GETC-ABET Level 4 Examination Guidelines
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. |INTRODUCTION |
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 |SUBFIELD |
|National Certificate |Field 05 - Education, Training and |Adult Learning |
| |Development | |
|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 |
| |
|One Official Language: 23 Credits |
|Mathematical Literacy: 16 Credits OR |
|Mathematics and Mathematical Sciences: 14 Credits NOT BOTH |
|CORE COMPONENT: COMPULSORY 32 CREDITS |
| |
|Life Orientation: 32 Credits |
|ELECTIVES COMPONENT: OPTIONAL 49 OR 51 CREDITS |
| |
|Academic Learning Areas: |
| |
|Human and Social Sciences: 23 Credits |
|Natural Sciences: 15 Credits |
|Economic and Management Sciences: 21 Credits |
|Arts and Culture: 17 Credits |
|Technology: 11 Credits |
|One Additional Official Language (Excluding the language chosen as a Fundamental): 23 Credits |
| |
|Vocational Learning Areas: |
| |
|Applied Agriculture and Agricultural Technology: 20 Credits |
|Ancillary Health Care: 45 Credits |
|Small, Medium and Micro Enterprises: 17 Credits |
|Travel and Tourism: 38 Credits |
|Information Communication Technology: 23 Credits |
|Early Childhood Development: 26 Credits |
|Wholesale and Retail: 30 Credits |
|OPTION 1 |OPTION 2 |OPTION 3 |
|( 5 Learning Areas) |( 6 Learning Areas) |( 7 or more Learning Areas) |
| | | |
|TWO Fundamentals |TWO Fundamentals |TWO Fundamentals |
|ONE Core and |ONE Core and |ONE Core and |
|TWO Electives |THREE Electives |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 |CREDITS |
|7448 |Work with patterns in various context |4 |
|7452 |Describe , represent and interpret mathematical models in different context |6 |
|7453 |Use algebraic notations, conventions and terminology to solve problems |3 |
|7464 |Analyse cultural products and processes as representations of shape, space and time |3 |
| | Total |16 |
|SAQA US ID |US TITLE |CREDITS |
|7448 |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.
SPECIFIC OUTCOMES AND ASSESSMENT CRITERIA:
|SPECIFIC OUTCOME 1 |SPECIFIC OUTCOME 2 |SPECIFIC OUTCOME 3 |SPECIFIC OUTCOME 4 |SPECIFIC OUTCOME 5 |
|Recognise, identify and describe patterns |Complete, extend and generate patterns in a|Devise processes for a general rule |Represent patterns using different |Use general rules to generate |
|in various contexts |variety of contexts | |generalised mathematical forms |patterns. |
| | |OUTCOME RANGE | | |
|ASSESSMENT CRITERIA |OUTCOME RANGE |Processes include: systematic counting, |OUTCOME RANGE |OUTCOME RANGE |
|ASSESSMENT CRITERION 1 |Numeric, geometric, patterns from a variety|sequencing numbers, tables, drawings, pictures, |Graphs, formulae, expressions and other |Processes include: systematic counting,|
|Patterns are recognised in terms of the |of contexts |classification, organised lists, mathematical |rules for expressing patterns |sequencing numbers, tables, drawings, |
|relationship between the elements of the | |and models such as graphs | |pictures, classification, organised |
|pattern. |ASSESSMENT CRITERIA | |ASSESSMENT CRITERIA |lists, mathematical models such as |
| |ASSESSMENT CRITERION 1 |ASSESSMENT CRITERIA |ASSESSMENT CRITERION 1 |graphs. |
|ASSESSMENT CRITERION 2 |Completed patterns are internally |ASSESSMENT CRITERION 1 |Appropriate mathematical forms are used to | |
|Patterns are correctly identified in terms |consistent with respect to the relationship|Appropriate processes are devised according to |represent patterns |ASSESSMENT CRITERIA |
|of the relationship between the elements of|between elements of the pattern. |the context | |ASSESSMENT CRITERION 1 |
|the pattern. | | |ASSESSMENT CRITERION 2 |Patterns generated are consistent with |
| |ASSESSMENT CRITERION 2 |ASSESSMENT CRITERION 2 |The representation is consistent with |the general rule |
|ASSESSMENT CRITERION 3 |The extension is consistent with respect to|Processes have potential to lead to a general |relationships within the pattern and | |
|Patterns are correctly described in terms |the relationship between elements of the |rule |represents the pattern completely. |ASSESSMENT |
|of the relationship between the elements of|pattern | | |CRITERION 2 |
|the pattern and remain consistent through | |ASSESSMENT CRITERION 3 |ASSESSMENT CRITERION 3 |Patterns are generated to the extent |
|the pattern |ASSESSMENT CRITERION 3 |A general rule is devised such that it is |Conversions are made between various forms |that they enable the rule to be devised|
| |Generated patterns are internally |consistent with the relationship of the elements|of representations |from the patterns |
|ASSESSMENT CRITERION 4 |consistent |of the patterns | | |
|The language of comparison is appropriate |. | |ASSESSMENT CRITERION 4 | |
|and describes the relationship between the | | |Relationships between various possible | |
|elements of the pattern. | | |forms of representations are described | |
|SAQA US ID |US TITLE |CREDITS |
|7452 |Describe , represent and interpret mathematical models in different context | |
| | |6 |
PURPOSE OF THE UNIT STANDARD
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
LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING
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 1 |SPECIFIC OUTCOME 2 |SPECIFIC OUTCOME 3 |SPECIFIC OUTCOME 4 |SPECIFIC OUTCOME 5 |SPECIFIC OUTCOME 6 |
|Describe and represent relationships |Describe and represent relationships |Describe and represent relationships |Describe and represent relationships |Analyse and explain the behaviour of |Analyse and explain the behaviour of |
|in a variety of contexts using tables|in a variety of contexts using simple|in a variety of contexts using graphs|in a variety of contexts |graphs in terms of increasing and |general algebraic equations and |
| |algebraic expressions | |geometrically |decreasing trends. |formulae |
| | |OUTCOME RANGE | | | |
|OUTCOME RANGE |OUTCOME RANGE |Simple linear, quadratic and |OUTCOME RANGE |OUTCOME RANGE |OUTCOME RANGE |
|Simple linear, quadratic and |Simple linear, quadratic and |exponential relationships and simple |Heights and distances using |Limited to situations where the |Linear and quadratic equations |
|exponential relationships. |exponential relationships. |cyclical relationships such as trig |right-angled triangles. |information can be directly read off | |
|Relationships may be given in the |Relationships may be given in the |functions. | |the graph |ASSESSMENT CRITERIA |
|form of words, equations, and graphs |form of words, tables, and graphs or |Number lines for inequalities. |ASSESSMENT CRITERIA | |ASSESSMENT CRITERION 1 |
|or as a result of experiments |as a result of experiments |Relationships may be given in the |ASSESSMENT CRITERION 1 |ASSESSMENT CRITERIA |The dependent and independent |
| | |form of words, tables, and equations |The descriptions are consistent with |ASSESSMENT RITERION 1 |variables are identified |
|ASSESSMENT CRITERIA |ASSESSMENT CRITERIA |or as a result of experiments |the given relationship |The variables are identified | |
|ASSESSMENT CRITERION 1 |ASSESSMENT CRITERION 1 | | | |ASSESSMENT CRITERION 2 |
|Independent and dependent variables |Independent and dependent variables |ASSESSMENT CRITERIA |ASSESSMENT CRITERION 2 |ASSESSMENT CRITERION 2 |The potential or existing |
|are identified |are identified |ASSESSMENT CRITERION 1 |The representation is consistent with|The potential or existing |relationships between variables are |
| | |Independent and dependent variables |the given relationship |relationships between variables are |described |
|ASSESSMENT CRITERION 2 |ASSESSMENT CRITERION 2 |are identified | |described | |
|The descriptions are consistent with |The descriptions are consistent with | |ASSESSMENT CRITERION 3 | |ASSESSMENT CRITERION 3 |
|the given relationship |the given relationship |ASSESSMENT CRITERION 2 |Sufficient information is represented|ASSESSMENT CRITERION 3 |The increasing and decreasing trends |
| | |The descriptions are consistent with |in such a way that the relationship |The increasing and decreasing trends |are described |
|ASSESSMENT CRITERION 3 |ASSESSMENT CRITERION 3 |the given relationship |is evident. |are described | |
|The representation is consistent with|The representation is consistent with| | | | |
|the given relationship |the given relationship |ASSESSMENT CRITERION 3 | |ASSESSMENT CRITERION 4 | |
| | |The representation is consistent with| |The maximum and minimum are | |
|ASSESSMENT CRITERION 4 |ASSESSMENT CRITERION 4 |the given relationship | |identified | |
|Sufficient information is represented|Sufficient information is represented| | | | |
|in such a way that the relationship |in such a way that the relationship |ASSESSMENT CRITERION 4 | | | |
|is evident |is evident |Sufficient information is represented| | | |
| | |such that the relationship is evident| | | |
|SAQA US ID |US TITLE |CREDITS |
|7453 |Use algebraic notations, conventions and terminology to solve problems |3 |
PURPOSE OF THE UNIT STANDARD
People credited with this unit standard are able to:
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
LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING
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 OUTCOMES AND ASSESSMENT CRITERIA:
|SPECIFIC OUTCOME 1 |SPECIFIC OUTCOME 2 |SPECIFIC OUTCOME 3 |
|Form and use algebraic equations and inequalities to represent and |Manipulate algebraic expressions to find equivalent forms |Select and use algebraic formulae to solve problems |
|solve problems | | |
| |OUTCOME RANGE |OUTCOME RANGE |
|OUTCOME RANGE |Common factors, products and grouping using associative, distributive|Substitution into any formula, solve for one variable, supplied |
|Simple linear equations and inequalities |and commutative properties |formulae from any context |
| | | |
|ASSESSMENT CRITERIA |ASSESSMENT CRITERIA |ASSESSMENT CRITERIA |
|ASSESSMENT CRITERION 1 |ASSESSMENT CRITERION 1 |ASSESSMENT CRITERION 1 |
|The problem is represented completely through equations or |The manipulated form is equivalent to the original form |The correct formula is selected in terms of the problem context |
|inequalities, which are consistent with the problem. | | |
| | |ASSESSMENT CRITERION 2 |
|ASSESSMENT CRITERION 2 | |The formula is applied correctly to obtain a valid solution |
|The concepts of equations and inequalities are explained | | |
| | |ASSESSMENT CRITERION 3 |
|ASSESSMENT CRITERION 3 | |Units are used correctly |
|Situations requiring the use of equations as opposed to | | |
|inequalities, and vice versa, are identified | | |
| | | |
|ASSESSMENT CRITERION 4 | | |
|Algebraic rotation, conventions and terminology are used correctly | | |
| | | |
|ASSESSMENT CRITERION 5 | | |
|The solution is correct in terms of the problem context | | |
| | | |
|ASSESSMENT CRITERION 6 | | |
|The solution is verified through substitution or other verification | | |
|processes | | |
|SAQA US ID |US TITLE |CREDITS |
|7464 |Analyse cultural products and processes as representations of shape, space and time | |
| | |3 |
PURPOSE OF THE UNIT STANDARD
People credited with this unit standard are able to:
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
LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING
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 OUTCOMES AND ASSESSMENT CRITERIA:
|SPECIFIC OUTCOME 1 |SPECIFIC OUTCOME 2 |SPECIFIC OUTCOME 3 |
|Identify geometric shapes and patterns in cultural products |Analyse similarities & differences in shapes & patterns, & effect of |Analyse and explain the way shapes and space are used in different |
| |colour, used by cultures |epochs and cultures |
|OUTCOME RANGE | | |
|Shapes of and decorations on cultural products such as drums, pots, |ASSESSMENT CRITERIA |OUTCOME RANGE |
|mats, buildings, and necklaces |ASSESSMENT CRITERION 1 |Architecture, town and settlement planning |
| |Similarities in shapes and patterns are identified |ASSESSMENT CRITERIA |
|ASSESSMENT CRITERIA | | |
|ASSESSMENT CRITERION 1 |ASSESSMENT CRITERION 2 |ASSESSMENT CRITERION 1 |
|Basic transformations are identified |Differences in shapes and patterns are identified |Shapes used by different cultures are identified |
| | | |
|ASSESSMENT CRITERION 2 |ASSESSMENT CRITERION 3 |ASSESSMENT CRITERION 2 |
|Basic geometric shapes are identified |Possible reasons for similarities and/or differences in shapes and |The use of space in different cultures is analysed and explained |
| |patterns used by different cultures are identified. | |
|ASSESSMENT CRITERION 3 | |ASSESSMENT CRITERION 3 |
|Basic patterns are identified and described |ASSESSMENT CRITERION 4 |The use of space in different epochs is analysed |
| |The effect of colour on shape and symmetry is described and | |
|ASSESSMENT CRITERION 4 |illustrated | |
|Basic patterns are extended in a way that maintains the consistency | | |
|of the pattern | | |
|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: 7448 |4 |[pic]25 |
|Work with patterns in various context | | |
|US: 7452 |6 |[pic]38 |
|Describe, represent and interpret mathematical models in different contexts | | |
|US: 7453 |3 |[pic]18,5 |
|Use algebraic notation, conventions and terminology to solve problems | | |
|US: 7464 |3 |[pic] |
|Analyse cultural products and processes as representations of shape, space and time | | |
|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 |CLARIFICATION |
|Range 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 patterns |
|AC1: Completed patterns are internally consistent with respect to relationship between |Continue with patterns to show consistency between terms. |
|elements of pattern. | |
|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 |Check whether the rule is appropriate. |
|elements of the patterns. | |
|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 |Check for consistency in patterns. |
|the pattern completely. | |
|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 |Generate patterns from a description in words to deduce a general |
|the pattern. |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 |Use expressions or equations to describe relationships. |
|algebraic expressions. |Range: Linear relationships given in the form of words, tables or |
| |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 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. |
|AC1: Independent and dependent variables are identified. |The concepts will not be examined formally, but must be discussed.|
|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 inequalities |
| |Range: simple linear equations or inequalities. |
|AC1: Problem represented completely through equations or inequalities, which are |Solve linear equations/inequalities, including word problems. |
|consistent with the problem. | |
|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 |Translate from words to mathematical language, e.g. |
|versa, are identifies. | |
| |5 added to a number is less than 20 [pic] 5 + x < 20 |
| |increased by x is 15 [pic] 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: (+, -, [pic],[pic]) |
| |Products |
| |Factors: 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 [pic] binomial), (monomial [pic] |
| |trinomial), (binomial [pic] 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 |CLARIFICATION |
|SO 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 |Complete/extend given patterns. |
|pattern. | |
|SO 2: Analyse similarities and differences in shapes and patterns and effect of colour,|Similarities and differences |
|used by cultures. |Range: 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 |Explain the use of space in urban and rural areas. |
|cultures. |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 |Describe and represent relationships. |
| |(increasing/decreasing), minimum/maximum. | |
|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 |WEIGHTING |
|Knowledge |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 DEMONSTRATED |
|Knowledge (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: +, -, [pic] and [pic], including the use of the calculator |
| |Action 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 axes |
| |Action 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 differences |
| |Action 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 INFORMATION |
|TEST |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|Projects can be done at any time, preferable in the second quarter to provide |
| | | |rubric. |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: [pic] |
|E.g. [pic] = 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 SCIENCES |YEAR: 2009 |
|LEARNING AREA CODE: MMSC4 | |
|Assessment Tasks |1 |2 |3 |4 |5 |
|Form(s) of |Test |Assignment |Project |Worksheet | Investigation |
|assessment | | | | | |
|US |US 001 SO 1, 2, 3 |US 002 SO 5 |US 001 SO 2, 3 |US 003 SO 2, 3 |US 001 SO 1, 2, 3 |
| |US 002 SO 1, 3, 4 |US 004 SO 1 |US 002 SO 2, 3, 5 | | |
|SOs |US 003 SO 1 | |US 003 SO 1, 3 | | |
| | | |US 004 SO 3 | | |
|Tools of Assessment |Marking Memo |Marking Memo |Marking Memo/ Rubric |Marking Memo |Marking Memo/ Rubric |
|Date to be| |
|completed | |
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 |72; 75; 78; ___; ___ | |(2) |
| | | | | |
| |1.1.2 |4; -2; -8; ___; ___ | |(2) |
| | | | | |
| | |[pic] ; [pic]; [pic]; ___; ___ | | |
| |1.1.3 | | |(2) |
| | | | | |
| | |2; 8; 32; ___; ___ | | |
| |1.1.4 | | |(2) |
| | | | | |
| | |1; 1; 2; 3; 5; ___; ___ | | |
| |1.1.5 | | | |
| | | | |(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. | | |
| | | |
|[pic] | | |
|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 | |(5) |
| |3 | | |
| |5 | | |
| |8 | | |
| |10 | | |
| | | | |
| |Number of persons | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
|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 | |(5) |
| | |3 | | |
| | |4 | | |
| | |6 | | |
| | |10 | | |
| | | | | |
| | |Number of dots (d) | | |
| | |2 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| |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
|INSTRUCTIONS AND INFORMATION | | |
|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 | | |
| |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 | | |
| |f | |(3) |
| | | | |
| |9 | | |
| |40 | | |
| |9[pic] + 40[pic] = ( )[pic] | | |
| | | | |
| | | | |
| |5 | | |
| | | | |
| |5[pic] + ( )[pic] = (13)[pic] | | |
| |13 | | |
| | | | |
| | | | |
| |8 | | |
| |( )[pic] + (8)[pic] = (17)[pic] | | |
| |17 | | |
| | | | |
|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. | | |
| | | | |
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| | | | |
| |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 | | |
| | |Distance | | |
| | | | |(2) |
| | |AC | | |
| | | | |(2) |
| | | | | |
| | |CD | |(2) |
| | |400 m | | |
| | | | |(3) |
| | |DF | | |
| | | | |(2) |
| | | | |(3) |
| | |FG | | |
| | |250 m | |(3) |
| | | | |(2) |
| | |GI | | |
| | | | | |
| | | | | |
| | |IJ | | |
| | |800 m | | |
| | | | | |
| | |JL | | |
| | | | | |
| | | | | |
| | |LM | | |
| | |5000 m | | |
| | | | | |
| | |MO | | |
| | | | | |
| | | | | |
| | |OP | | |
| | | | | |
| | | | | |
| | |PQ | | |
| | |250 m | | |
| | | | | |
| | |QS | | |
| | | | | |
| | | | | |
| | |TOTAL(A to S) | | |
| | | | | |
| | | | | |
| |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. | | |
| | | | |
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| | | | |
| |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 | | | |
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| | | | |(3) |
| |2.1.2 | | | |
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| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | |(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
|INSTRUCTIONS AND INFORMATION | | |
|1. |Answer ALL the questions. | | |
|2. |Calculators may be used, but you must show all calculations. ALL answers should be rounded off to one decimal place. | | |
|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. | | |
|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 cm | | |
|Minimum width: 1,1 m | | |
|Gradient 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 | |(4) |
| | |5 | | |
| | |x | | |
| | | | | |
| | |Length/ base | | |
| | | | | |
| | |12 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |Gradient | | |
| | |[pic] | | |
| | |[pic] | | |
| | |[pic] | | |
| | |[pic] | | |
| | |[pic] | | |
| | | | | |
| |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) | |(2) |
| | |Plot the points on the axes and join them with a straight line. | | |
| | |Give a suitable name for your graph. | |(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 = ___ 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 ( width | | |
| |Calculate 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) |
| |Rubric for 2.3 and 2.4 |
|Criteria | |
| |Levels |Mark |
| | |16 |
| |1 |2 |3 |4 | |
|Mathematical |Used no concepts. No |Used 1 – 2 concepts. Made some |Used 3 – 4 concepts. Used |Used more than 4 concepts. | |
|concepts/ language |attempt to use |attempt to use mathematical |mathematical language |Used appropriate mathematical | |
|used |mathematical language. |language. Did not communicate |clearly and correctly. |language. Good communication. | |
| |Communication poor. |ideas clearly. | | | |
|Explanation |No effort made to |Inconsistent explanation of |Explanations clear and |Clear, unambiguous and | |
| |explain. |concepts. |appropriate. |detailed explanation. | |
|Scale Model |Not to scale. |Only one dimension to scale |Two dimensions to scale. |All dimensions to scale. | |
|Presentation/ |Offered untidy model. |Made an effort to decorate model.|Model neatly decorated. |Model exceeds immediate | |
|Decoration |Loose structure. |Structure not firm enough. |Structure firm. |requirements. Structure | |
| | | | |extremely firm. | |
|TOTAL |[23] |
|TOTAL | |50 |
TASK 3: WORKSHEET
|INSTRUCTIONS AND INFORMATION | | |
|1. |Answer ALL the questions ON THE WORKSHEET. | | |
|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. | | |
|QUESTION 1 | | |
|Study the FOIL-rule to simplify (a + b)[pic] | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
|= a.a + a.b + b.a + b.b | | |
| | | |
|F O I L | | |
| | | |
|= a[pic] + ab + ab + b[pic] | | |
| | | |
|= a[pic] + 2ab + b[pic] | | |
| | | |
|Therefore ( a + b )[pic] = a[pic] + 2ab + b[pic] . . . . . . . . . Square Rule | | |
| | | |
|term 1 term 2 term 3 | | |
| | | |
|1.1 |Calculate (p – q)[pic] in two different ways: | | |
| |1.1.1 |Using the FOIL-rule: | | |
| | |(p – q)[pic] = _____________________________________________ | | |
| | |__________________________________________________________________________________________________________ | | |
| | | | |(2) |
| |1.1.2 |Using the Square rule directly: | | |
| | |(p – q)[pic] = ____________________________________________ | |(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)[pic] in two different ways: | | |
| |1.2.1 |Using the FOIL-rule: | | |
| | |(3x + y )[pic] = ___________________________________________ | | |
| | |_____________________________________________________ | | |
| | |_____________________________________________________ | |(2) |
| |1.2.2 |Using the Square rule directly: | | |
| | |(3x + y )[pic] = ___________________________________________ | |(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)[pic] = ____________________________________________ | |(2) |
| |1.3.2 |(x + 3y)[pic] = ____________________________________________ | |(2) |
| |1.3.3 |(2x – y)[pic] = ____________________________________________ | |(2) |
| |1.3.4 |(3x + 2y)[pic] = ___________________________________________ | |(2) |
| |1.3.5 |(4p – 3q)[pic] = ___________________________________________ | |(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[pic] – ab + ab – b[pic] | | |
| | | |
|= a[pic] – b[pic] | | |
| | | |
|Therefore ( a + b )(a – b) = a[pic] – b[pic] . . . . .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: | | |
| |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 | | |
| | | |
|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: [pic] [the sign comes from term2) | | |
| | | |
|Example: Factorise: 4a[pic] – 4ab + b[pic] | | |
|Check for Squares rule: | | |
|three terms: Yes. | | |
|4a[pic] and + b[pic] are squares. | | |
|middle term is 2(2a)(b) | | |
|answer: (2a – b)[pic] | | |
| | | |
|CHECKPOINTS FOR DIFFERENCE-OF-SQUARES RULE: | | |
|two terms | | |
|first term and second term are squares | | |
|sign between terms is a minus | | |
|answer: [pic] | | |
| | | |
|Example: Factorise: 9a[pic] – b[pic] | | |
|Check for Difference-of-squares rule: | | |
|two terms: Yes | | |
|9a[pic] and b[pic] are squares | | |
|– between terms | | |
|answer: (3a – b)(3a + b) | | |
| | | |
|Factorise the following completely: | | | |
|3.1 |4p[pic] – 1 = _____________________________________________________ | |(1) |
|3.2 |9x[pic] – 4 = _____________________________________________________ | |(1) |
|3.3 |16x[pic] – 25 = ___________________________________________________ | |(1) |
|3.4 |[pic] = __________________________________________________ | |(2) |
|3.5 |[pic] = __________________________________________________ | |(2) |
| | | |[7] |
|TOTAL: | |50 |
TASK 4: INVESTIGATION
|INSTRUCTIONS AND INFORMATION | | |
|1. |Answer ALL the questions. | | |
|2. |Calculators may be used. | | |
|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. | | |
|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 7th number. Determine the difference. | | |
| | | | |(2) |
| |1.3.2 |Add the first 6 numbers and compare the answer with the 8th | | |
| | |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 | | |
| | |1 | | |
| | |2 | | |
| | |-1 | | |
| | | | | |
| | |1; 2; 3 | | |
| | |4 | | |
| | |3 | | |
| | |+1 | |(7) |
| | | | | |
| | |2; 3; 5 | | |
| | |9 | | |
| | |10 | | |
| | |-1 | | |
| | | | | |
| | |3; 5; 8 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |5; 8; 13 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |8; 13; 21 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |13; 21; 34 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |21; 34; 55 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |34; 55; 89 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | |55; 89; 144 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| |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÷1 | | |
| | | | |
| | | | |
| |2; 1 | |(5) |
| |2÷1 | | |
| | | | |
| | | | |
| |3; 2 | | |
| |3÷2 | | |
| | | | |
| | | | |
| |5; 3 | | |
| |5÷3 | | |
| | | | |
| | | | |
| |Continue for at least six more pairs | | |
| | | | |
| | | | |
| | | | |
| |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 [pic] for each. | | |
|2.2 |Identify the envelope with a shape nearest to the Golden ratio, that is where [pic]( 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 [pic]. 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
| |Level | |
|Criteria | |Mark |
| | |12 |
| |1 |2 |3 |4 | |
|Organisation and |Made no attempt to organize |Did some classification. |Classified data |Organised results well. Classified | |
|recording of data |data, Did not use tables. |Used tables. Made minor |correctly. Worked in an |correctly and recorded results | |
| |Recorded in a muddled way |errors in recording. |organized way. Recorded |clearly in a table. | |
| | | |results in a table. | | |
|Correctness of |Made major mistakes in |Made minor mistakes in |Made no errors in |Carried out operations accurately | |
|calculations |calculation. |calculations. |calculations. |and completely. | |
|Identification of |Found no patterns, Showed no|Identified some patterns.|Identified and described |Identified and described patterns | |
|patterns/ mathematical|logical reasoning. |Did not reason clearly |patterns correctly. Was |correctly. Used variables and used | |
|reasoning | |and consistently. |able to reach a |them effectively. Offered strong | |
| | | |consistent conclusion. |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 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 COVER
Gives 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 1
1.1 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.
[pic]
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: 100 |
This question paper consists of 8 pages.
|INSTRUCTIONS AND INFORMATION | | |
|1. |Answer ALL the questions in your ANSWER BOOK. | | |
|2. |Calculators may be used, but you must show ALL calculations. | | |
|3. |Read the questions carefully before you write your answers. | | |
|4. |Write legibly and present your work clearly. | | |
|5. |Number the answers correctly and clearly. | | |
|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 |[pic]; [pic]; [pic]; … ; …; | | |
| | | | |(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. | | |
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| |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. | | |
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| | |Number of blocks | | |
| | |1 | |(3) |
| | |2 | | |
| | |3 | | |
| | |4 | | |
| | |5 | | |
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| | |Number of matches | | |
| | |4 | | |
| | |7 | | |
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| |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. | | |
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|2.1 |Calculate the gradient of AB using the formula | | |
| |[pic] , where m is the gradient and | | |
| |[pic]and [pic]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. | | |
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|3.1 |Copy and complete the following table to show the amount paid for a certain number of hamburgers. | | |
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| |Number of hamburgers | | |
| |1 | | |
| |2 | |(4) |
| |3 | | |
| |4 | | |
| |8 | | |
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| |Amount in Rand | | |
| |9 | | |
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|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. | |(2) |
| |Use a suitable scale and show the number of hamburgers on the horizontal axis. | |(2) |
| |Give a suitable title for the graph. | |(1) |
| |Plot the points and join them with a broken line. | |(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 = 2(r, where | | |
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| |C = circumference, | | |
| |r = radius and | | |
| |( = 3,14 | |(2) |
| |Calculate the circumference of the circle if the radius = 8 cm. | | |
|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. | | |
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| |5.4.1 |Complete the following: | | |
| | |The ladder, the building and the road form a … triangle. | |(1) |
| | |State the Theorem of Pythagoras in words. | |(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(. | | |
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|6.2 |Describe the transformation from C to D completely in the diagram below: | | |
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|6.3 |Choose the correct word from those given in brackets. Write only the word next to the question number in the answer book: | | |
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| |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. | | |
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|6.4 |Study the picture below which shows part of a woven cushion, and answer the questions that follow: | | |
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| |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] |
| | |TOTAL: | |100 |
This memorandum consists of 7 pages
|QUESTION 1 | |[24] |
|US 001 SO 1, 2, 3 | | |
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|NUMBER |EXPECTED ANSWER(S) |COMMENTS |MARKS |
|1.1.1 |20 ; 26 |Correct terms |(2) |
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|1.1.2 |( 12 ; (17 |Correct terms |(2) |
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|1.1.3 |[pic] ; [pic] OR [pic]; [pic] OR [pic];[pic] |Correct terms | |
| | | |(2) |
|1.2. |Decreasing. Each time 5 |Correct choice. | |
| |is subtracted |Any valid reason showing decrease: 2 marks |(3) |
| |OR Decreasing –5 is added each time | | |
|1.3.1. | | | |
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| | |Correct number of| |
| | |matches | |
| | |(1 per pattern) |(2) |
|1.3.2 |Number of blocks |Correct table values | |
| |1 | | |
| |2 | |(3) |
| |3 | | |
| |4 | | |
| |5 | | |
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| |Number of matches | | |
| |4 | | |
| |7 | | |
| |10 | | |
| |13 | | |
| |16 | | |
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|1.3.3 |Pattern increasing by 3 matches each time |Increase/add (1 mark) | |
| |OR add 3 matches each time |3 (1 mark) | |
| |OR multiply number by 3 and add 1 | |(2) |
|1.3.4 |31 matches |Correct answer (2) | |
| |Multiply the number of blocks by 3 and add 1. |Valid reason(1) |(3) |
|1.3.5 |n = 3b + 1 |3b (1 mark) + 1 ( 1 mark) |(2) |
|1.3.6 |3b + 1 = 100 |n= 100 ( Formula from 1.3.5) | |
| |3b = 99 |Simplify | |
| |b = 33 blocks |Correct answer |(3) |
|QUESTION 2 | | |
|US 002 SO 2, 3, 5 | |[12] |
|NUMBER |EXPECTED ANSWER(S) |COMMENTS |MARKS |
|2.1 | [pic] = [pic] = [pic] = (2 | | |
| | |Substitution in formula | |
| |OR [pic]= [pic] = (2 | | |
| | |Correct answer (accept any one) | |
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| | | |(2) |
|2.2 | y = mx + c | | |
| |= (2x + c |Substitute m | |
| |Subst. ((3; 4): 4 = (2((3) + c |Substitute point | |
| |4 – 6 = c | | |
| |– 2 = c |Finding c | |
| |OR y = mx + c |Answer only: No marks | |
| |= –2 x + c | | |
| |Subst. (5; (12): (12 = (2(5) + c | | |
| |(c = (2 | | |
| |(y = (2x ( 2 | | |
| |OR y – y1 = m(x – x1) | | |
| |Subst. ((3; 4): y – 4 = -2(x – (-3)) | | |
| |= -2(x + 3) = -2x -6 | | |
| |y = -2x - 2 | | |
| |OR | | |
| |Subst. (5; (12): y – (-12) = -2(x – 5) | | |
| |y + 12 = -2x + 10 | |(3) |
| |y = -2x - 2 | | |
|2.3 | (2 OR y = (2 OR (0; (2) |Correct answer |(1) |
|2.4 | y = (2x ( 2 | | |
| |Let y = 0 ( -2x (2 = 0 |Letting y = 0 | |
| |((2x = 2 |Correct answer | |
| |( x = (1 OR ((1; 0) |Answer 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 |Subtract 3 | |
| |OR y = (5 |Correct answer | |
| |OR (0; (5) |Answer only: 2 marks |(2) |
|QUESTION 3 | | |
|US 002 SO 1, 3 | |[19] |
|NUMBER |EXPECTED ANSWER(S) |COMMENTS |MARKS |
|3.1 |Number of Hamburgers |Correct table values | |
| |1 | | |
| |2 | |(4) |
| |3 | | |
| |4 | | |
| |8 | | |
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| |Amount in Rand | | |
| |9 | | |
| |18 | | |
| |27 | | |
| |36 | | |
| |72 | | |
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|3.2 | | | |
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| | | |Graph: |
| | | |3.2 |
| | | |(8) marks on graph |
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| | | |[3.3 |
| | | |(2) marks on graph] |
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| | | |If axes swapped: |
| | | |subtract 2 marks |
| | | |(if everything else |
| | | |is correct) |
|3.3 |R63 |Correct value from graph (can also be | |
| |Dotted line |given on graph) | |
| |Position of A on graph |Dotted line | |
| | |Position of A |(3) |
|3.4 |Hamburgers sold: [pic] = 43 |Divide amount by 9 | |
| | |Correct answer | |
| |Profit: 43 X R3 = R129 |Multiply answer by R3 | |
| |OR [pic] = R 129 |Correct answer | |
| | |Full marks |(4) |
| | | | |
| | |Answer only: 2 marks | |
|QUESTION 4 US 003 SO 2, 3 | |[15] |
|NUMBER |EXPECTED ANSWER(S) |COMMENTS |MARKS |
|4.1.1 | ab² ( c | | |
| |ab² ( c + 4 | | |
| |2c ( 5 |2ab² | |
| |2ab² ( 1 |0c | |
| | |( 1 |(3) |
|4.1.2 | ab² ( c + 4 | | |
| |=(2)(5)² ( (4) + 4 |Substitution | |
| |=2(25) ( 4 + 4 |Squaring 5 | |
| |= 50 oranges |Correct answer |(3) |
|4.2 |2a² ( 6a + 4a(a + 3) | | |
| |= 2a² ( 6a + 4a² + 12a |Simplify bracket: 4a² + 12a | |
| |= 6a² + 6a |Correct answer | |
| | | |(4) |
|4.3.1 |(x ( 3)(a + b) + 3(a + b) | | |
| |=(a + b)(x (3 + 3) |Taking out common factor(a + b) | |
| |=x(a + b) OR (a + b)x |Grouping: (x -3 + 3) | |
| | |Simplify (x ( 3 + 3) = x |(3) |
| | | | |
| |OR: xa + xb – 3a – 3b + 3a + 3b | | |
| |= xa + xb | | |
| |= x(a + b) | | |
|4.3.2 |x² ( 5x ( 6 = (x + 1)(x ( 6) |Correct terms |(2) |
|QUESTION 5 | | |
|US 004 SO 3 | |[16] |
|NUMBER |EXPECTED ANSWER(S) |COMMENTS |MARKS |
|5.1 |3x ( 10 ( 2x ( 2 | | |
| |(x ( 8 |Solving x | |
| | |Arrow to right | |
| | |Including 8 |(3) |
| | | | |
|5.2 |Let number of learners = x | | |
| |( [pic]x = 14 |Equating | |
| |([pic] = 14 x [pic] |Multiply by [pic] | |
| |= 35 learners |Correct answer | |
| |OR [pic] of learners = 7 | | |
| |(Total learners = 7 x 5 =35 | | |
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| | | |(3) |
|5.3 |C = 2(r | | |
| |= 2(3,14)(8) cm |Substitution | |
| |= 50,24 cm |Correct answer |(2) |
|5.4.1 |(a) right-angled |Correct answer |(1) |
| |(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 | |
| | |Accept: AC2 =BC2 + AB2 |(1) |
|5.4.2 |(Ladder)² = (Building)² + (Road)² |Formula | |
| |((41 m)² = (40 m)² + (Road)² |Substitution | |
| |( 1681 m² = 1600 m² + (Road)² |Correct Squaring | |
| |( (Road)² = 1681 m² ( 1600 m² | | |
| |= 81 m² |Simplifying | |
| |( Road = 9 m |Square root | |
| |OR |Correct unit | |
| |(Road)² = (Ladder)² - (Building)² | | |
| |=(41 m)² ( (40 m)² | | |
| |= 1681 m² ( 1600 m² | | |
| |= 81 m² | | |
| |( Road = 9 m | | |
| |OR | | |
| |BC2 + 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 | | |
| | | |(6) |
|QUESTION 6 | | |
|US 004 SO 1, 2, 3 | |[14] |
|NUMBER |EXPECTED ANSWER(S) |COMMENTS |MARKS |
|6.1 |A(((4; 5) |Correct coordinates |(2) |
|6.2 |Reflection about the y-axis |Reflection | |
| | |y-axis |(2) |
|6.3 |vertical |Correct answer |(1) |
|6.4.1 |Squares, rectangles, rhombi, parallelograms, triangles, kites, |Any 3 correct shapes | |
| |quadrilaterals, diamond shape | | |
| | | |(3) |
|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 / |Any 2 differences | |
| |diagonals bisect each other | | |
| |perpendicularly (with an angle of 90°) | |(2) |
|6.4.4 |Makes different patterns OR shapes visible OR Give strong effect to |Any relevant role. | |
| |picture OR Makes picture viewable. | |(1) |
|6.5 |Rectangles fit nicely together (can tessellate). OR Rectangular shapes |Any relevant reason | |
| |are easy to built OR rectangular forms are more stable than round forms,| | |
| |etc. | |(1) |
| |TOTAL: | |100 |
MARKING THE QUESTION PAPER
i. Follow-up principal
If 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 answer
When 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 marks
The 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 unambiguous |
| |Assessment criteria are strictly adhered to |
| |Marking 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 candidates |
| |Covers different cognitive levels |
| |Nature 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 |Forms |Instruments/Tools |Purposes |
|(WHO) |(WHAT) |(HOW) |(WHY) |
|Educator assessment, |Tests, Drawings, |Assessment grids, |Baseline, |
|Self-assessment, |Paintings, Graphs, |Rubrics, |Diagnostic, |
|Peer-assessment and |Physical activities, Projects, |Memoranda and |Formative, |
|Group-assessment. |Demonstrations, |Observation sheets. |Summative and |
| |Poems, Dramas, Role-plays, Stories, | |Systemic. |
| |Songs/music, | | |
| |Oral presentations, | | |
| |Written presentations, | | |
| |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.
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A
3rd arrangement
[pic]
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
2nd arrangement
1st arrangement
1 block
c
2 blocks
B
b
a
[pic]
[pic]
D 2015
2nd arrangement
1st arrangement
1 block
c
2 blocks
B
b
a
[pic]
[pic]
Diagram B
Diagram A
-3
5
x
y
0
A
A′
-3
3
x
y
0
A
A′
-3
3
x
y
0
A
A′
1
2
3
4
5
6
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0
-1
x
y
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-5
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-4
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-7
1
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5
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-1
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(
A(5;-4)
length/base
12x
x
height
Last terms
First terms
(a + b)[pic] = ( a + b ) ( a + b )
Inner terms
Outer terms
First terms
Last terms
(a + b)(a – b) = ( a + b ) ( a – b )
Inner terms
Outer terms
1; 1; 2; 3; 5; 8; 13; …
1; 1; 2; 3…
3 blocks
(
(
B(5; (12)
A((3; 4)
y
x
0
(
(
Ladder = 41 m
Road
Height = 40 m
A
B
C
y
x
0
A(–4; –1)
(
(
A(
y
x
0
C
D
y
x
0
A
B
E
D
C
B
A
K
L
F
G
H
I
J
KEY: A Accuracy
CA Consistent Accuracy
M Method
(A
(A
(A[pic]
(A
(A
(A
(A
(A
(A
(A
(CA
(A
(CA
(CA
(CA
(A
4 blocks
(A
(A
5 blocks
(A
(CA
(CA
(A
(A
(A
(A
(CA
(A
(A
(A
(CA
(CA
(CA
(A
(A
(CA
(A
(A
(CA
(A
(A
(CA
(A
(A
(CA
(A
(A
(CA
(A
(M
(CA
(CA
(M
(A
(A
(CA
(A
(CA
(A
(A
(CA
(A
(A
(A
(A
(3.3)
(position of A)
Selling hamburgers
A
(3.2)
(scale on vertical axis)
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
Amount in Rand
(M
Number of Hamburgers
(M
(CA
(CA
(M
(M
.
7
.
8
(CA
.
.
.
(3.2)
(labeling horizontal axis)
(3.2)
(labeling vertical axis)
.
0
(CA
(CA
(M
(CA
(CA
(CA
(A
(A
(A
(A
(A
(A
(A
(A
(A
(CA
(CA
(CA
(A
(A
(CA
(A
(CA
(CA
(A
(CA
(A
(A
(A
(A
(CA
8
0
(CA
(A
(M
(CA
(CA
(M
(A
(M
(CA
(A
(M
(A
(A
(CA
(CA
(A
(CA
(M
(A
(CA
(CA
(A
(CA
(A
(M
(CA
(CA
(A
(CA
(A
(A
(A
(A
(A
(A
(A
(A
(A
(A
(A
(A
(A
(A
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