a measure of central tendency to summarise ungrouped data.

SPECIFIC OUTCOME 3 Display data in diagrams.

OUTCOME RANGE Bar diagrams; double bar diagrams; pie diagrams in terms of proper fractions, decimals or percentages of circles; line diagrams.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1

Data is displayed manually or electronically in bar diagrams and double bar diagrams with appropriate scales and keys.

ASSESSMENT CRITERION 2 Data is displayed manually or electronically in pie diagrams in terms of proper fractions, decimals or percentages of the circle.

ASSESSMENT CRITERION 3 Data is displayed manually or electronically in line diagrams.

SPECIFIC OUTCOME 4 Critically analyse data in tables and diagrams in order to draw conclusions and make predictions.

OUTCOME RANGE Tally tables; frequency tables; two-way tables; stem-and-leaf diagrams; bar diagrams; double bar diagrams; pie diagrams; line diagrams.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Data in tally tables, frequency tables, two-way tables and stem-and-leaf diagrams is critically read and interpreted with an awareness of sources of error and data manipulation (e.g. grouping, scale, choice of summary statistics) to draw conclusions and make predictions.

ASSESSMENT CRITERION 2 Data in bar diagrams, double bar diagrams, pie diagrams and line diagrams (own and in the media) is correctly read and interpreted with an awareness of sources of error and data manipulation (e.g. grouping, scale, choice of summary statistics) to draw conclusions and make predictions.

ASSESSMENT CRITERION 3 The most suitable measure of central tendency is chosen correctly.

ASSESSMENT CRITERION 4 The misuse of scales in diagrams as a source of error and bias is understood and explained with examples.

ASSESSMENT CRITERION 5 The misuse of grouping in tables and

SPECIFIC OUTCOME 5 Interpret and determine chance variation.

OUTCOME RANGE Possible outcomes (using two-way tables and tree diagrams) and their probability; actual outcomes and their relative frequencies.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 The possible outcomes of simple experiments (of which the possible outcomes are equally likely) are determined by using two-way tables and tree diagrams.

ASSESSMENT CRITERION 2 The list of possible outcomes is used to calculate the probability of each possible outcome.

ASSESSMENT CRITERION 3 Simple experiments are performed and the frequencies of the actual outcomes are counted correctly.

ASSESSMENT CRITERION 4 The frequencies of the actual outcomes are used to calculate the relative frequency of each actual outcome (the number of times the outcome happens divided by the number of trials in the experiment).

ASSESSMENT CRITERION 5 The probability of an outcome (calculated on the basis of equally likely events) is compared with its relative frequency (determined after many trials) and possible differences are explained.

ASSESSMENT CRITERION 6



ASSESSMENT CRITERION 8 The range is used as a measure of dispersion (spread) to summarise ungrouped data.

diagrams as a source of error and data manipulation is explained with examples.

ASSESSMENT CRITERION 6 Predictions are made about social, environmental and political issues (e.g. crime, national expenditure, conservation, HIV/AIDS), characteristics of target groups (e.g. age, gender, race, socio-economic), attitudes or opinions of people on issues (e.g. smoking, tourism, sport) and other human rights and inclusivity issues.

The probability of an outcome of an experiment is used to predict the relative frequency of that outcome.





Moderation option: Moderation will be overseen by the relevant ETQA according to moderation guidelines in the relevant qualification and the agreed ETQA procedures.

UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE N/A

UNIT STANDARD DEVELOPMENTAL OUTCOME N/A

UNIT STANDARD LINKAGES N/A

SAQA US ID US TITLE CREDITS119362 Work with numbers, operations with numbers and relationships between

numbers4


People credited with this unit standard are able to: Recognise, order, describe and compare numbers Perform calculations to solve realistic and abstract problems Use different techniques and strategies to calculate efficiently and accurately Solve problems in contexts (social, economic, environmental, human rights) Describe and illustrate the development of number systems in different cultures e.g. Babylonian (base 60) or Mayan (base 20)


It is assumed that learners undertaking the learning of this unit standard have prior knowledge and skills for working with numbers, operations with numbers and relationships between numbers and reading and writing at ABET level 3.

UNIT STANDARD RANGE N/A.




SPECIFIC OUTCOME 1 Recognise, order, describe and compare numbers.

OUTCOME RANGE Rational numbers including: common fractions; decimal fractions and percentages; numbers in exponential forms; large and small numbers in scientific notation; irrational numbers in context of measurement ( ; square and cube roots where applicable).

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Numbers are expressed using the correct number names and symbols.

ASSESSMENT CRITERION 2 Place value of digits in any number is used correctly.

ASSESSMENT CRITERION 3 Multiplicative inverses are recognised, described and used correctly.

ASSESSMENT CRITERION 4 Equivalent forms of rational numbers are recognised and used correctly.

ASSESSMENT CRITERION 5 The difference between rational and irrational numbers is recognised.

SPECIFIC OUTCOME 2 Perform calculations to solve realistic and abstract problems.

OUTCOME RANGE Multiple operations with rational numbers; approximations of rational numbers; finding exponents; finding squares of natural numbers; finding square roots of natural numbers.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Appropriate operations are used to find squares and square roots of numbers.

ASSESSMENT CRITERION 2 Rational numbers are converted to equivalent forms, e.g. recurring decimals to proper fractions.

ASSESSMENT CRITERION 3 The distributive, associative and commutative properties are recognised and used correctly.

ASSESSMENT CRITERION 4 The meaning of exponents in numerical examples is recognised and used correctly.

ASSESSMENT CRITERION 5 The laws of exponents are used correctly in numerical examples.

SPECIFIC OUTCOME 3 Use different techniques and strategies to calculate efficiently and accurately.

OUTCOME RANGE Working in columns; long division e.g. repeated subtraction of the divisor; estimating answers; available technologies e.g. calculators, spreadsheets, etc.; algorithms to find equivalent fractions.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Numbers are rounded off correctly.

ASSESSMENT CRITERION 2 Techniques are chosen which are suited to the problem.

ASSESSMENT CRITERION 3 Estimates are reasonably close to the answers.

ASSESSMENT CRITERION 4 Estimates made facilitate easy calculations.

ASSESSMENT CRITERION 5 Calculations on a calculator are done correctly.

SPECIFIC OUTCOME 4 Solves problems in contexts.

OUTCOME RANGE Problems involving financial aspects e.g. budgets, accounts, loans, simple interest, hire purchase; other Learning Areas, e.g. measurement in Technology and Natural Sciences contexts.; ratio, rate and proportion (direct and indirect). Contexts include: Social, economic, environmental human rights.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 The problem is expressed using words, mathematical expressions, equations and/or drawings.

ASSESSMENT CRITERION 2 Appropriate operations are used correctly.

ASSESSMENT CRITERION 3 Solutions are offered which make sense within the context of the problem and the validity of solutions is checked.

ASSESSMENT CRITERION 4 Methods to solve problems and check solutions are explained.

ASSESSMENT CRITERION 5 Calculator answers are interpreted realistically in context.

ASSESSMENT CRITERION 6

SPECIFIC OUTCOME 5 Describe and illustrate the development of numbers by using a different number base than base 10.

OUTCOME RANGE e.g. binary.

ASESSMENT CRITERIA ASSESSMENT CRITERION 1

How the system works is illustrated correctly.

ASSESSMENT CRITERION 2 Counting and recording is done in accordance with the logic of the system.

ASSESSMENT CRITERION 3 A quantity is expressed correctly within the system.



Explanations of methods are given which are in line with practical considerations.





Moderation will be overseen by the relevant ETQA according to moderation guidelines in the relevant qualification and the agreed ETQA procedures.

UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE N/A.

UNIT STANDARD DEVELOPMENTAL OUTCOME N/A.

UNIT STANDARD LINKAGES N/A.

SAQA US ID US TITLE CREDITS7450 Work with measurement in a variety of contexts 2


People credited with this unit standard are able to:

Demonstrate understanding of the relationships between common quantities in various contexts; Use measuring instruments to measure and calculate quantities in various contexts; and Solve measurement problems in various contexts.


The following competency at ABET Numeracy level 3 is assumed to be in place:

Demonstrate understanding of appropriate measurements and relationships between different units of measure, solve problems involving measurement, perimeter, area, volume and time.




SPECIFIC OUTCOME 1 Apply relationships between common quantities in various contexts.

OUTCOME RANGE Mass and weight, distance and displacement, speed and velocity, volume and density, volume and surface area, area and perimeter, distance and time, volume and capacity.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Terms are used in the proper context.

ASSESSMENT CRITERION 2 Comparisons between quantities are made and differences and relationships described.

ASSESSMENT CRITERION 3 Formulae and units are described in context to show the relationships and differences.

SPECIFIC OUTCOME 2 Use measuring instruments to measure and calculate quantities in various contexts.

OUTCOME RANGE Quantities include all of: length, distance, mass, time, temperature, volumes of regular prisms, perimeter, area, weight, surface area, density, displacement and angles. Measuring instruments include all of: rulers, tape measures, scale, clocks, thermometers, capacity measuring instruments, and protractors.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Measuring instruments are used correctly.

ASSESSMENT CRITERION 2 Readings are recorded and reported within the margin of error as limited by the instrument and as is appropriate within the context.

ASSESSMENT CRITERION 3 Measuring instruments are chosen to comply with the accuracy requirements of the context.

SPECIFIC OUTCOME 3 Solve measurement problems in various contexts.

OUTCOME RANGE Practical and non-practical processes, trigonometric right-angled heights and distances.

ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 Solutions are correct within margins of error allowed within the context.

ASSESSMENT CRITERION 2 Units are used correctly.

ASSESSMENT CRITERION 3 Methods and solutions are justified.



4. LTSM IN PALCs

The recommended Learning and Teaching Support Materials for this learning area are listed in the catalogue provided by the AET Directorate of the Department of Higher Education and Training.

A variety of LTSM is used in various contexts in ABET Centres across the country and these are sourced or adapted from a variety of sources. Given this background, it is not yet possible to propose a set body of material to be studied (e.g. prescribed poems or short stories). This allows educators to use their own discretion and creativity in the selection of materials, but it must be reiterated that the choice must be informed by the applicable Unit Standards.

5. WEIGHTING OF THE SPECIFIC OUTCOMES AND ASSESSMENT CRITERIA

Unit standard title Credits Approx Marks Weighting

Describe and represent objects in terms of shape space and measurement.

5 ±31 ±31%

Evaluate and solve data handling and probability problems within given contexts.

5 ± 31 ± 31 %

Work with numbers; operations with numbers and relationships between numbers

4 ± 25 ± 25 %

Work with measurement in a variety of contexts. 2 ± 13 ± 13%Total: 16 100 100%

6. CORE KNOWLEDGE AREAS

This section unpacks the Unit Standards and their Specific Outcomes, summarising the core knowledge areas of each, and suggesting activities and applicable assessment tools, as well as the skills tested or practiced in each activity. It then locates each US and SO in either the Summative or Formative Assessment, specifying which question or task in the assessment will be covered.

The unpacking of the US & SO is done sequentially here, in order to provide educators with a broad overview of the total scope of the US in the learning area (as circumscribed by the Range Statements of each SO), in preparation for the assessments. Examiners will make any selection of these activities to include in both the question paper as well as the SBA tasks. By working through them, the educator is thus preparing learners for the full range of possible tasks in the assessment.

Unit Standard Title: Describe and represent objects in terms of shape, space and measurement.

Specific Outcome Assessment Criteria Core KnowledgeRecognize, identify, name, compare, sort and visualise geometric figures and solids, including cultural forms and products.

Basic geometric shapes are identified correctly. Identification of basic geometric shapes, for example triangles, quadrilaterals, circles, cylinders, prisms and spheres.

Basic transformations are identified correctly. Identification of translations, reflections and rotations.

Analyze properties of geometric figures and solids

Geometric shapes are drawn and models of solids are constructed in order to investigate and compare their properties.

Draw basic geometric shapes, for example triangle, quadrilaterals, circles, cylinders, prisms and spheres.Build models, for example a box, a pyramid and a cylinder to compare and investigate their properties.

Geometry of straight lines and triangles are used to solve problems and justify relationships in

Draw angles of specific sizes.Indicating perpendicular and parallel lines.



geometric figures. Identification and usage of different types of triangles to solve problems.

Transformations, congruency and similarity are used to investigate, describe and justify properties of geometric figures and solids.

Understand and apply the concepts of congruency, similarity and transformations (Reflections, Rotation and translation) within real life situations.

The theorem of Pythagoras is used to solve problems involving missing lengths in known geometric figures and solids.

Application of the theorem of Pythagoras to solve problems.

Use scales to interpret maps and draw simple maps to scale.

Scales are used correctly to find distance and length.

Use of scales to find the real distance and length on maps.

Maps are drawn as accurately as the context requires.

Draw simple maps.

Solve problems in a range of measurements contexts.

Appropriate formulae are selected and used correctly.

Selection and use of appropriate formulae to solve problems.

Solutions are given with appropriate SI units. Knowledge of Correct SI units. Perimeters of polygons and circles are calculated correctly from given dimensions.

Calculate perimeters of polygons and circles from given dimensions.

Areas of triangles, rectangles and circles are calculated correctly from given dimensions.

Calculate areas of triangles, rectangles and circles.

Areas of polygons are calculated by decomposition into triangles and rectangles.

Calculate areas of polygons by decomposing them into triangles and rectangles.

Volumes of triangular and rectangular prisms and cylinders are calculated correctly.

Calculate volumes of triangular and rectangular prisms and cylinders.

Draw different views of objects in real-life situations.

Views from different viewing sites are given which are consistent with the shape of the object from that view.

Give views on the shape of objects from different viewing sites.

Scales are used correctly. Correct choice and use of scales.

Unit Standard title: Evaluate and solve data handling and probability problems within given contexts

Specific Outcome Assessment Criteria Core KnowledgeCollect data to answer questions.

Appropriate sources of data (peers, family, newspapers, books, magazines, Internet) are identified.

Identification of sources of data for example from newspapers, the internet, etc.

A distinction between populations and samples is made.

A definition of the difference between a sample and a population should be defined.

The data that is collected (alone and/or as a member of a group or team) is appropriate to answer questions related to the investigation.

Collection of appropriate data.

Data collection sheets are designed and used to collect data.

Design and use of data collection sheets.

Questionnaires are designed and used to collect data.

Design and use of questionnaires to collect data.

Experiments involving random number generators, coins, spinners, dice and cards are designed and used to collect data.

Design and use of experiments involving random number generators, coins, spinners, dice and cards.

Interviews are used to collect data. Conduct interviews to collect data.Summarise data into tables and summary statistics.

Data is organised and recorded in tally tables. Organise and record data in tally tables.Data is organised and recorded in frequency tables.

Organise and record data in frequency tables.

Data is organised and recorded in two-way tables.

Organise and record data recorded in two-way tables.

Data is organised and recorded in stem-and-leaf diagrams.

Organise and record data in stem-and-leaf diagrams.

The mode is used as a measure of central tendency to summarise ungrouped data.

Calculation of the mode.

The range is used as a measure of dispersion (spread) to summarise ungrouped data.

Calculation of the range.

Display data in diagrams. Data is displayed manually or electronically in bar diagrams and double bar diagrams with appropriate scales and keys.

Drawing of bar diagrams and double bar diagrams using appropriate scales and keys. Manually for exam purposes and SBA’s, but electronically only for SBA’s only.



Data is displayed manually or electronically in pie diagrams in terms of proper fractions, decimals or percentages of the circle.

Drawing of pie diagrams. Manually for exam purposes and SBA’s, but electronically only for SBA’s only)

Data is displayed manually or electronically in line diagrams.

Drawing of straight line graphs using appropriate scales and keys. Manually for exam purposes and SBA’s, but electronically only for SBA’s only)

Critically analyse data in tables and diagrams in order to draw conclusions and make predictions.

Data in tally tables, frequency tables, two-way tables and stem-and-leaf diagrams is critically read and interpreted with an awareness of sources of error and data manipulation (e.g. grouping, scale, choice of summary statistics) to draw conclusions and make predictions

Read an interpret data in the given tables with an awareness of the sources of error.

Data in bar diagrams, double bar diagrams, pie diagrams and line diagrams (own and in the media) is correctly read and interpreted with an awareness of sources of error and data manipulation (e.g. grouping, scale, choice of summary statistics) to draw conclusions and make predictions.

Read and interpret data in diagrams, double bar diagrams, pie diagrams and line diagrams to draw conclusions and make predictions.

The most suitable measure of central tendency is chosen correctly.

Choose the most suitable measure of central tendency.

The misuse of scales in diagrams as a source of error and bias is understood and explained with examples.

Recognize and explain the misuse of scales in diagrams as a source of error and bias.

The misuse of grouping in tables and diagrams as a source of error and data manipulation is explained with examples.

Explain with examples the misuse of grouping in diagrams as a source of error and data manipulation.

Predictions are made about social, environmental and political issues (e.g. crime, national expenditure, conservation, HIV/AIDS), characteristics of target groups (e.g. age, gender, race, socio-economic), attitudes or opinions of people on issues (e.g. smoking, tourism, sport) and other human rights and inclusivity issues.

Make use of the given data and graphs to make predictions about social, environmental and political issues.

Interpret and determine chance variation.

The possible outcomes of simple experiments (of which the possible outcomes are equally likely) are determined by using two-way tables and tree diagrams.

Determine the possible outcomes of simple experiments by using two way tables and tree diagrams.

The list of possible outcomes is used to calculate the probability of each possible outcome.

Calculate the probability of each possible outcome.

Simple experiments are performed and the frequencies of the actual outcomes are counted correctly.

Count the frequencies of actual outcomes.

The frequencies of the actual outcomes are used to calculate the relative frequency of each actual outcome (the number of times the outcome happens divided by the number of trials in the experiment).

Calculate the relative frequency of each actual outcome.

The probability of an outcome (calculated on the basis of equally likely events) is compared with its relative frequency (determined after many trials) and possible differences are explained.

Compare and explain the possible differences between the probabilities of an outcome with its relative frequency.

The probability of an outcome of an experiment is used to predict the relative frequency of that outcome.

Predict the relative frequency of an outcome using its probability.

Unit Standard title: Work with numbers; operations with numbers and relationships between numbers

Specific Outcome Assessment Criteria Core KnowledgeRecognise, order, describe and compare numbers.

Numbers are expressed using the correct number names and symbols.

Write numbers in symbols and in words.



Place value of digits in any number is used correctly.

Determine the place value of digits.

Multiplicative inverses are recognised, described and used correctly.

Give the multiplicative inverse of a number.

Equivalent forms of rational numbers are recognised and used correctly.

Give the equivalent form of a rational number.

The difference between rational and irrational numbers is recognised.

Recognise the difference between rational and irrational number.

Perform calculations to solve realistic and abstract problems

Appropriate operations are used to find squares and square roots of numbers.

Find squares and square roots of numbers.

Rational numbers are converted to equivalent forms, e.g. recurring decimals to proper fractions.

Convert rational number to their equivalent forms.

The distributive, associative and commutative properties are recognised and used correctly.

Recognise the difference between the distributive, associative and commutative properties

The meaning of exponents in numerical examples is recognised and used correctly.

Recognise and apply exponents.

The laws of exponents are used correctly in numerical examples.

The laws of exponents.

Use different techniques and strategies to calculate efficiently and accurately.

Numbers are rounded off correctly Rounding off numbers within its context.

Techniques are chosen which are suited to the problem

Correct techniques within the context are used to solve problems.

Estimates are reasonably close to the answers. Estimations.Estimates made facilitate easy calculations. Use estimations to ease calculations.Calculations on a calculator are done correctly. Use of a calculator.

Solves problems in contexts. The problem is expressed using words, mathematical expressions, equations and/or drawings.

Changing of a word problem to a mathematical expression, equation or drawing or vice versa to solve the problem.

Appropriate operations are used correctly. Appropriate use of correct operations (+;-;×;÷) to solve problems.

Solutions are offered which make sense within the context of the problem and the validity of solutions is checked.

Check the validity of solutions within the context.

Methods to solve problems and check solutions are explained.

Exposure to solve a problem using different methods.

Calculator answers are interpreted realistically in context.

Realistic interpretation of calculator given answers.

Explanations of methods are given which are in line with practical considerations.

Practical considerations of the given context in solving problems.

Describe and illustrate the development of numbers by using a different number base than base 10

How the system works is illustrated correctly. Correct application of a number system other than base 10 e.g. the Roman numerals IV; XII

Counting and recording is done in accordance with the logic of the system.

Count and record using the given number system.

A quantity is expressed correctly within the system.

Expression of numbers within a number system e.g. 8 = VIII or IIII III = 8

Unit Standard title: Work with measurement in a variety of contexts Specific Outcome Assessment Criteria Core Knowledge

Apply relationships between common quantities in various contexts

Terms are used in the proper context. Concepts in the context of measurement.Comparisons between quantities are made and differences and relationships described.

Comparisons within the given context between quantities are made and their relationships described.

Formulae and units are described in context to show the relationships and differences.

Correct use of formulae and units within given contexts.

Use measuring instruments to measure and calculate quantities in various contexts

Measuring instruments are used correctly. Correct use of measuring instruments.Readings are recorded and reported within the margin of error as limited by the instrument and as is appropriate within the context

Appropriate use of measuring instruments and allowance for the margin of error within the given contexts.



Measuring instruments are chosen to comply with the accuracy requirements of the context.

Correct choice of measuring instruments as required within the context.

Solve measurement problems in various contexts.

Solutions are correct within margins of error allowed within the context.

Define the allowance for the margin of error within the given contexts.

Units are used correctly. Application of the correct units within the context.

Methods and solutions are justified. Verification of solutions.

7. TAXONOMIES USED IN SCAFFOLDING QUESTIONS

In setting the examination question paper and the SBA Tasks, Bloom’s Taxonomy is used to scaffold the degrees of complexity of questions and tasks. Each question in a Mathematical Literacy question paper is scaffolded according to Bloom’s Taxonomy in the following order.

Level of question Description Approximate Weighting per question

Level 1 Low order questions 40%Level 2 Middle order questions 30%Level 3 Higher order questions 30%

Mark allocation according to levels of Questions:

Question Approximate total marks per question

Level of question Approximate marks per level of question

1 251 102 83 7

2 201 82 63 6

3 251 102 83 7

4 151 62 53 6

5 151 62 53 4

C

8. SITE-BASED ASSESSMENT (FORMATIVE)

The ABET level 4 site-based assessment tasks are part of a developmental process aimed at increasing capacity in the ABET sector and enhancing the level of teaching and learning in the PALCs. The tasks are also aimed at quality assurance and standardisation of site based assessment in all PALCs across the country. In delivering the ABET level 4 curriculum, it is suggested that the assessment tasks should be integrated into planning for teaching and learning and implemented in conjunction with the assessment guidelines for ABET. Teaching, learning and assessment are intertwined and planning for assessment is an integral part of planning for teaching and learning. It is therefore strongly recommended that the assessment tasks should be conducted as part of the teaching and learning process. This means that the assessment tasks should be



incorporated into an educator’s work schedule for the year. It is further recommended that educators use different teaching strategies and informal assessment to ensure that learners are adequately prepared for the formal assessment tasks. The tasks were carefully designed to ensure that a variety of skills are assessed in each learning area and that the unit standards and assessment criteria are adequately covered. The performance-based tasks are to be completed or administered over a period of time whilst the pen-and–paper tasks should be administered under controlled conditions.

It is recommended that the tasks be used as part of the formal site based assessment programme at PALCs. All formal assessment must be recorded and ongoing feedback must be given to learners. Evidence of the formally recorded assessment tasks should be included in the educator’s portfolio while the learners’ evidence of learning must contain the recorded pieces of evidence for each assessment. Continuous moderation at site level, cluster level, district level and provincial level is strongly recommended.

The results of assessment should be used to support the learners’ development and make improvements to the learning and teaching process. It is important that learners who might experience barriers to learning and development are identified early, assessed, and provided with learning support. In such cases the assessment tasks should be adapted to accommodate these learning needs. We expect you to critically engage with the assessment tasks as we are aware that they do not reflect a “zero-defect” or a “one-answer-solution”.

8.1 STRUCTURE OF SBA TASKS

The SBA is made out of an educator’s guide and a learner’s tasks. The learner’s tasks for each learning area contain five assessment tasks focusing on the unit standards that should be covered in formative assessment. The educator’s guide contains the assessment instrument(s) (memorandum, rubric and/or checklist) for each of the assessment tasks. The tasks include a variety of appropriate assessment strategies and different forms of assessment of which one is a project as prescribed by Umalusi.

Additional is a learning area assessment plan which is aimed at assisting the educator with the spreading of the formal assessment tasks throughout the year.

Each SBA task is worth 50 marks and the five SBA tasks total 250 marks. All formal and informal assessment leading to formal moderation must be recorded accordingly. These marks should be converted to 50% which is the weighting of the site-based assessment. Moderation of these SBA tasks must be done according to the provincial management plan on the conduct, administration and management of the GETC-ABET Level 4 examinations and assessment.The following section provides an overview of the nature of the tasks for the Site-based Assessment Tasks, preceded by a few guidelines to educators on how to prepare their learners for each task. More detailed instructions on how to execute each task are provided in the Learners’ tasks, while detailed guidelines on how to prepare learners for each task are provided in the accompanying educator guide.

An analysis grid of the SBAs pertaining to US, ID, SO, AC and marks will be included.

EXAMPLE OF A LEARNING AREA ASSESSMENT PLAN

LEARNING AREA: MATHEMATICAL LITERACY

LEARNING AREA CODE: MLMS4

YEAR: 2009

Assessment Tasks 1 2 3 4 5

Form(s) of assessment

Test Assignment / Tutorial

Project Investigation Worksheet



Unit Standard ID/’s

119362 119362 119362 19368 119373

SO’s and AC’s SO2 (AC 1,2,3)SO3 (AC 3 & 4)SO4 (AC 1 & 3)

SO2 (AC 1,2,3)SO3 (AC 1 & 2)

SO4 (AC 1)

SO2 (AC 1)SO3 (AC 1,2 &4)SO4 (AC 1 &3)

SO1 (AC 1,2,&4)

SO2 (AC 1; 2 &3)

SO3 (AC 1,2,3 & 4)

SO (AC 1)SO2 (AC)

SO3(AC1,2,3&4)

Unit Standard ID/’s

119364

SO’s and AC’s SO 5 (AC 1 &2)

Tools of assessment Memorandum Rubric Memorandum Memorandum MemorandumDates to be completed

8.2 EXEMPLAR SBA TASKS

TASK 1: TEST

INSTRUCTIONS AND INFORMATION

1. Answer ALL the questions in the ANSWER BOOK.

2. Calculators may be used, and ALL calculations must be shown.

3. Number the answers correctly according to the numbering system used in this question paper.

5. Questions must be answered in blue or black ink.6. A formula sheet is provided.

QUESTION 1

1.1 Answer question 1.1 WITHOUT USING A CALCULATOR. Determine the following, and give answers in the simplest form.

1.1.1 450 – 610 + 360 (1)

1.1.2 Write down the time as shown on the following digital clocks. Indicate whether morning, afternoon or evening. Example: 8: 15 is fifteen minutes past eight or quarter past eight in the morning.

(a)… (b)… (2)

1.1.34 – 3 (3)

1.1.4 South African time is 7 hours ahead of New York. I want to phone someone in New York at 9 a.m. when their office opens. At what time (South African time) must I phone? (1)

1.1.5 When a boxing match starts at 8 o'clock at night in New York, what time is it here? (1)GETC-ABET Level 4 ~ @ NQF Level 1 24 | P a g e

12:25 20:50


1.1.6 Write this number in expanded form to show the real value of the digits.Example: 325, 87 = 300 + 20 + 5 + 0,8 + 0,07

a. 975, 3 …b. 8 925, 61… (2)

1.2 Arrange the following decimal fractions from smallest to largest: 0,231 : 2,31 : 0,0231 (3)

1.3 Brenda has to post a parcel. There are 5 books in the parcel, each with a mass of 160 g. The wrapping of the parcel has a mass of 10 g. What is the total mass of the parcel in kilograms? (2)

1.4 Convert the following fractions in the table below to decimals and percentages. Redraw the table and write your answers in the table. Decimals should be rounded off to two decimal places and percentages to the nearest percentage.

Decimals Percentages

(a) (b)

(2)

1.5 David and Sophie collected the following coin balls

Indicate which of these coin balls will they need to balance the scales below. Use the least number of discs or coins balls. Coins may be used more than once.

(a) (b) 80 g

335 g(2)

1.6 20% of … = 1360 (1)

1.7 Which is colder - 15°C or 0°C (1)

1.8 10,05 – 3,24 = (1)

1.9 15% of 200 + 5% of 300 = (1)

1.10 Simplify the ratios below.

16: 64 (1)[24]


5ggg

10 g

20 g

30 g

40 g

100 g


QUESTION 2

2.1 Themba has plastic rods of equal lengths, and fasteners to join them. He uses four rods to build the following figure:

2.1.1 What do we call the figure that he made? (1)

2.1.2 What is the size of each angle in the shape above? (1)

2.1.3 He takes three of the same equal rods and makes a separate closed figure. Draw the figure he made. (2)

2.2 Draw the mirror image and two sketches of each shape after you have rotated it.

Shape Mirror image Rotation 1: 90° anti-clockwise

Rotation 2: A further 90° anti- clock-wise, (180° in total)

(a) (b) (c)

(d) (e) (f)

(6)

2.3 Which of the following diagrams will represent the view from the left?

(1)



(a) (b) (c) (d)

2.4 Look at the picture of this cardboard box.

If you cut the box and flatten it (fold it open) the flat cardboard may look like this.

Which of the following will give you a cube again if you fold along the lines?Draw the correct one in your ANSWERBOOK

(a) (b) (c) (d)

(1)

2.5 Draw a Cartesian plane and plot the following points on your Cartesian plane. The points must be clearly indicated.A (3:2) , B (-2:-3) and C (4:0) (4)

2.6 The following map below shows directions from Longwe to different places.



2.6.1 The scale of the map is 1:500. Use your ruler to measure distances on the map. Use your measurement to estimate the total distance from Longwe to Castress in km (show your workings). (5)

2.6.2 A taxi can travel 9 km per litre of petrol. Work out how many litres of petrol are needed to travel from Mutale to Longwe. ( Round off your answer to 2 decimal places). (5)

[26]

[50]



FORMULA SHEET: MLSC4

2-DIMENSIONAL FIGURES:

FIGURE PERIMETER AREATriangle Sum of sides

bh

Rectangle 2( + b) bSquare 4s sCircle 2 r OR d r

3-DIMENSIONAL FIGURES:

FIGURE VOLUME SURFACE AREARegular Prism A H P H + 2ATriangular Prism

h H(s + s + s) H + bh

Rectangular Prism b H 2( + b)H + 2 b OR2 H + 2bH + 2 b

Circular Prism (Cylinder) r H 2 r(r+H) OR 2 r +2 rH

Key: = length

b = breadth (width)s = sideh = height of triangleH = perpendicular heightr = radiusd = diameterA = AreaP = perimeterV = Volume

=

TASK 2: ASSIGNMENT

INSTRUCTIONS AND INFORMATION FOR THE LEARNER

1. The assignment should be done in groups. Each section of the assignment will be evaluated on weekly basis to establish the progress made by the group.

2. You are given the instruction as a group to paint the interior of your community hall/school hall/classroom with specific dimensions pertaining to the building/room.

3. Refer to the assignment rubric for the evidence required.

4. The group will submit the complete assignment on or before the due date.

Tools required to complete the assignment


Examinations and Assessment Guidelines: MLMS41. Measuring tape, pair of scissors, glue, and floor plan.2. Detailed budget.3. The decisions, motivations and calculations will be assessed for each individual group member.

SECTION 1 (MEASUREMENT)

Measure all the walls of the interior of the building / room. Provide a floor plan of the interior of the building / room. Show all the calculations.

SECTION 2 (QUOTATIONS FOR PAINT)

Find quotations from any paint company on the price for four different types of paints. (Use any of the following to gather information, Internet, Magazines, News papers).

Include all other materials required to complete the paint job in the quotations . In case where paint is not used any other usable product can be defined. All quotations should be included in the assignment and then the quotation accepted with

the motivation for the choice of quotation.

SECTION 3 (QUOTATIONS FOR LABOUR)

Find quotations from any four painters on the asking rate per square meter to do the job. Let the painters also give you the estimated time it will take them to complete the entire job as well as more specifics on the paint job.

All quotations should be included in the assignment and then the quotation accepted with the motivation for the choice of quotation.

The group will make a decision and give motivation on which painter to employ.

SECTION 4 (FINAL ASSIGNMENT DOCUMENT)

Assignment draft (history). Calculation showing the total cost for paint based on your group decision. Total cost for labour job based on your group decision. Total cost for the entire job (paint and labour).

TOTAL: [50]



RUBRIC FOR ASSESSING THE ASSIGNMENT:

UNIT STANDARDS: 119373(SO. 3, 4) & 119362 (SO. 2, 3, 4)COMPETENCIES 1 2 3 4 5 Scores

Measurements done No or unrealistic dimensions

little work done Floor plan and measurements not completed

Floor plan drawn up. But no measurements given

All measurements

indicated on floor plan

X2

10

Calculations No or incorrect formulae Just formulae given Formulae (F) and substitution (S) done.

F, S and answer (A) given F, S, A and unit (U) given 5

Quotations for paint No or unrealistic 1 or no Quotation 2 Quotations 3 Quotations 4 Quotations 5

Decision on paint No or unrealistic choice Decision and no motivation

Decision and reasonable motivation

Decision and good motivation

Decision and very good motivation

5

Quotations for labour No or unrealistic choice 1 or no Quotation 2 Quotations 3 Quotations 4 Quotations 5

Decision on labour No or unrealistic choice Decision and no motivation




5

Analysis of advertisement on various paints

No or incorrect analysis Incorrect/ incomplete analysis of paints

Minor errors in analysis of paints

Correct analysis of advertisements

Detailed analysis of advertisements

5

Final calculations No or incorrect calculations

No final calculations done Total cost for one of above criteria

Total cost for two of above criteria

Total cost for paint and labour

X2

10

TOTAL SCORE FOR ASSIGNMENT 40


TASK 3: PROJECT


1. This project must be completed over a period of four weeks.

2. The project can be done in pairs or in groups. Each group member should however write his or her own answers.

3. Indicate the names of group members who worked on the project.

5. Your educator will assess this project at regular intervals to ensure a good quality project and completion on time.

6. Read the instruction and questions carefully and do thorough planning before you start with the project.

7. Answer ALL the questions.

8. You will need the following resources for the project:Advertisements on cellphones from news papers, magazines and cell phone dealersA4 papers, pair of scissors and glue and a calculator.

9. Write neatly and legibly using blue or black ink and present your work clearly.

QUESTION 1

In your class, your group decides to buy your teacher a cellphone as a token of appreciation. For a group to reach a good decision, an investigation had to be carried out. The group then decided to investigate the costs, advantages and disadvantages of different offers that different service providers have on similar phones. Answer the following questions to help you reach a good decision:

1.1 Visit cellphone dealers, go onto the internet, newspapers or from magazines collect THREE different advertisement offers of cellphones and paste them in your ANSWERBOOK. (3)

1.2. Redraw the table given below. Use your THREE adverts to complete the table.

Offer First Second ThirdBrand (cellphone) nameCost of cellphoneName ProvidersFree minutesFree SMSSIM and connection feeCall ratesAdditional benefits (8)

1.3 Do you think the table could help you to decide which offer is the best? Give TWO reasons for your answer.

(2)

1.4 Which of the THREE providers offer the best benefits with regard to call rates? Provide reasons for your answer. (3)

1.5 Show by calculations the cost difference between the best and least offers. (3)

Copyright reserved Please turn over


1.6 Draw a bar graph to show how the costs of the three offers compare (3)

1.7 What is the difference between contract and prepaid cellphone services? (4)

1.8 What is the difference between peak and off-peak times? (2)

1.9 Did the introduction of cell-phones in our country improve communication between people? Explain your answer. (2)

[30]

QUESTION 2

2. The following data represent the life span of a light bulb in days.

133 83 82 109 121 105 105 73 117 109 83 97 138 85 104 79 106 82 80 92 132 91 83 108

2.1 Redraw and complete the table below to show the tallies and frequencies for the different class intervals:

Class intervals in days Tallies Frequency 70 – 79 // 280 – 89 90 – 99 100 – 109 110 – 119 120 – 129 130 – 139

(6)

2.2 Represent the data above in a stem-and-leaf diagram. (5)

2.3 Calculate the mean life span of the light bulb. (3)

2.4 Calculate the range of the data. (2)

2.5 Compare the median and the mode of the data. (4) [20]

TOTAL: 50

TASK 4: INVESTIGATION

INSTRUCTIONS AND INFORMATION TO LEARNERS

1. This investigation must be completed over a period of four weeks.

2. The investigation can be done in pairs or in groups. Each group member should however write his or her own answers.

3. Indicate the names of group members who worked on the investigation.

5. Your educator will assess this investigation at regular intervals to ensure a good quality GETC-ABET Level 4 ~ @ NQF Level 1 33 | P a g e


investigation and completion on time.

6. Read the instruction and questions carefully and do thorough planning before you start with the investigation.


8. You will need the following resources for the investigation:- advertisements on cell phones from news papers, magazines and cell phone dealers- A4 papers, pair of scissors and glue- a calculator

9. Write neatly and legibly. Use blue or black ink and present your work clearly

THE INVESTIGATION: SMALL BUSINESS

INSTRUCTIONS

You have identified the need for a small business in your community. You do not want to run the risk of starting a business that will fail. As a result you conduct an investigation to reduce the risk. Your community has 200 households. Collect data on the five basic needs of each house-hold.

1. Design the form that will be used to collect the data about basic needs of the house holds. (4)

2. How much money will be required to start the small business? Show all the calculations (4)

3. Explain how the money needed to start a small business will be raised? Give reasons. (4)

4. In 200 households, calculate 10% of the households that you will sample. (1)

5. From the data collected, state the basic needs of the community to help you decide on the most viable small business.

NEED TALLY FREQUENCY (F)e.g. sport and recreation //// 4

Sum of (f) = ______(7)

6. Represent the frequencies on a pie chart. (4)

7. What type of small business will you start based on the information above? (5)

8. Give reasons why the small business above is required in the community. (2)

9. In your group identify FIVE most important activities that should be considered to start a small business. (5)

10. Most people start businesses that do not last for long. Explain how the small business will



survive in this hard time of high employment. (5)

11. It is a wish of every entrepreneur to grow the business and probably establish branches. Provide a three year plan to grow the small business. (6)

12. What social values can the Small business shop add to the upliftment of the community? Name THREE. (3)

TOTAL: 50

TASK 5: WORKSHEET

Surname: _________________________

First names _________________________

Centre Name _________________________

Date: __________________________ Learner’s Signature __________________________



2. Calculators may be used, but you must show ALL calculations.

3. This question paper serves as the ANSWER BOOK

4. Questions must be answered in blue or black ink.

QUESTION 1

1.1 Determine the following without the use of a calculator. Answers must be written in a simplified form.

1.1.1 = (1)

1.1.2 125% of 125 = (1)

1.1.3 3,85 – 1,38 = (1)

1.1.4 (–5) x (–8) 4 = (1)

1.1.53 + 5 – 2 = (3)

1.1.6 2 million + 2220 = (1)

1.1.7 7 2 = (2)

1.2 Arrange the following numbers from the smallest to the largest:



; ; (3)

1.3 Choose the correct answer:

1.3.1 75% of 120 has the same value as …

(a) 2 x 45 (b) 120 (c) 120 – 75 (d) 25 x 3(1)

1.3.2 = (a) 0.03 (b) 0.9 (c) 3 (d) 9 (1)

1.3.3 If p = -4, then p =

(a) (b) 16 (c) 256 (d) (1)

1.4 Fill in the correct symbol in the box [ = ; ‹ ; › ]

1.4.1-0, 5 -5 (1)

1.4.2

60% (1)

1.4.32 x 4 + 3 2 + 3 x 4 (1)

1.5 Draw the mirror image and TWO sketches of each shape after you have rotated it.


Rotation 2:A further 90° anti- clock-wise, (180° in total)

(a) (b) (c)

(d) (e) (f)

(6)[25]

QUESTION 2

2.1 The father wants his three children to inherit his money when he dies. The will states that that the children will inherit the money according to their ages. At the time of his death, Pule was 31, Susan was 27 and Alfred was 24. The total estate is R4 100 000. Calculate how much each child will inherit? (4)



2.2 Three different cars, each moving at a constant speed, covers a distance of 240km between two towns as indicated in the table below:

Cars A B CSpeed in km/h 120 (a) 100Time in hours 2 2,18 (b)

Calculate the values of (a) and (b) in the table above. Round your answers off to two decimal places. (4)

2.3 Use the following flow diagram to answer the questions that follows:Input number

Output number

2.3.1 Find the output number if the input number is 24. (2)

2.3.2 Give the output number if the input number is k. (2)

2.3.3 Calculate the input number if the output is 9. (3) [15]


Half the input number

Add 3 from the answer


QUESTION 3

Refer to the map below to answer the following questions:

3.1 In which province do we find Springbok town? (1)

3.2 Which country is found inside South Africa but is not part of South Africa? (1)

3.3 Which coastal city lies to the south-west of Pretoria? (1)

3.4 In what compass direction is Upington to Richards Bay? (1)

3.5 Use a ruler to measure the distance on the map (in centimetres) between Durban and Johannesburg. (2)

3.2.3 If 1 centimetre on the map represents 290 km on the road, calculate the distance between Durban and Johannesburg. (2)

3.3 Plot the following points on a Cartesian plane. The points must be clearly indicated.

P (2 ; 4)Q (-3 ; -1)R (3 ; 0)S (1 ; -2) (2)

[10]

TOTAL: 50

TOOL 1: TEST of 63


QUESTION 1: US ID : 119362 SO’2(AC 1,2,3,4), US ID :119364: SO 4(AC3,4) 1 – 2SO3(AC1) SO4(AC, 2) SO5(AC 1,2)

1.1.1 200 1 mark for the answer (1)

1.1.2 (a) Twenty five past twelve 1 mark for the answer(b) Ten to nine 1 mark for the answer

(2)

1.1.3 1 mark for conversion

- 1 mark for equivalent fraction

1 mark for simplification

OR

= ( 4-3 ) + ( - )

= 1 -

= (3)

1.1.4 16h00 1 mark for the answer (1)

1.1.5 3 am 1 mark for the answer 1 mark for conversion. (1)

1.1.6 (a) 900 + 70+ 5 + 0,3 1 mark for simplification(b) 8000 + 900+ 20 + 5 + 0.6 +0.01 1 mark for the answer (2)

1.2 2,31; 0,231; 0,0231 all terms to be in the right sequence (3)

1.3 5 x 160g = 800 +10 1 mark for simplification = 810g1 mark for the answer OR =0.81 kg (2)

1.4 (a) 0,5 (b) 50 1 mark for the correct answer (2)

1.5 (a) 80 = 40+ 40 or 10 +30 + 40 or any correct possible combination(b) 335 = 100 + 100 + 100 + 30 + 5 any correct possible combination (2)

1.6 6800 1 mark for the correct answer (1)

1.7 - 15 C 1 mark for the correct answer (1)



1.8 6.81 1 mark for the correct answer (1)

1.9 30 + 15 = 45 1 mark for the correct answer (1)

1.10 1:4 1 mark for the correct ratio A square 1 mark for deduction 1 mark for answer (1)

[24]

QUESTION 2: Unit Standard ID:119373 SO1(AC 1,2) SO2(AC 1,2,) SO3(AC 1,2,5 3)

2.1.1 A square 1 mark for deduction 1 mark for answer (1)

2.1.2 A Right Angle ( 90 ) 1 mark for answer (1)

2.1.3 An Equilateral triangle ( in the drawing all sides must be equal) 1 mark for the reason (2)

2.2

(a) (b) (c)

(d) (e) (f)

1 mark for each correct diagram (6)

2.3

(a) (1)

2.4

(b) 1 mark for correct drawing made of squares

(1)

2.5 1 mark for the Cartesian plane 1 mark for each correct placed coordinates (4)

2.6.1 From Longwe – Tomkins = 4.8 1 mark for correct measurement From Tomkins – Bherma = 2.5 1 mark for correct measurement From Bherma – Castress = 3 Total = 10.3 units500 x 10.3 = 5 150. 1 mark total correct conversion (5)

2.6.2 From Longwe – Tomkins = 4.8 From Tomkins – Bherma = 2.51 mark for correct measurement

of 63


From Bherma – Mutale = 4 1 mark for correct measurement

Total =.11.3 units

500 x 11.3 = 5 650.1 mark total correct conversion

=627 ,78 L 1 mark total correct answer (5) [26]

TOTAL: 50

TOOL 2: ASSIGNMENT

INSTRUCTIONS AND INFORMATION FOR THE LEARNER

1. You are given the instruction to paint the interior of your community hall/school hall/classroom/room at home with specific dimensions pertaining to the building / room.

2. Three different learners do the three different sections and present it then to the entire group to make their individual decisions and write-up.

3. A weekly progress analysis will be done to ensure that each member did his/her section for the other group members to move on with the assignment.

4. The entire group will be penalised for a section not done by the group member responsible for that section.

5. The decisions, motivations and calculations will be assessed for each individual group member.

Section 1 (Measurement)

Measurement of the interior walls of the building / room together of the windows doors or parts which should be subtracted together with floor plan: (Max score of 4)

Each member does the calculations of the total surface area and write-up individually. Formulae, Substitution, Answer and Unit receive marks. (Max score of 4 marks)

Section 2 (Quotations for paint)

Quotations from any paint company on the price for four different types of paints. All quotations should be included. (max 4 marks)

Decision and motivation by each group member on decision of the paint they will take depending on their individual needs and does the write-up individually. (max of 4 marks)

Section 3 (Quotations for labour)

Quotations from any four painters on the asking rate per square meter to do the job. Let the painters also give you the estimated time it will take them to complete the entire job as well as more specifics on the paint job. All quotations should be included. (max of 4 marks)

Each group member’s decision and motivation on which painter to employ. (max of 4 marks)

in the assignment and then the quotation accepted with the motivation for the choice of quotation

Section 4 (Final calculations)

Total cost for paint based on your individual decision. (2 marks) Total cost for labour job based on your individual decision. (+ 1 mark) Total cost for the entire job (paint and labour). (+ 1 mark)

RUBRIC FOR ASSESSING THE ASSIGNMENT:



UNIT STANDARDS: 119373 & 1193621 2 3 4 Scores

Measure-ments done

No or little work done

Floor plan and measurements not completed

Floorplan drawn up. But no measurements given

All measurements indicated on floor plan 5

Calculations Just formulae given

Formulae (F) and substitution (S) done.

F, S and answer (A) given

F, S, A and unit (U) given

5

Quotations for paint

1 or no Quotation 2 Quotations 3 Quotations 4 Quotations 5

Decision on paint

Decision and no motivation




5

Quotations for labour

1 or no Quotation 2 Quotations 3 Quotations 4 Quotations 5

Decision on labour

Decision and no motivation




5

Analysis of advertisement on various paints

Incorrect/ incomplete analysis of paints

Minor errors in analysis of paints

Correct analysis of advertisements

Detailed analysis of advertisements

5

Final calcula-tions

No final calculations done

Total cost for one of above criteria

Total cost for two of above criteria

Total cost for paint and labour

5

TOTAL SCORE FOR ASSIGNMENT: 40

TOOL 3: PROJECT


1. This project must be completed over a period of four weeks.

2. Learners should be encouraged to work in groups. Ensure participation by all group members

3. Explain the project to the learners including all requirements before starting on it.

4. The educator should assess the project at regular intervals to ensure a good quality project and completion on time.

QUESTION 1

In your class, your group decides to buy your teacher a cell phone as a token of appreciation. For a group to reach a good decision, an investigation had to be carried out. The group then decided to investigate the costs, advantages and disadvantages of different offers that different providers have on similar phones. Answer the following questions to help you reach a good decision:

1.1 1 mark for each a cell phone advertisement from each provider. (3)

1.2 1 mark for each for each row correctly completed. (8)

1.3 Open ended answer. Any reasonable answer. Reasons provided (2)

1.4 3 marks for each of the offers correctly responded to (3)

1.5 1 mark for the scale1 mark for labelling the x axis



1 mark for labelling the y axis2 marks for all three bars correct (3)

1.6 Open ended answer. Any 3 reasonable answer based on the information from the graph

(3)

1.7 A contract: commit yourself to a particular service provider for a particular term/ timeframe/ 12 or 24 moths

a prepaid: airtime paid in advance/ or any related reasonable answer (4)

1.8 peak time: between 7am to 7 pm / busy time off- peak time: between 8pm to 7 am (2)

1.9 Open ended answer. Any reasonable answer (2) [30]

QUESTION TWO

The following data represent the life span of a light bulb in days.

133 83 82 109 121 105 105 73 117 109 83 97 138 85 104 79 106 82 80 92 132 91 83 108

2.1 Complete the table below to show the tallies and frequency for the different class intervals:

Class intervals in days Tallies Frequency 70 – 79 // 280 – 89 //// // 790 – 99 //// 4100 – 109 //// // 7110 – 119 / 1120 – 129 / 1130 – 139 /// 3 (6)

2.2 Represent the data above in a stem-and-leaf diagram

7 39 8 022 3335 9 1237 10 4556899 11 7 12 1 13 238 (5)

2.3 Calculate the mean life span of the light bulb = 2 490, n = 25

Mean = 99,6 (3)

2.4 Calculate the range of the data



Range = 138 – 73 = 65 (2)

2.5 Compare the median and the mode of the dataMedian = 97 and mode = 83

median mode But median closer to the mean (4)

[20]

[50]

TOOL 4: WORKSHEET

QUESTION 1

1.1 1.1.1 =

= 10 (1)

1.1.2 125% of 125 = 125 + 31.25

= 156.25 (1)

1.1.3 3,85 – 1,38 = 2,47 (1)

1.1.4 (–5) x (–8) 4 = 40 4

= 10 (1)

1.1.53 + 5 – 2 = 6 + + -

= 6 +

= 6 (3)

1.1.6 2 million + 2220 = 2 002 220 (1)

1.1.7 7 2 = 7 x 7 x 2 x 2 x 2 x 2 x 2 = 49 x 32 = 1568 (2)

1.2 ; ;

; ; (3)

1.3 1.3.1

75% of 120 has the same value as

2 x 45 120 120 – 75 25 x 3

(1)



1.3.2 =

0.9 3 9 (1)

1.3.3 If p = -4, then p =

16 (1)

1.4 1.4.1-0, 5 -5

(1)

1.4.2 60% (1)

1.4.32 x 4 + 3 2 + 3 x 4 (1)


›

=

‹

0.3

256


1.5 1.5.1 Draw the mirror image and two sketches of each shape after you have rotated it.


Rotation 2: A further 90° anti- clock-wise, (180° in total)

(a) (b) (c)

(d) (e) (t)

1 mark for each correct sketch

(6)[25]

QUESTION 2

2.1 Total parts = 31 + 27 + 24 = 82

Pule = x R 4 100 000

= R 1 550 000 Suzan = R 1 350 000 and Alfred = R 1 200 000 (4)

2.2 (a) 110.1 km/h

(b) 2.4 hours (4)

2.3

2.3.1 24 x 0.5 + 3 = 15 (2)

2.3.2k + 3 (2)

2.3.3 Calculate the input number if the output is 9.

(9 – 3) x 2 = 6 (3) [15]

QUESTION 3

3.1 Western Cape (1)

3.2 Lesotho (1)

3.3 Cape Town (1)

3.4 East (1)



3.5 Allow 2mm error (2)

3.2.3 Follow on (2)

3.3 P(2 ; 4)Q(-3 ; -1)R(3 ; 0)S(1 ; -2)

mark for each correct point on Cartesian plane (2) [10]

TOTAL: [50]

TOOL 5: INVESTIGATION

INSTRUCTIONS AND INFORMATION TO EDUCATORS

1. This investigation must be completed over a period of four weeks.

2 Learners should be encouraged to work in groups. Ensure participation by all group members.

3. Explain the project to the learners including all requirements before starting on it.

5. The educator should assess the project at regular intervals to ensure a good quality project and completion on time.

THE INVESTIGATION: ESTABLISHMENT OF SMALL BUSINESS

QUESTION 1: INTRODUCTION

1. Open ended answer. Any reasonable answer. Reasons given. (4)

2. Open ended answer. Any reasonable answer. Reasons given. . (4)

3. Open ended answer. Any reasonable answer. Reasons given. . (4)

4. 200 =20 (1)

5. 2 marks for all ten items2 marks for all ten tallies2 marks for all ten frequencies1 mark for the sum of the frequency (7)

6. Pie chart diagram1 mark for the correct sectors 2 marks for showing the calculations 1 mark for labeling the graph (4)

7. Any reasonable answer based on the data given (5)



8. Open ended answer. Any reasonable answer. Reasons given. (2)

9. Open ended answer. Any reasonable answer. Reasons given (5)




TOTAL: [50]

9. EXTERNAL ASSESSMENT (SUMMATIVE)

The summative assessment component of the MLMS4 learning comprises 50% of the total assessment. The policy on the Conduct, Administration and Management of the GETC-ABET Level 4 Examinations gives details on how this component of assessment should be managed. It prescribes the examination processes like registration of PALCs as examination centres, registration of candidates, conduct of examinations, marking, capturing of marks, standardization, resulting, to mention but a few.

9.1 STRUCTURE OF A QUESTION PAPER

This section provides an overview of the structure of the question paper as a summative assessment tool. It indicates the nature of an assessment task or activity in each section and question of the paper, the mark allocation of each question/section, and what US & SOs are covered in each question/section.Educators are advised to refer to section 8 of this document, to view the broad overview of the Core Knowledge Areas to be covered in each US & SO, so that the selection for the different questions/sections of the question paper can be contextualised. In addition, educators are provided with some guidelines on how best to prepare learners for each question/section of the paper. The final paper will consist of three sections:

The general layout of the Mathematical Literacy examination paper consists of:

A front page (cover page) giving clear indication of the learning area, the code of the learning area, the date, the time allocation for writing the paper and the total marks. At the bottom of the page an indication is also given of the number of pages the paper consists of. If a formula sheet is attached, it will also be indicated on the front page. The logo of the examining body, DoE is also very prominent in the centre of the cover page.

All instructions and other information are specified on page two. This should be regarded as very important and learners should be advised to thoroughly study this page before attempting the paper.

Question 1 usually starts on page 3, followed by the rest of the questions. All diagrams and sketches are within the question itself. The numbering order is as follows :

Example: Question 2 2.1………………………. 2.1.1…………………….. 2.1.2 (a)…………………

A header, indicating the code of the learning area and the date of the examination is on each page. A footer on each page, indicating the copyright of the paper as well as the instruction to please turn over,

giving an indication that more questions follow on the next page.



All marks are indicated next to each question. The total marks are indicated at the end of the question, bolded and in square brackets.

A formula sheet might be included as an annexure.

9.2 EXEMPLAR QUESTION PAPER

An exemplar of a sample question paper and marking memorandum is included below for reference. Educators are advised to study the mark allocation and instructions, so they can coach their learners on how to answer questions more effectively. This will hopefully inform individual assessment and marking practice.

GENERAL EDUCATION AND TRAINING CERTIFICATE

NQF LEVEL 1

ABET LEVEL 4 SUMMATIVE ASSESSMENT

LEARNING AREA: MATHEMATICAL LITERACY

CODE : MLSC

DATE : JUNE 2008

TIME : 3 HOURS

MARKS : 100This question paper consists of 9 pages and a formula sheet.



2. Show ALL calculations.

3. Number the answers correctly according to the numbering system used in this question paper.

4. Calculators may be used except where otherwise indicated.

5. Questions must be answered in blue or black ink.

6. Write neatly and legibly.

QUESTION 1

1.1 Determine the following without the use of a calculator. Answers must be given in simplified form.

1.1.1 785 - 297 (1)



1.1.2 75 30 (2)

1.1.3 16,58 - 5,2 (1)

1.1.4 16 9 4 (1)

1.1.53 + 5 (3)

1.1.6 45% of R900 (2)

1.1.7 2 4 (2)

1.1.8 (2)

1.2 Arrange the following numbers from the largest to the smallest:

1.2.1 0,02331; 0,231; 2,31; 0,0231 (1)

1.2.2 ; ; (2)

1.3 Convert the following:

1.3.1 0,25 to a common fraction in its simplest form (2)

1.3.2 45 percent to a common fraction in the simplest form (2)

1.4 A bookseller bought 200 books at R60 each. He/she sold them at R80 each.

1.4.1 Calculate the total cost of the 200 books. (2)

1.4.2 Calculate the income from the sale of the 200 books. (2)

1.4.3 Calculate the profit the bookseller will make if he/she sells all the books. (2)

1.4.4 Express the profit in QUESTION1.4.3 as a percentage of the total cost. (2)

1.4.5 How many books must he/she sell in order to recover his/her cost? (2) [31]

QUESTION 2

2.1 Convert the following to the unit as indicated:

2.1.1 630 minutes = … hours … minutes (1)

2.1.2 685 = … m (1)

2.2 A circular plot of land has a radius of 28 metres as shown in the sketch below. The sketch is NOT drawn to scale.



2.2.1 Calculate the perimeter of the plot. (3)

2.2.2 Calculate the area of the plot. (3)

2.2.3 If the radius of the plot is halved, calculate the new area. (3)

2.2.4 What is the ratio of the new area to the old area? (2)

2.3 A cube has sides of 5 cm each as shown in the sketch below.

2.3.1 Calculate the volume of the cube. Give the answer correct to THREE decimal places. (3)

2.3.2 Draw a net (i.e. opened and flattened surface area) representing the diagram of the cube. (3)

2.3.3 Calculate the total surface area of the cube (correct to THREE decimal places) (3) [22]

QUESTION 3

3.1 The following are the attendance figures for the last six games played by the local soccer team:

3 852; 2 638; 2 525; 1 954; 2 911; 1 948

3.1.1 Determine the average attendance. (3)

3.1.2 Determine the range of the attendance figures. (1)

3.1.3 What can you conclude from the figures? (2)

3.2 A bag contains 6 black balls and 4 white balls. Chris puts his hand into the bag and draws out one ball. Calculate the following probabilities:

3.2.1 That he will draw a white ball (1)


28 m

5 cm

5 cm

5 cm


3.2.2 That he will draw a black ball (1)

3.2.3 If he draws out two balls, what is the chance that both will be black? (2)

3.3 The following straight-line graph shows the relationship/conversions between units of distance, namely kilometres and miles.

Use the graph to complete the following:

3.3.1 50 miles = … km (1)

3.3.2 120 km = … miles (1)

3.3.3 The conversion factor for converting miles to kilometres is … (1)

3.4 The following table shows the number of loaves of bread sold daily by the corner café:

Day Mon Tues Wed Thurs Fri Sat SunLoaves 180 160 120 100 100 60 40

3.4.1 Represent the data graphically by means of a pictograph.HINT: Use any suitable symbol to represent 20 loaves. (3)

3.4.2 On which day was the bread sales the highest? (1)

3.4.3 Discuss any pattern of sales that you see. (2) [19]

QUESTION 4

4.1 Simplify the following ratio: 24:64:40 (1)

4.2 After deduction of taxes and duties, Piet’s estate was left with R 1 362 248. It was to be distributed amongst his wife and two children in the ratio 2:1:1

4.2.1 Determine how many portions the estate was divided into. (1)

4.2.2 Determine the value of each portion of the distribution. (1)



4.2.3 Determine the value of each person’s inheritance. (2)

4.3 At 06:00, Johann left Johannesburg for Durban. At 07:00, Thabo left Durban for Johannesburg. Suppose each travelled a total distance of 640 km. Both agreed to meet at Montrose, exactly halfway between Durban and Johannesburg.

4.3.1 Johann travelled at an average speed of 100 km/h. He stopped after 2 hours. What distance did he travel in that time? (1)

4.3.2 At 09:00 Thabo reached Estcourt, 220 km from Durban. Calculate the average speed he travelled for this part of his journey. (2)

4.3.3 After stopping for 30 minutes, Johann left for Montrose. Calculate how far he had to travel to get there. (1)

4.3.4 Determine the time at which Johann reaches Montrose. (2)

4.3.5 Thabo’s car uses 1 litre of petrol for every 8 km. Calculate how many litres his car uses for the full journey. (1)

4.3.6 Petrol costs R5,80 per litre. Calculate Thabo’s petrol costs for the trip from Durban to Johannesburg. (1)

4.3.7 Calculate Thabo’s total travelling cost for the trip from Durban to Johannesburg if he paid a further R145 in toll fees in addition to his petrol cost. (1)

[14]

QUESTION 5



5.1 The Cartesian Plane below has not been drawn to scale. Give the Cartesian coordinates of the points (A to F) indicated.

5.2 Use the sketch below to describe the movement from P to S passing through Q and R.

P S N 5km 45 º Q 8km R (3)

[9]

QUESTION 6

Look at this kilometre chart which shows the distance between different places in kilometres.If you want to find the distance between Maseru and Welkom you would look down the column of figures under Welkom and along the line next to Maseru. The figure in the box where the two meet is the distance.


7km

-8

8

7

6

5

4

3

2

1

Y

X

–1

–2

–3

–4 –3 –2 –1 1 2 3 4 5

D

E

C

F

A

B

-5-6-7

C

– 4

8

7

6

5

4

2

1

Y

X

–1

–2

–

–4 –3 –2 –1 1 2 3 4 5

D

E

C

F

A

B

-5-6-7

C

–5

--3


Windhoek

1 679 Welkom

2 066 718 Umtata

1 859 316 928 Pretoria

1 950 830 545 1 133 Port Elizabeth

2 162 451 1 003 372 1 548 Mbabane

1 750 249 616 488 822 633 Maseru

2 400 813 1 064 583 1 690 223 853 Maputo

1 577 321 1 034 294 1 141 648 544 886 Mafikeng2 008 340 517 414 1 062 386 366 567 597 Ladysmith

6.1 What is the distance between Pretoria and Maputo? (1)

6.2 Which TWO places are closest to each other? (1)

6.3 What is the distance between Mafikeng and Umtata? (1)

6.4 If you want to go from Windhoek to Maputo, would you go via Pretoria or direct? Show calculations to justify your choice. (2)

[5]

TOTAL: 100

FORMULAE2-dimensional figures:

FIGURE PERIMETER AREATriangle Sum of sides

bh

Rectangle 2( + b) bSquare 4s sCircle 2 r OR d r3-dimensional figures:

FIGURE VOLUME TOTAL SURFACE AREARegular Prism A H P H + 2 A

Triangular Prismh H

(s + s + s) H + bh

Rectangular Prism b H 2( + b) H + 2lb OR2[(l+b) H+lb]

Cube s 4s + 2s = 6sCircular Prism (Cylinder)

r H 2 rH + 2 r OR2 r (H+r)

Key:l lengthB breadth (width)S side



height of triangle= perpendicular height= radius= diameter= area= perimeter= volume

MEMORANDUM

QUESTION 1: US 1: SO’S 1 – 4; US 2: SO’S 1 –

1.1.1 488 (1)

1.1.2 (75 10) + (75 10) + (75 10) 1 mark for distribution = 2250 1 mark for the answer OR 75 10 3 = 2 250 OR 75 30 2 250 Full marks for answer only (2)

1.1.3 11,38 (1)

1.1.4 36 (1)

1.1.5 + 1 mark for conversion into improper fractions

= + 1 mark for equivalent fractions/ LCD

= = 8 1 mark for simplification

OR (3 + 5) + ( + ) 1 mark for separation of whole

numbers and fractions

= 6 + ( + ) 1 mark for equivalent fractions

= 6 1 mark for simplification (3)

1.1.6 900 1 mark for writing percentage

as a fraction= 405 1 mark for answerFull marks for answer only

(2)

1.1.7 16 16 1 mark for expansions= 1 1 mark for simplificationOR

=1

Full marks for answer only(2)



1.1.8 1 mark for simplification= 10 1 mark for finding rootsFull marks for answer only (2)

1.2.1 2,31; 0,231; 0,02331; 0,0231 all terms to be in the right sequence (1)

1.2.2; ; 1 mark for equivalent fractions

Order: ; ; Each term to be in the right place order

Full marks for correct order (2)

1.3.10,25 = = (2)

1.3.245% = = (2)

1.4.1 Total cost = 200 R60 1 mark for deduction = R 12 000 1 mark for simplification (2)

1.4.2 Total income = 200 R80 1 mark for deduction = R16 000 1 mark for answer (2)

1.4.3 Profit = R16 000 – R12 000 1 mark for deduction = R4 000 1 mark for simplification (2)

1.4.4% profit = 100 % 1 mark for deduction

= 33,33% 1 mark for simplification (2)

1.4.5 No. of books= R12 000 80 1 mark for deduction = 150 1 mark for simplification (2)

[31]

QUESTION 2: US 4: SO’S 1 – 3

2.1.1 10 hours 30 minutes (1)

2.1.2 685 000ml (1)

2.2.1Perimeter = 2 28m 1 mark for substitution in correct formula

= 176m 1 mark for answer and 1 mark for the correct unit (3)

2.2.2Area = 28 28m 1 mark for substitution in correct formula

= 2464m 1mark for answer and 1 mark for the correct unitFull marks for answer only (3)

2.2.3New Area = 14 14m 1 mark for substitution in correct

formula and 1 mark for halving length = 616m 1 mark for answer (3)

2.2.4 New Area: Old Area = 616: 2464



= 1:4 full marks for answer (2)

2.3.1 V =s = 5 m 1 mark for substitution in correct formula = 125 m 1 mark for correct answer and 1 for correct unit (3)

2.3.2

Six squares Three squares in one plane Four squares in the other planeOther possible orientations must be considered. (3)



2.3.3 Surface area = 6S = 6 25 m 1 mark for substitution in formula = 150 m 1 mark for answer and 1 mark for the correct unit (3)

[22]

QUESTION 3: US 5: SO’S 1 - 5

3.1.1Average = 1 mark for

substitution in formula 1 mark for operation = 2638 1 mark for answerFull marks answer only (3)

3.1.2 Range = 3852 -1948 =1904 1 mark for the answer (1)

3.1.3 Open- ended. Any feasible explanation in respect of attendances and differences to be accepted. (2)

3.2.1 = (1)

3.2.2= (1)

3.2.3 1 mark for deduction

= OR 0,33 OR 1 mark for simplification (2)

3.3.1 50miles = 80km (1)

3.3.2 120km = 75miles (1)

3.3.3 (1)

3.4.1 Key: represents 20 loaves

Day LoavesMonday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday



I mark for choice of key2 marks for graph (3)

3.4.2 Monday (1)

3.4.3 Open – ended. Any feasible explanation with regard to sales and days. (2)

[19]

QUESTION 4: US 2: SO’S 1 – 2

4.1 3: 8: 5 (1)

4.2.1 2 + 1 + 1 =4 (1)

4.2.2 R1 362 248 4 = R340 562 (1)

4.2.3 Wife gets R340 562 2 = R681 124Each child gets R340 562 (2)

4.3.1 Distance = 2 100 km = 200 km (1)

4.3.2 Speed = 220 2 km/h = 110 Km/h (2)

4.3.3 320km – 200km= 120 km (1)

4.3.4 To reach Montrose he has to travel for hours =1 hr. 12min.

Hence he reaches Montrose at 09:42 (2)

4.3.5 No. of litres = 640 8 = 80l (1)

4.3.6 Petrol cost = R5,80 80 = R464 (1)

4.3.7 Total cost = R464 + R145 = R609 (1)

[14]

QUESTION 5: US 4: US 9: SO 1

5.1 A (2;8) B (0; 6) C (3;0) D (5; -4) E (-8; -5) F (-6; 3) (6)

5.2 Travel 5km south from P to Q, then 8km east from Q to R, and finally 7km north-east from R to S. 1 mark for each move. (3)

[9]

QUESTION 6: US 8 SO’S 1 – 2

6.1 583km (1)



6.2 Mbabane and Maputo (1) 6.3 1034km (1) 6.2 Direct – Direct distance is 2400 km compared to 2442km via Pretoria. (2)

[5]

TOTAL: 100

HINTS FOR MARKING OF THE ANSWER SCRIPTS:

A good practice at marking centres is to actually conduct a thorough marking memorandum discussion before the actual marking starts. After the marking memorandum discussion it is also advised that the markers mark a few scripts and submit these scripts for moderation. Markers should also fully adhere to the concept of CA marking where applicable. Two different methods of marking that could be used in the provincial-based marking are as follows:

1. Marking a full script per marker :

Scripts were distributed equally at the beginning of the marking session between all markers. The specific marker marks the entire script and after marking the entire batch, the scripts are submitted for moderation to the chief marker and the moderator. The marker is liable for the entire script.

2. Parallel marking:

The scripts are divided between groups of three or four members. Each marker marks specific allocated questions. The amount of questions that needs to be marked amongst members in a group is distributed on a more or less equal mark allocation e.g. three in a group, approximately thirty three marks per marker or four in a group, approximately 25 marks per marker, depending on the mark allocation per question in the set paper. The first marker marks his/her questions and moves the entire batch of scripts to the next marker in the group etc. Once the scripts have moved between all the members in the group, it is deemed to be completed and is then sent for moderation.

Following this way of marking usually ease the whole process of marking because the marker get acquainted to the memorandum of his/her questions very quickly, hence less mistakes in the marking of the paper.

10. PROMOTING THE PRINCIPLES OF QUALITY ASSESSMENT PRACTICES

The Department views assessment as a process of making decisions about a learner’s performance. It involves gathering and organising evidence of learning, in order to review what learners have achieved. It informs decision making in education, and helps educators to establish whether learners are performing according to their full potential and are making process towards the required unit standards credits as outlined in the qualification cited above. Principles of assessment that are always considered when assessment tasks and tools are developed include among others the following:

Validity Assess what is supposed to be assessed. Examination question papers and SBAs take the US, and their related assessment criteria into account in setting appropriate types of questions.

Reliability Assessment should produce reliable results instructions are clear, consistent and unambiguousAssessment criteria are strictly adhered toMarking guidelines/memoranda are clear and markers apply the same standard.



Transparency Accomplished through guidelines, uniform SBAs and national examinations are moderated internally.Papers and SBAs are moderated externally by Umalusi. Stakeholders know what to expect and candidates have the right to appeal.

Fairness Assessment does not disadvantage anybody (based on age, race, gender, ethnicity, geographic location)Assessment is accessible to all candidatesCovers different cognitive levelsNature of the learning environment of learners is considered.

Currency Assessment keeps up with current events and life-world of ABET learners. This is reflected in the content and nature of the texts selected, and the topics offered for interaction.

Authenticity Assessment is original and encourages originality, creativity and avoids repetition. It consciously tries to avoid predictability.

The different types, descriptions and uses of assessments are given below to serve as a reminder to everybody with an interest in adult education that only quality assessment practices is suitable for this sector of our education system.

Baseline Assessment: Usually used at the beginning of a learning experience to establish what learners already know, can do or value. It assists educators with the planning of learning programmes and learning activities.

Formative Assessment: It is developmental and used to inform both the teacher and the learner about how the learner has progressed (or not). It enhances teaching and learning. Teachers use it to adapt learning activities to the learner needs. It is also known as assessment for learning

Summative Assessment:

It gives an overall and final picture of the achievements of a learner at a given time. The examination is an example of summative assessment for ABET Level 4. This could be viewed as a “snapshot” whilst formative assessment is viewed as a “video” of a learner’s progress.

Diagnostic Assessment: It is a form of formative assessment that leads to intervention, remedial action or revision programme. It identifies both the strengths and weaknesses of either the learner or the teaching methodology

Systemic Assessment: It is an external way of monitoring the education system by comparing learners’ performance to national indicators of learner achievement. It involves monitoring learner attainment at regular intervals using national or provincially defined measuring instruments.

Note of the following Assessment Strategies should also be taken.Methods (WHO)

Forms (WHAT)

Instruments/Tools (HOW)

Purposes (WHY)

Educator assessment,Self-assessment,Peer-assessment andGroup-assessment.

Tests, Drawings,Paintings, Graphs,Physical activities, Projects,Demonstrations,Poems, Dramas, Role-plays, Stories,Songs/music,Oral presentations,Written presentations,Worksheets,Questionnaires,Cassettes, Posters,

Assessment grids,Rubrics,Memoranda andObservation sheets.

Baseline,Diagnostic,Formative,Summative andSystemic.



In conclusion, assessment must always be fair to learners and all possible barriers preventing learners from expressing their knowledge, skills and values in an assessment task, must be considered when developing, assessing and moderating the assessment task.


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