GETC-ABET Level 4 Examination Guidelines Draft Curriculum Statements... · Web viewPythagoras (570 BC to 500 BC) was a Greek mathematician and philosopher, who was credited with the

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

MATHEMATICS AND MATHEMATICAL SCIENCES L4

CODE: MMSC4

2013 - 2015

Examinations and Assessment Guidelines: MMSC4

TABLE OF CONTENTS

1. Introduction 3

2. The GETC-ABET Level 4 Qualification 4

3. Unit Standards for MMSC4 Learning Area 7

4. LTSM in PALCs 16

5. Weighting of the Specific Outcomes and Assessment Criteria 16

6. Core Knowledge Areas 17

7. Taxonomies used in scaffolding questions 21

8. Site-Based Assessment (Formative) 21

8.1 Structure of SBA Tasks 22

8.2 Exemplar SBA Tasks 23

9. External Assessment (Summative) 39

9.1 Structure of a question paper 39

9.2 Exemplar question paper 40

10. Promoting the Principles of quality assessment practices 51

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 MMSC4 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 MMSC4 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 MMSC4 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 Credits6. 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 MMSC4 LEARNING AREA

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

Critical Cross-field Outcomes (CCFO):



UNIT STANDARD CCFO IDENTIFYING Identify and solve problems: using context to decode and make meaning individually and in groups in

oral/signed activities. Reflect on and explore a variety of strategies to learn more effectively: listening skills include listening

for meaning in order to promote study skills such as note-taking, asking for clarification etc. Explore education and career opportunities: speaking/signing and listening skills at this level enable

access to information on such opportunities, and provides the foundation for successful engagement in such opportunities.

Develop entrepreneurial opportunities: speaking/signing and listening skills at this level enable access to information on such opportunities, and provides the foundation for successful engagement in such opportunities.

UNIT STANDARD CCFO WORKING Work effectively with others and in teams: using interactive speech/signing in activities, discussion and research projects.

UNIT STANDARD CCFO ORGANISING Organise and manage oneself and one`s activities responsibly and effectively: through using language

UNIT STANDARD CCFO COLLECTING Collect, analyse, organise and critically evaluate information: fundamental to the process of growing language capability across language applications and fields of study.

UNIT STANDARD CCFO COMMUNICATING Communicate effectively using visual, mathematical and/or language skills: in formal and informal communications.

UNIT STANDARD CCFO SCIENCE Use science and technology effectively and critically: language makes it possible for people to access and use scientific and technological information and applications.

UNIT STANDARD CCFO DEMONSTRATING Understand the world as a set of related systems: through using language to investigate and express

links, and to explore a global range of contexts and texts. Be culturally and aesthetically sensitive across a range of social contexts: listening and speaking skills

enhance understanding and discussion of such issues.

UNIT STANDARD CCFO CONTRIBUTING Participate as responsible citizens in the life of local, national and global communities: listening and

speaking/signing skills enable people to participate effectively in such processes.

The MMSC4 Learning Area comprises 6 unit standards:

SAQA US ID US TITLE CREDITS7448 Work with patterns in various context 47452 Describe , represent and interpret mathematical models in different context 67453 Use algebraic notations, conventions and terminology to solve problems 37464 Analyse cultural products and processes as representations of shape, space

and time3

Total 16

SAQA US ID US TITLE CREDITS7448 Work with patterns in various context 4

PURPOSE OF THE UNIT STANDARD



People credited with this unit standard are able to recognise, identify, describe, generate, complete and extend numeric, geometric and other patterns in various contexts

LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING

The following competencies at ABET Numeracy level 3 are assumed to be in place: Work with number patterns and relationships involving multiples, factors, even numbers, odd numbers and prime numbers. Describe, draw, analyse and construct planar shapes and patterns and spatial objects and describe, interpret and represent the environment geometrically.


Examinations and Assessment Guidelines: MMSC4SPECIFIC OUTCOMES AND ASSESSMENT CRITERIA:

SPECIFIC OUTCOME 1Recognise, identify and describe patterns in various contexts

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Patterns are recognised in terms of the relationship between the elements of the pattern.

ASSESSMENT CRITERION 2Patterns are correctly identified in terms of the relationship between the elements of the pattern.

ASSESSMENT CRITERION 3Patterns are correctly described in terms of the relationship between the elements of the pattern and remain consistent through the pattern

ASSESSMENT CRITERION 4The language of comparison is appropriate and describes the relationship between the elements of the pattern.

SPECIFIC OUTCOME 2Complete, extend and generate patterns in a variety of contexts

OUTCOME RANGE Numeric, geometric, patterns from a variety of contexts

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Completed patterns are internally consistent with respect to the relationship between elements of the pattern.

ASSESSMENT CRITERION 2The extension is consistent with respect to the relationship between elements of the pattern

ASSESSMENT CRITERION 3Generated patterns are internally consistent

.

SPECIFIC OUTCOME 3Devise processes for a general rule

OUTCOME RANGE Processes include: systematic counting, sequencing numbers, tables, drawings, pictures, classification, organised lists, mathematical and models such as graphs

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Appropriate processes are devised according to the context

ASSESSMENT CRITERION 2Processes have potential to lead to a general rule

ASSESSMENT CRITERION 3A general rule is devised such that it is consistent with the relationship of the elements of the patterns

SPECIFIC OUTCOME 4Represent patterns using different generalised mathematical forms

OUTCOME RANGE Graphs, formulae, expressions and other rules for expressing patterns

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Appropriate mathematical forms are used to represent patterns

ASSESSMENT CRITERION 2The representation is consistent with relationships within the pattern and represents the pattern completely.

ASSESSMENT CRITERION 3Conversions are made between various forms of representations

ASSESSMENT CRITERION 4Relationships between various possible forms of representations are described

SPECIFIC OUTCOME 5Use general rules to generate patterns.

OUTCOME RANGE Processes include: systematic counting, sequencing numbers, tables, drawings, pictures, classification, organised lists, mathematical models such as graphs.

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Patterns generated are consistent with the general rule

ASSESSMENT CRITERION 2Patterns are generated to the extent that they enable the rule to be devised from the patterns



SAQA US ID US TITLE CREDITS7452 Describe , represent and interpret mathematical models in

different context 6


People credited with this unit standard are able to:

Describe and represent relationships in a variety of contexts using tables; Describe and represent relationships in a variety of contexts using simple algebraic expressions and/or equations; Describe and represent relationships in a variety of contexts using graphs; Describe and represent relationships in a variety of contexts geometrically; Analyse and explain the behaviour of graphs in terms of increasing and decreasing trends; Analyse and explain the behaviour of general algebraic equations and formulae in terms of increasing and decreasing relationships between variables


The following learning at ABET Numeracy level 3 is assumed to be in place: Construct and use tables and graph to organise and interpret information



SPECIFIC OUTCOMES AND ASSESSMENT CRITERIA:

SPECIFIC OUTCOME 1Describe and represent relationships in a variety of contexts using tables

OUTCOME RANGE Simple linear, quadratic and exponential relationships. Relationships may be given in the form of words, equations, and graphs or as a result of experiments

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Independent and dependent variables are identified

ASSESSMENT CRITERION 2The descriptions are consistent with the given relationship

ASSESSMENT CRITERION 3The representation is consistent with the given relationship

ASSESSMENT CRITERION 4Sufficient information is represented in such a way that the relationship is evident

SPECIFIC OUTCOME 2Describe and represent relationships in a variety of contexts using simple algebraic expressions

OUTCOME RANGE Simple linear, quadratic and exponential relationships. Relationships may be given in the form of words, tables, and graphs or as a result of experiments




ASSESSMENT CRITERION 4Sufficient information is represented in such a way that the relationship is evident

SPECIFIC OUTCOME 3Describe and represent relationships in a variety of contexts using graphs

OUTCOME RANGESimple linear, quadratic and exponential relationships and simple cyclical relationships such as trig functions. Number lines for inequalities. Relationships may be given in the form of words, tables, and equations or as a result of experiments




ASSESSMENT CRITERION 4Sufficient information is represented such that the relationship is evident

SPECIFIC OUTCOME 4Describe and represent relationships in a variety of contexts geometrically

OUTCOME RANGE Heights and distances using right-angled triangles.

ASSESSMENT CRITERIAASSESSMENT CRITERION 1The descriptions are consistent with the given relationship


ASSESSMENT CRITERION 3Sufficient information is represented in such a way that the relationship is evident.

SPECIFIC OUTCOME 5Analyse and explain the behaviour of graphs in terms of increasing and decreasing trends.

OUTCOME RANGE Limited to situations where the information can be directly read off the graph

ASSESSMENT CRITERIAASSESSMENT RITERION 1The variables are identified

ASSESSMENT CRITERION 2The potential or existing relationships between variables are described

ASSESSMENT CRITERION 3The increasing and decreasing trends are described

ASSESSMENT CRITERION 4The maximum and minimum are identified

SPECIFIC OUTCOME 6Analyse and explain the behaviour of general algebraic equations and formulae

OUTCOME RANGE Linear and quadratic equations

ASSESSMENT CRITERIAASSESSMENT CRITERION 1The dependent and independent variables are identified

ASSESSMENT CRITERION 2The potential or existing relationships between variables are described

ASSESSMENT CRITERION 3The increasing and decreasing trends are described



SAQA US ID US TITLE CREDITS7453 Use algebraic notations, conventions and terminology to solve problems 3



Form and use algebraic equations and inequalities to represent and solve practical and abstract problems; Manipulate algebraic expressions to find equivalent forms; and Select and use algebraic formulae to solve problems


The following learning at ABET Numeracy level 4 is assumed to be in place: Describe and represent relationships in a variety of contexts using simple algebraic expressions and/or equations.




SPECIFIC OUTCOME 1Form and use algebraic equations and inequalities to represent and solve problems

OUTCOME RANGE Simple linear equations and inequalities

ASSESSMENT CRITERIAASSESSMENT CRITERION 1The problem is represented completely through equations or inequalities, which are consistent with the problem.

ASSESSMENT CRITERION 2The concepts of equations and inequalities are explained

ASSESSMENT CRITERION 3Situations requiring the use of equations as opposed to inequalities, and vice versa, are identified

ASSESSMENT CRITERION 4Algebraic rotation, conventions and terminology are used correctly

ASSESSMENT CRITERION 5The solution is correct in terms of the problem context

ASSESSMENT CRITERION 6The solution is verified through substitution or other verification processes

SPECIFIC OUTCOME 2Manipulate algebraic expressions to find equivalent forms

OUTCOME RANGE Common factors, products and grouping using associative, distributive and commutative properties

ASSESSMENT CRITERIAASSESSMENT CRITERION 1The manipulated form is equivalent to the original form

SPECIFIC OUTCOME 3Select and use algebraic formulae to solve problems

OUTCOME RANGESubstitution into any formula, solve for one variable, supplied formulae from any context

ASSESSMENT CRITERIAASSESSMENT CRITERION 1The correct formula is selected in terms of the problem context

ASSESSMENT CRITERION 2The formula is applied correctly to obtain a valid solution

ASSESSMENT CRITERION 3Units are used correctly



SAQA US ID US TITLE CREDITS7464 Analyse cultural products and processes as representations of shape, space

and time 3



Identify geometric shapes and patterns in cultural products; Analyse similarities and differences in shapes and patterns, and the effect of colour, used by different cultures; and Analyse and explain the way shapes and space are used in different epochs


The following learning at ABET Numeracy level 3 is assumed to be in place: Describe, draw, analyse and construct planar shapes and patterns and spatial objects; Describe, interpret and represent the environment geometrically.




SPECIFIC OUTCOME 1Identify geometric shapes and patterns in cultural products

OUTCOME RANGE Shapes of and decorations on cultural products such as drums, pots, mats, buildings, and necklaces

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Basic transformations are identified

ASSESSMENT CRITERION 2Basic geometric shapes are identified

ASSESSMENT CRITERION 3Basic patterns are identified and described

ASSESSMENT CRITERION 4Basic patterns are extended in a way that maintains the consistency of the pattern

SPECIFIC OUTCOME 2Analyse similarities & differences in shapes & patterns, & effect of colour, used by cultures

ASSESSMENT CRITERIAASSESSMENT CRITERION 1Similarities in shapes and patterns are identified

ASSESSMENT CRITERION 2Differences in shapes and patterns are identified

ASSESSMENT CRITERION 3 Possible reasons for similarities and/or differences in shapes and patterns used by different cultures are identified.

ASSESSMENT CRITERION 4The effect of colour on shape and symmetry is described and illustrated

SPECIFIC OUTCOME 3Analyse and explain the way shapes and space are used in different epochs and cultures

OUTCOME RANGEArchitecture, town and settlement planningASSESSMENT CRITERIA

ASSESSMENT CRITERION 1Shapes used by different cultures are identified

ASSESSMENT CRITERION 2The use of space in different cultures is analysed and explained

ASSESSMENT CRITERION 3The use of space in different epochs is analysed



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

RATIO OF COMPLEXITY:

Both the Summative Question Paper and the Site-based Assessment Tasks attempt to strike a balance in the complexity of the questions and tasks that are fair to learners, but also conform to standard assessment practices. In general, all assessments in the language learning areas are structured around the following ratios:

40% literal (recall from text; listing; extracting; verifying)30% interpretative (analyse, understand, verify)30% synthesis (apply, give own opinions, produce)

WEIGHTING:

Since the credits assigned to a unit standard gives it a particular weighting value in relation to other unit standards, an attempt will be made to balance the relative value of unit standards in assessments. The following weighting ratios reflect the composition of the summative assessment tool (question paper):

TABLE 1: Suggested weighting per Unit Standard

UNIT STANDARD ID CREDITS WEIGHTING % / MARKS

US: 7448Work with patterns in various context

4 25

US: 7452Describe, represent and interpret mathematical models in different contexts

6 38

US: 7453Use algebraic notation, conventions and terminology to solve problems

3 18,5

US: 7464Analyse cultural products and processes as representations of shape, space and time

3

TOTAL: 16 100

This table does not necessarily give the order of questions set in the examination.

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.

SAQA US ID 7448: WORK WITH PATTERNS IN VARIOUS CONTEXT

DESCRIPTION CLARIFICATIONRange for Unit Standard: numeric (limited to integers and fractions) and geometric shapes. SO 1: Recognise, identify and describe patterns in various contexts. Describe patterns AC1: Patterns recognised in terms of relationships between

elements of the pattern Classify patterns as increasing or decreasing

AC2: Patterns identified in terms of relationship between elements of the pattern.

AC3: Patterns described in terms of relationship between elements of pattern.

Use appropriate language to describe patterns/relationship (terms, twice, multiply, add, subtract, etc.) AC4: Appropriate language of comparison and describes

relationships between elements of pattern.SO 2: Complete, extend and generate patterns in a variety of contexts. Extend patternsAC1: Completed patterns are internally consistent with respect to relationship between elements of pattern.

Continue with patterns to show consistency between terms.

AC2: The extension is consistent with respect to the relationship between elements of the pattern.AC3: Generated patterns are internally consistent. Own patterns are generated, given a description

in words.SO 3: Devise processes for a general rule. Determine general rule in words or in formula.

Range: use counting, sequencing, tables, drawings, pictures, classifications, lists, graphs.

AC1: Appropriate processes are devised according to the content. Use different methods to determine the general rule.AC2: Processes have potential to lead to a general rule.

AC3: General rule devised such that it is consistent with the relationship of the elements of the patterns.

Check whether the rule is appropriate.

SO 4: Represent patterns using different generalised mathematical forms.

Represent patterns in words, graphs or formula.Range: graphs, formulae, words.

AC1: Appropriate mathematical forms used to represent patterns. Represent patterns in graphs, formula or words.AC2: Representation is consistent with relationships within the pattern and represents the pattern completely.

Check for consistency in patterns.

AC3: Conversions are made between various forms of representations.

Convert with confidence between different forms.

AC4. Relationships between various possible forms of representations are described.SO 5: Use general rules to generate patterns. Use general rules to form patterns.

Range: use counting, sequencing, tables, drawings, pictures, classifications, lists, graphs.

AC1: Patterns generated are consistent with the general rule. Use given general rule to generate patterns.AC2: Patterns are generated to the extent that they enable the rule to be devised from the pattern.

Generate patterns from a description in words to deduce a general rule.

SAQA US ID 7452: DESCRIBE, REPRESENT AND INTERPRET MATHEMATICAL MODELS IN DIFFERENT CONTEXTS



DESCRIPTION CLARIFICATION



SO 1: Describe and represent relationships in variety of contexts using tables.

Use tables to describe relationships.Range: linear, quadratic and exponential relationships given in the form of words, equations, graphs

AC1: Independent and dependent variables are identified. The concepts will not be examined formally, but must be discussed.

AC2: The descriptions are consistent with the given relationship. Check table entries for consistency.AC3: Representation is consistent with given relationship. Represent relationship given in words, equations

or graphs using tables.AC4: Sufficient information is represented in such a way that the relationship is evident.SO 2: Describe and represent relationships in a variety of contexts using simple algebraic expressions.

Use expressions or equations to describe relationships.Range: Linear relationships given in the form of words, tables or graphs


AC2: The descriptions are consistent with the given relationships. Check linear equation/expression for consistency by substitution.

AC3: The representation is consistent with the given relationship. Represent relationship given in words, tables or graphs using equations/expressions.

AC4: Sufficient information is represented in such a way that the relationship is evident.SO 3: Describe and represent relationships in a variety of contexts using graphs.

Use graphs or number line to describe relationships.Range: linear relationships given in the form of words, tables, inequalities and equations.


AC2: Descriptions are consistent with the given relationship. Check coordinates in graphs for consistency AC3: Representation is consistent with the given relationship. Represent relationship given in words, tables or

equations using graphs.AC4: Sufficient information is represented such that the relationship is evident.SO 4: Describe and represent relationships in a variety of contexts geometrically.

Use Pythagoras to calculate any sides/distances in a right-angled triangle.

AC1: Descriptions are consistent with the given relationship. Apply the theorem of Pythagoras for different right-angled triangles.

AC2: The representation is consistent with the given relationship. Use the theorem of Pythagoras to calculate a missing side.AC3: Sufficient information is represented in such a way that the

relationship is evident. SO 5: Analyse and explain the behaviour of graphs Reading from a graph.

Range: any given graph AC1: The variables are identified. Read from the graph.AC2: The potential or existing relationships between variables are described. AC3: The increasing and decreasing trends are described. Analyse and make decisions from graph about

the trend.AC4: The maximum and minimum are identified. Read maximum and minimum values from graph.SO 6: Analyse and explain the behaviour of general algebraic equations

Describe relationship between variables in an equation/formula.Range: linear and quadratic equations.

AC1: The dependent and independent variables are identified. The concepts will not be examined formally, but must be discussed.

AC2: The potential or existing relationships between variables are described.

Describe relationships in algebraic equations/formulae in words or tables.

AC3: The increasing and decreasing trends are described. Use words or tables to describe trends.

SAQA US ID 7453: USE ALGEBRAIC NOTATION, CONVENTIONS AND TERMINOLOGY TO SOLVE PROBLEMS

DESCRIPTION CLARIFICATION



SO 1: Form and use algebraic equations and inequalities to represent and solve problems.

Form and/or solve equations and inequalitiesRange: simple linear equations or inequalities.

AC1: Problem represented completely through equations or inequalities, which are consistent with the problem.

Solve linear equations/inequalities, including word problems.

AC2: Concept of equations and inequalities are explained. Concepts will not be formally examined. AC3: Situations requiring the use of equations as opposed to inequalities, and vice versa, are identifies.

Translate from words to mathematical language, e.g. o 5 added to a number is less than 20 5

+ x < 20o increased by x is 15 4 + x = 15

AC4: Algebraic notations, conventions and terminology are used correctly.

Penalised if terminology and notations are not used correctly.

AC5: The solution is correct in terms of the problem context. Validate answers according to contexts, e.g. 2½ men, negative length, etc.

AC6: The solution is verified through substitution or other verification processes.

Check solutions through substitution.

SO2: Manipulate algebraic expressions to find equivalent forms Simplification: (+, -, , )ProductsFactors: common factors; difference of squares, grouping, quadratic trinomials.

AC1: Manipulated form is equivalent to the original form. Simplification of algebraic expressions, including fractions and the use of exponents.

Products: (monomial binomial), (monomial trinomial), (binomial binomial).

Factors: common factor, grouping of terms, difference of 2 squares, quadratic trinomial (in the form x² + bx + c).

SO 3: Select and use algebraic formulae to solve problems. Use formulae from any context.Range: substitution into formula to solve for one variable.

AC1: The correct formula is selected in terms of the problem context. Substitute into formula to solve the problem.AC2: The formula is applied correctly to obtain a valid solution. AC3: Units are used correctly. Incorrect or no use of units will be penalised.

SAQA US ID 7464: ANALYSE CULTURAL PRODUCT AND PROCESSES AS REPRESENT

DESCRIPTION CLARIFICATIONSO 1: Identify geometric shapes and patterns in cultural products. Shapes and decorations on cultural products in SA

using basic transformations (translation, reflection, rotation).Range: drums, beads, pots, mats, buildings, necklaces, flags, etc.

AC1: Basic transformations are identified. Transformations including translations (up, down, right, left), reflections (limited to the horizontal/x-axis, vertical/y-axis and the line y=x) and rotations (90°, 180° clock/anti-clockwise about the origin).

Symmetry should be covered in terms of reflection.

Describe transformations completely, e.g. translation of 3 units upwards, reflection about the y-axis or rotation of 90° in a clockwise direction about the origin.

AC2: Basic geometric shapes are identified. Shapes such as triangles, circles, ovals, all types of quadrilaterals in different contexts.

AC3: Basic patterns are identified and described. Identify patterns in cultural products e.g. parallel lines, number images, etc.



AC4: Basic patterns are extended in a way that maintains the consistency of the pattern.

Complete/extend given patterns.

SO 2: Analyse similarities and differences in shapes and patterns and effect of colour, used by cultures.

Similarities and differencesRange: circles, rectangles, squares, parallelograms, trapezium, kites.

AC1: Similarities in shapes and patterns are identified. Analyse and compare patterns in terms of similarities and differences.AC2: Differences in shapes and patterns are identified.

AC3: Possible reasons for similarities and/or differences in shapes and patterns used by different cultures are identified. AC4: The effect of colour on shape and symmetry is described and illustrated.

Explain why certain colours are used for specific purposes.

This aspect can be done informally. SO 3: Analyse and explain the way shape and space are used in different epochs and cultures.

Explain the use of space in urban and rural areas.Range: architecture, town and settlement planning.

AC1: Shapes used by different cultures are identified. Shapes identified such as circles, rectangles, squares, parallelograms, trapezium, kites.

AC2: The use of space in different cultures is analysed and explained. Space in architectures e.g. in settlements in KwaZulu Natal (huts) and in a city such as Johannesburg (double story buildings).

AC3: The use of space in different epochs is analysed. Space in different periods/ages e.g. town and settlement planning.

SUMMARY OF COMPETENCIES IN THE UNIT STANDARDS

UNIT STANDARD

KNOWLEDGE COMPETENCY/SKILL

US 7448 Patterns Recognise, identify, complete, generate, represent and describe patterns.

US 7452 Tables, algebraic expressions, graphs, theorem of Pythagoras, trends (increasing/decreasing), minimum/maximum.

Describe and represent relationships.

US 7453 Algebraic expressions, equations, inequalities and formulae.

Simplify, factorise, solve, check and substitute algebraic expressions/equations/inequalities/formulae.

US 7464 Shape, space, transformations, patterns. Identify, describe, extend, analyse, explain, compare shapes and space in cultural context.

7. TAXONOMIES USED IN SCAFFOLDING QUESTIONS

In setting the examination question paper and the SBA Tasks, Barrett’s Taxonomy is used to scaffold the degrees of complexity of questions and tasks. The following table is a simplified and summarised overview of Barrett’s Taxonomy:

TABLE 2: Taxonomy for question papers in MMSC4

CATEGORIES WEIGHTINGKnowledge 20%Routine procedures 35%Complex procedures 30%Problem solving 15%



TABLE 3: Table describing the cognitive levels and their related skills

COGNITIVE LEVEL EXPLANATION OF SKILLS TO BE DEMONSTRATEDKnowledge (20%) Straight recall

Estimation: appropriate rounding off Reading from graphs Substituting in given formulae Stating theorems and definitions Know and use of appropriate vocabulary Use of basic operations: +, -, and , including the use of the calculatorAction verbs: list, define, tell, complete, label, name

Routine Procedures (35%)

Routine calculations: BODMAS, etc. Changing the subject of the formula Manipulation of algebraic expressions: products, factors. Identify patterns and shapes Completion of graphs on given axesAction verbs: Describe, predict, calculate, solve, determine, choose, simplify, extend, complete

Complex Procedures (30%)

Calculations involving more than one step Mathematical reasoning Deductions of rules/formulae Drawing of graph (axes not given)Action verbs: Motivate, determine, calculate, compare, explain

Problem Solving (15%) Analysis of situation Deductions from graphs Explanations of problem situations Identify similarities and differencesAction verbs: Motivate, justify, create/design, explaining, generate

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.

TASK DURATION MARKS TOOL ADDITIONAL INFORMATIONTEST 2 hours 50 Marking

memo Done under controlled conditions. The test can be completed as a whole or be done in parts. A

relevant part of the test can be selected and completed. Time should be adapted accordingly.

By the end of the year, marks should be added to have a total mark out of 50.

ASSIGNMENT 2 weeks 50 Marking memo

Not done under controlled conditions. Learners may use their textbooks or other materials to

complete an assignment.PROJECT 3 weeks 50 Marking

memo or rubric.

Projects can be done at any time, preferable in the second quarter to provide ample time to complete and assess.

The process should be monitored on a regular basis to ensure that learners complete it in time.

WORKSHEET 2 hours 50 Memo Not necessarily completed under controlled conditions. Learners may use their textbooks or other materials to

complete a worksheet. Some parts can be done at home. The worksheet can be completed as a whole or be done in

parts. A relevant part of the worksheet can be selected and completed. Time should be adapted accordingly.

By the end of the year, marks should be added to have a total mark out of 50.

INVESTIGATION

3 hours 50 Memo and rubric

Provided that learners do not copy, the investigation can be given to complete at home.

TOTAL: 250

Convert to 100:

E.g. = 32 (rounded off to nearest integer)

These tasks should be reflected in the Learning Area Assessment Plan (see example below).



EXAMPLE OF A LEARNING AREA ASSESSMENT PLAN

LEARNING AREA: MATHEMATICS AND MATHEMATICAL SCIENCESLEARNING AREA CODE: MMSC4

YEAR: 2009

Assessment Tasks 1 2 3 4 5Form(s) of assessment

Test Assignment Project Worksheet Investigation

US

SOs

US 001 SO 1, 2, 3US 002 SO 1, 3, 4

US 003 SO 1

US 002 SO 5US 004 SO 1

US 001 SO 2, 3US 002 SO 2, 3, 5US 003 SO 1, 3US 004 SO 3

US 003 SO 2, 3

US 001 SO 1, 2, 3

Tools of Assessment

Marking Memo Marking Memo Marking Memo/ Rubric

Marking Memo Marking Memo/ Rubric

Date 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, but you must show ALL calculations.

3. Read the questions carefully before you write the answers.

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

5. Number the answers clearly and in accordance with the numbering system used in this question paper.

QUESTION 1

1.1 Complete the following number patterns by adding two more terms in each case:

1.1.1

1.1.2

1.1.3

1.1.4

1.1.5

72; 75; 78; ___; ___

4; -2; -8; ___; ___

; ; ; ___; ___

2; 8; 32; ___; ___

1; 1; 2; 3; 5; ___; ___

(2)

(2)

(2)

(2)

(2)

1.2 Describe EACH of the number patterns in QUESTION 1.1 (5)

1.3 Write down the first 3 terms of a sequence by following the guidelines:



the first term is 20 divide by 2 to get the next term. (2)

[17]

QUESTION 2

The bar graph below illustrates the relationship between the number of persons per number of rooms in a hostel. Use this information to answer the questions that follow.

Accommodation in Hostel

048

121620242832364044

1 2 3 4 5 6 7 8 9 10

Number of rooms

Num

ber o

f per

sons

2.1 If the number of rooms increases, does the number of persons increase or decrease? (1)

2.2 Describe the pattern of persons in terms of the number of rooms as illustrated by the bar graph. (2)

2.3 Complete the following table by using the bar graph:Number of rooms 1 3 5 8 10Number of persons (5)

2.4 How many people can be accommodated in 19 rooms? (2)

2.5 If half of the rooms can accommodate 4 persons and the other half 2 persons, how many persons can be accommodated in a hostel of 10 rooms? (3)

[13]

QUESTION 3

3.1 Dots are arranged as in the diagram below. Study the pattern of the dots and answer the questions that follow.

3.1.1 Draw the lay-out of the dots for the 4th arrangement. (2)

3.1.2 Copy and complete the following table to show the number of dots required for different arrangements.

Arrangement (n) 1 2 3 4 6 10Number of dots (d) 2 (5)


1st arrangement 2nd arrangement 3rd arrangement


3.1.3 Describe the pattern in your own words. (2)

3.1.4 Hilton wants to find the general term which will express the number of dots (d) in terms of each of the different arrangements (n).He says that since this pattern is linear, the relationship should be in the form d = an + c where

a is the number added each time and c is the number added to a to get the first term

So a = 3 and c = –1 which gives him d = 3n -1.

(a) Show how Hilton got c = –1. (2)

(b) Show through substituting n = 2 and n = 4 whether Hilton’s formula d = 3n – 1 was correct or wrong.

(3)

3.1.5 Determine the number of dots needed for the 20th arrangement. (2)

3.1.6 Which arrangement can be made with 47 dots? (2)

3.2 Use Hilton’s method to determine the general term for the number sequence: 2; 6; 10; 14;… in the form Term n = an + c, where n is the number of the term. Determine a and c first. (2)

[20]

TOTAL: 50

TASK 2: ASSIGNMENT


1. Answer ALL the questions.

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

3. Read the questions carefully before you write down your answers.

4. Write legibly and present your work clearly.

5. Number the answers correctly and clearly.

QUESTION 1

Pythagoras (570 BC to 500 BC) was a Greek mathematician and philosopher, who was credited with the most famous geometric theorem of all time, known as the theorem of Pythagoras. He spent many years in Egypt, studying the Mathematics of the ancient Egyptians, before settling in Italy, where he founded a school of Mathematics and Philosophy. He was also the founder of a secret society, only for men! They believed that the soul was immortal and they were not allowed to eat beans.

1.1 State the theorem of Pythagoras in your own words. (4)

1.2 Consider the given triangle.Complete the following statements with reference to the triangle:

(a) b2 = ………(b) a2 = ………(c) c2 = ……....

(3)

1.3 Three numbers that comply to Pythagoras’s theorem, are called Pythagorean


A

CB

cb

a


Triplets. For example: 3, 4 and 5 is a Pythagorean triplet because 52 = 42 + 32.

Copy and complete the following table to show Pythagorean triplets:

d e d2 + e2 = f2 f9 40 9 + 40 = ( )5 5 + ( ) = (13) 13

8 ( ) + (8) = (17) 17(3)

1.4 Princess Fiona has been captured and is being held captive in a castle by a ferocious dragon. The diagram below shows the journey Shrek and Donkey must take to find Fiona. Note that the diagram is not drawn to scale. All distances are given in metres. The suspension bridge is an arc of a circle with a radius of 100 metres. Use = 3, 1416 in your calculation.

1.4.1 Find the distance that Shrek and Donkey must travel from Duloc (at A) to rescue Princess Fiona (at S). Copy and complete the following table. Round off answers to the nearest metre. Show all your calculations.

Section of journey DistanceACCD 400 m DFFG 250 m GIIJ 800 mJLLM 5000 mMOOPPQ 250 m

(2)

(2)

(2)

(3)

(2)(3)



QSTOTAL(A to S)

(3)(2)

1.4.2 Convert your final answer to kilometers and round it off to the nearest kilometer. (2)

1.5 To reach and work on high spots on the construction site, the builders are using a variety of cherry-picker type cranes as indicated in diagram A below.Diagram B is a simplified diagram with the various lengths indicated.

Use your knowledge of the theorem of Pythagoras to calculate the height AE at which the person is working (see Diagram A). You may use diagram B to assist you to calculate the height AE.Note that ACG is not a straight line. Round off your answer to two decimal places.

(9) [40]

QUESTION 2

2.1 Fully describe the transformation of A to A′ in each of the following diagrams:

2.1.1

(3)


-3 5x

y

0

A A′

Diagram A Diagram B


2.1.2

(3)

2.1.3

(2)

2.2 Find the coordinates of the image of point A(5 ; -4;) after a translation of 6 units upwards and 3 units to the left in the Cartesian plane below.

(2) [10]

TOTAL 50

TASK 3: PROJECT



2. Calculators may be used, but you must show all calculations. ALL answers should be rounded off to one decimal place.


1 2 3 4 5 6 7 80-1 x

y

-2-5 -3-4-6-7

12345

-2-1

-3-4

A(5;-4)

-3 3x

y

0

AA′

-3 3x

y

0

A A′





ACTIVITY 1

Discuss in class whether your ABET centre is accessible for physically disabled persons. Also discuss what can be done to make the centre more accessible.

In this task we will focus on building a ramp to make the centre more accessible. In your discussions identify a suitable area to build the ramp.

Study the specifications for a wheelchair ramp and use it when necessary.

SOUTH AFRICAN BURO OF STANDARDS(SABS)

SPECIFICATIONS FOR CONSTRUCTION OF A WHEELCHAIR RAMP

Minimum length/ base: 40 cmMinimum width: 1,1 mGradient must be 1 : 12

1.1 Let’s take a closer look at the gradient :

1.1.1 Complete the following table:

Height 0,5 1 2 5 xLength/ base 12Gradient

(4)

1.1.2 Use the table to draw a neat line graph by using the following guidelines: Use a suitable scale and show the length/ base on the horizontal axis. (up

to 60 units). Use a suitable scale and show the height on the vertical axis (make

provision for 0,5 unit intervals) Plot the points on the axes and join them with a straight line. Give a suitable name for your graph.

(2)

(2)(3)(1)

1.1.3 Write the gradient of the graph, using the sketch of the triangle in QUESTION 1.1. (1)

1.1.4 Without doing any calculations, write the equation of this straight line in the form h


length/base

12x

x

heig

ht


= ___ where h is the height of the ramp. (1)

1.2 Now we are going to design and build the ramp. The measurements can be done as a class group, but the calculations and drawing must be done individually.

1.2.1 Measure the height of the stairs/ step where you plan to build the ramp. (1)

1.2.2 Use the specifications for the wheelchair ramp to calculate the length of the foundation(base) for your ramp.

(3)

1.2.3 Measure the width of the planned ramp. (1)

1.2.4 Measure the length of the gradient (slope) of the planned ramp. (1)

1.2.5 Check your answer by using the theorem of Pythagoras (4)

1.2.6 With the information available, draw a three-dimensional sketch of the ramp. Include all labels and dimensions.

(3) [27]

ACTIVITY 2

We are going to use concrete, consisting of stone, sand and cement in the proportion 3 : 2 : 1, to build the ramp.

2.1 From your drawings you would have noticed that the ramp has the shape of a triangular prism. The volume of this prism is given by V = ½ base height widthCalculate the volume of concrete needed to build the ramp.

(3)

2.2 Use the proportion given above to calculate the volume of stone, sand and cement needed to build the ramp.

(4)

2.3 Using mathematical language/ concepts, write a report on how you designed the ramp and how you calculated the volumes for mixing the concrete.

(8)

2.4 Construct/ build a neat scale model of your ramp by using cheap material and hand it in. (8)

CriteriaRubric for 2.3 and 2.4

Levels Mark161 2 3 4

Mathematical concepts/ language used

Used no concepts. No attempt to use mathematical language.

Used 1 – 2 concepts. Made some attempt to use mathematical language. Did not communicate ideas

Used 3 – 4 concepts. Used mathematical language clearly and correctly.

Used more than 4 concepts. Used appropriate mathematical language. Good



Communication poor.

clearly. communication.

Explanation No effort made to explain.

Inconsistent explanation of concepts.

Explanations clear and appropriate.

Clear, unambiguous and detailed explanation.

Scale Model Not to scale. Only one dimension to scale

Two dimensions to scale.

All dimensions to scale.

Presentation/ Decoration

Offered untidy model. Loose structure.

Made an effort to decorate model. Structure not firm enough.

Model neatly decorated. Structure firm.

Model exceeds immediate requirements. Structure extremely firm.

TOTAL [23]

TOTAL 50

TASK 3: WORKSHEET


1. Answer ALL the questions ON THE WORKSHEET.


3. Read the questions carefully before you write the answers.

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

QUESTION 1

Study the FOIL-rule to simplify (a + b)

= a.a + a.b + b.a + b.b

F O I L

= a + ab + ab + b = a + 2ab + b

Therefore ( a + b ) = a + 2ab + b . . . . . . . . . Square Rule

term 1 term 2 term 3

1.1 Calculate (p – q) in two different ways:

1.1.1 Using the FOIL-rule:(p – q) = _____________________________________________


(a + b) = ( a + b ) ( a + b )

Inner terms

First terms Last terms

Outer terms


__________________________________________________________________________________________________________ (2)

1.1.2 Using the Square rule directly: (p – q) = ____________________________________________ (2)

1.1. 3 When using the Square rule, explain:

(a) How did you determine term 1?__________________________________________________________________________________________________________

(1)

(b) How did you determine term 2?__________________________________________________________________________________________________________

(1)

(c) How did you determine term 3?_________________________________________________________________ (1)

1.2 Calculate (3x + y) in two different ways:

1.2.1 Using the FOIL-rule: (3x + y ) = ___________________________________________ _____________________________________________________ _____________________________________________________ (2)

1.2.2 Using the Square rule directly: (3x + y ) = ___________________________________________ (2)

1.2.3 When using the Square rule, explain:

(a) How did you determine term 1?__________________________________________________________________________________________________________ (1)

(b) How did you determine term 2?__________________________________________________________________________________________________________ (1)

(c) How did you determine term 3?________________________________________________________________________________________________________

(1)

1.3 Calculate the following by using only the Square rule:

1.3.1 (2a – b) = ____________________________________________ (2)

1.3.2 (x + 3y) = ____________________________________________ (2)

1.3.3 (2x – y) = ____________________________________________ (2)

1.3.4 (3x + 2y) = ___________________________________________ (2)

1.3.5 (4p – 3q) = ___________________________________________ (2)

[24]QUESTION 2



Study the FOIL-rule to solve (a + b)(a – b)

= a.a – a.b + b.a – b.b

F O I L

= a – ab + ab – b = a – b

Therefore ( a + b )(a – b) = a – b . . . . .Difference-of-squares rule term 1 term 2

REMEMBER: For this rule, always use minus between squares.

2.1 Calculate (x – y)(x + y) in two different ways:

2.1.1 Using the FOIL-rule:(x – y)(x + y) = _________________________________________ (2)

2.1.2 Using the Difference-of-squares rule directly: (x – y)(x + y) = ________________________________________ (2)

2.2 When using the Difference-of-squares rule, explain:

2.2.1 What do you notice about the first terms in each of the given brackets? __________________________________________________________________________________________________________ (1)

2.2.2 What do you notice about the second terms in each of the given brackets ?__________________________________________________________________________________________________________

(1)

2.2.3 How did you determine term 1 of your answer?__________________________________________________________________________________________________________ (1)

2.2.4 How did you determine term 2 of your answer? (Note the sign in particular)__________________________________________________________________________________________________________ (1)

2.2.5 What do you notice about the number of terms? Explain your answer. __________________________________________________________________________________________________________ (1)

2.3 Write down only answers by using the difference-of-squares rule:


(a + b)(a – b) = ( a + b ) ( a – b )

Inner terms

First terms Last terms

Outer terms


2.3.1 (x + 2) (x – 2) = ________________________________________ (2)

2.3.2 (2a – b) (2a + b) = ______________________________________ (2)

2.3.3 (3x + y) (3x – y) = _______________________________________ (2)

2.3.4 (4p – q) (4p + q) = _______________________________________ (2)

2.4 Study your answers and explain why you think this rule is called the Difference-of-squares rule.____________________________________________________________________________________________________________________________ (2)

[19]

QUESTION 3

REVERSING THE PROCESS TO DETERMINE FACTORS

1. CHECKPOINTS FOR SQUARES RULE: three terms first term and last terms are squares middle term is 2(square root of term1)(square root of term3) answer: [the sign comes from term2)

Example: Factorise: 4a – 4ab + b Check for Squares rule:

three terms: Yes. 4a and + b are squares. middle term is 2(2a)(b) answer: (2a – b)

2. CHECKPOINTS FOR DIFFERENCE-OF-SQUARES RULE: two terms first term and second term are squares sign between terms is a minus answer:

Example: Factorise: 9a – b Check for Difference-of-squares rule:

two terms: Yes 9a and b are squares – between terms answer: (3a – b)(3a + b)

Factorise the following completely:

3.1 4p – 1 = _____________________________________________________ (1)

3.2 9x – 4 = _____________________________________________________ (1)

3.3 16x – 25 = ___________________________________________________ (1)

3.4 = __________________________________________________ (2)

3.5 = __________________________________________________ (2)[7]



TOTAL: 50

TASK 4: INVESTIGATION



2. Calculators may be used.




6. Hand in the envelopes that you used in ACTIVITY 2 together with your answers as evidence.

ACTIVITY 1

Fibonacci sequences is a special kind of number pattern developed by Leonardo Pisano (1170 B.C – 1250 B.C), better known as Fibonacci. This sequence looks like this:

It is extremely useful and appears in many different areas in science, mathematics and daily life. In this activity we are going to investigate Fibonacci sequences more.

1.1 Look at the pattern above and write down the first 12 terms in the sequence. (2)

1.2 Can the following be classified as Fibonacci numbers? Explain your answer.

1.2.1 610 (2)

1.2.2 2 584 (2)

1.3 Use the first 12 Fibonacci numbers.

1.3.1 Add the first 5 numbers and compare the answer with the 7 th number. Determine the difference.

(2)

1.3.2 Add the first 6 numbers and compare the answer with the 8 th Number. Determine the difference.

(2)

1.3.3 Describe any pattern you observed while answering ACTIVITY 1.3.1 and ACTIVITY 1.3.2.

(2)

1.3.4 Do you think this observation will hold for any series of Fibonacci numbers? Check by doing it for the first 12 numbers (i.e. add the first 12 numbers and compare the answer with the 14th number).

(3)

1.4 Choose any three consecutive Fibonacci numbers. Do the following: Square the middle number(A) Find the product of the numbers on either side of the middle number(B) Find the difference between A and B

1.4.1 Copy and complete the following table:Consecutive Fibonacci numbers

Square of the middle number(A)

Product of numbers on either side(B)

Difference between A and B


1; 1; 2; 3; 5; 8; 13; …


1; 1; 2 1 2 -11; 2; 3 4 3 +12; 3; 5 9 10 -13; 5; 85; 8; 13

8; 13; 2113; 21; 3421; 34; 5534; 55; 8955; 89; 144

(7)

1.4.2 What do you observe? (2)

1.4.3 Will this observation hold for the continued Fibonacci sequence?Check the truth of your observation by using a set of 3 consecutive Fibonacci numbers that is not in the table and write down your conclusion.

(3)

1.5 Divide any two consecutive Fibonacci numbers. Write the answer as a decimal. You may use a calculator.

1.5.1 Use a table like below to organise your results.Consecutive Fibonacci numbers

Division of Fibonacci numbers

Answer as a decimal. (approaches Golden ratio)

1; 1 1÷12; 1 2÷13; 2 3÷25; 3 5÷3

Continue for at least six more pairs

(5)

1.5.2 Choose any number from your answers you think could be the Golden Ratio. (1) [33]

ACTIVITY 2

The number 1,618 is called the GOLDEN RATIO. Let’s investigate the Golden ratio on envelopes.Collect at least 5 envelopes of different sizes.Hand in your envelopes as evidence.

2.1 Measure the length and width of the envelopes. Record your data in an ordered way and

calculate the ratio for each.

2.2Identify the envelope with a shape nearest to the Golden ratio, that is where 1,618.

2.2.1 Cut off a square (with side length equal to the width) from your identified envelope.

2.2.2 Measure the sides of the remaining rectangle. Record your results

and calculate . Is the remaining rectangle golden?

2.2.3 Repeat ACTIVITY 2.2.1 and ACTIVITY 2.2.2 for the remaining rectangle.



2.2.4 Continue the process of cutting off a square for as long as you can. After each cutting off of a square, repeat ACTIVITY 2.2.1 and ACTIVITY 2.2.2

2.2.4 Write down your findings.

This activity will be assessed using the rubric that follows after ACTIVITY 3. [12]

ACTIVITY 3

Make your own Fibonacci sequence:

3.1 Take any two numbers between 0 and 10.

3.2 Apply Fibonacci’s method by adding the two numbers to get the following number and continue for up to 12 numbers.

(2)

3.3 Name your sequence. (1)

3.4 Show by giving an example that your sequence tends to be Golden. (2) [5]

Assessment rubric for ACTIVITY 2

CriteriaLevel

Mark121 2 3 4

Organisation and recording of data

Made no attempt to organize data, Did not use tables. Recorded in a muddled way

Did some classification. Used tables. Made minor errors in recording.

Classified data correctly. Worked in an organized way. Recorded results in a table.

Organised results well. Classified correctly and recorded results clearly in a table.

Correctness of calculations

Made major mistakes in calculation.

Made minor mistakes in calculations.

Made no errors in calculations.

Carried out operations accurately and completely.

Identification of patterns/ mathematical reasoning

Found no patterns, Showed no logical reasoning.

Identified some patterns. Did not reason clearly and consistently.

Identified and described patterns correctly. Was able to reach a consistent conclusion.

Identified and described patterns correctly. Used variables and used them effectively. Offered strong supporting arguments and proper logical reasoning.

Total[Acknowledgement: Adapted from My Clever Mathematics through Issues Gr 9 – Ina Nel, Marilyn Schmidt and Gerrit Stols. Copyright Clever Books]

TOTAL 50

9. EXTERNAL ASSESSMENT (SUMMATIVE)

The summative assessment component of the MMSC4 learning comprises 50% of the total assessment. The policy on the Conduct, Administration and Management of the GETC-ABET Level 4 Examinations gives details


1; 1; 2; 3…


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:

GENERAL LAYOUT OF THE QUESTION PAPER

a) FRONT COVERGives information regarding:

Learning Area: MMSC4 Examination: date and year Duration: 3 hours Total of marks: 100 Number of pages including diagram sheets

b) INSTRUCTIONS The following general instructions are usually given at the beginning of the paper:

1. Answer all questions.2. Calculators may/may not be used.3. Read the questions carefully.4. Write legibly and clearly.5. Show all your calculations.6. Number the answers correctly and clearly.7. Write in blue or black ink.

Specific instructions can be given in certain questions, e.g. round off to one decimal place, use the formula given, etc.

c) QUESTIONS All questions must be answered. The following numbering system is followed:

QUESTION 11.1 Solve …….. 1.1.1 ……….. (2)

1.1.2 ……….(a) …………. (4)

(b) …………. (i) ……….. (2) (ii) ……….. (3)

1.2 Determine ………. (5) (Total for question) [16] (Total for paper) TOTAL: 100

The structure of questions usually progress from easy to more complex. Questions usually cover one Unit Standard at a time, assessing different competencies. However, it may

happen that more than one Unit Standard can be assessed in an integrated way in a question. Accompanying diagrams are not drawn to scale, except when stated.

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: MATHEMATICS AND MATHEMATICAL SCIENCES

CODE: MMSC4

DATE: OCTOBER 2008

TIME: 3 HOURS

MARKS: 100This question paper consists of 8 pages.


1. Answer ALL the questions in your ANSWER BOOK.


3. Read the questions carefully before you write your answers.



6. Write the answers in blue or black ink.

QUESTION 1

1.1 Continue the following number patterns by adding two more terms to each pattern.

1.1.1 2 ; 8; 14; … ; …; (2)

1.1.2 3; 2; 7; … ; …; (2)

1.1.3; ; ; … ; …; (2)

1.2 Is the pattern in QUESTION 1.1.2 increasing or decreasing? Motivate your answer. (3)



1.3 Study the patterns of blocks made with matches in the diagrams given below and then answer the questions that follow.

1.3.1 Continue the pattern by drawing the patterns for 4 blocks and 5 blocks in the answer book. (2)

1.3.2 Redraw the following table and use the patterns in QUESTIONS 1.3 and 1.3.1, amongst others, to complete the table that shows the number of matches used for different blocks.

Number of blocks 1 2 3 4 5Number of matches 4 7

(3)

1.3.3 Describe the pattern(s) in your own words. (2)

1.3.4 How many matches are required to build 10 blocks? Explain in words how to determine this answer. (3)

1.3.5 Determine a general rule for the number of matches (n) needed to build a certain number of blocks (b) in the form n = … (2)

1.3.6 Use your rule, or any other method, to determine how many blocks can be built using 100 matches.

(3) [24]

QUESTION 2

The diagram below shows a straight line which is drawn through the points A(3; 4) and B(5; 12) on a Cartesian plane.

2.1 Calculate the gradient of AB using the formula

, where m is the gradient and


B(5; 12)

A(3; 4)y

x0

1 block

2 blocks

3 blocks


and are two points on AB. (2)

2.2 Show that the equation of AB is given by y = 2x 2. (3)

2.3 Write down the value of the y-intercept of AB. (1)

2.4 Determine the x-intercept of the graph of AB. (2)

2.5 Choose the correct word from those given in brackets. Write only the word next to the question number (2.5.1 – 2.5.2) in the answer book:

2.5.1 The gradient of the graph is (positive / negative) (1)

2.5.2 The value of y (increases / decreases) as the x-values increase. (1) 2.6 If AB is shifted 3 units downwards, what will be the value of the new y-intercept? (2)

[12]

QUESTION 3

For some extra income, Tracy sells hamburgers at R9 a piece at the market.

3.1 Copy and complete the following table to show the amount paid for a certain number of hamburgers.

Number of hamburgers 1 2 3 4 8Amount in Rand 9 (4)

3.2 Use the information in the table in QUESTION 3.1 and draw a line graph using the following guidelines:

Use a suitable scale and show the amount in Rand on the vertical axis. Use a suitable scale and show the number of hamburgers on the horizontal axis. Give a suitable title for the graph. Plot the points and join them with a broken line.

(2)(2)(1)(3)

3.3 Use the graph to determine the amount paid for 7 hamburgers. Draw dotted lines and indicate with the letter A where you read the answer on the graph. (3)

3.4 Tracy makes a profit of R3 per hamburger sold. If she had R387 in her pocket from selling hamburgers after a day’s work, what was her total profit? (4)

[19]

QUESTION 4

4.1 Jabu bought (ab² c) apples, (ab² c + 4) oranges and (2c 5) bananas.

4.1.1 Calculate the total number of fruits he bought. (3)

4.1.2 If a = 2; b = 5 and c = 4, how many oranges did he buy? (3)

4.2 Simplify the following: 2a² 6a + 4a(a + 3) (4)

4.3 Factorise the following expressions completely:

4.3.1 (x 3)(a + b) + 3(a + b) (3)



4.3.2 x² 5x 6 (2)

[15]

QUESTION 5

5.1 Solve the following inequality and represent the solution on a number line.3x 10 2x 2 (3)

5.2 Two-fifths of the learners in an ABET class were absent one day. If 14 learners were absent, how many learners are there in the class in total?

(3)

5.3 The circumference of a circle is given by C = 2r, where

C = circumference, r = radius and = 3,14Calculate the circumference of the circle if the radius = 8 cm.

(2)

5.4 To extinguish a fire on the tenth floor, 40 metres from the ground, the fire brigade uses a ladder that is 41 metres tall and places it across the width of a road on ground level to lean against the building as in the illustration below.

5.4.1 Complete the following: (a) The ladder, the building and the road form a … triangle.(b) State the Theorem of Pythagoras in words.

(1)(1)

5.4.2 Calculate the width of the road (BC) using the Theorem of Pythagoras. (6)[16]

QUESTION 6

6.1 The point A(–4; –1) in the diagram below is translated (shifted) 6 units upwards in the Cartesian plane. Give the coordinates of the image A, if A is translated to A.


Ladder = 41 m

Road

Heig

ht

= 40

mA

B C

y

x0A(–4; –1)

A


(2)

6.2 Describe the transformation from C to D completely in the diagram below:

(2)

6.3 Choose the correct word from those given in brackets. Write only the word next to the question number in the answer book:

If the horizontal line AB in the diagram below is rotated through 90° in a clockwise direction about the origin, the image will be a (horizontal/vertical) line.

(1)

6.4 Study the picture below which shows part of a woven cushion, and answer the questions that follow:

6.4.1 Name THREE different shapes that can be found in the picture. (3)

6.4.2 Give TWO lines of symmetry in the picture. (2)

6.4.3 Name TWO properties that are found in all squares, but not in all parallelograms. (2)

6.4.4 What role does the different shades of black and white play in the picture? (1)

6.5 Why do you think buildings are mostly built in a rectangular form and not round? (1) [14]


y

x0

C D

y

x0A B

B C D EA

K

L F

GHIJ


TOTAL: 100

This memorandum consists of 7 pages

QUESTION 1 US 001 SO 1, 2, 3

[24]

NUMBER EXPECTED ANSWER(S) COMMENTS MARKS

1.1.1

1.1.2

1.1.3

20 ; 26

12 ; 17

; OR ; OR ;

Correct terms

Correct terms

Correct terms

(2)

(2)

(2)

1.2. Decreasing. Each time 5 is subtracted OR Decreasing –5 is added each time

Correct choice.Any valid reason showing decrease: 2 marks

(3)

1.3.1.

Correct number of matches(1 per pattern)

(2)

1.3.2 Number of blocks 1 23

45

Number of matches 4 7 10 13 16

Correct table values

(3)

1.3.3 Pattern increasing by 3 matches each time OR add 3 matches each time OR multiply number by 3 and add 1

Increase/add (1 mark)3 (1 mark) (2)

1.3.4 31 matches Multiply the number of blocks by 3 and add 1.

Correct answer (2)Valid reason(1) (3)

1.3.5 n = 3b + 1 3b (1 mark) + 1 ( 1 mark) (2)


A

KEY: A Accuracy

CA Consistent Accuracy

AA

A

A A AAA

CA

4 blocks

5 blocks

A

A

CA

A

A

AAA

A A

A

CA

CA

CA

A A

CA CAA


1.3.6 3b + 1 = 1003b = 99 b = 33 blocks

n= 100 ( Formula from 1.3.5)SimplifyCorrect answer (3)

QUESTION 2 US 002 SO 2, 3, 5 [12]


2.1 = = = 2

OR = = 2

Substitution in formula

Correct answer (accept any one)

(2)

2.2 y = mx + c = 2x + cSubst. (3; 4): 4 = 2(3) + c 4 – 6 = c – 2 = cOR y = mx + c = –2 x + cSubst. (5; 12): 12 = 2(5) + c c = 2y = 2x 2OR y – y1 = m(x – x1)Subst. (3; 4): y – 4 = -2(x – (-3)) = -2(x + 3) = -2x -6 y = -2x - 2OR Subst. (5; 12): y – (-12) = -2(x – 5) y + 12 = -2x + 10 y = -2x - 2

Substitute m Substitute point

Finding cAnswer only: No marks

(3)

2.3 2 OR y = 2 OR (0; 2) Correct answer (1)

2.4 y = 2x 2 Let y = 0 -2x 2 = 0 2x = 2 x = 1 OR (1; 0)

Letting y = 0Correct answerAnswer only: Full marks (2)

2.5.1 Negative Correct answer (1)

2.5.2 Decreases. Correct answer (1)

2.6 y-intercept = –2 – 3 = 5 OR y = 5 OR (0; 5)

Subtract 3Correct answerAnswer only: 2 marks (2)

QUESTION 3


CACA

ACA

CA

A

A

A

M

CAA

A

A

A

A CA

CAM

CA

CA

A

A

CAACA

CA

A A

A

CA

A


US 002 SO 1, 3 [19]


3.1 Number of Hamburgers 1 2 3 4 8Amount in Rand 9

18273672

Correct table values

(4)

3.2

Graph:3.2(8) marks on graph

[3.3(2) marks on graph]

If axes swapped: subtract 2 marks(if everything else is correct)

3.3 R63Dotted linePosition of A on graph

Correct value from graph (can also be given on graph)Dotted line Position of A (3)


A

AAA

CAM

CA

CA

(3.3)

(position of A)

Selling hamburgers

A

(3.2

)

(sca

le o

n ve

rtica

l axi

s)

36.45.

.1

.2

.3

.4

9..5

.6

18.27.

54. 63.72.

.(3.2)

(scale on horizontal axis)

(plotting first 3 points)

(plotting last 2 points)

(title of graph)

(dotted lines)

(3.2)

(3.2)

(3.3)

(3.2)

(3.2)

(broken line)

M

M

M

Am

ount

in R

and

M

Number of HamburgersM

CA

CA

M

M

.7

.8

CA

..

.

(3.2)

(labeling horizontal axis)

(3.2

)

(lab

elin

g ve

rtica

l axi

s)

.

0


3.4Hamburgers sold: = 43

Profit: 43 X R3 = R129

OR = R 129

Divide amount by 9Correct answerMultiply answer by R3Correct answerFull marks

Answer only: 2 marks

(4)

QUESTION 4 US 003 SO 2, 3 [15]

NUMBER EXPECTED ANSWER(S) COMMENTS MARKS4.1.1 ab² c

ab² c + 4 2 c 5 2ab² 1

2ab² 0c 1 (3)

4.1.2 ab² c + 4=(2)(5)² (4) + 4=2(25) 4 + 4= 50 oranges

SubstitutionSquaring 5Correct answer (3)

4.2 2a² 6a + 4a(a + 3)= 2a² 6a + 4a² + 12a = 6a² + 6a

Simplify bracket: 4a² + 12aCorrect answer

(4)

4.3.1 (x 3)(a + b) + 3(a + b)=(a + b)(x 3 + 3)=x(a + b) OR (a + b)x

OR: xa + xb – 3a – 3b + 3a + 3b= xa + xb= x(a + b)

Taking out common factor(a + b)Grouping: (x -3 + 3)Simplify (x 3 + 3) = x

(3)

4.3.2 x² 5x 6 = (x + 1)(x 6) Correct terms (2)

QUESTION 5 US 004 SO 3 [16]


5.1 3x 10 2x 2x 8 Solving x

Arrow to rightIncluding 8 (3)

5.2 Let number of learners = x

x = 14

= 14 x

= 35 learners

OR of learners = 7

Equating

Multiply by

Correct answer


AA A

A

CACA

A ACA

AA

CA

A A

A CA

80

CA

M

CA

A

A

CACA

CA

MA CA

A

ACA

A

CA

A A


Total learners = 7 x 5 =35 (3)

5.3 C = 2r = 2(3,14)(8) cm = 50,24 cm

SubstitutionCorrect answer (2)

5.4.1 (a) right-angled(b) In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.

Correct answer

Correct answerAccept: AC2 =BC2 + AB2

(1)

(1)

5.4.2 (Ladder)² = (Building)² + (Road)²(41 m)² = (40 m)² + (Road)² 1681 m² = 1600 m² + (Road)² (Road)² = 1681 m² 1600 m² = 81 m² Road = 9 m

OR(Road)² = (Ladder)² - (Building)² =(41 m)² (40 m)² = 1681 m² 1600 m² = 81 m² Road = 9 m

ORBC2 + AB2 = AC2 BC2 + (40 m)2 = (41 m)2 BC2 = (41 m)² (40 m)² =1681 m² 1600 m² = 81 m² BC = 9 m

FormulaSubstitutionCorrect Squaring

SimplifyingSquare rootCorrect unit

(6)

QUESTION 6 US 004 SO 1, 2, 3 [14]


6.1 A(4; 5) Correct coordinates (2)

6.2 Reflection about the y-axis Reflectiony-axis (2)

6.3 vertical Correct answer (1)

6.4.1 Squares, rectangles, rhombi, parallelograms, triangles, kites, quadrilaterals, diamond shape

Any 3 correct shapes

(3)


CAMA

A M

CAA

CAA

MACA

CAA

CA

CA

CA

M A

CACA

A

A A

AA A

A A

A A

A


6.4.2 CI , LF, BJ or DH Any 2 correct lines (2)

6.4.3 Square: All sides equal / all angles = 90° / diagonals are equal / diagonals bisect each other perpendicularly (with an angle of 90°)

Any 2 differences

(2)

6.4.4 Makes different patterns OR shapes visible OR Give strong effect to picture OR Makes picture viewable.

Any relevant role.(1)

6.5 Rectangles fit nicely together (can tessellate). OR Rectangular shapes are easy to built OR rectangular forms are more stable than round forms, etc.

Any relevant reason

(1)

TOTAL: 100

MARKING THE QUESTION PAPER

i. Follow-up principalIf a sum is incorrect, the mark will not be 0 out of the total, but only the mistake is penalised. The learner can still obtain the rest of the marks if the other steps are done correctly.

ii. Writing down only answerWhen a learner write down only the answer and does not show any calculations, he/she should be penalised. The learner must consider the instruction: “Show all the calculations”.

iii. Symbols used with marksThe symbols accompanying the marks indicated on the memo are A, CA and M. The explanation if these symbols are: A = Accuracy: The answer should be exactly what is on the memorandum.CA = Consistent Accuracy: The answer must be checked according to the previous step of the learner,

even if the previous step is incorrect. M = Method: This answer usually is a formula/theorem or directly derived from a formula/theorem and is

mathematical concepts.

iv. Guidelines Marking at site level is done with a red pen, while moderation is done with a green pen. The memorandum serves as a guideline to teachers to standardise the allocation of marks. It is

important for learners to know how marks are allocated in the examination/tests.

10. PROMOTING THE PRINCIPLES OF QUALITY ASSESSMENT PRACTICES

The Department of Higher Education and Training 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


A A

A

A


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,

Assessment grids,Rubrics,Memoranda andObservation sheets.

Baseline,Diagnostic,Formative,Summative andSystemic.



Worksheets,Questionnaires,Cassettes, Posters,

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.


GETC-ABET Level 4 Examination Guidelines Draft Curriculum Statements... · Web viewPythagoras (570 BC to 500 BC) was a Greek mathematician and philosopher, who was credited with the

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