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Curriculum and Assessment Policy Statement
Further Education and Training PhaseGrades 10-12
National Curriculum Statement (NCS)
CAPS
CurriCulum and assessment PoliCy statement Grades 10-12
matHematiCal literaCy
MATHEMATICAL LITERACY GRADES 10-12
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
department of Basic education
222 Struben StreetPrivate Bag X895Pretoria 0001South AfricaTel: +27 12 357 3000Fax: +27 12 323 0601
120 Plein Street Private Bag X9023Cape Town 8000South Africa Tel: +27 21 465 1701Fax: +27 21 461 8110Website: http://www.education.gov.za
© 2011 department of Basic education
isBn: 978-1-4315-0574-6
Design and Layout by: Ndabase Printing Solution
Printed by: Government Printing Works
MATHEMATICAL LITERACY GRADES 10-12
CAPS
FOREWORD by thE ministER
Our national curriculum is the culmination of our efforts over a period of seventeen years to transform the curriculum bequeathed to us by apartheid. From the start of democracy we have built our curriculum on the values that inspired our Constitution (Act 108 of 1996). the Preamble to the Constitution states that the aims of the Constitution are to:
�� KHDO� WKH�GLYLVLRQV�RI� WKH�SDVW�DQG�HVWDEOLVK�D�VRFLHW\�EDVHG�RQ�GHPRFUDWLF�values, social justice and fundamental human rights;
�� LPSURYH�WKH�TXDOLW\�RI�OLIH�RI�DOO�FLWL]HQV�DQG�IUHH�WKH�SRWHQWLDO�RI�HDFK�SHUVRQ�
�� OD\�WKH�IRXQGDWLRQV�IRU�D�GHPRFUDWLF�DQG�RSHQ�VRFLHW\�LQ�ZKLFK�JRYHUQPHQW�LV�EDVHG�RQ�WKH�ZLOO�RI�WKH�SHRSOH�DQG�HYHU\�FLWL]HQ�LV�HTXDOO\�SURWHFWHG�E\�ODZ��and
�� EXLOG�D�XQLWHG�DQG�GHPRFUDWLF�6RXWK�$IULFD�DEOH�WR�WDNH�LWV�ULJKWIXO�SODFH�DV�D�VRYHUHLJQ�VWDWH�LQ�WKH�IDPLO\�RI�nations.
Education and the curriculum have an important role to play in realising these aims.
in 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience RI�LPSOHPHQWDWLRQ�SURPSWHG�D�UHYLHZ�LQ�������7KLV�OHG�WR�WKH�¿UVW�FXUULFXOXP�UHYLVLRQ��WKH�Revised National Curriculum Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).
Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National Curriculum Statement (2002) and the National Curriculum Statement Grades 10-12 to produce this document.
From 2012 the two national Curriculum statements, for Grades R-9 and Grades 10-12 respectively, are combined LQ�D�VLQJOH�GRFXPHQW�DQG�ZLOO�VLPSO\�EH�NQRZQ�DV�WKH�National Curriculum Statement Grades R-12. the National Curriculum Statement for Grades R-12 builds on the previous curriculum but also updates it and aims to provide FOHDUHU�VSHFL¿FDWLRQ�RI�ZKDW�LV�WR�EH�WDXJKW�DQG�OHDUQW�RQ�D�WHUP�E\�WHUP�EDVLV��
the National Curriculum Statement Grades R-12 represents a policy statement for learning and teaching in south African schools and comprises of the following:
(a) Curriculum and Assessment Policy statements (CAPs) for all approved subjects listed in this document;
(b) National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(c) National Protocol for Assessment Grades R-12.
MRS ANGIE MOTSHEKGA, MP MINISTER OF BASIC EDUCATION
MATHEMATICAL LITERACY GRADES 10-12
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
MATHEMATICAL LITERACY GRADES 10-12
1CAPS
CONTENTS
seCtion 1: introduCtion to tHe CurriCulum and assessment PoliCy statements .. 3
1.1 Background .....................................................................................................................................................3
1.2 overview ..........................................................................................................................................................3
1.3 General aims of the south african Curriculum ............................................................................................4
1.4 time allocation ................................................................................................................................................6
1.4.1 Foundation Phase ...................................................................................................................................6
1.4.2 Intermediate Phase .................................................................................................................................6
1.4.3 Senior Phase ...........................................................................................................................................7
1.4.4 Grades 10-12 ..........................................................................................................................................7
seCtion 2: introduCtion to matHematiCal literaCy ............................................................8
2.1 What is mathematical literacy ...................................................................................................................... 82.2 Progression in mathematical literacy........................................................................................................ 112.3 overview and weighting of topic ................................................................................................................ 122.4 suggested time allocation ........................................................................................................................... 15
2.5 suggested work schedule ........................................................................................................................... 15
seCtion 3: Content and sCoPe oF ConteXts Per toPiCs ...................................................20
3.1 introduction .................................................................................................................................................. 203.2 overview of contexts, content and/or skills per topic and grade ............................................................ 21
3.3 detailed outline of content/skills to be taught per grade ......................................................................... 25
Part 1 Basic Skills Topics ................................................................................................................................ 25
%� Interpreting and communicating answers and calculations ....................................................................... 26
%� Numbers and calculations with numbers .................................................................................................. 27
%� Patterns, relationships and representations .............................................................................................. 36
Part 2 Application Topics ................................................................................................................................ 47
%� Finance ..................................................................................................................................................... 48
%� Measurement ............................................................................................................................................ 61
%� Maps, plans and other representations of the physical world ................................................................... 72
%� Data handling ............................................................................................................................................ 81
%� Probability ................................................................................................................................................. 90
MATHEMATICAL LITERACY GRADES 10-12
2 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
seCtion 4: assessment in matHematiCal literaCy ...............................................................96
4.1 introduction ................................................................................................................................................. 964.2 informal or daily assessment ...................................................................................................................... 974.3 Formal assessment ...................................................................................................................................... 974.4 Programme of assessment ......................................................................................................................... 98
4.4.1 Programme of assessment in Mathematical Literacy ......................................................................... 98
�� Programme of assessment for Mathematical Literacy in Grades 10 and 11 .................................. 98
�� Programme of assessment for Mathematical Literacy in Grade 12 ................................................ 99
�� Description of the assessment tasks in Mathematical Literacy ..................................................... 100
�� Summary of the formal assessment tasks listed in the CAPS document ..................................... 102
4.4.2 Examinations for Grades 10, 11 and 12 ............................................................................................. 104
�� Overview ....................................................................................................................................... 104
�� Time and mark allocation .............................................................................................................. 104
�� Additional information regarding examination papers ................................................................... 105
�� Paper 1 and Paper 2 compared .................................................................................................... 108
�� Contexts ........................................................................................................................................ 108
�� Weighting of topics ........................................................................................................................ 109
�� Distribution of marks according to taxonomy levels ...................................................................... 109
�� Additional information on the mid-year examinations ................................................................... 109
4.5 recording and reporting ........................................................................................................................... 1104.6 moderation of assessment .........................................................................................................................1114.7 appendices ................................................................................................................................................. 112
�� Appendix 1 Description of the levels in the mathematical literacy assessment taxonomy ...................... 112
�� Appendix 2 Assessment task example: Responsible use of paracetamol .............................................. 117
�� Appendix 3 Further interpretation of the levels in the mathematical literacy assessment taxonomy ..... 120
4.8 General ........................................................................................................................................................ 128
MATHEMATICAL LITERACY GRADES 10-12
3CAPS
SECTION 1
introduCtion to tHe CurriCulum and assessment PoliCy statements For matHematiCal literaCy Grades 10-12
1.1 Background
The National Curriculum Statement Grades R-12 (NCS) stipulates policy on curriculum and assessment in the schooling sector.
To improve implementation, the National Curriculum Statement was amended, with the amendments coming into effect in January 2012. A single comprehensive Curriculum and Assessment Policy document was developed for each subject to replace Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines in Grades R-12.
1.2 overview
(a) The National Curriculum Statement Grades R-12 (January 2012) represents a policy statement for learning and teaching in South African schools and comprises the following:
(i) Curriculum and Assessment Policy Statements for each approved school subject;
(ii) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(iii) The policy document, National Protocol for Assessment Grades R-12 (January 2012).
(b) The National Curriculum Statement Grades R-12 (January 2012) replaces the two current national curricula statements, namely the
(i) Revised National Curriculum Statement Grades R-9, Government Gazette No. 23406 of 31 May 2002, and
(ii) National Curriculum Statement Grades 10-12 Government Gazettes, No. 25545 of 6 October 2003 and No. 27594 of 17 May 2005.
(c) The national curriculum statements contemplated in subparagraphs b(i) and (ii) comprise the following policy documents which will be incrementally repealed by the National Curriculum Statement Grades R-12 (January 2012) during the period 2012-2014:
(i) The Learning Area/Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines for Grades R-9 and Grades 10-12;
�LL�� 7KH� SROLF\� GRFXPHQW�� 1DWLRQDO� 3ROLF\� RQ� DVVHVVPHQW� DQG� TXDOL¿FDWLRQV� IRU� VFKRROV� LQ� WKH� *HQHUDO�Education and Training Band, promulgated in Government Notice No. 124 in Government Gazette No. 29626 of 12 February 2007;
�LLL�� 7KH� SROLF\� GRFXPHQW�� WKH� 1DWLRQDO� 6HQLRU� &HUWL¿FDWH�� $� TXDOL¿FDWLRQ� DW� /HYHO� �� RQ� WKH� 1DWLRQDO�4XDOL¿FDWLRQV�)UDPHZRUN��14)���SURPXOJDWHG�LQ�*RYHUQPHQW�*D]HWWH�1R�������RI����-XO\������
MATHEMATICAL LITERACY GRADES 10-12
4 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
�LY�� 7KH� SROLF\� GRFXPHQW�� $Q� DGGHQGXP� WR� WKH� SROLF\� GRFXPHQW�� WKH� 1DWLRQDO� 6HQLRU� &HUWL¿FDWH�� $�TXDOL¿FDWLRQ�DW�/HYHO���RQ�WKH�1DWLRQDO�4XDOL¿FDWLRQV�)UDPHZRUN��14)���UHJDUGLQJ�OHDUQHUV�ZLWK�VSHFLDO�needs, published in Government Gazette, No.29466 of 11 December 2006, is incorporated in the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
�Y�� 7KH� SROLF\� GRFXPHQW�� $Q� DGGHQGXP� WR� WKH� SROLF\� GRFXPHQW�� WKH� 1DWLRQDO� 6HQLRU� &HUWL¿FDWH�� $�TXDOL¿FDWLRQ�DW�/HYHO���RQ�WKH�1DWLRQDO�4XDOL¿FDWLRQV�)UDPHZRUN��14)���UHJDUGLQJ�WKH�1DWLRQDO�3URWRFRO�for Assessment (Grades R-12), promulgated in Government Notice No.1267 in Government Gazette No. 29467 of 11 December 2006.
(d) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, and the sections on the Curriculum and Assessment Policy as contemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the National Curriculum Statement Grades R-12. It will therefore, in terms of section 6A of the South African Schools Act, ������$FW�1R�����RI������� form the basis for the Minister of Basic Education to determine minimum outcomes and standards, as well as the processes and procedures for the assessment of learner achievement to be applicable to public and independent schools.
1.3 General aims of the south african Curriculum
(a) The National Curriculum Statement Grades R-12 gives expression to the knowledge, skills and values worth learning in South African schools. This curriculum aims to ensure that children acquire and apply knowledge and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge in local contexts, while being sensitive to global imperatives.
(b) The National Curriculum Statement Grades R-12 serves the purposes of:
%� equipping learners, irrespective of their socio-economic background, race, gender, physical ability or LQWHOOHFWXDO� DELOLW\�� ZLWK� WKH� NQRZOHGJH�� VNLOOV� DQG� YDOXHV� QHFHVVDU\� IRU� VHOI�IXO¿OPHQW�� DQG� PHDQLQJIXO�participation in society as citizens of a free country;
%� providing access to higher education;
%� facilitating the transition of learners from education institutions to the workplace; and
%� SURYLGLQJ�HPSOR\HUV�ZLWK�D�VXI¿FLHQW�SUR¿OH�RI�D�OHDUQHU¶V�FRPSHWHQFHV�
(c) The National Curriculum Statement Grades R-12 is based on the following principles:
%� Social transformation: ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of the population;
%� Active and critical learning: encouraging an active and critical approach to learning, rather than rote and uncritical learning of given truths;
%� High knowledge and high skills: the minimum standards of knowledge and skills to be achieved at each JUDGH�DUH�VSHFL¿HG�DQG�VHW�KLJK��DFKLHYDEOH�VWDQGDUGV�LQ�DOO�VXEMHFWV�
%� Progression: content and context of each grade shows progression from simple to complex;
MATHEMATICAL LITERACY GRADES 10-12
5CAPS
%� Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social and HQYLURQPHQWDO�MXVWLFH�DQG�KXPDQ�ULJKWV�DV�GH¿QHG�LQ�WKH�&RQVWLWXWLRQ�RI�WKH�5HSXEOLF�RI�6RXWK�$IULFD��7KH�National Curriculum Statement Grades R-12 is sensitive to issues of diversity such as poverty, inequality, race, gender, language, age, disability and other factors;
%� Valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country as important contributors to nurturing the values contained in the Constitution; and
%� &UHGLELOLW\��TXDOLW\�DQG�HI¿FLHQF\��SURYLGLQJ�DQ�HGXFDWLRQ�WKDW�LV�FRPSDUDEOH�LQ�TXDOLW\��EUHDGWK�DQG�GHSWK�WR�those of other countries.
(d) The National Curriculum Statement Grades R-12 aims to produce learners that are able to:
%� identify and solve problems and make decisions using critical and creative thinking;
%� work effectively as individuals and with others as members of a team;
%� organise and manage themselves and their activities responsibly and effectively;
%� collect, analyse, organise and critically evaluate information;
%� communicate effectively using visual, symbolic and/or language skills in various modes;
%� use science and technology effectively and critically showing responsibility towards the environment and the health of others; and
%� demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.
(e) Inclusivity should become a central part of the organisation, planning and teaching at each school. This can only happen if all teachers have a sound understanding of how to recognise and address barriers to learning, and how to plan for diversity.
� 7KH�NH\�WR�PDQDJLQJ�LQFOXVLYLW\�LV�HQVXULQJ�WKDW�EDUULHUV�DUH�LGHQWL¿HG�DQG�DGGUHVVHG�E\�DOO�WKH�UHOHYDQW�VXSSRUW�structures within the school community, including teachers, District-Based Support Teams, Institutional-Level Support Teams, parents and Special Schools as Resource Centres. To address barriers in the classroom, teachers should use various curriculum differentiation strategies such as those included in the Department of %DVLF�(GXFDWLRQ¶V�Guidelines for Inclusive Teaching and Learning (2010).
MATHEMATICAL LITERACY GRADES 10-12
6 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
1.4 time allocation
1.4.1 Foundation Phase
(a) The instructional time in the Foundation Phase is as follows:
suBJeCtGrade r (Hours)
Grades 1-2 (Hours)
Grade 3 (Hours)
Home Language 10 8/7 8/7
First Additional Language 2/3 3/4
Mathematics 7 7 7
Life Skills
%� Beginning Knowledge
%� Creative Arts
%� Physical Education
%� Personal and Social Well-being
6
(1)
(2)
(2)
(1)
6
(1)
(2)
(2)
(1)
7
(2)
(2)
(2)
(1)
total 23 23 25
(b) Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.
(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours for Additional Language in Grades 1-2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional Language.
(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R-2 and 2 hours as indicated by the hours in brackets for Grade 3.
1.4.2 intermediate Phase
(a) The instructional time in the Intermediate Phase is as follows:
suBJeCt Hours
Home Language 6
First Additional Language 5
Mathematics 6
Natural Sciences and Technology 3,5
Social Sciences 3
Life Skills
%� Creative Arts
%� Physical Education
%� Personal and Social Well-being
4
(1,5)
(1)
(1,5)
total 27,5
MATHEMATICAL LITERACY GRADES 10-12
7CAPS
1.4.3 senior Phase
(a) The instructional time in the Senior Phase is as follows:
suBJeCt Hours
Home Language 5
First Additional Language 4
Mathematics 4,5
Natural Sciences 3
Social Sciences 3
Technology 2
Economic Management Sciences 2
Life Orientation 2
Creative Arts 2
total 27,5
1.4.4 Grades 10-12
(a) The instructional time in Grades 10-12 is as follows:
suBJeCt time alloCation Per Week (Hours)
Home Language 4.5
First Additional Language 4.5
Mathematics 4.5
Life Orientation 2
A minimum of any three subjects selected from Group B Annexure B, Tables B1-B8 of the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, subject to the provisos stipulated in paragraph 28 of the said policy document.
12 (3x4h)
total 27,5
7KH�DOORFDWHG�WLPH�SHU�ZHHN�PD\�EH�XWLOLVHG�RQO\�IRU�WKH�PLQLPXP�UHTXLUHG�1&6�VXEMHFWV�DV�VSHFL¿HG�DERYH��and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wish to offer additional subjects, additional time must be allocated for the offering of these subjects.
MATHEMATICAL LITERACY GRADES 10-12
8 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
SECTION 2
matHematiCal literaCy
2.1 What is mathematical literacy?
The competencies developed through Mathematical Literacy allow individuals to make sense of, participate in and FRQWULEXWH� WR� WKH� WZHQW\�¿UVW� FHQWXU\� ZRUOG�²� D�ZRUOG� FKDUDFWHULVHG� E\� QXPEHUV�� QXPHULFDOO\� EDVHG� DUJXPHQWV�and data represented and misrepresented in a number of different ways. Such competencies include the ability to reason, make decisions, solve problems, manage resources, interpret information, schedule events and use and apply technology. Learners must be exposed to both mathematical content and real-life contexts to develop these competencies. Mathematical content is needed to make sense of real-life contexts; on the other hand, contexts determine the content that is needed.
The subject Mathematical Literacy should enable the learner to become a self-managing person, a contributing worker and a participating citizen in a developing democracy. The teaching and learning of Mathematical Literacy should thus provide opportunities to analyse problems and devise ways to work mathematically in solving such problems. Opportunities to engage mathematically in this way will also assist learners to become astute consumers RI�WKH�PDWKHPDWLFV�UHÀHFWHG�LQ�WKH�PHGLD�
7KHUH�DUH�¿YH�NH\�HOHPHQWV�RI�0DWKHPDWLFDO�/LWHUDF\�
%� mathematical literacy involves the use of elementary mathematical content.
The mathematical content of Mathematical Literacy is limited to those elementary mathematical concepts and skills that are relevant to making sense of numerically and statistically based scenarios faced in the everyday lives of individuals (self-managing individuals) and the workplace (contributing workers), and to participating as critical citizens in social and political discussions. In general, the focus is not on abstract mathematical concepts. As a rule of thumb, if the required calculations cannot be performed using a basic four-function calculator, then the calculation is in all likelihood not appropriate for Mathematical Literacy. Furthermore, since the focus in Mathematical Literacy is on making sense of real-life contexts and scenarios, in the Mathematical Literacy classroom mathematical content should not be taught in the absence of context.
%� mathematical literacy involves authentic real-life contexts.
In exploring and solving real-world problems, it is essential that the contexts learners are exposed to in this subject are authentic (i.e. are drawn from genuine and reaslitic situations) and relevant, and relate to daily life, the workplace and the wider social, political and global environments. Wherever possible, learners must be able to work with actual real-life problems and resources, rather than with problems developed around constructed, semi-real, contrived and/RU�¿FWLWLRXV�VFHQDULRV��(�J��OHDUQHUV�PXVW�EH�H[SRVHG�WR�UHDO�DFFRXQWV�FRQWDLQLQJ�FRPSOH[�DQG�³PHVV\´�¿JXUHV�UDWKHU�WKDQ�FRQWULYHG�DQG�FRQVWUXFWHG�UHSOLFDV�FRQWDLQLQJ�RQO\�FOHDQ�DQG�URXQGHG�¿JXUHV�
Alongside using mathematical knowledge and skills to explore and solve problems related to authentic real-life contexts, learners should also be expected to draw on non-mathematical skills and considerations in making sense of those contexts. E.g. although calculations may reveal that a 10 kg bag of maize meal is the most cost-effective, FRQVLGHUDWLRQ�RI�WKH�FRQWH[W�PD\�GLFWDWH�WKDW�WKH���NJ�EDJ�ZLOO�KDYH�WR�EH�ERXJKW�EHFDXVH�WKH����NJ�EDJ�FDQQRW�¿W�inside the taxi and/or the buyer does not have enough money to buy the 10 kg bag and/or the buyer has no use for
MATHEMATICAL LITERACY GRADES 10-12
9CAPS
10 kg, etc. In other words, mathematical content is simply one of many tools that learners must draw on in order to explore and make sense of appropriate contexts.
%� mathematical literacy involves solving familiar and unfamiliar problems.
It is unrealistic to expect that in the teaching of Mathematical Literacy learners will always be exposed to contexts WKDW�DUH�VSHFL¿FDOO\� UHOHYDQW� WR� WKHLU� OLYHV��DQG� WKDW� WKH\�ZLOO� EH�H[SRVHG� WR�DOO� RI� WKH�FRQWH[WV� WKDW� WKH\�ZLOO� RQH�day encounter in the world. Rather, the purpose of this subject is to equip learners with the necessary knowledge and skills to be able to solve problems in any context that they may encounter in daily life and in the workplace, LUUHVSHFWLYH�RI�ZKHWKHU�WKH�FRQWH[W�LV�VSHFL¿FDOO\�UHOHYDQW�WR�WKHLU�OLYHV�RU�ZKHWKHU�WKH�FRQWH[W�LV�IDPLOLDU��/HDUQHUV�ZKR�DUH�PDWKHPDWLFDOO\�OLWHUDWH�VKRXOG�KDYH�WKH�FDSDFLW\�DQG�FRQ¿GHQFH�WR�LQWHUSUHW�DQ\�UHDO�OLIH�FRQWH[W�WKDW�WKH\�encounter, and be able to identify and perform the techniques, calculations and/or other considerations needed to make sense of the context. In this sense Mathematical Literacy develops a general set of skills needed to deal with a particular range of problems.
If Mathematical Literacy is seen in this way, then a primary aim in this subject is to equip learners with a set of skills that transcends both the mathematical content used in solving problems and the context in which the problem is situated. In other words, both the mathematical content and the context are simply tools: the mathematical content provides learners with a means through which to explore contexts; and the contexts add meaning to the mathematical content. But what is more important is that learners develop the ability to devise and apply both mathematical and non-mathematical techniques and considerations in order to explore and make sense of any context, whether the context is familiar or not.
The interplay between content, contexts and solving problems is illustrated in the following diagram:1
� Mathematical Content
Ratios
Linear graphs
Income and expenditure
Percentages
Statistics
Real-life Contexts
Baking
Tax
HIV/Aids
Cellphones
Running a business
Competencies/Skills
Drawing graphs
Budgeting Analysing
Estimation
Making comparisons
Figure 1: Interplay between content, context and problem-solving skills in Mathematical Literacy
%� mathematical literacy involves decision making and communication.
A mathematically literate individual is able to weigh up options by comparing solutions, make decisions regarding the most appropriate choice for a given set of conditions, and communicate decisions using terminology (both 1 Adapted from: Brombacher, A. 2007. 0DWKHPDWLFDO�/LWHUDF\�í�$�5HDGHU. Cape Town: Bateleur Books. p.15.
MATHEMATICAL LITERACY GRADES 10-12
10 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
mathematical and non-mathematical) appropriate to the context. In the teaching of Mathematical Literacy, teachers should provide learners with opportunities to develop and practise decision-making and communication skills.
�� mathematical literacy involves the use of integrated content and/or skills in solving problems.
The content, skills and contexts in this document are organised and categorised according to topics. However, problems encountered in everyday contexts are never structured according to individual content topics. Rather, the solving of real-life problems commonly involves the use of content and/or skills drawn from a range of topics, and so, being able to solve problems based in real-life contexts requires the ability to identify and use a wide variety of techniques and skills integrated from across a range of content topics.
MATHEMATICAL LITERACY GRADES 10-12
11CAPS
To illustrate these elements of Mathematical Literacy, consider the following two cellphone advertisements that appeared in the Sunday Times newspaper on 11 April 2010.
&RQWH[W��The context is authentic, as drawn from a newspaper, and is relevant in that many people often have to make a choice between different cellphone contract options.
Notice, however, that although the context is authentic, it is highly unlikely that this context will be relevant or familiar for all learners. Nonetheless, situations in life in which we are expected to make comparisons occur frequently and a mathematically literate individual is able to make sense of those situations irrespective of the context.
&RQWHQW��To determine the conditions under which each of these contracts will be the most cost-effective, we could perform calculations, complete tables or draw graphs. Whatever method we might choose, though, the method requires an understanding of only basic mathematical concepts and calculations, and does not require an understanding of complex and/or abstract mathematical principles.
It is also crucial to notice that the primary aim in working with these adverts is not to test understanding of a particular section of mathematical content or calculation. Rather, the primary aim is to make sense of the context in order to make a decision about which contract is the most cost-effective under a certain set of conditions.
1RQ�PDWKHPDWLFDO� FRQVLGHUDWLRQV��Although we can use mathematical calculations to determine the conditions for which one contract is more cost-effective than the other, many people will choose a particular contract not because of cost, but because of the make and model of cellphone that comes with the contract and/or the features attached to the phone. In other words, although mathematical calculations provide us with a deeper insight into a scenario, there are often non-mathematical considerations that affect the decisions we make. A mathematically literate person has the capacity to take into account both mathematical and non-mathematical considerations and to be aware that there are factors other than economy which may LQÀXHQFH�GHFLVLRQV�
'HFLVLRQ�PDNLQJ�DQG�FRPPXQLFDWLRQ��Although we can use mathematical tools to explore the options, what is equally important LV�EHLQJ�DEOH�WR� LQWHUSUHW�WKH�¿QGLQJV��PDNH�D�GHFLVLRQ�DERXW�ZKLFK�FRQWUDFW� LV�WKH�PRVW�FRVW�HIIHFWLYH�RSWLRQ�XQGHU�FHUWDLQ�conditions, and communicate the decision with an awareness of non-mathematical considerations such as preference for make, model, colour, features, etc. The mathematical calculations are meaningless without decision making and appropriate communication.
,QWHJUDWHG�FRQWHQW�� In order to make sense of each of the contracts, we could perform cost calculations involving addition, multiplication and division. An alternative approach would be to draw two graphs to represent each of the contract options on the same set of axes. A still further approach involves completing a table of values. Irrespective of the method used, interpretation and decision-making and communication skills will be needed to make sense of the calculated answers.
The point is that in order to make sense of the different cellphone contracts, a variety of techniques, calculations, skills and content topics can and should be utilised. This approach must be adopted for all problem-solving scenarios.
2.2 Progression in mathematical literacy
Progression refers to the process of developing more advanced and complex knowledge and skills. In Mathematical Literacy, progression occurs on three levels:
2.2.1 Content
One of the ways in which Mathematical Literacy develops across the grades is in terms of mathematical concepts/skills. E.g. in Grade 10 learners are expected to be able to work with one graph on a set of axes; in Grade 11 two
MATHEMATICAL LITERACY GRADES 10-12
12 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
graphs; and in Grade 12 two or more graphs on the same set of axes. This is not the case for all topics, though, and there are some instances where there is no new content in Grade 12 compared to Grades 10 and 11. In such cases progression may occur in relation to contexts and/or problem-solving processes.
2.2.2 Contexts
Progression also occurs in relation to the nature, familiarity and complexity of the context in which problems are encountered. Moving from Grade 10 to Grade 12, the contexts become less familiar and more removed from the experience of the learner and, hence, less accessible and more demanding. There are some topics in which the focus LQ�*UDGH����LV�RQ�FRQWH[WV�UHODWLQJ�WR�WKH�SHUVRQDO�OLYHV�RI�OHDUQHUV�DQG�RU�KRXVHKROG�LVVXHV��H�J��SHUVRQDO�¿QDQFH�ĺ�cell-phone accounts; household budget), in Grade11 on contexts relating to the workplace and/or business environment �H�J��EXVLQHVV�¿QDQFH�ĺ�SD\VOLSV��WD[DWLRQ���DQG�LQ�*UDGH����RQ�FRQWH[WV�UHODWLQJ�WR�VFHQDULRV�HQFRPSDVVLQJ�ZLGHU�VRFLDO�DQG�SROLWLFDO�FRQWH[WV�LQFRUSRUDWLQJ�QDWLRQDO�DQG�JOREDO�LVVXHV��H�J��H[FKDQJH�UDWHV�DQG�LQÀDWLRQ���
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One of the key characteristics of a mathematically literate individual is the ability to identify and apply appropriate mathematical and non-mathematical techniques needed to solve problems encountered in both familiar and unfamiliar contexts. However, this ability to solve problems without guidance is not something that develops naturally, but rather should be demonstrated and nurtured from Grade 10 to Grade 12. One of the key distinctions between Grade 10, ���DQG����OHDUQHUV�LV�WKH�FRQ¿GHQFH�ZLWK�ZKLFK�OHDUQHUV�DUH�DEOH�WR�LGHQWLI\�DQG�XWLOLVH�DSSURSULDWH�PDWKHPDWLFDO�content, techniques and other non-mathematical considerations in order to explore authentic real-life contexts without guidance and/or scaffolding.
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2.3 overview and weighting of topics
The content, skills and contexts appropriate to Mathematical Literacy are presented in topics in this document.
The topics have been separated into %DVLF�6NLOOV�7RSLFV comprising:
%� Interpreting and communicating answers and calculations
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%� Numbers and calculations with numbers
%� Patterns, relationships and representations
and Application Topics comprising:
%� Finance
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Much of the content in the Basic Skills Topics comprises elementary mathematical content and skills that learners have already been exposed to in Grade 9 (e.g. different number formats and conventions, calculating percentages, drawing graphs from tables of values, and so on). The inclusion of this content in this document provides teachers with the opportunity to revise these important concepts and provide learners with the opportunity to explore these FRQFHSWV�LQ�FRQWH[WV��,W�LV�H[SHFWHG�WKDW�D�¿UP�JUDVS�RI�WKH�FRQFHSWV�LQ�WKH�%DVLF�6NLOOV�7RSLFV is necessary for making sense of the content and contexts outlined in the Application Topics.
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Figure 2 shows an overview and weighting of the topics according to which the Mathematical Literacy curriculum has been organised for Grades 10, 11 and 12.
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Comments on the structure of topics
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MATHEMATICAL LITERACY GRADES 10-12
20 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
SECTION 3
Content and sCoPe oF ConteXts Per toPiC
3.1 introduction
This part of the CAPS document provides a detailed outline of the content and/or skills and suggested contexts to be taught in each grade. The content is organised according to topics and sections.
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MATHEMATICAL LITERACY GRADES 10-12
21CAPS
3.2
ove
rvie
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text
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10
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de 1
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12
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nd/o
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lls o
utlin
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the
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ic S
kills
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ics
to u
nder
stan
d si
tuat
ions
and
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ve p
robl
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cena
rios
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MATHEMATICAL LITERACY GRADES 10-12
22 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
cse
ctio
nG
rade
10
Gra
de 1
1G
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Gra
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MATHEMATICAL LITERACY GRADES 10-12
23CAPS
app
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topi
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MATHEMATICAL LITERACY GRADES 10-12
24 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
cse
ctio
nG
rade
10
Gra
de 1
1G
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12
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---
---
MATHEMATICAL LITERACY GRADES 10-12
25CAPS
3.3 detailed outline of content/skills to be taught per grade
Part 1: Basic skills topics
MATHEMATICAL LITERACY GRADES 10-12
26 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
inte
rpre
ting
and
com
mun
icat
ing
answ
ers
and
calc
ulat
ions
Gra
des
10, 1
1 an
d 12
sugg
este
d te
achi
ng ti
me:
r
ecom
men
ded
text
s an
d/or
reso
urce
s:%�
Text
book
s
The
skill
s as
soci
ated
with
inte
rpre
ting
and
com
mun
icat
ing
answ
ers
are
appl
icab
le to
eve
ry to
pic
and
sect
ion
in th
e cu
rric
ulum
and
acr
oss
ever
y gr
ade.
Lea
rner
s ha
ve to
be
show
n co
ntin
uous
ly h
ow to
inte
rpre
t ans
wer
s in
rela
tion
to th
e co
ntex
t in
whi
ch th
e an
swer
s ha
ve b
een
calc
ulat
ed a
nd h
ow to
com
mun
icat
e th
eir a
nsw
ers
in a
n ap
prop
riate
way
. For
this
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sect
ion
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tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Inte
rpre
tatio
n of
an
swer
s
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ck th
e ap
prop
riate
ness
of a
sol
utio
n by
com
parin
g it
to th
e es
timat
ed s
olut
ion.
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ify th
e so
lutio
n as
requ
ired
by th
e co
ntex
t of t
he p
robl
em.
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mor
e th
an 6
litre
s is
nee
ded
and
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calc
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ed 6
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unde
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litre
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nd n
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p, d
own,
or o
ff to
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opria
te n
umbe
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ecim
al p
lace
s de
pend
ing
on c
onte
xt.
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erm
ine
the
mos
t app
ropr
iate
uni
ts in
whi
ch to
exp
ress
the
answ
er a
s de
term
ined
by
the
cont
ext i
n w
hich
the
prob
lem
is p
osed
.
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)
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ork
a pr
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the
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ondi
tions
cha
nge.
(e.g
. Rec
alcu
latin
g th
e m
onth
ly re
paym
ent a
mou
nt o
n a
car l
oan
as a
resu
lt of
an
incr
ease
in th
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tere
st ra
te.)
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ogni
se th
at a
n er
ror i
n m
easu
rem
ent o
r a s
mal
l cha
nge
in ro
undi
ng c
an m
ake
a la
rge
diffe
renc
e to
an
answ
er if
the
erro
r or c
hang
e is
com
poun
ded
over
man
y ca
lcul
atio
ns o
r thr
ough
a la
rge
mul
tiplic
atio
n.
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dist
ance
.)
10, 1
1
and
12
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mun
icat
ion
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mun
icat
e so
lutio
ns u
sing
app
ropr
iate
term
inol
ogy,
sym
bols
and
uni
ts.
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arly
sta
te w
orki
ngs
and
met
hods
use
d fo
r sol
ving
a p
robl
em.
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ify c
ompa
rison
s an
d op
inio
ns w
ith c
alcu
latio
ns o
r with
info
rmat
ion
prov
ided
in th
e co
ntex
t.
10, 1
1
and
12
MATHEMATICAL LITERACY GRADES 10-12
27CAPS
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
sugg
este
d te
achi
ng ti
me:
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rec
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ende
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xts
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sour
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xtbo
oks
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exp
ecte
d th
at le
arne
rs w
ill m
ake
use
of a
var
iety
of n
umbe
r con
cept
s an
d ca
lcul
atio
ns a
s th
ey e
xplo
re c
onte
xts
and
solv
e pr
oble
ms
rela
ting
to s
ituat
ions
invo
lvin
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e to
pics
of
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nce,
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onte
nt a
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r ski
lls o
utlin
ed in
this
topi
c sh
ould
be
used
in
conj
unct
ion
with
the
cont
ent a
nd/o
r ski
lls a
nd c
onte
xts
outli
ned
in th
e ot
her a
pplic
atio
n to
pics
. How
lear
ners
mak
e us
e of
thes
e nu
mbe
r con
cept
s w
ill b
e de
term
ined
by
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cont
exts
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sion
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once
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in G
rade
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re n
o ne
w n
umbe
r con
cept
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xpec
ted
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rade
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umbe
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mat
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nven
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once
pts
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ed in
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cont
ext o
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Ope
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mbe
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kills
Rou
ndin
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Pro
porti
on
Rat
es
Per
cent
ages
MATHEMATICAL LITERACY GRADES 10-12
28 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
For a
ll ca
lcul
atio
ns in
volv
ing
num
bers
, lea
rner
s ar
e ex
pect
ed to
be
able
to w
ork
with
num
bers
exp
ress
ed in
the
follo
win
g fo
rmat
s: w
hole
num
bers
; dec
imal
s; fr
actio
ns; p
erce
ntag
es.
Num
ber
form
ats
and
conv
entio
ns
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k w
ith th
e fo
llow
ing
num
ber f
orm
ats:
%�de
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omm
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gativ
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ders
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and
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nven
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onte
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gnis
e th
at a
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gh th
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esen
tatio
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ke n
umbe
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anip
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ed in
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cena
rios
invo
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e to
pics
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inan
ce, M
easu
rem
ent, 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
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ndlin
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10, 1
1
and
12
MATHEMATICAL LITERACY GRADES 10-12
29CAPS
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Ope
ratio
ns
on n
umbe
rs
and
calc
ulat
or
skill
s
Per
form
the
follo
win
g ca
lcul
atio
ns fo
r num
bers
exp
ress
ed a
s w
hole
num
bers
, fra
ctio
ns, d
ecim
als
and
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enta
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ticip
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utio
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ivid
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ns
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umbe
rs
and
calc
ulat
or
skill
s (c
ontin
ued)
In o
rder
to:
Mak
e se
nse
of s
cena
rios
invo
lvin
g th
e to
pics
of F
inan
ce, M
easu
rem
ent, 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
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ition
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omm
ents
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imat
ing
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nsw
er to
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robl
em is
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ruci
al s
tep
in a
ny c
alcu
latio
n fo
r tw
o re
ason
s. F
irstly
, bef
ore
estim
atio
n ca
n oc
cur,
a pr
oper
und
erst
andi
ng o
f the
pro
blem
sh
ould
be
deve
lope
d. S
econ
dly,
an
estim
ated
ans
wer
pro
vide
s a
benc
hmar
k ag
ains
t whi
ch to
com
pare
the
calc
ulat
ed a
nsw
er: i
f the
cal
cula
ted
answ
er a
nd th
e es
timat
ion
are
very
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cent
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hem
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MATHEMATICAL LITERACY GRADES 10-12
30 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
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tent
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deve
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and
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31CAPS
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num
bers
Gra
des
10, 1
1 an
d 12
sect
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tent
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con
text
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MATHEMATICAL LITERACY GRADES 10-12
32 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
sect
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tent
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text
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latio
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10
MATHEMATICAL LITERACY GRADES 10-12
33CAPS
topi
c:
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cal
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num
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10, 1
1 an
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uy
10
MATHEMATICAL LITERACY GRADES 10-12
34 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
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deve
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text
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ave
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1
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12
MATHEMATICAL LITERACY GRADES 10-12
35CAPS
topi
c:
num
bers
and
cal
cula
tions
with
num
bers
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
a
Poss
ible
ass
essm
ent:
Ass
ignm
ent:
Com
parin
g ac
tual
and
rela
tive
size
Con
side
r tw
o di
ffere
nt it
ems
who
se p
rices
hav
e in
crea
sed
and
then
%�w
ork
out t
he a
ctua
l Ran
d in
crea
se in
pric
e fo
r eac
h of
the
item
s
%�w
ork
out t
he p
erce
ntag
e ch
ange
in p
rice
for e
ach
of th
e ite
ms
%�co
mpa
re th
e ac
tual
incr
ease
to th
e pe
rcen
tage
incr
ease
and
dis
cuss
the
usef
ulne
ss o
f per
cent
ages
.
10
MATHEMATICAL LITERACY GRADES 10-12
36 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sugg
este
d te
achi
ng ti
me:
*UDGH���������ZHHNV
Gra
de 1
1:
3-4
wee
ks
rec
omm
ende
d te
xts
and/
or re
sour
ces:
%�Te
xtbo
oks
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Lear
ners
will
mak
e us
e of
a v
arie
ty o
f pat
tern
s, re
latio
nshi
ps a
nd re
pres
enta
tions
of t
hose
rela
tions
hips
as
they
exp
lore
con
text
s an
d so
lve
prob
lem
s in
Fin
ance
, Mea
sure
men
t, M
aps,
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RUOG
, Dat
a ha
ndlin
g an
d P
roba
bilit
y. T
he c
onte
nt a
nd/o
r ski
lls o
utlin
ed in
this
topi
c sh
ould
t be
used
in c
onju
nctio
n w
ith th
e co
nten
t and
/or
ski
lls a
nd c
onte
xts
outli
ned
in th
e ot
her a
pplic
atio
n to
pics
. How
lear
ners
mak
e us
e of
thes
e co
ncep
ts w
ill b
e de
term
ined
by
the
cont
exts
in w
hich
par
ticul
ar p
robl
ems
are
situ
ated
, e.g
. WDULII�V\VWHPV�RU�EXVLQHVV�¿QDQFH�
Teac
hing
tim
e is
allo
cate
d on
ly to
the
revi
sion
and
/or t
each
ing
of th
ese
patte
rns,
rela
tions
hips
and
repr
esen
tatio
n co
ncep
ts in
Gra
des
10 a
nd 1
1. T
here
is n
o ne
w c
onte
nt in
Gra
de 1
2.
Rat
her,
it is
exp
ecte
d th
at le
arne
rs w
ill c
onst
ruct
and
inte
rpre
t tab
les,
equ
atio
ns a
nd g
raph
s to
mak
e se
nse
of a
ny c
onte
xt o
r pro
blem
in w
hich
thes
e co
ncep
ts h
ave
appl
icat
ion
and
in
parti
cula
r will
be
able
to w
ork
with
two
(Gra
de 1
1) o
r mor
e (G
rade
12)
rela
tions
hips
at t
he s
ame
time
in a
sin
gle
repr
esen
tatio
n (ta
ble
and/
or g
raph
).
scop
e of
con
text
s an
d/or
con
tent
per
sec
tion
and
grad
e:
sect
ion
Gra
de 1
0G
rade
11
Gra
de 1
2M
akin
g se
nse
of g
raph
s th
at te
ll a
stor
yIn
Gra
de 1
0, P
atte
rns,
rela
tions
hips
an
d re
pres
enta
tions
of r
elat
ions
hips
ar
e lim
ited
to c
onte
xts
invo
lvin
g:%�
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ortio
n re
latio
nshi
ps%�
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atio
nshi
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a t
able
or
on a
set
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xes
(e.g
. exp
lorin
g th
e co
st o
f a
sing
le c
ell-p
hone
con
tract
ra
ther
tha
n co
mpa
ring
two
diffe
rent
co
ntra
cts)
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rade
s 11
and
12,
Pat
tern
s, re
latio
nshi
ps a
nd re
pres
enta
tions
of
rela
tions
hips
are
lim
ited
to c
onte
xts
invo
lvin
g:%�
cons
tant
, lin
ear,
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rse
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ortio
n, e
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entia
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ompo
und
grow
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and
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lans
and
oth
er re
pres
enta
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he
SK\VLFDO�ZRUOG
, Dat
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roba
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rade
11,
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rela
tions
hips
in a
tabl
e or
on
a se
t of a
xes
(e.g
. com
parin
g tw
o di
ffere
nt c
ell p
hone
bill
ing
optio
ns)
%�in
Gra
de 1
2, tw
o or
mor
e re
latio
nshi
ps in
a ta
ble
or o
n a
set o
f axe
s (e
.g.
com
parin
g th
ree
diffe
rent
ele
ctric
ity b
illin
g op
tions
)
Pat
tern
s an
d re
latio
nshi
ps
Rep
rese
ntat
ions
of r
elat
ions
hips
in
tabl
es, e
quat
ions
and
gra
phs
Wor
king
with
two
or m
ore
rela
tions
hips
an
d/or
repr
esen
tatio
ns
MATHEMATICAL LITERACY GRADES 10-12
37CAPS
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Mak
ing
sens
e of
gr
aphs
that
tell
a st
ory*
Wor
k w
ith a
var
iety
of g
raph
s fo
und
in n
ewsp
aper
s, m
agaz
ines
and
oth
er re
sour
ces
for w
hich
ther
e ar
e no
obv
ious
or a
vaila
ble
equa
tions
and
/or
patte
rns
betw
een
the
varia
bles
repr
esen
ted
in th
e gr
aphs
.
In o
rder
to:
Rec
ogni
se th
at g
raph
s te
ll a
stor
y an
d be
abl
e to
exp
lain
the
stor
y/m
essa
ge/im
pres
sion
repr
esen
ted
in a
gra
ph
Rec
ogni
se th
at g
raph
s re
pres
ent a
rela
tions
hip
betw
een
two
or m
ore
item
s/qu
antit
ies
and
be a
ble
to id
entif
y th
ose
item
s an
d de
scrib
e th
e re
latio
nshi
p
Rec
ogni
se a
nd d
escr
ibe
how
the
shap
e an
d di
rect
ion
of a
gra
ph a
nd c
hang
es to
the
shap
e/di
rect
ion
affe
ct th
e st
ory/
mes
sage
repr
esen
ted
in th
e gr
aph
Rec
ogni
se a
nd d
escr
ibe
the
mea
ning
of d
iffer
ent p
oint
s on
the
grap
h, in
clud
ing:
%�th
e po
int w
here
the
grap
h(s)
cro
ss th
e ve
rtica
l and
hor
izon
tal a
xes;
%�m
axim
um a
nd m
inim
um p
oint
s on
the
grap
h;
%�th
e po
int w
here
diff
eren
t gra
phs
cros
s.
10, 1
1
and
12
add
ition
al c
omm
ents
:
* The
prim
ary
purp
ose
of th
is s
ectio
n is
to p
rovi
de le
arne
rs w
ith th
e op
portu
nity
to in
vest
igat
e a
varie
ty o
f diff
eren
t typ
es o
f gra
phs
in o
rder
to d
evel
op a
feel
for
wor
king
with
gra
phs
and
an u
nder
stan
ding
that
gra
phs
tell
a st
ory
and
pres
ent a
mes
sage
to th
e re
ader
, with
out g
ettin
g bo
gged
dow
n by
form
al m
athe
mat
ical
pr
oced
ures
invo
lvin
g eq
uatio
ns, p
lotti
ng p
oint
s, s
ubst
itutio
n, e
tc. T
his
sect
ion
is a
lso
inte
nded
to p
rovi
de le
arne
rs w
ith th
e op
portu
nity
to d
escr
ibe
grap
hs u
sing
ev
eryd
ay a
nd/o
r fam
iliar
term
inol
ogy
(e.g
. “go
ing
up”;
“top”
) rat
her t
han
expl
icit
mat
hem
atic
al te
rmin
olog
y (e
.g. “
incr
easi
ng”;
“max
imum
”). T
he fo
cus
in th
is s
ectio
n m
ust b
e on
und
erst
andi
ng th
e gr
aphs
and
the
mes
sage
dis
play
ed in
the
grap
hs ra
ther
than
on
form
al g
raph
ing
proc
edur
es a
nd te
rmin
olog
y.
MATHEMATICAL LITERACY GRADES 10-12
38 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Pat
tern
s an
d re
latio
nshi
ps
Wor
k w
ith th
e fo
llow
ing
type
s of
form
al re
latio
nshi
ps b
etw
een
quan
titie
s fo
und
in b
oth
num
eric
al (e
.g. c
ell p
hone
cos
ts) a
nd g
eom
etric
(e.g
. tili
ng
patte
rns)
form
s in
the
cont
ext o
f situ
atio
ns in
volv
ing
the
topi
cs o
f Fin
ance
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sure
men
t, 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
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nce
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onst
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tions
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irect
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MATHEMATICAL LITERACY GRADES 10-12
39CAPS
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
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tern
s an
d re
latio
nshi
ps
(con
tinue
d)
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MATHEMATICAL LITERACY GRADES 10-12
40 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
ion
Con
tent
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MATHEMATICAL LITERACY GRADES 10-12
41CAPS
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
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Con
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12
MATHEMATICAL LITERACY GRADES 10-12
42 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Patte
rns,
rela
tions
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and
repr
esen
tatio
nsG
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s 10
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and
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topi
c:
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and
repr
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tatio
nsG
rade
s 10
, 11
and
12
sect
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11
MATHEMATICAL LITERACY GRADES 10-12
44 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
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sol
ve p
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rela
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nd
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add
ition
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omm
ents
:*
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rade
11
it is
exp
ecte
d th
at le
arne
rs w
ill w
ork
with
two
rela
tions
hips
in a
repr
esen
tatio
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ble
and/
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raph
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paris
ons
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ose
rela
tions
hips
.
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rade
12
it is
exp
ecte
d th
at le
arne
rs w
ill w
ork
with
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ore
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in a
repr
esen
tatio
n (ta
ble
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raph
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paris
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ted
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eter
min
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e va
lues
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hich
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ore
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ulat
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atio
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sly)
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her,
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uld
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essa
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stim
ate
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valu
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ende
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phs
and/
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alue
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esen
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bles
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ovem
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and
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titut
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ctio
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e re
latio
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ps.
MATHEMATICAL LITERACY GRADES 10-12
45CAPS
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Wor
king
with
tw
o or
mor
e re
latio
nshi
ps
(con
tinue
d)
Com
pare
repr
esen
tatio
ns o
f tw
o (G
rade
11)
or m
ore
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de 1
2) re
latio
nshi
ps (f
rom
thos
e de
scrib
ed a
bove
) tha
t des
crib
e al
tern
ativ
e op
tions
/sol
utio
ns,
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%�di
ffere
nces
in th
e ra
tes
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hang
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n th
e de
pend
ent a
nd in
depe
nden
t var
iabl
es fo
r eac
h of
the
rela
tions
hips
*
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ffere
nces
in th
e st
eepn
ess
of g
raph
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pres
entin
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latio
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atio
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raph
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e re
latio
nshi
ps*
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valu
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e us
ed to
sol
ve p
robl
ems
rela
ting
to c
onte
xts
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sure
men
t, 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
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nd
12
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riff s
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nce�IRU�P
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e of
com
paris
ons
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o or
mor
e re
latio
nshi
ps.
MATHEMATICAL LITERACY GRADES 10-12
46 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Patte
rns,
rela
tions
hips
and
repr
esen
tatio
nsG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
a
Poss
ible
ass
essm
ent:
Inve
stig
atio
n: C
ompa
rison
of c
osts
on
diffe
rent
cel
l pho
ne s
yste
ms
%�Fi
nd a
dver
ts fo
r tw
o di
ffere
nt ty
pes
of c
ell p
hone
sys
tem
s in
a n
ewsp
aper
(e.g
. a p
re-p
aid
cell
phon
e an
d a
cont
ract
cel
l pho
ne)
%�Fi
nd o
ut th
e ta
riffs
cha
rged
for t
wo
diffe
rent
type
s of
cel
l pho
nes
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. pre
-pai
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stem
and
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ontra
ct s
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raw
gra
phs
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pres
ent t
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onth
ly c
ost o
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l pho
ne s
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m
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se th
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aphs
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ake
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duct
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t whi
ch c
ell p
hone
sys
tem
wou
ld b
e be
tter f
or y
ou b
ased
on
the
min
utes
of t
alkt
ime
that
you
use
dur
ing
the
mon
th.
11
Poss
ible
ass
essm
ent:
Inve
stig
atio
n: C
ompa
rison
of c
osts
on
diffe
rent
ele
ctric
ity s
yste
ms
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rged
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ree
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ems
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phs
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ent t
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onth
ly c
ost o
f ele
ctric
ity o
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ch o
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tem
s
%�U
se th
e gr
aphs
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ake
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duct
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t whi
ch e
lect
ricity
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tem
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t sui
tabl
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d co
st e
ffect
ive
for a
n in
divi
dual
with
par
ticul
ar n
eeds
.
12
MATHEMATICAL LITERACY GRADES 10-12
47CAPS
Part 2:
application topics
MATHEMATICAL LITERACY GRADES 10-12
48 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c: F
inan
ceG
rade
s 10
, 11
and
12
sugg
este
d te
achi
ng ti
me:
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*UDGH��������������ZHHNV
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rec
omm
ende
d te
xts
and/
or re
sour
ces:
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xtbo
oks
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HQWV�UHODWLQJ�WR�SHUVRQDO��KRXVHKROG��Z
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FRQWH[WV�DQG�PRUH�FRPSOH[�¿QDQFLDO�WRSLFV��H�J��KRXVHKROG�ELOOV��EDQN�DQG�VWRUH�DFFRXQW�VWDWHPHQWV��DGYHUWV�
show
ing
car a
nd h
ome
loan
con
ditio
ns; t
ax fo
rms)
scop
e of
con
text
s an
d/or
con
tent
per
sec
tion
and
grad
e:
sect
ion
Gra
de 1
0G
rade
11
Gra
de 1
2Fi
nanc
ial d
ocum
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text
s ar
e lim
ited
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ose
that
dea
l with
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ith p
erso
nal,
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lace
and
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orga
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MATHEMATICAL LITERACY GRADES 10-12
49CAPS
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Fina
ncia
l do
cum
ents
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old
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ctric
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ater
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ne, c
ell p
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shop
ping
doc
umen
ts (e
.g. t
ill s
lips,
acc
ount
sta
tem
ents
)�-
bank
ing
docu
men
ts*
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. ban
k st
atem
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ctur
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old
budg
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10, 1
1 an
d 12
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udge
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ns; i
nvoi
ces;
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ipts
; tra
vel a
llow
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im fo
rms;
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king
doc
umen
ts*
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nd
12
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te ta
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mpl
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me
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:o
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ondi
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stat
emen
ts fr
om b
anks
and
oth
er lo
an in
stitu
tions
sho
win
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an a
gree
men
t (e.
g. in
tere
st ra
te a
nd m
onth
ly re
paym
ent c
hang
es)
12
In o
rder
to�
Und
erst
and
term
inol
ogy
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in d
ocum
ents
, inc
ludi
ng:
Gra
des
10, 1
1 an
d 12
:G
rade
s 11
and
12:
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te o
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riod
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e do
cum
ent
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st ra
tes
%�re
paym
ent a
mou
nts
and
perio
ds%�
resi
dual
%�re
al c
ost o
r tot
al c
ost
Exp
lain
and
dem
onst
rate
how
the
valu
es a
ppea
ring
in th
e do
cum
ents
hav
e be
en d
eter
min
ed.
10, 1
1 an
d 12
MATHEMATICAL LITERACY GRADES 10-12
50 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Fina
ncia
l do
cum
ents
(con
tinue
d)
add
ition
al c
omm
ents
: �)RU�D�GHVFULSWLRQ�RI�WKH�WHUPLQRORJ\�UHODWLQJ�VSHFL¿FDOO\�WR�b
udge
ts a
nd b
anki
ng d
ocum
ents
, see
the
sect
ions
bel
ow o
n ,QFRPH��H[SHQGLWXUH��SUR¿W�ORVV��LQFRP
H�DQG�
expe
nditu
re s
tate
men
ts a
nd b
udge
ts a
nd %DQNLQJ��ORDQV�DQG�LQYHVWPHQWV
.
a
Poss
ible
ass
essm
ent:
Ass
ignm
ent:
Dem
onst
rate
the
unde
rsta
ndin
g of
a h
ouse
hold
bill
Ana
lyse
a h
ouse
hold
bill
(ele
ctric
ity, w
ater
, tel
epho
ne, e
tc.)
and
expl
ain
how
the
diffe
rent
cos
t val
ues
on th
e bi
ll ha
ve b
een
dete
rmin
ed.
10
Poss
ible
ass
essm
ent:
Ass
ignm
ent: 8QGHUVWDQGLQJ�WKH�³7D[�3RFNHW�*
XLGH´
5HDG�WKURXJK�DQG�DQVZ
HU�TXHVWLRQV�UHODWLQJ�WR�WKH�³7D[�3RFNHW�*
XLGH´�EURFKXUH�LVVXHG�E\�6$56�
12
Tarif
f sys
tem
s
Wor
k w
ith th
e fo
llow
ing
tarif
f sys
tem
s:%�
mun
icip
al ta
riffs
(e.g
. HOHFWULFLW\��Z
DWHU��VHZ
DJH)
%�te
leph
one
tarif
fs (e
.g. FHOO�SKRQH�DQG�¿[HG�OLQH)
%�tra
nspo
rt ta
riffs
(e.g
. bus
, tax
i and
trai
n ta
riffs
)%�
bank
fees
.In
ord
er to�
Cal
cula
te c
osts
usi
ng g
iven
tarif
fs a
nd/o
r for
mul
ae.
Dra
w a
nd in
terp
ret g
raph
s of
var
ious
tarif
fs s
yste
ms.
*10
, 11
and
12
Com
pare
two
(Gra
de 1
1) o
r mor
e (G
rade
12)
diff
eren
t opt
ions
for a
tarif
f sys
tem
to d
eter
min
e th
e m
ost a
ppro
pria
te o
ptio
n fo
r ind
ivid
uals
with
par
ticul
ar
need
s (e
.g. c
ompa
ring
pre-
paid
ver
sus
cont
ract
cel
l pho
ne c
osts
) by:
%�pe
rform
ing
calc
ulat
ions
%�dr
awin
g gr
aphs
to re
pres
ent t
he d
iffer
ent o
ptio
ns a
nd in
terp
retin
g th
e po
int(s
) of i
nter
sect
ion
and
othe
r reg
ions
on
the
grap
hs in
rela
tion
to th
e co
ntex
t+
11 a
nd
12
add
ition
al c
omm
ents
: �,Q�*UDGH����OHDUQHUV�DUH�H[SHFWHG�WR�EH�DEOH�WR�GUDZ�DQG�LQWHUSUHW�FRQVWDQW��¿[HG���OLQHDU�DQG�LQYHUVH�SURSRUWLRQ�JUDSKV��$
V�VXFK��*
UDGH����OHDUQHUV�FDQ�RQO\�EH�
H[SHFWHG�WR�GUDZ�JUDSKV�RI�WDULII�V\VWHPV�WKDW�UHODWH�WR�WKHVH�W\SHV�RI�JUDSKV��)RU�PRUH�VSHFL¿F�GHWDLOV��UHIHU�WR�WKH�WRSLF�
Pat
tern
s, re
pres
enta
tions
and
rela
tions
hips
.In
Gra
des
11 a
nd 1
2 th
ere
is n
o lim
itatio
n on
the
type
s of
gra
phs
that
lear
ners
are
exp
ecte
d to
be
able
to d
raw
to d
emon
stra
te th
eir u
nder
stan
ding
of t
ariff
sys
tem
s.+ �/
HDUQHUV�DUH�QRW�H[SHFWHG�WR�¿QG�EUHDN�HYHQ�YDOXHV�IRU�VFHQDULRV�LQYROYLQJ�GLIIHUHQW�WDULII�V\VWHPV�WKURXJK�DOJHEUDLF�FDOFXODWLRQV��WKDW�LV��VROYLQJ�HTXDWLRQV�
sim
ulta
neou
sly)
. Rat
her,
they
sho
uld
be a
ble
to re
ad o
ff an
d, if
nec
essa
ry, e
stim
ate
the
valu
es o
f the
dep
ende
nt a
nd in
depe
nden
t var
iabl
es fo
r whi
ch th
e gr
aphs
are
eq
ual d
irect
ly fr
om th
e ax
es.
)RU�P
RUH�VSHFL¿F�GHWDLOV�RQ�WKH�FRQWHQW�DQG�RU�VNLOOV�DQG�DSSURDFK�WKDW�OHDUQHUV�DUH�H[SHFWHG�WR�ZRUN�ZLWK�LQ�GHWHUPLQLQJ�SRLQWV�RI�LQWHUVHFWLRQ�RI�JUDSKV��UHIHU�WR�WKH�
sect
ion :RUNLQJ�ZLWK�WZ
R�RU�PRUH�UHODWLRQVKLSV
and
/or r
epre
sent
atio
ns in
the
topi
c P
atte
rns,
rela
tions
hips
and
repr
esen
tatio
ns.
a
Poss
ible
ass
essm
ent:
%�In
vest
igat
ion:
:KLFK�FHOO�SKRQH"
%�U
se c
alcu
latio
ns, g
raph
s an
d br
eak-
even
ana
lysi
s to
com
pare
the
optio
ns p
rese
nted
in tw
o di
ffere
nt c
ell p
hone
adv
erts
%�D
iscu
ss n
on-m
athe
mat
ical
con
side
ratio
ns th
at a
ffect
the
type
of c
ell p
hone
opt
ion
a pe
rson
may
cho
ose.
11
MATHEMATICAL LITERACY GRADES 10-12
51CAPS
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Inco
me,
ex
pend
iture
, SUR¿W�ORVV��
inco
me-
and-
expe
nditu
re
stat
emen
ts
and
budg
ets*
,GHQWLI\�DQG�SHUIRUP�FDOFXODWLRQV�LQYROYLQJ�LQFRPH��H[SHQGLWXUH��SUR¿W�DQG�ORVV�YDOXHV��LQFOXGLQJ�
%�Fi
xed,
var
iabl
e an
d oc
casi
onal
inco
me�YDOXHV�DQG�¿[HG��YDULDEOH��RFFDVLRQDO��KLJK�SULRULW\�DQG�ORZ�SULRULW\�
expe
nditu
re v
alue
s fro
m th
e fo
llow
ing
sour
ces:
�-pe
rson
al in
com
e:
o sa
larie
s, w
ages
and
com
mis
sion
o gi
fts a
nd p
ocke
t mon
ey
o bu
rsar
ies
and
loan
s
o sa
ving
s
o in
tere
st
o in
herit
ance
�-pe
rson
al e
xpen
ditu
re:
o liv
ing
expe
nses
(e.g
. foo
d, c
loth
ing,
ent
erta
inm
ent)
o ac
coun
ts (e
.g. HOHFWULFLW\�DQG�ZDWHU
)
o te
leph
one
o fe
es (e
.g.�VFKRRO�IHHV�DQG�EDQN�IHHV
)
o in
sura
nce
(e.g
. car
, hou
seho
ld a
nd m
edic
al a
id)
o pe
rson
al ta
xes
o lo
an re
paym
ents
(e.g
. sto
re a
ccou
nts)
o sa
ving
s
10, 1
1 an
d 12
�-bu
sine
ss a
nd/o
r wor
kpla
ce in
com
e:
o in
com
e fro
m s
ales
and
/or s
ervi
ces
rend
ered
o do
natio
ns a
nd/o
r gra
nts
o in
tere
st o
n m
oney
in a
ccou
nts
and/
or in
vest
men
ts
�-bu
sine
ss a
nd/o
r wor
kpla
ce e
xpen
ditu
re:
o sa
larie
s, w
ages
and
com
mis
sion
o ru
nnin
g ex
pens
es (e
.g. s
ervi
ces,
tele
phon
e, re
nt)
o in
vest
men
ts a
nd s
avin
gs
o ta
xes
11 a
nd
12
�-in
com
e fo
r lar
ger o
rgan
isat
ions
(e.g
. tax
es fo
r a g
over
nmen
t).�-
expe
nditu
re fo
r lar
ger o
rgan
isat
ions
(e.g
. mun
icip
ality
).12
In o
rder
to�
0DQDJH�¿QDQFHV�E\�
%�an
alys
ing
and
prep
arin
g in
com
e-an
d-ex
pend
iture
sta
tem
ents
and
bud
gets
, with
an
awar
enes
s of
the
diffe
renc
e be
twee
n th
ese
two
docu
men
ts, f
or:
�-an
indi
vidu
al a
nd/o
r hou
seho
ld
�-a
trip
(e.g
. hol
iday
)
�-SHUVRQDO�SURMHFWV��H�J��GLQQHU�SDUW\��VLJQL¿FDQW�SXUFKDVHV�VXFK�DV�D�FHOO�SKRQH��WHOHYLVLRQ�RU�IXUQLWXUH�
10, 1
1 an
d 12
�-a
smal
l bus
ines
s (e
.g. s
paza
sho
p), i
nclu
ding
:
o D�FRPSDULVRQ�RI�LQFRP
H�H[SHQGLWXUH�SUR¿W�YDOXHV�RYHU�WZ
R�\HDUV�
(ana
lysi
s on
ly)
o EXGJHWV�VKRZ
LQJ�D�FRPSDULVRQ�RI�SURMHFWHG�YHUVXV�DFWXDO�LQFRPH��H[SHQGLWXUH�DQG�SUR¿W�ORVV�YDOXHV�
(ana
lysi
s on
ly)
�-la
rge
proj
ects
and
/or e
vent
s (e
.g. f
und-
rais
ing
even
t or a
wed
ding
)
11 a
nd
12
MATHEMATICAL LITERACY GRADES 10-12
52 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Inco
me,
ex
pend
iture
, SUR¿W�ORVV��
inco
me-
and-
expe
nditu
re
stat
emen
ts
and
budg
ets
(con
tinue
d)
�-la
rge
orga
nisa
tions
(ana
lysi
s on
ly) (
e.g.
mun
icip
ality
or p
rovi
ncia
l/nat
iona
l gov
ernm
ent),
incl
udin
g:
o D�FRPSDULVRQ�RI�LQFRP
H�H[SHQGLWXUH�SUR¿W�YDOXHV�RYHU�WZ
R�\HDUV
o EXGJHWV�VKRZ
LQJ�D�FRPSDULVRQ�RI�SURMHFWHG�YV�DFWXDO�LQFRPH��H[SHQGLWXUH�DQG�SUR¿W�ORVV�YDOXHV
12
%�co
nsid
erin
g th
e im
porta
nce
of s
avin
g fo
r occ
asio
nal o
r fut
ure
expe
nses
.10
, 11
and
12
add
ition
al c
omm
ents
:*
In G
rade
s 10
and
11
it is
exp
ecte
d th
at le
arne
rs w
ill b
e ab
le to
wor
k w
ith in
com
e-an
d-ex
pend
iture
sta
tem
ents
and
bud
gets
con
tain
ing
reas
onab
ly s
mal
l and
sim
ple
mon
ey v
alue
s ap
prop
riate
to p
erso
nal,
hous
ehol
d, w
orkp
lace
and
sm
all b
usin
ess
cont
exts
. In
Gra
de 1
2, it
is e
xpec
ted
that
lear
ners
will
be
able
to w
ork
with
inco
me-
and-
expe
nditu
re s
tate
men
ts a
nd b
udge
ts c
onta
inin
g la
rge
and
com
plex
mon
ey v
alue
s, in
clud
ing
valu
es e
xpre
ssed
in th
ousa
nds,
hun
dred
s of
thou
sand
s, m
illio
ns a
nd
billi
ons.
a
Poss
ible
ass
essm
ent (
inco
rpor
atin
g Fi
nanc
e an
d d
ata
hand
ling,
i.e.
col
lect
ing
data
):A
ssig
nmen
t: D
evel
opin
g a
hous
ehol
d bu
dget
%�K
eep
a re
cord
of h
ouse
hold
inco
me
and
expe
nditu
re fo
r a ti
me
perio
d
%�D
raw
up
a st
atem
ent o
f inc
ome
and
expe
nditu
re fo
r the
hou
seho
ld
%�$QDO\VH�WKH�VWDWHP
HQW�DQG�VXJJHVW�KRZ
�WKH�¿QDQFLDO�SRVLWLRQ�RI�WKH�KRXVHKROG�FRXOG�EH�FKDQJHG�RU�LP
SURYHG�
10
Cos
t pric
e an
d se
lling
pric
e*
Iden
tify
the
cost
s as
soci
ated
with
pro
duci
ng/m
anuf
actu
ring
an it
em o
r ren
derin
g a
serv
ice
in th
e co
ntex
t of:
%�a
hom
e in
dust
ry (e
.g. EUHDG�EDNLQJ�EXVLQHVV
)
%�sm
all b
usin
ess
(e.g
. WXFN�VKRS��VWUHHW�YHQGRU��ÀHD�PDUNHW�VWDOO��FHOO�SKRQH�FRQWDLQHU�EXVLQHVV��JDUGHQ�VHUYLFHV��SDLQWLQJ�EXVLQHVV��FDU�ZDVK��KDLUGUHVVHU��FDWHULQJ�
busi
ness
; crè
che;
sub
sist
ence
farm
ing)
.
In o
rder
to�
Det
erm
ine
the
cost
of p
rodu
ctio
n an
d/or
cos
t pric
e of
an
item
or s
ervi
ce, w
ith a
n un
ders
tand
ing
of th
e di
ffere
nce
betw
een
thes
e tw
o co
sts.
'HFLGH�RQ�DQ�DSSURSULDWH�VHOOLQJ�SULFH�IRU�DQ�LWHP�DQG�RU�VHUYLFH�EDVHG�RQ�DQ�H[SHFWHG�SHUFHQWDJH�SUR¿W�
11 a
nd
12
Inve
stig
ate
the
runn
ing
of a
sm
all b
usin
ess
with
con
side
ratio
n of
the
follo
win
g fo
r the
bus
ines
s:
%�in
com
e-an
d-ex
pend
iture
sta
tem
ents
%�bu
dget
s
%�br
eak-
even
ana
lysi
s (s
ee th
e se
ctio
n be
low
on %UHDN�HYHQ�DQDO\VLV
)
%�th
e co
st o
f pro
duct
ion,
cos
t pric
e an
d se
lling
pric
e of
an
item
or s
ervi
ce s
old/
rend
ered
by
the
busi
ness
.
12
add
ition
al c
omm
ents
:* T
his
sect
ion
on C
ost p
rice
and
selli
ng p
rice
appl
ies
only
to G
rade
11
and
Gra
de 1
2 le
arne
rs.
MATHEMATICAL LITERACY GRADES 10-12
53CAPS
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Bre
ak-e
ven
anal
ysis
*
Det
erm
ine
brea
k-ev
en v
alue
s us
ing
the
follo
win
g m
etho
ds:
%�dr
awin
g tw
o (G
rade
11)
or m
ore
(Gra
de 1
2) g
raph
s on
a s
et o
f axe
s an
d re
adin
g of
f the
poi
nts
of in
ters
ectio
n of
the
grap
hs
%�tri
al a
nd im
prov
emen
t thr
ough
sub
stitu
tion
into
two
or m
ore
equa
tions
repr
esen
ting
the
scen
ario
and
/or g
raph
s.
Und
erst
and
the
follo
win
g co
mpo
nent
s of
bre
ak-e
ven
anal
ysis
:
%�th
e br
eak-
even
poi
nt is
alw
ays
mad
e up
of t
wo
valu
es (e
.g. t
he n
umbe
r of i
tem
s th
at s
houl
d be
sol
d an
d th
e am
ount
of m
oney
that
sho
uld
be m
ade
from
th
e sa
le o
f tho
se it
ems)
%�th
e re
leva
nce/
mea
ning
of t
he b
reak
-eve
n va
lues
is d
eter
min
ed b
y th
e co
ntex
t in
whi
ch th
e br
eak-
even
val
ues
occu
r.
In o
rder
to�
Mak
e se
nse
of s
ituat
ions
invo
lvin
g:
%�th
e br
eak-
even
val
ues
for a
bus
ines
s w
ith c
onsi
dera
tion
of c
ost p
rice,
sel
ling
pric
e, in
com
e an
d ex
pend
iture
val
ues
%�th
e va
lues
for w
hich
two
(Gra
de 1
1) o
r mor
e (G
rade
12)
diff
eren
t cos
ting
optio
ns a
re e
qual
(e.g
. diff
eren
t cel
l pho
ne o
r ele
ctric
ity c
ostin
g op
tions
).
11 a
nd
12
add
ition
al c
omm
ents
: �/HDUQHUV�DUH�QRW�H[SHFWHG�WR�¿QG�EUHDN�HYHQ�YDOXHV�IRU�VFHQDULRV�WKURXJK�DOJHEUDLF�FDOFXODWLRQV��WKDW�LV��VROYLQJ�HTXDWLRQV�VLPXOWDQHRXVO\���5
DWKHU��WKH\�VKRXOG�EH�
able
to re
ad o
ff an
d, if
nec
essa
ry, e
stim
ate
the
valu
es o
f the
dep
ende
nt a
nd in
depe
nden
t var
iabl
es fo
r whi
ch th
e gr
aphs
are
equ
al d
irect
ly fr
om th
e ax
es.
* Thi
s se
ctio
n on
%UHDN�HYHQ�DQDO\VLV
app
lies
only
to G
rade
11
and
Gra
de 1
2 le
arne
rs.
Exa
mpl
es o
f con
text
s an
d/or
reso
urce
s in
whi
ch th
e co
ncep
t of b
reak
-eve
n ca
n be
exp
lore
d:
%�sm
all h
ome
indu
stry
(e.g
. EUHDG�EDNLQJ�EXVLQHVV
)
%�sm
all b
usin
ess
(e.g
.�WXFN�VKRS��VWUHHW�YHQGRU��ÀHD�PDUNHW�VWDOO��FHOO�SKRQH�FRQWDLQHU�EXVLQHVV��JDUGHQ�VHUYLFHV��SDLQWLQJ�EXVLQHVV��FDU�ZDVK��FDWHULQJ�EXVLQHVV
)
%�su
bsis
tenc
e fa
rmin
g
%�el
ectri
city
tarif
f sys
tem
s
%�te
leph
one
tarif
f sys
tem
s
%�re
ntal
opt
ions
(e.g
. hiri
ng a
pho
toco
pier
);
%�et
c.
a
Poss
ible
ass
essm
ent:
Ass
ignm
ent:
Run
ning
a h
ome
indu
stry
bus
ines
s
%�In
vest
igat
e th
e va
rious
fact
ors
invo
lved
in ru
nnin
g a
smal
l hom
e in
dust
ry b
usin
ess
%�bu
dget
s an
d in
com
e-an
d-ex
pend
iture
sta
tem
ents
%�co
st p
rice
and
selli
ng p
rice
of it
ems
mad
e an
d so
ld fo
r the
bus
ines
s
%�th
e br
eak-
even
val
ues
for t
he b
usin
ess.
11
MATHEMATICAL LITERACY GRADES 10-12
54 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Inte
rest
:RUN�ZLWK�YDULRXV�EDQNLQJ�DQG�RWKHU�¿QDQFLDO�GRFXP
HQWV��H�J��EDQN�VWDWHP
HQWV��DFFRXQW�VWDWHPHQWV�VKRZLQJ�LQWHUHVW�UDWHV�RQ�D�GHELW�EDODQFH)
.
In o
rder
to�
'LVWLQJXLVK�EHWZHHQ�³LQWHUHVW�UDWH´�YDOXHV�DQG�³LQWHUHVW´�YDOXHV�
Inve
stig
ate
thro
ugh
calc
ulat
ion
how
inte
rest
val
ues
are
calc
ulat
ed u
sing
inte
rest
rate
val
ues.
10
Per
form
cal
cula
tions
invo
lvin
g si
mpl
e an
d co
mpo
und
inte
rest
thro
ugh
man
ual c
alcu
latio
ns a
nd w
ithou
t the
use
of f
orm
ulae
*.
Rep
rese
nt s
impl
e in
tere
st g
row
th s
cena
rios
usin
g lin
ear g
raph
s an
d co
mpo
und
inte
rest
gro
wth
sce
nario
s us
ing
grap
hs s
how
ing
com
poun
d ch
ange
.
In o
rder
to
Inve
stig
ate
the
follo
win
g sc
enar
ios+ :
%�lo
an a
gree
men
ts b
etw
een
fam
ily m
embe
rs w
here
repa
ymen
ts a
re m
ade
only
onc
e at
the
end
of th
e lo
an
%�LQYHVWPHQWV�LQ�¿[HG�GHSRVLW�DFFRXQWV�ZKHUH�WKH�PRQH\�LV�GHSRVLWHG�DQG�ZLWKGUDZ
Q�IURP�WKH�DFFRXQW�RQO\�RQFH
%�ba
nk a
ccou
nts
with
a c
hang
ing
bala
nce
11 a
nd
12
%�hi
re-p
urch
ase
agre
emen
ts a
nd lo
ans
(e.g
. per
sona
l, ca
r, ho
use)
whe
re a
repa
ymen
t is
mad
e ev
ery
mon
th
%�ot
her i
nves
tmen
ts (e
.g. r
etire
men
t ann
uitie
s, fu
nera
l pla
ns��Z
KHUH�D�¿[HG�GHSRVLW�LV�PDGH�HYHU\�PRQWK�
12
add
ition
al c
omm
ents
:
* Le
arne
rs a
re n
ot e
xpec
ted
to w
ork
with
any
form
ulae
her
e. T
he fo
cus
is o
n de
velo
ping
an
unde
rsta
ndin
g of
the
conc
ept o
f a c
ompo
undi
ng c
alcu
latio
n, th
at is
, whe
re
the
valu
es u
sed
in a
cal
cula
tion
draw
on
answ
ers/
valu
es fr
om a
pre
viou
s ca
lcul
atio
n.
Lear
ners
sho
uld
be a
ble
to:
%�pe
rform
sim
ple
and
com
poun
d in
tere
st c
alcu
latio
ns m
anua
lly u
sing
a b
asic
cal
cula
tor,
pen
and
pape
r, an
d/or
spr
eads
heet
s
%�in
terp
ret a
nd u
se ta
bles
sho
win
g co
mpo
unde
d va
lues
.+ F
or m
ore
info
rmat
ion
on th
ese
scen
ario
s, s
ee th
e se
ctio
n bel
ow o
n %DQNLQJ��ORDQV�DQG�LQYHVWPHQWV
a
Poss
ible
ass
essm
ent:
Inve
stig
atio
n��&RP
SDULQJ�VLPSOH�DQG�FRPSRXQG�LQWHUHVW�JUDSKLFDOO\
Inve
stig
ate
the
diffe
renc
e be
twee
n si
mpl
e an
d co
mpo
und
inte
rest
sce
nario
s by
dra
win
g an
d co
mpa
ring
grap
hs o
f the
se s
cena
rios.
11
MATHEMATICAL LITERACY GRADES 10-12
55CAPS
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Ban
king
, lo
ans
and
inve
stm
ents
(b
anki
ng)
Inve
stig
ate
the
follo
win
g ty
pes
of b
ank
acco
unts
:
%�sa
ving
s ac
coun
t
%�ch
eque
/cur
rent
acc
ount
%�¿[HG�GHSRVLW�DFFRXQW
%�cr
edit
acco
unt (
with
a c
redi
t car
d) a
nd a
deb
it ac
coun
t (w
ith a
deb
it ca
rd).
In o
rder
to�
10, 1
1 an
d 12
Inte
rpre
t ban
king
doc
umen
ts (e
.g. EDQN�VWDWHP
HQWV�DQG�IHHV�EURFKXUHV
) and
und
erst
and
the
follo
win
g te
rmin
olog
y in
the
docu
men
ts:
10
%�op
enin
g an
d cl
osin
g ba
lanc
e
%�de
bit
%�cr
edit
%�st
op o
rder
%�ba
nk c
harg
e or
tran
sact
ion
fee
%�de
bit o
rder
%�AT
M
%�el
ectro
nic
trans
fer
%�pa
ymen
t
%�in
tere
st
%�cr
edit
rate
s;
%�de
bit r
ates
%�br
anch
%�de
posi
t
%�w
ithdr
awal
Det
erm
ine
bank
cha
rges
for d
iffer
ent t
ypes
of a
ccou
nts
usin
g gi
ven
fee
tabl
es a
nd fo
rmul
ae.
Dra
w g
raph
s fro
m g
iven
ban
k ch
arge
form
ulae
to re
pres
ent b
ank
char
ges
for d
iffer
ent t
rans
actio
n am
ount
s on
diff
eren
t typ
es o
f acc
ount
s.
Com
pare
ban
k ch
arge
s of
diff
eren
t ban
ks u
sing
tarif
f tab
les,
giv
en fo
rmul
ae a
nd d
raw
n gr
aphs
to a
sses
s th
e su
itabi
lity
of d
iffer
ent a
ccou
nts
for i
ndiv
idua
ls
with
par
ticul
ar n
eeds
.
Inve
stig
ate
the
adva
ntag
es a
nd d
isad
vant
ages
of t
he d
iffer
ent t
ypes
of a
ccou
nts
rega
rdin
g ac
cess
to m
oney
, ban
k ch
arge
s an
d in
tere
st ra
tes.
Inve
stig
ate
the
impl
icat
ions
of l
ate
paym
ents
on
a cr
edit
card
acc
ount
.
Inve
stig
ate
the
diffe
rent
way
s in
whi
ch in
tere
st is
cal
cula
ted
on d
iffer
ent t
ypes
of a
ccou
nts
(e.g
. ,QWHUHVW�RQ�D�VDYLQJV�DFFRXQW�LV�FDOFXODWHG�GDLO\�EXW�FRP
SRXQGHG�PRQWKO\��RQ�D�¿[HG�GHSRVLW�DFFRXQW�VLPSOH�LQWHUHVW�LV�FDOFXODWHG�GXULQJ�WKH�PRQWK�
but i
s co
mpo
unde
d on
ly a
t the
end
of t
he m
onth
).
11 a
nd
12
a
Poss
ible
ass
essm
ent:
Ass
ignm
ent: :KLFK�EDQN"
%�Vi
sit t
wo
bank
s an
d co
llect
pric
ing
info
rmat
ion
on a
sim
ilar t
ype
of s
avin
gs a
ccou
nt a
t eac
h ba
nk
%�C
ompa
re th
e co
sts
asso
ciat
ed w
ith th
ese
acco
unts
at t
he tw
o ba
nks
%�D
ecid
e w
hich
ban
k w
ould
be
the
bette
r opt
ion
for a
par
ticul
ar c
usto
mer
.
11
MATHEMATICAL LITERACY GRADES 10-12
56 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Ban
king
, lo
ans
and
inve
stm
ents
(lo
ans
and
inve
stm
ent)*
Inve
stig
ate
the
follo
win
g ty
pes
of lo
an a
nd in
vest
men
t sce
nario
s:
%�in
form
al lo
an a
gree
men
ts b
etw
een
fam
ily m
embe
rs
%�LQYHVWPHQWV�LQ�¿[HG�GHSRVLW�DFFRXQWV�ZKHUH�WKH�PRQH\�LV�GHSRVLWHG�DQG�ZLWKGUDZ
Q�IURP�WKH�DFFRXQW�RQO\�RQFH
%�hi
re-p
urch
ase
agre
emen
ts (e
.g. b
uyin
g fu
rnitu
re o
n cr
edit)
11 a
nd
12
%�lo
ans
from
ban
ks a
nd m
icro
-lend
ers
whe
re th
ere
is a
mon
thly
repa
ymen
t (e.
g. p
erso
nal,
stud
ent,
car a
nd h
ouse
loan
s)
%�in
vest
men
ts w
here
ther
e is
a m
onth
ly d
epos
it, in
clud
ing:
�-st
okve
l
�-re
tirem
ent a
nnui
ties
�-pe
nsio
n fu
nds
�-fu
nera
l pla
ns
12
In o
rder
to��
Iden
tify
and
unde
rsta
nd th
e fo
llow
ing
elem
ents
of l
oan
and
inve
stm
ent s
ituat
ions
:
11 a
nd
12
%�Lo
ans:
�-bo
rrow
er
�-le
nder
�-in
tere
st ra
te
%�In
vest
men
ts:
�-pr
inci
pal
�-in
tere
st ra
te
�-m
onth
ly p
aym
ent
�-de
posi
t
�-re
paym
ent
�-lo
an te
rm (l
ife)
�-in
vest
men
t ter
m (l
ife)
�-in
tere
st
�-ch
arge
s
�-re
al (t
otal
) cos
t of a
loan
�-in
tere
st
�-re
sidu
al (f
or a
car
loan
)
Mod
el lo
an a
nd in
vest
men
t sce
nario
s us
ing
a pe
n, p
aper
, bas
ic c
alcu
lato
r and
tabl
es, s
prea
dshe
ets,
and
/or a
vaila
ble
loan
cal
cula
tors
(e.g
. cal
cula
tors
DYDLODEOH�RQ�EDQN�ZHEVLWHV)
.
Det
erm
ine
the
real
cos
t of a
loan
and
the
inte
rest
pai
d on
a lo
an.
Det
erm
ine
the
tota
l am
ount
of m
oney
in a
n in
vest
men
t at t
he e
nd o
f a c
erta
in ti
me
perio
d.
Mak
e se
nse
of g
raph
s sh
owin
g lo
an a
nd in
vest
men
t sce
nario
s.+
MATHEMATICAL LITERACY GRADES 10-12
57CAPS
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Ban
king
, lo
ans
and
inve
stm
ents
(lo
ans
and
inve
stm
ent)*
(c
ontin
ued)
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Inve
stig
ate
the
effe
ct o
f cha
nges
in th
e m
onth
ly re
paym
ent a
mou
nt o
n th
e re
al c
ost o
f a lo
an.
,QYHVWLJDWH�WKH�HIIHFW�RI�FKDQJHV�LQ�WKH�PRQWKO\�LQYHVWPHQW�DPRXQW�RQ�WKH�YDOXH�RI�WKH�¿QDO�LQYHVWPHQW�
12
add
ition
al c
omm
ents
: �/HDUQHUV�DUH�QRW�H[SHFWHG�WR�NQRZ�FRP
SOH[�¿QDQFLDO�IRUPXODH��5
DWKHU��LW�LV�H[SHFWHG�WKDW�WKH\�ZLOO�GHYHORS�DQ�XQGHUVWDQGLQJ�RI�ORDQV�XVLQJ�D�SHQ��SDSHU�DQG�
calc
ulat
or te
chni
ques
and
thro
ugh
mod
ellin
g lo
an s
cena
rios
usin
g ta
bles
and
gra
phs.
+ �)RU�PRUH�VSHFL¿F�GHWDLOV�RQ�WKH�FRQWHQW�DQG�RU�VNLOOV�DQG�DSSURDFK�WKDW�OHDUQHUV�DUH�H[SHFWHG�WR�ZRUN�ZLWK�LQ�*UDGH����UHJDUGLQJ�GUDZ
LQJ��LQWHUSUHWLQJ�DQG�DQDO\VLQJ�
grap
hs, s
ee th
e se
ctio
n R
epre
sent
atio
ns o
f rel
atio
nshi
ps (g
raph
s) in
the
topi
c P
atte
rns,
rela
tions
hips
and
repr
esen
tatio
ns.
Exa
mpl
es o
f add
ition
al c
onte
xts
in w
hich
the
conc
epts
of l
oans
and
inve
stm
ents
can
be
expl
ored
incl
ude:
%�ed
ucat
ion
inve
stm
ent s
chem
es
%�lif
e in
sura
nce
polic
ies
%�an
y ot
her f
orm
al o
r inf
orm
al lo
an a
nd in
vest
men
t sce
nario
s.
a
Poss
ible
ass
essm
ent
Ass
ignm
ent:
Mod
ellin
g a
loan
%�U
se ta
bles
and
/or s
prea
dshe
ets
to c
onst
ruct
a m
odel
of a
loan
sce
nario
%�In
vest
igat
e th
e im
pact
of i
ncre
asin
g m
onth
ly re
paym
ents
on
the
real
cos
t of t
he lo
an
%�In
vest
igat
e th
e im
pact
of c
hang
es in
the
inte
rest
rate
on
the
loan
.
12
MATHEMATICAL LITERACY GRADES 10-12
58 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
,QÀDWLRQ
Inve
stig
ate
chan
ges
in th
e pr
ices
of g
oods
and
/or s
ervi
ces.
In o
rder
to�
Rec
ogni
se th
at:
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HU�RI�P
RQH\�RYHU�WLPH
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aver
age�LQFUHDVH�LQ�WKH�SULFHV�RI�D�YDULHW\�RI�JRRGV�DQG�VHUYLFHV�RYHU�WLPH�DQG�WKDW�GLIIHUHQW�LWHPV�FDQ�KDYH�GLIIHUHQW�LQÀDWLRQ�UDWHV
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%�pu
rcha
sing
pow
er (e
.g. T
hem
bi s
pend
s an
ave
rage
of R
2 20
0,00
per
mon
th o
n gr
ocer
ies.
If h
er s
alar
y re
mai
ns th
e sa
me
but h
er g
roce
ry b
ill in
crea
ses
at
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e va
lue
of a
n ite
m o
ver t
ime
(e.g
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)
%�th
e va
lue
of m
oney
in a
ban
k ac
coun
t and
/or i
nves
tmen
t (di
scus
sion
onl
y).
Com
pare
the
rate
s of
incr
ease
/dec
reas
e in
pric
es th
roug
h ca
lcul
atio
n (e
.g. $
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se fr
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11 a
nd
12
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luat
e si
tuat
ions
invo
lvin
g pr
opos
ed p
rice
incr
ease
s (e
.g. s
alar
y ne
gotia
tions
, sch
ool f
ee in
crea
ses)
.12
a
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Inve
stig
atio
n: 7UDFLQJ�LQÀDWLRQ�LQ�WKH�UHDO�ZRUOG
%�In
vest
igat
e an
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12
MATHEMATICAL LITERACY GRADES 10-12
59CAPS
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
/ski
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deve
lope
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app
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text
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llow
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men
ts:
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tax)
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yslip
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inco
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tax
brac
kets
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ulae
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tabl
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SA
RS
to e
mpl
oyer
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elop
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ndin
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rmin
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AR
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ease
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alar
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ome
tax
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ition
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omm
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se b
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12
MATHEMATICAL LITERACY GRADES 10-12
60 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Fina
nce
Gra
des
10, 1
1 an
d 12
sect
ion
Con
tent
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text
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urre
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imat
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val
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urre
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coun
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lue
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cur
renc
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rela
tion
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ther
cur
renc
ies
and
on th
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lue
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par
ticul
ar c
urre
ncy
in
rela
tion
to th
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st o
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ing
in a
cou
ntry
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han
on re
petit
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rmal
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hem
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to w
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are
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MATHEMATICAL LITERACY GRADES 10-12
61CAPS
topi
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mea
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men
tG
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12
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conv
ersi
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MATHEMATICAL LITERACY GRADES 10-12
62 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c: m
easu
rem
ent
Gra
des
10, 1
1 an
d 12
scop
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con
text
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d/or
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tent
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sec
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grad
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sect
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tent
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topi
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tG
rade
s 10
, 11
and
12
sect
ion
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tent
/ski
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deve
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text
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surin
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65CAPS
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tG
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s 10
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and
12
sect
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tent
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topi
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tG
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s 10
, 11
and
12
sect
ion
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tent
/ski
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deve
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ropr
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text
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surin
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ater
ials
nee
ded
to b
uild
an
RD
P ho
use)
(Gra
de 1
2)
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rder
to:
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sure
out
qua
ntiti
es to
com
plet
e a
task
(e.g
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.
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itor q
uant
ities
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. rai
nfal
l ove
r tim
e).
10, 1
1 an
d 12
Cal
cula
te:
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e co
st o
f a c
erta
in v
olum
e of
a p
rodu
ct (e
.g. FDOFXODWH�WKH�FRVW�RI�����OLWUHV�RI�PLON�DW������OLWUH
)10
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form
ula
invo
lvin
g vo
lum
e (e
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tes
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11 a
nd
12
MATHEMATICAL LITERACY GRADES 10-12
67CAPS
topi
c:
mea
sure
men
tG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Mea
surin
g vo
lum
e*
(con
tinue
d)
add
ition
al c
onte
xts/
reso
urce
s an
d co
mm
ents
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on d
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r mea
surin
g ou
t the
vol
umes
of d
iffer
ent q
uant
ities
of l
iqui
d ob
ject
s us
ing
vario
us m
easu
ring
inst
rum
ents
(e.g
. mea
surin
g ju
gs, a
nd c
ups
and
spoo
ns).
Gra
de 1
0 le
arne
rs a
re n
ot e
xpec
ted
to h
ave
to p
erfo
rm c
alcu
latio
ns o
f vol
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usi
ng a
ppro
pria
te fo
rmul
ae: r
athe
r, em
phas
is m
ust b
e pl
aced
on
unde
rsta
ndin
g th
e co
ncep
t of v
olum
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d m
easu
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volu
mes
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se th
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tern
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r tim
e.
11
Mea
surin
g te
mpe
ratu
re
Mea
sure
, mon
itor a
nd in
terp
ret t
empe
ratu
re v
alue
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ing
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men
ts a
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ourc
es, i
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ding
:
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omet
er
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mpe
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ials
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ports
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e co
ntex
t of:
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mpl
e ta
sks
in th
e fa
mili
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onte
xt o
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hou
seho
ld (e
.g.�KRXVHKROG�EDNLQJ�FRRNLQJ�FDWHULQJ�SURMHFWV
) (G
rade
10)
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text
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hool
and
/or w
ider
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mun
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rade
11)
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roje
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oth
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rder
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plet
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tem
pera
ture
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rtain
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itor t
he h
ealth
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ld o
r adu
lt (e
.g.�WDNLQJ�WKH�WHPSHUDWXUH�RI�D�VLFN�FKLOG
).
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1 an
d 12
Con
vert
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pera
ture
val
ues
from
deg
rees
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sius
(°C
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degr
ees
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enhe
it (°
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sing
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follo
win
g gi
ven
form
ulae
:*
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2°
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rder
to:
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rpre
t res
ourc
es th
at re
fer t
o te
mpe
ratu
re v
alue
s in
diff
eren
t uni
ts (e
.g.�UHFLSHV��WUDYHO�GRFXP
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).
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n tri
ps, i
nclu
ding
wor
king
with
cur
renc
y co
nver
sion
s (e
xcha
nge
rate
s), t
rave
l bud
gets
, tra
nspo
rt tim
e an
d fa
re ta
bles
(e.g
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), tra
vel m
aps
and
othe
r nec
essa
ry tr
avel
reso
urce
s.+
11 a
nd
12
MATHEMATICAL LITERACY GRADES 10-12
68 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
mea
sure
men
tG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Mea
surin
g te
mpe
ratu
re(c
ontin
ued)
add
ition
al c
onte
xts/
reso
urce
s an
d co
mm
ents
:*
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verti
ng b
etw
een
diffe
rent
tem
pera
ture
uni
ts a
nd/o
r sys
tem
s is
als
o in
clud
ed in
the
sect
ion
on C
onve
rsio
ns (s
ee a
bove
). + T
his st
atem
ent s
houl
d be
taug
ht in
con
junc
tion
with
the
stat
emen
t in
the
sect
ion
on M
aps
in th
e to
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fers
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ust a
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tegr
ated
with
the
sect
ions
on
Bud
gets
and
Exc
hang
e ra
tes
desc
ribed
in th
e to
pic
Fina
nce,
and
tim
etab
les
in th
e to
pic
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sure
men
t (se
e be
low
).
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cula
ting
perim
eter
, ar
ea a
nd
volu
me
Cal
cula
te/m
easu
re th
e pe
rimet
er, a
rea
(incl
udin
g su
rface
are
a) a
nd/o
r vol
ume
of o
bjec
ts*
by:
%�di
rect
mea
sure
men
t (pe
rimet
er u
sing
rule
rs, e
tc.;
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usi
ng g
rids,
etc
.; an
d vo
lum
e us
ing
mea
surin
g ju
gs, e
tc.)
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lcul
atio
n fo
r eac
h of
the
follo
win
g:�-
rect
angl
es, t
riang
les
and
circ
les
(qua
rter,
sem
i and
thre
e-qu
arte
rs) u
sing
kno
wn
form
ulae
+10
, 11
and
12
�-re
ctan
gula
r pris
ms
and
cylin
ders
usi
ng k
now
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rmul
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lcul
atio
n fo
r obj
ects
that
can
be
deco
mpo
sed
into
thos
e lis
ted
abov
e.11
and
12
In th
e co
ntex
t of:
%�si
mpl
e ta
sks
in th
e fa
mili
ar c
onte
xt o
f the
hou
seho
ld (e
.g.�KRXVHKROG�EDNLQJ�FRRNLQJ�FDWHULQJ�SURMHFWV
) (G
rade
10)
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larg
er p
roje
cts
in th
e fa
mili
ar c
onte
xts
of th
e ho
useh
old
and
scho
ol a
nd/o
r wid
er c
omm
unity
(e.g
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ntin
g a
clas
sroo
m) (
Gra
de 1
1)%�
com
plex
pro
ject
s in
bot
h fa
mili
ar a
nd u
nfam
iliar
con
text
s (e
.g. d
eter
min
ing
quan
titie
s of
mat
eria
ls n
eede
d to
bui
ld a
n R
DP
hous
e) (G
rade
12)
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riate
map
s, p
lans
and
mod
els+
(all
grad
es).
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rder
to:
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ve p
robl
ems
and
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plet
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sks/
proj
ects
, inc
ludi
ng:
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ting
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ater
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pone
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ed to
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plet
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clas
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side
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ven
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opria
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aps,
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ns a
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odel
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nd d
ecis
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text
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pact
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ound
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and/
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rror
s in
mea
sure
men
t (e
.g. 2
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e co
st o
f mat
eria
ls/c
ompo
nent
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eded
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ompl
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sk/p
roje
ct:
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ing
cost
of m
ater
ials
sup
plie
d by
the
teac
her (
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de 1
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usin
g co
st o
f mat
eria
ls d
eter
min
ed th
roug
h re
sear
ch (G
rade
s 11
and
12)
%�de
term
inin
g a
requ
ired
budg
et fo
r a g
iven
pro
ject
10, 1
1 an
d 12
%�m
akin
g ch
oice
s re
gard
ing
cost
s an
d/or
qua
ntiti
es a
nd/o
r mat
eria
ls u
sed
in o
rder
to c
ompl
ete
the
task
/pro
ject
with
in a
giv
en b
udge
t.(c
ontin
ued)
12
MATHEMATICAL LITERACY GRADES 10-12
69CAPS
topi
c:
mea
sure
men
tG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Cal
cula
ting
perim
eter
, ar
ea a
nd
volu
me
(con
tinue
d)
add
ition
al c
omm
ents
:*
In G
rade
10,
prim
ary
focu
s is
on
wor
king
with
2-d
imen
sion
al s
hape
s an
d ca
lcul
atio
ns o
f per
imet
er a
nd a
rea
of s
uch
shap
es.
In G
rade
s 11
and
12,
focu
s sh
ifts
to in
clud
e 3-
Dim
ensi
onal
sha
pes,
with
cal
cula
tions
of p
erim
eter
, are
a an
d vo
lum
e ex
tend
ed a
ccor
ding
ly.+ A
ll fo
rmul
ae fo
r cal
cula
tions
invo
lvin
g pe
rimet
er, a
rea,
sur
face
are
a an
d vo
lum
e w
ill b
e pr
ovid
ed in
ass
essm
ents
. Not
e th
at in
all
form
ulae
lear
ners
are
exp
ecte
d to
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rea
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ctan
gle
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ngth
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ngle
= ½
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ase
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lar
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ius)
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ce a
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ctan
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r box
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here
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= w
idth
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ght
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inde
r with
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bas
e
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us ×
hei
ght)
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me:
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me
of re
ctan
gula
r box
= a
rea
of b
ase/
lid ×
hei
ght
= le
ngth
× w
idth
× h
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t/dep
th
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me
of c
ylin
der =
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for m
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aps,
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ns a
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at le
arne
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re e
xpec
ted
to w
ork
with
in e
ach
grad
e.
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cula
ting
perim
eter
, ar
ea a
nd
volu
me
(con
tinue
d)
a
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ignm
ent:
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ng a
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ostin
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the
quan
tity
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ncin
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how
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part
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tabl
es m
ust b
e pl
ante
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any
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tabl
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e ga
rden
can
acc
omm
odat
e%�
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t rel
evan
t sto
res
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dwar
e st
ore,
nur
sery
, etc
.) to
inve
stig
ate
the
cost
of t
he m
ater
ials
for t
he g
arde
n.
10
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ignm
ent:
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seho
ld ZDWHU�FRQVXPSWLRQ
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e th
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ily w
ater
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sum
ptio
n of
a h
ouse
hold
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ing
into
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side
ratio
n vo
lum
es o
f wat
er u
sed
in a
sho
wer
, bat
h, s
ink
and
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r lo
catio
ns%�
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11
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ible
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essm
ent:
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stig
atio
n: 7LOLQJ�D�ÀRRU
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OR
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stig
atio
n: H
ousi
ng d
ensi
ty (i
ncor
pora
ting
area
and
sur
face
are
a, a
nd d
ata
hand
ling,
that
is, c
olle
ctin
g da
ta)
Cal
cula
te th
e ac
tual
hou
sing
den
sity
for a
sub
urb,
set
tlem
ent o
r tow
nshi
p by
com
parin
g th
e nu
mbe
r of p
eopl
e liv
ing
in a
hou
seho
ld to
the
area
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12
MATHEMATICAL LITERACY GRADES 10-12
70 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
mea
sure
men
tG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Tim
e
Rea
d, re
cord
and
per
form
cal
cula
tions
invo
lvin
g tim
e va
lues
, inc
ludi
ng:
%�tim
e va
lues
exp
ress
ed a
nd/o
r rec
orde
d on
wat
ches
, clo
cks
and
stop
wat
ches
%�tim
e va
lues
exp
ress
ed in
the
follo
win
g fo
rmat
s:
�-WLP
H�RI�GD\�IRUPDWV��H�J����R¶FORFN�������DP
�������SP
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�-tim
e re
cord
ing
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ats
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12
min
20
sec)
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des
11 a
nd 1
2)
%�co
nver
ting
betw
een
diffe
rent
uni
ts o
f tim
e:
�-se
cond
s - m
inut
es -
hour
s
�-da
ys -
wee
ks -
mon
ths
%�ca
lcul
atin
g el
apse
d tim
e in
volv
ing
the
diffe
rent
tim
e fo
rmat
s (e
.g.�WKH�DPRXQW�RI�WLPH�WKDW�KDV�SDVVHG�IURP������DP
�WR������DP
��WKH�GLIIHUHQFH�LQ�WLPH�EHWZHHQ���K�
23 m
in 1
2 se
c an
d 1
h 39
min
4 s
ec)
%�ca
lend
ars
show
ing
days
, wee
ks a
nd m
onth
s
%�tim
etab
les,
incl
udin
g:
�-st
udy
timet
able
s an
d te
levi
sion
tim
etab
les
(Gra
de 1
0)
�-le
sson
/exa
m ti
met
able
s (G
rade
11)
�-tra
nspo
rt tim
etab
les
(e.g
. bus
, tra
in, t
axi);
pro
duct
ion
timet
able
s e.
g. fo
r man
ufac
turin
g an
obj
ect o
r for
con
stru
ctin
g a
hous
e); a
nd ti
de ti
met
able
s (G
rade
12)
In th
e co
ntex
t of:
%�si
mpl
e ta
sks
in th
e fa
mili
ar c
onte
xt o
f the
hou
seho
ld (e
.g.�KRXVHKROG�EDNLQJ�FRRNLQJ�FDWHULQJ�SURMHFWV
) (G
rade
10)
%�la
rger
pro
ject
s in
the
fam
iliar
con
text
s of
the
hous
ehol
d an
d sc
hool
and
/or w
ider
com
mun
ity (e
.g. s
choo
l spo
rts e
vent
) (G
rade
11)
%�co
mpl
ex p
roje
cts
in b
oth
fam
iliar
and
unf
amili
ar c
onte
xts
(e.g
. tim
etab
le fo
r a c
onst
ruct
ion
proj
ect)
(Gra
de 1
2)
%�ap
prop
riate
map
s* (a
ll gr
ades
)
In o
rder
to�
Pla
n an
d co
mpl
ete
activ
ities
and
pro
ject
s (e
.g. a
rriv
ing
at s
choo
l on
time;
EDNLQJ�D�FDNH��GUDZLQJ�XS�DQ�H[DP
�VWXG\�WLPHWDEOH��P
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timet
able
). 10
, 11
and
12
Rec
ord
times
(e.g
. rec
ordi
ng ru
nnin
g tim
es a
t a s
choo
l spo
rts e
vent
).11
and
12
Pla
n tri
ps, i
nclu
ding
:
%�es
timat
ing
trave
lling
tim
es
%�de
term
inin
g tra
vel c
osts
%�de
term
inin
g ap
prop
riate
sto
ppin
g lo
catio
ns w
ith c
onsi
dera
tion
of p
etro
l con
sum
ptio
n an
d fa
tigue
11 a
nd
12
MATHEMATICAL LITERACY GRADES 10-12
71CAPS
topi
c:
mea
sure
men
tG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Tim
e (c
ontin
ued)
%�de
term
inin
g de
partu
re/a
rriv
al a
nd/o
r sta
rt/en
d tim
es fr
om ti
met
able
s
%�pr
epar
ing
budg
ets
for
the
trip
by m
akin
g us
e of
rel
evan
t map
s, ti
met
able
s an
d fa
re ta
bles
, veh
icle
ope
ratin
g co
st ta
bles
from
the
AA
and
othe
r tra
vel
reso
urce
s+
12
Cal
cula
te s
peed
(dis
tanc
e tra
velle
d in
term
s of
tim
e ta
ken)
+ (e
.g. a
vera
ge s
peed
trav
elle
d du
ring
a jo
urne
y; th
e av
erag
e ra
cing
spe
ed o
f a p
artic
ipan
t in
a sp
orts
eve
nt).
11 a
nd
12
add
ition
al c
onte
xts/
reso
urce
s an
d co
mm
ents
:*
Ref
er to
the
topi
c 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
RUOG
for m
ore
deta
ils o
n th
e m
aps,
pla
ns a
nd m
odel
s th
at le
arne
rs a
re e
xpec
ted
to w
ork
with
in G
rade
12.
+ Ref
er to
the
topi
c 1XP
EHUV�DQG�FDOFXODWLRQV�ZLWK�QXP
EHUV
and
the
sect
ion
on R
ates�IRU�P
RUH�GHWDLOV�RQ�VSHFL¿F�FRQWHQW�DQG�RU�VNLOOV�UHODWLQJ�WR�FDOFXODWLRQV�LQYROYLQJ�
spee
d. a
Poss
ible
ass
essm
ent (
inco
rpor
atin
g co
nver
sion
s, te
mpe
ratu
re, m
easu
ring
wei
ght a
nd v
olum
e, a
nd ti
me)
:A
ssig
nmen
t: %DNLQJ�D�FDNH
%�U
se m
easu
ring
cups
and
/or a
sca
le to
mea
sure
ingr
edie
nts
for a
reci
pe
%�B
ake
the
cake
acc
ordi
ng to
the
give
n in
stru
ctio
ns.
10
Poss
ible
ass
essm
ent (
inco
rpor
atin
g m
easu
ring
leng
th a
nd ti
me)
:A
ssig
nmen
t: M
ini-O
lym
pics
%�D
ivid
e th
e cl
ass
into
gro
ups
and
each
gro
up is
resp
onsi
ble
for a
diff
eren
t spo
rts a
ctiv
ity
%�S
ports
act
iviti
es m
ust i
nvol
ve m
easu
rem
ent (
e.g.
long
jum
p) a
nd ti
me
(e.g
. run
ning
tim
es)
%�E
ach
grou
p is
resp
onsi
ble
for m
anag
ing
thei
r ow
n sp
orts
act
ivity
and
for r
ecor
ding
mea
sure
men
t val
ues
and
times
%�E
ach
grou
p pa
rtici
pate
s in
all
of th
e sp
orts
act
iviti
es.
11
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HQW��LQFRUSRUDWLQJ�¿Q
DQFH��P
DSV�DQG�WLP
HWDEOHV��
Ass
ignm
ent:
Pla
nnin
g a
trip
(The
sam
e as
sign
men
t is
prov
ided
in th
e se
ctio
n on
Map
s in
the
topi
c 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
RUOG
.)
3ODQ�D�WULS�EHWZHHQ�WZR�FLWLHV�RU�FRXQWULHV��PDNLQJ�XVH�RI�PDSV��EXV�WUDLQ�WD[L�ÀLJKW�WLPHWDEOHV��WDULII�WDEOHV��H[FKDQJH�UDWHV��LI�QHFHVVDU\��DQG�
WKH�$$�¿[HG��UXQQLQJ�DQG�RSHUDWLQJ�FRVW�WDEOHV��LI�QHFHVVDU\��
12
MATHEMATICAL LITERACY GRADES 10-12
72 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sugg
este
d te
achi
ng ti
me:
G
rade
10:
5
-6 w
eeks
Gra
de 1
1:
5-6
wee
ks
Gra
de 1
2:
4-5
wee
ks
rec
omm
ende
d te
xts
and/
or re
sour
ces:
%�Te
xtbo
oks
%�S
treet
map
s, p
rovi
ncia
l and
nat
iona
l roa
d m
aps,
and
map
s sh
owin
g ra
ilway
rout
es; t
imet
able
s, fa
re ta
bles
and
dis
tanc
e FKDUWV�DSSURSULDWH�ÀRRU�SODQV�DQG�HOHYDWLRQ�SODQV��FDUGERDUG�IRU�P
DNLQJ�PRGHOV
scop
e of
con
text
s an
d/or
con
tent
per
sec
tion
and
grad
e:
sect
ion
Gra
de 1
0G
rade
11
Gra
de 1
2
Sca
leM
aps
and
plan
s of
fam
iliar
con
text
s an
d/or
si
mpl
e st
ruct
ures
(e.g
. sch
ool).
Map
s an
d pl
ans
of le
ss fa
mili
ar c
onte
xts
and/
or s
truct
ures
(e.g
. RI¿FH�VSDFH
) and
m
odel
s of
pac
kagi
ng c
onta
iner
s.
Map
s an
d pl
ans
of p
ossi
bly
unfa
mili
ar
cont
exts
and
/or c
ompl
ex s
truct
ures
(e.g
. R
DP
hous
e) a
nd m
odel
s of
pac
kagi
ng
cont
aine
rs a
nd b
uild
ings
.M
aps
Map
s an
d pl
ans
of le
ss fa
mili
ar c
onte
xts
and/
or s
truct
ures
.M
aps
and
plan
s of
pos
sibl
y un
fam
iliar
co
ntex
ts a
nd/o
r com
plex
stru
ctur
es.
Pla
ns
Mod
els
Wor
k w
ith a
ctua
l tin
s an
d bo
xes
to e
xplo
re
pack
agin
g ar
rang
emen
ts.
Bui
ld 3
D s
cale
mod
els
of p
acka
ging
co
ntai
ners
to in
vest
igat
e pa
ckag
ing
arra
ngem
ents
.
Dra
w 2
D s
cale
pic
ture
s of
3D
pac
kagi
ng
cont
aine
rs.
Bui
ld 3
D s
cale
mod
els
of p
acka
ging
co
ntai
ners
and
bui
ldin
gs to
exp
lore
wha
t WKH�¿QDO�SURGXFW�ZLOO�ORRN�OLNH�
Dra
w 2
D s
cale
pic
ture
s of
3D
bui
ldin
gs a
nd
pack
agin
g co
ntai
ners
.
MATHEMATICAL LITERACY GRADES 10-12
73CAPS
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Sca
le*
Wor
k w
ith th
e fo
llow
ing
type
s of
sca
les
on m
aps,
pla
ns a
nd in
the
cons
truct
ion
of m
odel
s:+
%�nu
mbe
r sca
les
expr
esse
d in
the
form
1:5
00
%�ba
r sca
les
expr
esse
d in
the
form
� 0 m
10
m
20 m
with
an
unde
rsta
ndin
g of
the
adva
ntag
es a
nd d
isad
vant
ages
of e
ach
type
of s
cale
and
the
situ
atio
ns in
whi
ch o
ne ty
pe o
f sca
le is
mor
e ap
prop
riate
than
the
othe
r.
In o
rder
to:
Cal
cula
te a
ctua
l len
gth
and
dist
ance
whe
n m
ap a
nd/o
r pla
n m
easu
rem
ents
are
kno
wn.
10, 1
1 an
d 12
Cal
cula
te m
ap a
nd/o
r pla
n m
easu
rem
ents
whe
n ac
tual
leng
ths
and
dist
ance
s ar
e kn
own
usin
g a
give
n sc
ale
to in
form
the
draw
ing
of 2
-dim
ensi
onal
pla
ns
and
pict
ures
and
the
cons
truct
ion
of 3
-dim
ensi
onal
mod
els.
+
Det
erm
ine
the
mos
t app
ropr
iate
sca
le in
whi
ch to
dra
w/c
onst
ruct
a m
ap, p
lan
and/
or m
odel
, and
use
this
sca
le to
com
plet
e th
e ta
sk.
11 a
nd
12
Det
erm
ine
the
scal
e in
whi
ch a
map
and
/or p
lan
has
been
dra
wn
in th
e fo
rm 1
:… a
nd u
se th
e sc
ale
to d
eter
min
e ot
her d
imen
sion
s on
the
map
and
/or p
lan.
12
add
ition
al c
omm
ents
:* A
lthou
gh s
cale
is a
form
of m
easu
rem
ent,
the
sect
ion
on S
cale
has
bee
n in
clud
ed a
s pa
rt of
the
topi
c 0DSV��SODQV�DQG�RWKHU�UHSUHVHQWDWLRQV�RI�WKH�SK\VLFDO�Z
RUOG
ra
ther
than
in th
e to
pic
Mea
sure
men
t ow
ing
to th
e di
rect
rele
vanc
e of
sca
le in
the
cont
ext o
f cal
cula
tions
invo
lvin
g m
aps,
pla
ns a
nd m
odel
s.
It is
ess
entia
l tha
t thi
s se
ctio
n on
Sca
le b
e ta
ught
in c
onju
nctio
n w
ith th
e co
nten
t and
/or s
kills
out
lined
in th
e se
ctio
n on
Mea
surin
g le
ngth
and
dis
tanc
e in
the
topi
c M
easu
rem
ent.
+ S
ee th
e se
ctio
ns b
elow
on
Map
s, P
lans
and
Mod
els�IRU�VSHFL¿F�GHWDLOV�RI�WKH�W\SHV�RI�PDSV��SODQV�DQG�PRGHOV�WKDW�OHDUQHUV�DUH�H[SHFWHG�WR�ZRUN�ZLWK�LQ�*UDGH�����
a
Poss
ible
ass
essm
ent (
inco
rpor
atin
g m
aps
and/
or p
lans
):In
vest
igat
ion:
Wha
t hap
pens
if y
ou re
size
a m
ap o
r pla
n?
%�In
vest
igat
e th
e ef
fect
that
resi
zing
a m
ap o
r pla
n w
ith a
num
ber s
cale
has
on
the
scal
e of
the
plan
or m
ap
%�In
vest
igat
e th
e ef
fect
that
resi
zing
a m
ap o
r pla
n w
ith a
bar
sca
le h
as o
n th
e sc
ale
of th
e pl
an o
r map
%�D
iscu
ss th
e ad
vant
ages
and
dis
adva
ntag
es o
f usi
ng n
umbe
r and
bar
sca
les
on m
aps
and
plan
s
10
MATHEMATICAL LITERACY GRADES 10-12
74 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Map
s
Wor
k w
ith th
e fo
llow
ing
map
s:
%�m
ap s
how
ing
the
seat
ing
plan
and
/or l
ayou
t of a
cla
ssro
om
%�PDS�VKRZLQJ�WKH�OD\RXW�RI�WKH�EXLOGLQJV�DQG�RU�VSRUWV�¿HOGV�DW�D�VFKRRO
%�m
ap s
how
ing
the
layo
ut o
f the
sto
res
in a
sho
ppin
g ce
ntre
%�se
atin
g pl
ans
for c
inem
as a
nd a
spo
rts s
tadi
um
10, 1
1 an
d 12
%�st
reet
map
s w
ith a
nd w
ithou
t a g
rid re
fere
nce
syst
em
%�na
tiona
l and
pro
vinc
ial r
oad
and
rail
map
s
%�st
rip c
harts
sho
win
g di
stan
ces
on a
por
tion
of ro
ad
%�el
evat
ion
map
s (e
.g. t
he C
omra
des
Mar
atho
n ro
ute)
%�re
side
ntia
l or h
ousi
ng e
stat
e m
aps.
11 a
nd
12
In o
rder
to�
Des
crib
e th
e po
sitio
n of
an
obje
ct (e
.g. b
uild
ings
, fur
nitu
re, s
eats
) in
rela
tion
to s
urro
undi
ng o
bjec
ts.
Des
crib
e th
e po
sitio
n of
a b
uild
ing
in re
latio
n to
sur
roun
ding
bui
ldin
gs (e
.g. WKH�EXLOGLQJ�LV�GLUHFWO\�DFURVV�WKH�URDG�IURP
�WKH�GRXEOH�VWRUH\�EULFN�EXLOGLQJ)
.
Find
loca
tions
, fol
low
dire
ctio
ns a
nd d
evel
op d
irect
ions
for t
rave
lling
bet
wee
n tw
o or
mor
e lo
catio
ns u
sing
the
follo
win
g m
appi
ng re
fere
nce
syst
ems
and/
or
tech
niqu
es:
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Q´
%�ho
use
and/
or b
uild
ing
num
berin
g sy
stem
s
%�nu
mbe
ring
syst
ems
used
for s
eatin
g in
spo
rts s
tadi
ums
10, 1
1 an
d 12
%�gr
id re
fere
nce
syst
em (e
.g. N
orth
Stre
et is
loca
ted
on A
D14
)
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HV�LQGH[´�ORFDWHG�DW�WKH�EDFN�RI�VWUHHW�PDSV�VKRZ
LQJ�WKH�SDJH�DQG�RU�JULG�UHIHUHQFH�IRU�YDULRXV�VWUHHWV�
11 a
nd
12
Est
imat
e*:
%�di
stan
ces
usin
g m
easu
rem
ent a
nd a
giv
en s
cale
(num
ber o
r bar
sca
le)
10, 1
1 an
d 12
%�th
e tim
e it
will
take
to tr
avel
bet
wee
n tw
o or
mor
e lo
catio
ns
%�th
e am
ount
and
cos
t of f
uel t
hat w
ill b
e us
ed in
trav
ellin
g be
twee
n tw
o or
mor
e lo
catio
ns
%�th
e av
erag
e sp
eed
trave
lled
durin
g a
trip
(that
is, d
ista
nce
trave
lled
in te
rms
of ti
me
take
n).
Det
erm
ine
appr
opria
te s
topp
ing
loca
tions
with
con
side
ratio
n of
pet
rol c
onsu
mpt
ion
and/
or fa
tigue
.
11 a
nd
12
'HWHUPLQH�WKH�³RSHUDWLQJ�FRVW´�RI�D�YHKLFOH�XVLQJ�WKH�¿[HG��UXQQLQJ�DQG�RSHUDWLQJ�FRVW�WDEOHV�GLVWULEXWHG�E\�WKH�$XWRP
RELOH�$VVRFLDWLRQ�RI�6RXWK�$IULFD��
Pla
n an
d co
st tr
ips
usin
g tim
etab
les,
fare
cha
rts, d
ista
nce
char
ts a
nd b
udge
ts.+
12
MATHEMATICAL LITERACY GRADES 10-12
75CAPS
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Map
s (c
ontin
ued)
Wor
k w
ith a
com
bina
tion
of m
aps
show
ing
diffe
rent
per
spec
tives
and
sca
les
to n
avig
ate
the
rout
e to
a d
estin
atio
n.
(e.g
.�:KHQ�WUDYHOOLQJ�EHWZHHQ�WZR�FLWLHV��D�PDS�ZLWK�D�ODUJH�VFDOH�VKRZ
LQJ�QDWLRQDO�URDGV�DQG�WRZQV�ZLOO�EH�XVHIXO��8
SRQ�DSSURDFKLQJ�RQH�RI�WKH�FLWLHV��
D�PDS�VKRZLQJ�WKH�VXEXUEV�DQG�PDMRU�URDGV�LQ�DQG�DURXQG�WKH�FLW\�ZLOO�EH�PRUH�SUDFWLFDO�WR�GHWHUPLQH�LQ�ZKLFK�GLUHFWLRQ�WR�WUDYHO�WR�JHW�WR�D�SDUWLFXODU�
GHVWLQDWLRQ�LQ�WKH�FLW\��8
SRQ�DUULYDO�LQ�D�SDUWLFXODU�VXEXUE��D�VWUHHW�PDS�ZLWK�D�PXFK�VP
DOOHU�VFDOH�ZLOO�EHFRP
H�PRUH�SUDFWLFDO�WR�QDYLJDWH�WKH�URXWH�WR�D�
parti
cula
r des
tinat
ion.
)
12
Inte
rpre
t the
follo
win
g co
mpa
ss d
irect
ions
in th
e co
ntex
t of a
ppro
pria
te m
aps
and
plan
s:
%�³1RUWK´��³6RXWK´��³(DVW´�DQG�³:
HVW´
%�³1RUWK�HDVW´��³1
RUWK�ZHVW´��³6
RXWK�HDVW´�DQG�³6RXWK�ZHVW´�
In o
rder
to�
Und
erst
and
dire
ctio
ns a
nd s
ignb
oard
s on
road
s an
d in
map
boo
ks th
at re
fer t
o co
mpa
ss d
irect
ions
(e
.g. “
Trav
el N
orth
on
the
M3”
).
,QWHUSUHW�HOHYDWLRQ�SODQV�RI�EXLOGLQJV�WKDW�LQFOXGH�WKH�ZRUGV�³1
RUWK�(OHYDWLRQ´��³6RXWK�(OHYDWLRQ´��³(DVW�(
OHYDWLRQ´�DQG�³:
HVW�(
OHYDWLRQ´��
Dec
ide
on w
here
to p
ositi
on a
hou
se o
r a g
arde
n in
rela
tion
to th
e po
sitio
n of
the
sun
at d
iffer
ent t
imes
of t
he d
ay.
12
add
ition
al c
omm
ents
:*
Whe
n w
orki
ng w
ith m
aps,
it is
unr
easo
nabl
e to
exp
ect l
earn
ers
to m
easu
re a
nd d
eter
min
e di
stan
ces,
trav
ellin
g tim
e, p
etro
l con
sum
ptio
n an
d/or
ave
rage
spe
ed
DFFXUDWHO\��7KHUH�VLPSO\�DUH�WRR�PDQ\�IDFWRUV�WKDW�LQÀXHQFH�WKH�DFFXUDF\�RI�VXFK�FDOFXODWLRQV�ZKHQ�ZRUNLQJ�ZLWK�PDSV��H�J��Z
KHWKHU�\RX�FXW�WKH�FRUQHU�RU�WXUQ�WKH�
FRUQHU�RQ�WKH�RXWVLGH�RI�WKH�URDG��RU�Z
KHWKHU�WKHUH�DUH�WUDI¿F�OLJKWV�RU�RWKHU�REVWUXFWLRQV�OLNH
URDGZRUNV�RQ�D�VWUHWFK�RI�URDG
.
For t
his
reas
on, m
aps
shou
ld b
e us
ed o
nly
for e
stim
atin
g di
stan
ces,
trav
ellin
g tim
es a
nd p
etro
l con
sum
ptio
n be
twee
n di
ffere
nt lo
catio
ns.
$�PRUH�DSSURSULDWH�FRQWH[W�LQ�ZKLFK�WR�WHVW�DFFXUDWH�PHDVXUHPHQW�LQYROYHV�ZRUNLQJ�ZLWK�ÀRRU�DQG�HOHYDWLRQ�SODQV�
+ Ref
er to
the
sect
ion
on T
ime
in th
e to
pic
Mea
sure
men
t for
mor
e in
form
atio
n on
exp
ecte
d ca
lcul
atio
ns in
volv
ing
time
and
rele
vant
tim
etab
les.
a
Poss
ible
ass
essm
ent:
Ass
ignm
ent: )LQGLQJ�\RXU�ZD\
8VH�D�JLYHQ�PDS�WR�¿QG�\RXU�Z
D\�WR�D�GHVWLQDWLRQ�
OR
Sel
ect t
he s
eats
with
the
best
vie
w fo
r an
even
t fro
m th
e re
mai
ning
ava
ilabl
e se
ats.
10
3RVVLEOH�DVVHVVP
HQW��LQFRUSRUDWLQJ�¿Q
DQFH��P
DSV�DQG�WLP
HWDEOHV��
Ass
ignm
ent:
Pla
nnin
g a
trip
3ODQ�D�WULS�EHWZHHQ�WZR�FLWLHV�RU�FRXQWULHV��XVLQJ�PDSV��EXV�WUDLQ�WD[L�ÀLJKW�WLPHWDEOHV��WDULII�WDEOHV��H[FKDQJH�UDWHV��LI�QHFHVVDU\��DQG�WKH�$$�
¿[HG��UXQQLQJ�DQG�RSHUDWLQJ�FRVW�WDEOHV��LI�QHFHVVDU\��
12
MATHEMATICAL LITERACY GRADES 10-12
76 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Pla
ns
(inst
ruct
ion/
as
sem
bly
diag
ram
s)
Use
inst
ruct
ion/
asse
mbl
y di
agra
ms,
con
tain
ing
wor
ds a
nd/o
r pic
ture
s, fo
und
in m
anua
ls fo
r:
%�pl
ugs
%�pl
astic
mod
els
%�un
asse
mbl
ed w
oode
n fu
rnitu
re u
nits
%�ce
ll-ph
ones
(e.g
. ins
talli
ng a
bat
tery
and
sim
car
d; o
r ope
ratin
g in
stru
ctio
ns)
%�el
ectri
cal a
pplia
nces
that
requ
ire in
divi
dual
com
pone
nts
to b
e co
nnec
ted
(e.g
. FRQQHFWLQJ�VSHDNHUV�WR�D�KL�¿��RU�FRQQHFWLQJ�DQ�DHULDO�WR�D�WHOHYLVLRQ
)
%�FKLOGUHQ¶V�WR\V�LQFOXGLQJ�
Lego
-type
kits
.
In o
rder
to�
Com
plet
e th
e ta
sk p
rese
nted
in th
e in
stru
ctio
ns a
nd/o
r exp
lain
wha
t the
inst
ruct
ions
mea
n an
d/or
repr
esen
t, us
ing
ever
yday
lang
uage
.
10, 1
1 an
d 12
a
Poss
ible
ass
essm
ents
:A
ssig
nmen
t: W
ritin
g in
stru
ctio
ns
Stu
dy th
e in
stru
ctio
n/as
sem
bly
diag
ram
s fo
r an
appl
ianc
e an
d w
rite
a de
taile
d se
t of i
nstru
ctio
ns in
wor
ds to
acc
ompa
ny a
nd/o
r exp
lain
the
diag
ram
s.
OR
Dra
w in
stru
ctio
n/as
sem
bly
diag
ram
s fo
r an
appl
ianc
e w
here
the
inst
ruct
ions
are
giv
en o
nly
in w
ords
.
Ass
ignm
ent/d
emon
stra
tion:
Ass
embl
ing
an o
bjec
t
$VVHP
EOH�DQ�REMHFW�EDVHG�RQ�WKH�LQVWUXFWLRQV�SURYLGHG��LQFOXGLQJ�FKLOGUHQ¶V�WR\V��WR�VKRZ
�WKH�OHDUQHU¶V�DELOLW\�WR�IROORZ�LQVWUXFWLRQV�
10
MATHEMATICAL LITERACY GRADES 10-12
77CAPS
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Pla
ns
�ÀRRU��
elev
atio
n an
d de
sign
pla
ns)
Use
the
follo
win
g pl
ans:
%�ro
ugh
and
scal
ed ÀRRU�OD\RXW�SODQV
sho
win
g a
top
view
per
spec
tive
(Gra
de 1
0)
%�ro
ugh
and
scal
ed e
leva
tion
plan
s (fr
ont,
back
and
sid
e) s
how
ing
a si
de v
iew
per
spec
tive
(Gra
des
11 a
nd 1
2)
%�ro
ugh
and
scal
ed d
esig
n dr
awin
gs o
f ite
ms
to b
e m
anuf
actu
red
(e.g
. clo
thin
g; fu
rnitu
re) (
Gra
des
11 a
nd 1
2)
In th
e co
ntex
t of:
%�a
fam
iliar
stru
ctur
e (e
.g.�FODVVURRP
��URRP�LQ�D�KRXVH�ĺ
�EHGURRP
�RU�ORXQJH)
(Gra
de 1
0)
%�a
less
fam
iliar
stru
ctur
e (e
.g.�RI¿FH�VSDFH�FRQWDLQLQJ�FXELFOHV��D�JDUGHQ�WRRO�VKHG)
(Gra
de 1
1)
%�a
com
plex
stru
ctur
e (e
.g.�KRXVH�ĺ
�5'3�KRXVH)
(Gra
de 1
2)
In o
rder
to�
Und
erst
and
the
sym
bols
and
not
atio
n us
ed o
n pl
ans
(e.g
. WKH�V\P
ERO�IRU�D�ZLQGRZ�LV�D�GRXEOH�OLQH��WKH�V\PERO�IRU�D�GRRU�LV�D�YHUWLFDO�OLQH�DWWDFKHG�WR�D�TXDUWHU�FLUFOH�LQGLFDWLQJ�WKH�VZ
LQJ�GLUHFWLRQ�RI�WKH�GRRU
).
Des
crib
e w
hat i
s be
ing
repr
esen
ted
on th
e pl
ans.
Ana
lyse
the
layo
ut o
f the
stru
ctur
e sh
own
on th
e pl
an a
nd s
ugge
st a
ltern
ativ
e la
yout
opt
ions
.
Det
erm
ine
actu
al le
ngth
s of
obj
ects
sho
wn
on p
lans
usi
ng m
easu
rem
ent a
nd a
giv
en s
cale
(num
ber o
r bar
sca
le).
Det
erm
ine
quan
titie
s of
mat
eria
ls n
eede
d by
usi
ng th
e pl
ans
and
perim
eter
, are
a an
d vo
lum
e ca
lcul
atio
ns.
10, 1
1 an
d 12
Und
erst
and
the
term
s
%�³1RUWK�(OHYDWLRQ´�
%�³6RXWK�(OHYDWLRQ´�
%�³(DVW�(
OHYDWLRQ´�
%�³:
HVW�(
OHYDWLRQ´�
and
the
rele
vanc
e of
com
pass
dire
ctio
ns in
the
cons
truct
ion
of b
uild
ings
.
&RQQHFW�WKH�IHDWXUHV�VKRZQ�RQ�HOHYDWLRQ�SODQV�ZLWK�IHDWXUHV�DQG�SHUVSHFWLYHV�VKRZQ�RQ�D�ÀRRU�SODQ�RI�WKH�VDPH�VWUXFWXUH�
11an
d 12
MATHEMATICAL LITERACY GRADES 10-12
78 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Pla
ns
�ÀRRU��
elev
atio
n an
d de
sign
pla
ns)
(con
tinue
d)
Det
erm
ine
the
mos
t app
ropr
iate
sca
le (G
rade
12)
in w
hich
to d
raw
a p
lan
and
use
the
scal
e (G
rade
10
and
11).
In o
rder
to�
Det
erm
ine
how
long
/wid
e/hi
gh a
n ob
ject
sho
uld
be d
raw
n on
a p
lan
whe
n ac
tual
dim
ensi
ons
are
know
n.
'UDZ�VFDOHG��'
�ÀRRU�DQG�HOHYDWLRQ�SODQV�IRU�
%�a
fam
iliar
stru
ctur
e (e
.g.�FODVVURRP
��URRP�LQ�D�KRXVH�ĺ
�EHGURRP
�RU�ORXQJH)
(Gra
de 1
0)
%�a
less
fam
iliar
stru
ctur
e (e
.g. RI¿FH�VSDFH�FRQWDLQLQJ�FXELFOHV��D�JDUGHQ�WRRO�VKHG)
(Gra
de 1
1)
%�a
com
plex
stru
ctur
e (e
.g.�KRXVH�ĺ
�5'3�KRXVH)
(Gra
de 1
2).
10, 1
1 an
d 12
add
ition
al c
omm
ents
:$GGLWLRQDO�FRQWH[WV�DQG�RU�UHVRXUFHV�LQFOXGH�DQ\�RWKHU�SODQV�LQ�WKH�FRQWH[W�RI�WKH�OHDUQHU¶V�GDLO\�OLIH�DQG�LQ�OHVV�IDPLOLDU�FRQWH[WV�UHODWLQJ�WR�VLPSOH�DQG�FRPSOH[�
stru
ctur
es.
a
3RVVLEOH�DVVHVVP
HQW��LQFRUSRUDWLQJ�SODQV��FRQ
YHUVLRQV��DUHD�DQG�VXUIDFH�DUHD��DQG
�¿QDQFH��
Ass
ignm
ent:
Pai
ntin
g a
clas
sroo
m
%�C
reat
e ac
cura
te 2
-dim
ensi
onal
sca
led
draw
ings
of t
he in
side
wal
ls o
f a c
lass
room
%�U
se th
e pl
ans
to d
eter
min
e th
e qu
antit
y of
pai
nt n
eede
d to
pai
nt th
e cl
assr
oom
%�P
repa
re a
bud
get t
o sh
ow th
e pr
ojec
ted
cost
of p
aint
ing
the
clas
sroo
m.
11
3RVVLEOH�DVVHVVP
HQW��LQFRUSRUDWLQJ�¿Q
DQFH��P
RGHOV��SODQV��SHULPHWHU��DUHD�DQG�YROXPH��
Ass
ignm
ent:
Bui
ldin
g a
hous
e
%�In
vest
igat
e th
e co
nsid
erat
ions
invo
lved
in th
e co
nstru
ctio
n of
a h
ouse
%�A
fter i
nter
pret
ing
the
plan
s of
a h
ouse
, bui
ld a
sca
le m
odel
and
per
form
per
imet
er, a
rea
and
volu
me
calc
ulat
ions
in th
e co
ntex
t of f
enci
ng,
pain
t, co
ncre
te, e
tc.
%�A
naly
se a
bud
get f
or th
e bu
ildin
g pr
ojec
t
%�$QDO\VH�LQÀDWLRQ�¿JXUHV�WR�SUHGLFW�SRVVLEOH�DGMXVWPHQWV�WR�EXLOGLQJ�FRVWV�
12
MATHEMATICAL LITERACY GRADES 10-12
79CAPS
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Mod
els*
Inve
stig
ate
pack
agin
g ar
rang
emen
ts u
sing
act
ual c
ans
and
a ra
nge
of a
ctua
l box
es.
In o
rder
to�
Det
erm
ine
the
mos
t app
ropr
iate
way
to p
acka
ge c
ans
and/
or b
oxes
for o
ptim
al u
se o
f spa
ce.
Det
erm
ine
the
mos
t cos
t-effe
ctiv
e w
ay to
pac
kage
a n
umbe
r of c
ans
and/
or b
oxes
.
10
(onl
y)
Mak
e an
d us
e:
%�3-
dim
ensi
onal
sca
le m
odel
s of
pac
kagi
ng c
onta
iner
s (e
.g.�SDFNDJLQJ�FRQWDLQHUV�IRU�EDOOV��ELVFXLWV��HWF�)
%�2-
dim
ensi
onal
sca
le c
ut-o
uts/
pict
ures
of a
ppro
pria
te v
iew
s of
3-d
imen
sion
al m
odel
s of
pac
kagi
ng c
onta
iner
s.
In o
rder
to�
Inve
stig
ate
the
best
pac
kagi
ng s
hape
to u
se fo
r pac
kagi
ng a
par
ticul
ar p
rodu
ct (e
.g.�6
KRXOG�EDOOV�EH�SDFNDJHG�LQ�D�F\OLQGULFDO�RU�UHFWDQJXODU�FRQWDLQHU")
.
Inve
stig
ate
the
best
pac
kagi
ng s
hape
to u
se fo
r fra
gile
and
irre
gula
r-sh
aped
obj
ects
(e.g
. a te
levi
sion
set
), w
hile
tryi
ng to
min
imis
e w
aste
d sp
ace
and
cost
.
Inve
stig
ate
the
amou
nt o
f mat
eria
l use
d to
mak
e a
box.
,QYHVWLJDWH�WKH�QXPEHU�RI�IXUQLWXUH�LWHP
V�WKDW�FDQ�¿W�LQWR�D�YHQXH��ZKLOH�FRQVLGHULQJ�WKH�VSDFH�QHHGHG�IRU�WDEOHV��FKDLUV�DQG�ZDONLQJ�DURXQG�
Est
imat
e qu
antit
ies
of m
ater
ials
nee
ded
(e.g
. pai
nt; t
iles)
usi
ng p
erim
eter
, are
a an
d vo
lum
e ca
lcul
atio
ns
11 a
nd
12
Mak
e an
d us
e:
%�3-
dim
ensi
onal
sca
le m
odel
s of
bui
ldin
gs (e
.g. c
lass
room
; sto
rero
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choo
l hal
l; ho
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plan
s
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ensi
onal
sca
le c
ut-o
uts/
pict
ures
of a
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pria
te v
iew
s of
bui
ldin
gs.
In o
rder
to�
Inve
stig
ate
poss
ible
way
s to
sta
ck/a
rran
ge b
oxes
in a
sto
rero
om in
ord
er to
min
imis
e w
aste
d sp
ace.
Crit
ique
asp
ects
of t
he la
yout
and
/or d
esig
n of
a s
truct
ure
and
mak
e su
gges
tions
for a
ltera
tions
.
Inve
stig
ate
the
plac
emen
t of f
urni
ture
in a
room
.
Est
imat
e qu
antit
ies
of m
ater
ials
nee
ded
(for e
xam
ple,
pai
nt; t
iles)
usi
ng p
erim
eter
, are
a an
d vo
lum
e ca
lcul
atio
ns+ .
12
MATHEMATICAL LITERACY GRADES 10-12
80 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
map
s, p
lans
and
oth
er re
pres
enta
tions
of t
he p
hysi
cal w
orld
G
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Mod
els*
(c
ontin
ued)
add
ition
al c
omm
ents
:*
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els
are
cons
truct
ed to
repr
esen
t the
phy
sica
l wor
ld fo
r tw
o m
ain
reas
ons:
1.
3D-s
cale
mod
els
mad
e fro
m 2
D-d
iagr
ams/
plan
s he
lp u
s to
bet
ter v
isua
lise
obje
cts
(e.g��Z
KDW�D�EXLOGLQJ�ZLOO�ORRN�OLNH�RQFH�LW�KDV�EHHQ�FRQVWUXFWHG
);2.
sc
ale
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els
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udin
g m
aps
and
diag
ram
s) c
an h
elp
us to
inve
stig
ate
prob
lem
s an
d de
velo
p so
lutio
ns (e
.g. KRZ
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�EHVW�WR�
plac
e fu
rnitu
re in
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rade
10,
lear
ners
are
exp
ecte
d to
wor
k w
ith a
ctua
l can
s an
d bo
xes
to in
vest
igat
e pa
ckag
ing
arra
ngem
ents
and
con
side
ratio
ns o
f spa
ce a
nd c
ost.
In G
rade
11,
the
focu
s is
prim
arily
on
help
ing
lear
ners
to d
evel
op th
e sk
ills
to c
reat
e sc
ale
mod
els
or d
raw
ings
to in
vest
igat
e pr
oble
ms
whe
re a
ctua
l res
ourc
es a
re
unav
aila
ble
or im
prac
tical
ly la
rge.
In G
rade
12,
the
prim
ary
focu
s is
on
usin
g sc
ale
mod
els
and
draw
ings
to s
olve
pro
blem
s.Th
e m
odel
s an
d/or
dra
win
gs s
houl
d be
dra
wn
to s
cale
.+ S
ee th
e se
ctio
n on
Per
imet
er, a
rea
and
volu
me
in th
e to
pic
Mea
sure
men
t for
mor
e de
tails
on
expe
cted
cal
cula
tions
invo
lvin
g pe
rimet
er, a
rea
and
volu
me.
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ition
al c
onte
xts
and/
or re
sour
ces
invo
lvin
g 3D
mod
els
and
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raw
ings
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hich
the
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epts
des
crib
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bove
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ored
incl
ude:
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aine
rs:
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ned
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nis
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f bal
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ntai
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Poss
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ignm
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ldin
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choo
l hal
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12
MATHEMATICAL LITERACY GRADES 10-12
81CAPS
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sugg
este
d te
achi
ng ti
me:
Gra
de 1
0:
4-5
wee
ks
Gra
de 1
1:
4-5
wee
ks
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de 1
2:
5-6
wee
ks
rec
omm
ende
d te
xts
and/
or re
sour
ces:
%�Te
xtbo
oks
%�O
ther
sou
rces
of s
tatis
tics
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educ
atio
n st
atis
tics)
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; cla
ssify
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nisi
ng d
ata;
sum
mar
isin
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ta; r
epre
sent
ing
data
; and
inte
rpre
ting/
anal
ysin
g da
ta. E
very
sta
ge in
the
proc
ess
is d
epen
dent
on
the
stag
e th
at p
rece
des
it an
d di
rect
ly im
pact
s on
the
stag
e th
at fo
llow
s. If
the
data
that
is c
olle
cted
is
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anal
ysis
of t
he d
ata
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inco
rrec
t.
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impo
rtant
that
lear
ners
und
erst
and
the
inte
r-co
nnec
tedn
ess
of th
e st
atis
tical
pro
cess
and
that
thes
e pr
oces
ses
are
taug
ht a
nd a
sses
sed
at re
late
d st
ages
.
MATHEMATICAL LITERACY GRADES 10-12
82 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
type
and
sco
pe o
f dat
a pe
r gra
de:
sect
ion
Gra
de 1
0G
rade
11
Gra
de 1
2D
evel
opin
g qu
estio
nsIn
Gra
de 1
0, th
e ty
pe o
f dat
a de
alt w
ith
is li
mite
d pr
imar
ily (b
ut n
ot e
xclu
sive
ly) t
o da
ta in
clud
ing:
%�si
ngle
set
s of
dat
a co
ntai
ning
mul
tiple
ca
tego
ries
(H�J��Z
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WHVW�VFRUHV�FDWHJRULVHG�LQWR�PDUN�
cate
gorie
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r an
entir
e cl
ass,
but
not
so
rted
acco
rdin
g to
gen
der)
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lues
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read
dire
ctly
from
gr
aphs
and
/or t
able
s w
ithou
t the
nee
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r est
imat
ion
%�da
ta re
latin
g to
the
pers
onal
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ners
and
/or t
o is
sues
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mili
ar to
the
lear
ners
, e.g
.:
�-te
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rts re
sults
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ight
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ght d
ata
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arne
rs
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ss
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hool
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tistic
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.g. n
umbe
r of
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ners
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ach
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umbe
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mal
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mal
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ount
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ario
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seho
ld
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ta o
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leph
one
call
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and
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tion
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cket
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ey d
ata.
In G
rade
11,
the
type
of d
ata
deal
t with
is
limite
d pr
imar
ily (b
ut n
ot e
xclu
sive
ly) t
o da
ta in
clud
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ts o
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tiple
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tego
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cate
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sed
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nder
)
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lues
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dire
ctly
from
gr
aphs
and
/or t
able
s w
ithou
t the
nee
d fo
r est
imat
ion
%�da
ta re
latin
g to
the
wid
er c
omm
unity
an
d m
ore
com
plex
soc
ial i
ssue
s th
at
are
less
fam
iliar
to le
arne
rs, e
.g.:
�-sp
orts
resu
lts/s
tatis
tics
for p
rovi
ncia
l an
d/or
nat
iona
l spo
rts e
vent
s
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cent
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e st
atis
tics
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dica
tion
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vel)
of s
hopp
ers
at a
sh
oppi
ng c
entre
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ice
hist
ory
data
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roce
ry it
ems
�-da
ta o
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usin
g, to
ilet,
wat
er a
nd
elec
trici
ty fa
cilit
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for a
sm
all
com
mun
ity
�-da
ta o
n em
ploy
men
t rat
es fo
r a
smal
l com
mun
ity
In G
rade
12,
the
type
of d
ata
deal
t with
is
lim
ited
prim
arily
(but
not
exc
lusi
vely
) to
data
incl
udin
g:
%�m
ultip
le s
ets
of d
ata
cont
aini
ng m
ultip
le
cate
gorie
s (H�J��Z
RUNLQJ�ZLWK�YHKLFOH�
stat
istic
s co
ntai
ning
info
rmat
ion
on th
e nu
mbe
r of d
iffer
ent t
ypes
of
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in S
outh
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ex v
alue
s (th
at is
, val
ues
expr
esse
d in
mill
ions
or l
arge
dat
a va
lues
con
tain
ing
com
plex
dec
imal
va
lues
) for
whi
ch e
stim
atio
n m
ay b
e ne
cess
ary
to d
eter
min
e va
lues
on
grap
hs a
nd in
tabl
es
%�da
ta re
latin
g to
nat
iona
l and
glo
bal
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es, e
.g.:
�-na
tiona
l and
/or p
rovi
ncia
l hea
lth
stat
istic
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ourc
ed fr
om th
e D
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ealth
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/or p
rovi
ncia
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catio
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atis
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rced
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Dep
artm
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tiona
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ncia
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rced
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�-na
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ourc
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tatis
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Sou
th A
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rate
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Cla
ssify
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and
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nisi
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ata
Sum
mar
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ta
Rep
rese
ntin
g da
ta
Ana
lysi
ng d
ata
MATHEMATICAL LITERACY GRADES 10-12
83CAPS
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Dev
elop
ing
ques
tions
Dev
elop
a q
uest
ion
or s
et o
f que
stio
ns th
at re
quire
s th
e co
llect
ion
of a
sin
gle
set (
Gra
de 1
0), t
wo
sets
(Gra
de 1
1) a
nd m
ultip
le s
ets
(Gra
de 1
2) o
f dat
a.
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In o
rder
to�
Inve
stig
ate
prob
lem
s re
latin
g to
the
pers
onal
live
s of
lear
ners
(Gra
de 1
0), t
he w
ider
com
mun
ity (G
rade
11)
, and
nat
iona
l and
glo
bal i
ssue
s (G
rade
12)
.
10, 1
1 an
d 12
Col
lect
ing
data
Dev
elop
and
use
an
appr
opria
te fo
rm/in
stru
men
t for
col
lect
ing
a si
ngle
set
(Gra
de 1
0), t
wo
sets
(Gra
de 1
1) a
nd m
ultip
le s
ets
(Gra
de 1
2) o
f dat
a, in
clud
ing:
%�ob
serv
atio
n
%�in
terv
iew
%�qu
estio
nnai
re o
r sur
vey
with
an
awar
enes
s of
the
follo
win
g:
�-th
e si
tuat
ions
for w
hich
the
diffe
rent
type
s of
dat
a co
llect
ion
inst
rum
ents
are
mos
t app
ropr
iate
and
the
adva
ntag
es a
nd d
isad
vant
ages
of e
ach
type
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�-ho
w to
sel
ect a
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riate
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ple
from
a p
opul
atio
n
�-th
e im
pact
that
the
choi
ce o
f sam
ple
will
hav
e on
the
relia
bilit
y of
the
data
col
lect
ed
In o
rder
to�
Col
lect
dat
a on
pro
blem
s be
ing
inve
stig
ated
rela
ting
to th
e pe
rson
al li
ves
of le
arne
rs (G
rade
10)
, the
wid
er c
omm
unity
(Gra
de 1
1), a
nd n
atio
nal a
nd g
loba
l is
sues
(Gra
de 1
2).
10, 1
1 an
d 12
Cla
ssify
ing
and
orga
nisi
ng d
ata
Cla
ssify
col
lect
ed d
ata
as:
%�ca
tego
rical
dat
a (e
.g. m
ale/
fem
ale;
type
of c
ar)
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umbe
r of p
eopl
e; n
umbe
r of c
ars)
and
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tinuo
us d
ata
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. ZHLJKWV��UDLQIDOO)
Sor
t col
lect
ed n
umer
ical
dat
a ac
cord
ing
to o
ne (G
rade
10)
, tw
o (G
rade
11)
or m
ore
than
two
cate
gorie
s (G
rade
12)
.
(e.g
. Sor
t dat
a re
latin
g to
the
heig
hts
of th
e le
arne
rs in
a c
lass
acc
ordi
ng to
hei
ght o
nly;
or a
ccor
ding
to b
oth
gend
er a
nd h
eigh
t; or
acc
ordi
ng to
gen
der,
heig
ht a
nd c
lass
.)
Gro
up c
olle
cted
dat
a us
ing
inte
rval
s (w
here
app
ropr
iate
) (e.
g.�,W�LV�RIWHQ�DSSURSULDWH�WR�JURXS�WHVW�VFRUHV�LQ�WKH�PDUN�LQWHUYDOV�³����´��³�����´��HWF�).
Org
anis
e co
llect
ed d
ata
usin
g:
%�ta
llies
%�fre
quen
cy ta
bles
10, 1
1 an
d 12
Cla
ssify
ing
and
orga
nisi
ng d
ata
(con
tinue
d)
5HFRJQLVH�WKDW�WKH�ZD\�LQ�ZKLFK�GDWD�LV�FODVVL¿HG��VRUWHG�DQG�RU�JURXSHG�ZLOO�DIIHFW�KRZ
�GDWD�LV�RUJDQLVHG��VXP
PDULVHG�DQG�UHSUHVHQWHG�
In o
rder
to�
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PDULVHG�DQG�RU�UHSUHVHQWHG��WR�¿QG�DQVZ
HUV�WR�WKH�
ques
tion(
s) p
osed
on
issu
es re
latin
g to
the
pers
onal
live
s of
lear
ners
(Gra
de 1
0), t
he w
ider
com
mun
ity (G
rade
11)
, and
nat
iona
l and
glo
bal i
ssue
s (G
rade
12
).
MATHEMATICAL LITERACY GRADES 10-12
84 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Sum
mar
isin
g da
ta
Sum
mar
ise
sing
le s
ets
of c
olle
cted
dat
a (G
rade
10)
; sum
mar
ise
and
com
pare
two
(Gra
de 1
1) a
nd m
ultip
le (G
rade
12)
set
s of
col
lect
ed d
ata
usin
g th
e fo
llow
ing
mea
sure
s of
cen
tral t
ende
ncy
and
spre
ad (f
or u
ngro
uped
dat
a on
ly):
%�m
ean
%�m
edia
n
%�m
ode
%�ra
nge
10 a
nd
11
%�qu
artil
es a
nd in
ter-
quar
tile
rang
e va
lues
* (in
con
junc
tion
with
box
-and
-whi
sker
dia
gram
s - s
ee “R
epre
sent
ing
data
” bel
ow)
%�pe
rcen
tiles
(int
erpr
etat
ion
only
)+12
with
an
unde
rsta
ndin
g of
the
follo
win
g:
%�th
e fu
nctio
n/pu
rpos
e of
the
mea
sure
s of
cen
tral t
ende
ncy
and
spre
ad
%�WKH�PHDVXUH�RI�FHQWUDO�WHQGHQF\�UHIHUUHG�WR�ZKHQ�WKH�WHUP�³DYHUDJH´�LV�XVHG
10, 1
1 an
d 12
%�th
e ro
le a
nd im
pact
of o
utlie
rs o
n th
e m
easu
res
of c
entra
l ten
denc
y an
d/or
spr
ead
%�th
e st
reng
ths
and
limita
tions
of e
ach
type
of m
easu
re o
f cen
tral t
ende
ncy
and
spre
ad a
nd th
e si
tuat
ions
in w
hich
one
mea
sure
is m
ore
or le
ss a
ppro
pria
te
than
the
othe
r m
easu
res
(e.g
.�,I�WKHUH�LV�DQ�RXWOLHU�LQ�D�GDWD�VHW��WKH�PHDQ�DYHUDJH�PD\�EH�VNHZ
HG�E\�WKH�RXWOLHU��$
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RXOG�EH�DGYLVDEOH�WR�
FDOFXODWH�WKH�PHDQ��PHGLDQ�DQG�PRGDO�DYHUDJHV��FRP
SDUH�WKHVH�DYHUDJHV��DQG�WKHQ�GHFLGH�ZKLFK�DYHUDJH�LV�WKH�PRVW�UHSUHVHQWDWLYH�RI�WKH�PDMRULW\�
of th
e da
ta v
alue
s.)
11 a
nd
12
Ana
lyse
cal
cula
ted
and/
or g
iven
mea
sure
s of
cen
tral t
ende
ncy
and/
or s
prea
d.10
, 11
and
12
In o
rder
to�
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(Gra
de 1
0), t
he w
ider
com
mun
ity (G
rade
11)
, and
nat
iona
l and
glo
bal i
ssue
s (G
rade
12)
.10
, 11
and
12
MATHEMATICAL LITERACY GRADES 10-12
85CAPS
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Sum
mar
isin
g da
ta
(con
tinue
d)
Use
qua
rtile
and
per
cent
ile v
alue
s, to
geth
er w
ith v
ario
us m
easu
ring
inst
rum
ents
# , in
the
follo
win
g co
ntex
ts:
%�R
oad
to H
ealth
cha
rt an
d ot
her g
row
th c
harts
for c
hild
ren
%�te
st a
nd e
xam
resu
lts.
In o
rder
to�
Ana
lyse
the
grow
th p
atte
rn o
f a b
aby/
todd
ler.
Ana
lyse
the
heal
th s
tatu
s of
a c
hild
usi
ng c
alcu
late
d B
ody
Mas
s In
dex
valu
es.
Det
erm
ine
the
quan
tity
of p
arac
etam
ol (a
dru
g fo
und
in s
ever
al m
edic
ines
, inc
ludi
ng P
anad
o) to
be
adm
inis
tere
d to
a c
hild
.
Ana
lyse
the
perfo
rman
ce o
f a g
roup
of l
earn
ers
in a
test
and
/or e
xam
inat
ion.
12
add
ition
al c
omm
ents
:C
omm
on c
onte
xts
invo
lvin
g qu
artil
es a
nd p
erce
ntile
s in
clud
e:
%�gr
owth
cha
rts fo
r bab
ies
and
child
ren
%�qu
artil
e an
d pe
rcen
tile
cate
gorie
s us
ed in
ana
lysi
ng re
sults
(e.g
. for
the
Gra
de 1
2 ex
amin
atio
n re
sults
)
%�te
st a
nd/o
r exa
m re
sults
for a
larg
e gr
oup
of le
arne
rs (e
.g.�IRU�WKH�ZKROH�VFKRRO)
* In
wor
king
with
qua
rtile
s, le
arne
rs a
re e
xpec
ted
to:
%�id
entif
y th
e qu
artil
e va
lues
in a
set
of d
ata
%�ex
plai
n th
e pr
oces
s in
volv
ed in
det
erm
inin
g gi
ven
quar
tile
valu
es in
a s
et o
f dat
a
%�ca
lcul
ate
inte
r-qu
artil
e ra
nge
valu
es
%�in
terp
ret q
uarti
le v
alue
s, in
ter-
quar
tile
rang
e va
lues
, and
box
-and
-whi
sker
dia
gram
s in
ord
er to
mak
e de
duct
ions
rega
rdin
g tre
nds
in th
e da
ta
Lear
ners
are
not
exp
ecte
d to
:
%�ca
lcul
ate
quar
tile
valu
es u
sing
form
ulae
.+ Le
arne
rs a
re n
ot e
xpec
ted
to p
erfo
rm a
ny c
alcu
latio
ns in
volv
ing
perc
entil
es. I
f pre
sent
ed w
ith p
erce
ntile
val
ues
in ta
bles
or g
raph
s, le
arne
rs s
houl
d be
abl
e to
ex
plai
n w
hat t
hose
val
ues
indi
cate
abo
ut th
e da
ta.
# S
ee th
e to
pic
Mea
sure
men
t and
the
sect
ions
on
Mea
surin
g le
ngth
and
dis
tanc
e an
d 0HDVXULQJ�PDVV��ZHLJKW�
for a
des
crip
tion
of th
e ty
pes
of m
easu
ring
inst
rum
ents
to b
e us
ed in
this
con
text
.
MATHEMATICAL LITERACY GRADES 10-12
86 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Rep
rese
ntin
g da
ta
Rep
rese
nt s
ingl
e (G
rade
10)
, tw
o (G
rade
11)
and
mul
tiple
(Gra
de 1
2) s
ets
of c
olle
cted
dat
a us
ing:
%�pi
e ch
arts
*
%�hi
stog
ram
s
%�si
ngle
bar
gra
phs
%�lin
e an
d br
oken
line
gra
phs
10, 1
1 an
d 12
%�m
ultip
le b
ar g
raph
s an
d co
mpo
und/
verti
cal s
tack
gra
phs
%�sc
atte
r plo
t gra
phs+
11 a
nd
12
%�bo
x-an
d-w
hisk
er p
lots
(as
grap
hica
l rep
rese
ntat
ions
of q
uarti
les)
(int
erpr
etat
ion
only
) #12
with
an
unde
rsta
ndin
g of
the
follo
win
g:
%�th
at e
ach
type
of r
epre
sent
atio
n of
fers
a d
iffer
ent p
ictu
re o
f the
dat
a an
d th
at c
erta
in ty
pes
of re
pres
enta
tions
are
mor
e ap
prop
riate
for p
artic
ular
type
s of
dat
a
(e.g
. $OWKRXJK�LW�ZRXOG�EH�SRVVLEOH�WR�XVH�D�SLH�FKDUW�WR�VKRZ�WKH�PRQWKO\�UDLQIDOO�LQ�D�WRZQ��LW�ZRXOG�EH�GLI¿FXOW�WR�LGHQWLI\�WUHQGV�LQ�WKH�UDLQIDOO�SDWWHUQ�
IURP�WKLV�FKDUW��$�EDU�JUDSK�DQG�HVSHFLDOO\�D�OLQH�JUDSK�ZRXOG�DOORZ�IRU�D�PXFK�PRUH�LQ�GHSWK�DQDO\VLV�RI�WKH�WUHQGV�LQ�WKH�UDLQIDOO�GDWD�)
%�th
e ef
fect
that
the
scal
e of
a s
et o
f axe
s an
d th
e po
int a
t whi
ch th
e ax
es c
ross
can
hav
e on
the
impr
essi
on c
reat
ed b
y a
grap
h.
Rea
d in
form
atio
n fro
m g
raph
s an
d, if
nec
essa
ry, u
se e
stim
atio
n to
det
erm
ine
valu
es o
n th
e gr
aphs
.¨
Ana
lyse
dat
a pr
esen
ted
in g
raph
s.
10, 1
1 an
d 12
In o
rder
to�
Iden
tify
trend
s in
dat
a to
ans
wer
the
ques
tions
on
the
pers
onal
live
s of
lear
ners
(Gra
de 1
0), t
he w
ider
com
mun
ity (G
rade
11)
, and
nat
iona
l and
glo
bal
issu
es (G
rade
12)
.
10, 1
1 an
d 12
add
ition
al c
omm
ents
:*
Lear
ners
are
not
exp
ecte
d to
dra
w p
ie c
harts
in a
n ex
amin
atio
n. R
athe
r, th
ey m
ust b
e ab
le to
inte
rpre
t and
read
val
ues
from
a p
ie c
hart
and,
if n
eces
sary
, exp
lain
ho
w th
e si
zes
of th
e di
ffere
nt s
egm
ents
of a
pie
cha
rt ha
ve b
een
dete
rmin
ed.
+ In
wor
king
with
sca
tter p
lot g
raph
s le
arne
rs a
re n
ot e
xpec
ted
to d
raw
OLQHV�RI�EHVW�¿W.
They
sho
uld,
how
ever
, ide
ntify
and
des
crib
e ob
serv
able
tren
ds in
the
plot
s.
# Le
arne
rs a
re n
ot e
xpec
ted
to d
raw
box
-and
-whi
sker
plo
ts. T
hey
shou
ld b
e ab
le to
:
%�lo
cate
min
imum
, max
imum
, med
ian
and
quar
tile
valu
es o
n th
e pl
ot
%�LQWHUSUHW�WKH�SORW�DQG�H[SODLQ�ZKDW�WKH�VKDSH�RI�WKH�SORW�VLJQL¿HV�LQ�WHUPV�RI�WKH�VSUHDG�RI�WKH�GDWD�YDOXHV�
MATHEMATICAL LITERACY GRADES 10-12
87CAPS
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Rep
rese
ntin
g da
ta
(con
tinue
d)
¨ In G
rade
10,
it is
exp
ecte
d th
at it
will
be
poss
ible
to re
ad a
nd id
entif
y va
lues
in g
raph
s di
rect
ly fr
om th
e va
lues
pro
vide
d on
the
axes
and
with
out t
he n
eed
for
estim
atio
n.
In G
rade
11,
it is
exp
ecte
d th
at s
ome
estim
atio
n m
ay b
e re
quire
d, b
ut th
at th
e es
timat
ion
will
invo
lve
estim
atin
g be
twee
n tw
o gi
ven
valu
es o
r est
imat
ing
valu
es w
here
tic
k m
arks
are
pro
vide
d on
the
axes
but
onl
y ce
rtain
tick
mar
ks a
re la
belle
d.
In G
rade
12,
ow
ing
to th
e la
rge
and
com
plex
nat
ure
of th
e da
ta d
ealt
with
in re
latio
n to
nat
iona
l and
/or g
loba
l iss
ues,
it is
exp
ecte
d th
at m
ore
com
plex
est
imat
ion
will
be
requ
ired
(e.g
. *LYHQ�WKDW�D�EDU�UHSUHVHQWLQJ�WKH�SRSXODWLRQ�RI�D�SDUWLFXODU�DJH�JURXS�OLHV�EHWZHHQ������������DQG�������������WKH�SRSXODWLRQ�LQ�WKDW�DJH�JURXS�LV�
appr
oxim
atel
y 23
500
000
).
Inte
rpre
ting
and
anal
ysin
g da
ta*
Rea
d an
d se
lect
dat
a fro
m re
pres
enta
tions
(tha
t is,
tabl
es a
nd g
raph
s) c
onta
inin
g da
ta in
ord
er to
ans
wer
que
stio
ns re
latin
g to
the
data
.
Iden
tify
and
desc
ribe
trend
s/pa
ttern
s in
dat
a pr
esen
ted
in ta
bles
/gra
phs
and
expl
ain
wha
t the
dat
a in
dica
tes
abou
t the
que
stio
n/pr
oble
m fo
r whi
ch th
e da
ta
was
col
lect
ed.
Inve
stig
ate
how
the
choi
ce o
f rep
rese
ntat
ion
of th
e da
ta im
pact
s on
the
impr
essi
ons
crea
ted
and
conc
lusi
on(s
) tha
t can
be
draw
n, ta
king
into
acc
ount
that
:
%�us
ing
perc
enta
ges
to re
pres
ent d
ata
valu
es in
a ta
ble
or g
raph
is u
sefu
l for
com
parin
g re
latio
nshi
ps in
siz
e, b
ut d
oes
not r
evea
l the
siz
e of
the
popu
latio
n/sa
mpl
e
%�us
ing
actu
al v
alue
s to
repr
esen
t dat
a va
lues
in a
tabl
e or
gra
ph s
how
s th
e po
pula
tion/
sam
ple
size
, but
is o
ften
not u
sefu
l for
sho
win
g th
e re
latio
nshi
p be
twee
n ca
tego
ries
clea
rly
%�w
hen
com
parin
g di
ffere
nt c
ateg
orie
s of
dat
a, if
ther
e is
an
uneq
ual n
umbe
r of d
ata
item
s in
eac
h ca
tego
ry, t
hen
the
use
of a
ctua
l val
ues
or p
erce
ntag
e va
lues
to re
pres
ent t
he d
ata
will
affe
ct th
e im
pres
sion
cre
ated
by
the
data
%�th
e ch
oice
of s
cale
on
the
axes
and
/or t
he p
oint
at w
hich
the
axes
cro
ss im
pact
on
the
impr
essi
on c
reat
ed b
y th
e gr
aph
%�ta
bles
will
ofte
n co
ntai
n m
ore
info
rmat
ion
than
gra
phs,
but
tren
ds/p
atte
rns
are
not e
asy
to o
bser
ve.
Ask
que
stio
ns a
bout
the
way
in w
hich
dat
a ha
s be
en c
olle
cted
, org
anis
ed, s
umm
aris
ed a
nd re
pres
ente
d to
reve
al p
ossi
ble
sour
ces
of e
rror
/bia
s/m
isin
terp
reta
tion.
Lear
ners
sho
uld
know
to a
sk q
uest
ions
abo
ut:
%�th
e si
ze o
f the
sam
ple
%�th
e re
pres
entiv
ity o
f the
sam
ple
%�th
e m
etho
ds u
sed
for c
olle
ctin
g da
ta
%�th
e ne
utra
lity
of th
e da
ta c
olle
ctio
n pr
oces
s
%�w
heth
er th
e da
ta c
olle
cted
was
fact
or o
pini
on
%�th
e w
ay in
whi
ch th
e da
ta w
as s
orte
d an
d/or
gro
uped
%�th
e si
zes
of th
e gr
oups
use
d in
gro
upin
g th
e da
ta
%�th
e ty
pe o
f mea
sure
use
d to
det
erm
ine
the
aver
age
of th
e da
ta
%�th
e sp
read
(ran
ge) o
f the
dat
a an
d w
hat t
his
spre
ad s
ugge
sts
abou
t the
dat
a.
10, 1
1 an
d 12
Com
pare
diff
eren
t rep
rese
ntat
ions
of m
ultip
le s
ets
of d
ata
and
expl
ain
diffe
renc
es.
Inve
stig
ate
situ
atio
ns in
whi
ch s
umm
aris
ed a
nd/o
r rep
rese
nted
dat
a is
inte
rpre
ted
in d
iffer
ent w
ays.
(e.g
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.)
11 a
nd
12
MATHEMATICAL LITERACY GRADES 10-12
88 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Inte
rpre
ting
and
anal
ysin
g da
ta*
(con
tinue
d)
Dev
elop
opp
osin
g ar
gum
ents
usi
ng th
e sa
me
sum
mar
ised
and
/or r
epre
sent
ed d
ata.
(e.g
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QHZVSDSHU�MRXUQDOLVWV
.)12
In o
rder
to�
Find
ans
wer
s to
the
ques
tions
pos
ed re
gard
ing
issu
es re
latin
g to
the
pers
onal
live
s of
lear
ners
, the
wid
er c
omm
unity
, and
nat
iona
l and
glo
bal i
ssue
s.10
, 11
and
12
add
ition
al c
omm
ents
:* A
lthou
gh th
e se
ctio
n on
Inte
rpre
ting
and
anal
ysin
g da
ta h
as b
een
incl
uded
as
a se
para
te s
ectio
n, it
is e
ssen
tial t
hat t
he in
terp
reta
tion
and
anal
ysis
of d
ata
occu
r at
ever
y st
age
durin
g th
e st
atis
tical
cyc
le:
%�w
hen
draw
ing
up a
que
stio
nnai
re, q
uest
ions
sho
uld
be a
sked
abo
ut th
e re
liabi
lity
of th
e qu
estio
nnai
re
%�w
hen
orga
nisi
ng d
ata,
dec
isio
ns s
houl
d be
mad
e ab
out w
heth
er to
exp
ress
dat
a as
act
ual v
alue
s or
per
cent
ages
, and
the
impl
icat
ions
of e
ach
form
at
%�on
ce m
easu
res
of c
entra
l ten
denc
y an
d sp
read
hav
e be
en c
alcu
late
d, th
e m
eani
ng o
f the
se m
easu
res
in re
latio
n to
the
data
sho
uld
be d
eter
min
ed
%�on
ce g
raph
s ha
ve b
een
draw
n to
repr
esen
t dat
a, th
e gr
aphs
sho
uld
be a
naly
sed
to d
eter
min
e tre
nds
or m
eani
ng in
the
data
%�w
hen
conc
lusi
ons
are
mad
e fro
m o
rgan
ised
, sum
mar
ised
and
repr
esen
ted
data
on
a qu
estio
n or
pro
blem
, tho
se c
oncl
usio
ns s
houl
d be
ana
lyse
d in
term
s of
eac
h st
age
of th
e st
atis
tical
cyc
le to
det
erm
ine
the
relia
bilit
y an
d va
lidity
of t
he c
oncl
usio
ns.
MATHEMATICAL LITERACY GRADES 10-12
89CAPS
topi
c:
dat
a ha
ndlin
gG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
a
Poss
ible
ass
essm
ent (
inco
rpor
atin
g al
l the
sta
ges
of th
e st
atis
tical
cyc
le):
Ass
ignm
ent:
Ele
ctric
ity u
sage
%�D
esig
n a
data
col
lect
ion
tool
for r
ecor
ding
how
long
diff
eren
t ele
ctric
app
lianc
es a
re u
sed
in a
hou
seho
ld
%�R
ecor
d, o
rgan
ise,
sum
mar
ise
and
repr
esen
t dat
a on
the
usag
e an
d co
nsum
ptio
n of
var
ious
ele
ctric
app
lianc
es
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10
Poss
ible
ass
essm
ent (
inco
rpor
atin
g m
easu
ring
leng
th a
nd w
eigh
t, w
orki
ng w
ith e
quat
ions
and
dat
a ha
ndlin
g, th
at is
, col
lect
ing,
org
anis
ing
and
anal
ysin
g da
ta):
Inve
stig
atio
n: H
ealth
y liv
ing
for a
dults
%�Th
e sa
me
inve
stig
atio
n is
pro
vide
d fo
r the
sec
tion
on W
eigh
t in
the
topi
c M
easu
rem
ent.
In o
ther
wor
ds, i
t is
expe
cted
that
this
inve
stig
atio
n w
ill d
raw
on
cont
ent a
nd/o
r ski
lls fr
om b
oth
Mea
sure
men
t and
Dat
a ha
ndlin
g
%�C
olle
ct h
eigh
t and
wei
ght d
ata
from
a s
ampl
e of
adu
lts in
clud
ing
an e
qual
num
ber o
f fem
ales
and
mal
es
%�D
eter
min
e th
e B
ody
Mas
s In
dex
(BM
I) va
lues
and
wei
ght s
tatu
s fo
r eac
h of
the
fem
ales
and
mal
es in
the
grou
p, a
nd u
se a
ppro
pria
te fr
eque
ncy
tabl
es
and/
or g
raph
s to
com
pare
the
wei
ght s
tatu
s da
ta
%�M
ake
dedu
ctio
ns a
bout
the
heal
th o
f the
who
le g
roup
and
of t
he fe
mal
es c
ompa
red
to th
e m
ales
.
11
Poss
ible
ass
essm
ent (
inco
rpor
atin
g al
l the
sta
ges
of th
e st
atis
tical
cyc
le):
Ass
ignm
ent: 5LVN\�EHKDYLRXU
%�C
olle
ct, o
rgan
ise,
sum
mar
ise
and
repr
esen
t dat
a on
dru
g an
d al
coho
l usa
ge d
raw
n fro
m le
arne
rs in
diff
eren
t gra
des
and
from
diff
eren
t gen
der a
nd ra
cial
gr
oups
%�A
naly
se th
e da
ta in
rela
tion
to th
e na
tiona
l res
ults
pre
sent
ed in
the
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12
MATHEMATICAL LITERACY GRADES 10-12
90 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Prob
abili
tyG
rade
s 10
, 11
and
12
sugg
este
d te
achi
ng ti
me:
Gra
de 1
0:
1-
2 w
eeks
Gra
de 1
1:
1-
2 w
eeks
Gra
de 1
2:
1-
2 w
eeks
rec
omm
ende
d te
xts
and/
or re
sour
ces:
%�Te
xtbo
oks
%�C
oins
and
dic
e
%�G
ames
invo
lvin
g co
ins
and
dice
; wea
ther
repo
rts; n
ewsp
aper
arti
cles
refe
rrin
g to
pro
babi
lity;
cos
met
ic a
nd o
ther
pro
duct
s m
akin
g st
atem
ents
rega
rdin
g pr
obab
ility
(H�J�����
�RI�WKH�ZRP
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…);
prod
ucts
sho
win
g su
cces
s an
d fa
ilure
rate
s fo
r the
ir us
age
(e.g
. pre
gnan
cy te
sts;
dru
g te
sts)
; inf
orm
atio
n on
a lo
ttery
; etc
.
&DOFXODWLRQV�LQYROYLQJ�SUREDELOLW\�DUH�RIWHQ�FRQ¿QHG�WR�m
athe
mat
ical
cal
cula
tions
prim
arily
in th
e co
ntex
t of d
ice,
coi
ns a
nd g
ames
. Alth
ough
we
may
enc
ount
er s
ituat
ions
invo
lvin
g pr
obab
ility
and
cha
nce
on a
regu
lar b
asis
in d
aily
life
, it i
s ve
ry s
eldo
m th
at m
athe
mat
ical
cal
cula
tions
are
nee
ded
in o
rder
to m
ake
sens
e of
thos
e si
tuat
ions
. E.g
. you
don
’t ne
ed to
be
DEOH�WR�FDOFXODWH�WKH�SUREDELOLW\�RI�Z
LQQLQJ�D�ORWWHU\�WR�NQRZ�WKDW�HYHQ�WKRXJK�WKHUH�LV�D�FKDQFH�RI�ZLQQLQJ��WKDW�FKDQFH�LV�YHU\�VP
DOO�
Wha
t is
mor
e im
porta
nt is
hav
ing
an u
nder
stan
ding
of
the
conc
ept o
f pro
babi
lity,
toge
ther
with
a s
ense
of w
heth
er a
n ev
ent i
s m
ore
or le
ss li
kely
to ta
ke p
lace
.
In li
ght o
f the
abo
ve, t
he d
escr
iptio
ns g
iven
bel
ow e
ncou
rage
teac
hers
to fo
cus
mor
e on
inte
rpre
ting
situ
atio
ns in
volv
ing
prob
abili
ty th
an o
n th
e m
athe
mat
ical
cal
cula
tion
of p
roba
bilit
y.
This
invo
lves
dev
elop
ing
an u
nder
stan
ding
of t
he c
once
pt o
f pro
babi
lity,
fam
iliar
ity w
ith th
e di
ffere
nt n
otat
ions
use
d in
exp
ress
ions
of p
roba
bilit
y an
d de
velo
ping
a s
ense
of w
heth
er a
si
tuat
ion
is m
ore
or le
ss li
kely
to o
ccur
. Alte
rnat
ive
cont
exts
out
side
of t
he re
alm
of d
ice,
coi
ns a
nd g
ames
hav
e al
so b
een
sugg
este
d to
rein
forc
e th
is fo
cus.
scop
e of
con
text
s an
d/or
con
tent
per
sec
tion
and
grad
e:
sect
ion
Gra
de 1
0G
rade
11
Gra
de 1
2E
xpre
ssio
ns o
f pro
babi
lity
Exp
lore
pro
babi
lity
in s
cena
rios
invo
lvin
g:
%�ga
mes
usi
ng c
oins
and
dic
e
%�w
eath
er p
redi
ctio
ns
Exp
lore
pro
babi
lity
in s
cena
rios
invo
lvin
g:
%�ga
mes
usi
ng c
oins
and
dic
e
%�w
eath
er p
redi
ctio
ns
%�te
sts
whe
re
ther
e is
th
e ch
ance
of
in
accu
rate
resu
lts
%�co
smet
ic
and
othe
r pr
oduc
ts
mak
ing
stat
emen
ts re
gard
ing
prob
abili
ty
Exp
lore
pro
babi
lity
in s
cena
rios
invo
lvin
g:
%�ga
mes
usi
ng c
oins
and
dic
e
%�w
eath
er p
redi
ctio
ns
%�te
sts
whe
re
ther
e is
th
e ch
ance
of
in
accu
rate
resu
lts
%�co
smet
ic
and
othe
r pr
oduc
ts
mak
ing
stat
emen
ts re
gard
ing
prob
abili
ty
%�lo
ttery
and
oth
er g
ambl
ing
gam
es
%�ris
k as
sess
men
ts
%�ne
wsp
aper
ar
ticle
s co
ntai
ning
re
fere
nces
to p
roba
bilit
y
Pre
dict
ion
Rep
rese
ntat
ions
for d
eter
min
ing
poss
ible
ou
tcom
es
---
---
Eva
luat
ing
expr
essi
ons
invo
lvin
g pr
obab
ility
MATHEMATICAL LITERACY GRADES 10-12
91CAPS
topi
c:
Prob
abili
tyG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Exp
ress
ions
of
pro
babi
lity
Wor
k w
ith s
ituat
ions
invo
lvin
g pr
obab
ility
, inc
ludi
ng:
%�ga
mes
that
mak
e us
e of
coi
ns a
nd d
ice
%�w
eath
er p
redi
ctio
ns
10, 1
1 an
d 12
%�te
sts
whe
re th
ere
is th
e ch
ance
of i
nacc
urat
e re
sults
(e.g
. pre
gnan
cy te
st; d
rug
test
)
%�pr
oduc
ts m
akin
g st
atem
ents
rega
rdin
g pr
obab
ility
(e.g
.�D�FRVPHWLF�SURGXFW�WKDW�FODLPV�WKDW����
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)
%�ta
bles
and
gra
phs
cont
aini
ng d
ata
and
stat
istic
s*
11 a
nd
12
%�na
tiona
l lot
terie
s (e
.g. 3
RZHU%DOO)
%�ga
mbl
ing
scen
ario
s (e
.g. s
lot m
achi
nes)
%�ris
k as
sess
men
ts (e
.g. i
n ap
plic
atio
ns fo
r car
insu
ranc
e)
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12
In o
rder
to:
Rec
ogni
se th
e di
ffere
nce
betw
een
the
follo
win
g te
rms:
%�ev
ent
%�ou
tcom
e/re
sult
Rec
ogni
se th
at p
roba
bilit
y is
exp
ress
ed u
sing
a s
cale
that
rang
es b
etw
een:
%�0
(eve
nts
that
can
not t
ake
plac
e - i
mpo
ssib
le e
vent
s)
%�1
or 1
00%
(eve
nts
that
are
cer
tain
to ta
ke p
lace
)
Rec
ogni
se th
at th
e pr
obab
ility
of a
n ev
ent i
s ex
pres
sed
usin
g fra
ctio
ns, p
erce
ntag
es a
nd d
ecim
al n
otat
ion.
10, 1
1 an
d 12
add
ition
al c
omm
ents
:*
In G
rade
11,
the
scop
e of
the
data
that
lear
ners
are
exp
ecte
d to
wor
k w
ith re
late
s to
the
pers
onal
live
s of
lear
ners
and
the
wid
er c
omm
unity
. In
Gra
de 1
2, th
e sc
ope
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are
expe
cted
to e
xplo
re in
eac
h gr
ade,
refe
r to
the
topi
c D
ata
hand
ling
abov
e.
MATHEMATICAL LITERACY GRADES 10-12
92 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Prob
abili
tyG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Pre
dict
ion
Wor
k w
ith s
ituat
ions
invo
lvin
g pr
obab
ility
, inc
ludi
ng:
%�ga
mes
that
mak
e us
e of
coi
ns a
nd d
ice
%�w
eath
er p
redi
ctio
ns
10, 1
1 an
d 12
%�te
sts
whe
re th
ere
is th
e ch
ance
of i
nacc
urat
e re
sults
(e.g
. pre
gnan
cy te
st; d
rug
test
)
%�pr
oduc
ts m
akin
g st
atem
ents
rega
rdin
g pr
obab
ility
(e.g
. D�FRVPHWLF�SURGXFW�WKDW�FODLPV�WKDW����
�RI�WKH�ZRP
HQ�ZKR�XVHG�WKH�SURGXFW�QRZ
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)
11 a
nd
12
%�na
tiona
l lot
terie
s (e
.g. 3
RZHU%DOO)
%�ga
mbl
ing
scen
ario
s (e
.g. s
lot m
achi
nes)
%�ris
k as
sess
men
ts (e
.g. i
n ap
plic
atio
ns fo
r car
insu
ranc
e)
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12
In o
rder
to:
Rec
ogni
se th
at e
xpre
ssio
ns o
f pro
babi
lity
are
only
pre
dict
ions
abo
ut th
e ou
tcom
e of
an
even
t (e.
g.�$OWKRXJK�WKHUH�LV�DOZD\V�D�FKDQFH�WKDW�VRP
HRQH�PD\�ZLQ�
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)
Und
erst
and
the
diffe
renc
e be
twee
n th
e re
lativ
e fre
quen
cy a
nd th
e th
eore
tical
pro
babi
lity
of a
n ev
ent (
e.g.
The
theo
retic
al p
roba
bilit
y of
a to
ssed
coi
n la
ndin
g RQ�KHDGV�LV����
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d 12
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se th
at e
xpre
ssio
ns o
f pro
babi
lity
are
pred
ictio
ns a
bout
the
futu
re b
ased
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even
ts o
f the
pas
t (e.
g. &DU�LQVXUDQFH�UDWHV�IRU�SHRSOH�EHWZHHQ�WKH�DJHV�
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ogni
se th
at e
xpre
ssio
ns o
f pro
babi
lity
can
only
pre
dict
the
trend
of a
n ou
tcom
e ov
er a
long
per
iod
of ti
me
(for a
ver
y la
rge
num
ber o
f tria
ls) a
nd c
anno
t ac
cura
tely
pre
dict
the
outc
ome
of s
ingl
e ev
ents
(e.g
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er a
ge g
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s do
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eces
saril
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ean
that
it is
not
pos
sibl
e th
at a
noth
er a
ge g
roup
mig
ht e
xper
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e a
high
er n
umbe
r of
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11 a
nd
12
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ogni
se th
e di
ffere
nce
betw
een
situ
atio
ns w
here
the
outc
ome
of o
ne e
vent
impa
cts
on th
e ou
tcom
e of
ano
ther
and
situ
atio
ns w
here
the
two
outc
omes
do
not i
mpa
ct o
n ea
ch o
ther
. (e.
g.�,I�D�SHUVRQ�EX\V�PRUH�WKDQ�RQH�ORWWHU\�WLFNHW��GRHV�WKLV�LQFUHDVH�WKH�FKDQFH�RI�Z
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betw
een
pred
ictio
ns th
at a
re b
ased
on
know
ledg
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d in
tuiti
on a
bout
a s
ituat
ion
(e.g
. the
out
com
e of
a s
ports
mat
ch o
r hor
se ra
ce)
and
expr
essi
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of p
roba
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at a
re b
ased
on
long
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tren
ds in
dat
a.
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the
perfo
rman
ce o
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team
s ( i
njur
ies
of p
laye
rs; p
erfo
rman
ce o
f the
team
s on
the
day)
to b
e ab
le to
pre
dict
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MATHEMATICAL LITERACY GRADES 10-12
93CAPS
topi
c:
Prob
abili
tyG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Rep
rese
ntat
ions
fo
r det
erm
inin
g po
ssib
le o
utco
mes
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k w
ith s
ituat
ions
invo
lvin
g pr
obab
ility
, inc
ludi
ng:
%�ga
mes
that
mak
e us
e of
coi
ns a
nd d
ice
%�w
eath
er p
redi
ctio
ns
10, 1
1 an
d 12
%�te
sts
whe
re th
ere
is th
e ch
ance
of i
nacc
urat
e re
sults
(e.g
. pre
gnan
cy te
st; d
rug
test
)
%�pr
oduc
ts m
akin
g st
atem
ents
rega
rdin
g pr
obab
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(e.g
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)
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bles
and
gra
phs
cont
aini
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ata
and
stat
istic
s*
11 a
nd
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tiona
l lot
terie
s (e
.g. 3
RZHU%DOO)
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mbl
ing
scen
ario
s (e
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lot m
achi
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%�ris
k as
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men
ts (e
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n ap
plic
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r car
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12
In o
rder
to:
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tify
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ible
out
com
es fo
r com
poun
d ev
ents
by
mak
ing
use
of+ :
%�tre
e di
agra
ms
%�tw
o-w
ay ta
bles
.
10, 1
1 an
d 12
add
ition
al c
omm
ents
:*
In G
rade
11,
the
scop
e of
the
data
that
lear
ners
are
exp
ecte
d to
wor
k w
ith re
late
s to
the
pers
onal
live
s of
lear
ners
and
the
wid
er c
omm
unity
. In
Gra
de 1
2, th
e VFRSH�RI�WKH�GDWD�UHODWHV�WR�WKH�SHUVRQDO�OLYHV�RI�OHDUQHUV��WKH�ZLGHU�FRP
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that
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ach
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fer t
o th
e to
pic
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a ha
ndlin
g ab
ove.
+ The
sec
tions
on
tree
diag
ram
s an
d tw
o-w
ay ta
bles
hav
e be
en in
clud
ed to
pro
vide
lear
ners
with
exp
osur
e to
diff
eren
t too
ls a
nd re
pres
enta
tions
that
can
be
used
to
repr
esen
t eve
nts
invo
lvin
g pr
obab
ility
in a
gra
phic
al/p
icto
rial w
ay. T
he fo
cus
in th
ese
sect
ions
sho
uld
be o
n us
ing
thes
e re
pres
enta
tions
to id
entif
y al
l of t
he
poss
ible
out
com
es o
f an
even
t, es
peci
ally
in s
ituat
ions
whe
re th
e ou
tcom
es a
re n
ot im
med
iate
ly o
bvio
us.
Lear
ners
are
not
exp
ecte
d to
hav
e to
use
tree
dia
gram
s an
d tw
o-w
ay ta
bles
to p
erfo
rm m
athe
mat
ical
cal
cula
tions
of p
roba
bilit
y (e
.g. m
ultip
lyin
g pr
obab
ilitie
s al
ong
the
bran
ches
of t
ree
diag
ram
s).
MATHEMATICAL LITERACY GRADES 10-12
94 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
topi
c:
Prob
abili
tyG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
Eva
luat
ing
expr
essi
ons
invo
lvin
g pr
obab
ility
Wor
k w
ith s
ituat
ions
invo
lvin
g pr
obab
ility
, inc
ludi
ng:
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mes
that
mak
e us
e of
coi
ns a
nd d
ice
%�w
eath
er p
redi
ctio
ns
%�te
sts
whe
re th
ere
is th
e ch
ance
of i
nacc
urat
e re
sults
(e.g
. pre
gnan
cy te
st; d
rug
test
)
%�pr
oduc
ts m
akin
g st
atem
ents
rega
rdin
g pr
obab
ility
(e.g
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lot m
achi
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men
ts (e
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itiqu
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lidity
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xpre
ssio
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terp
reta
tions
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roba
bilit
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esen
ted
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ewsp
aper
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d ot
her s
ourc
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orm
atio
n.
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12
MATHEMATICAL LITERACY GRADES 10-12
95CAPS
topi
c:
Prob
abili
tyG
rade
s 10
, 11
and
12
sect
ion
Con
tent
/ski
lls to
be
deve
lope
d in
app
ropr
iate
con
text
sG
rade
a
Poss
ible
ass
essm
ent:
Ass
ignm
ent:
Unf
air p
lay
%�D
evel
op a
gam
e us
ing
coin
s an
d/or
dic
e an
d m
ake
the
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e un
fair
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is, t
here
is a
hig
her p
roba
bilit
y of
losi
ng)
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ive
the
gam
e to
you
r cla
ssm
ates
and
ask
them
to d
eter
min
e (w
ithou
t doi
ng a
ny c
alcu
latio
ns) w
heth
er th
e ga
me
is fa
ir an
d if
not,
why
not
.
10
Poss
ible
ass
essm
ent (
inco
rpor
atin
g al
l pro
babi
lity
conc
epts
):In
vest
igat
ion:
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sing
coi
ns
%�To
ss a
coi
n a
smal
l num
ber o
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ls a
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en d
eter
min
e th
e pr
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ility
of t
he to
ssed
coi
n la
ndin
g on
hea
ds fo
r thi
s ex
perim
ent
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e sa
me
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ver
y la
rge
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ls a
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en d
eter
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e th
e pr
obab
ility
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ssed
coi
n la
ndin
g on
hea
ds fo
r thi
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rger
exp
erim
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vest
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w b
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ports
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valu
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e od
ds
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vest
igat
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iona
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and
/or g
ambl
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12
MATHEMATICAL LITERACY GRADES 10-12
96 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
SECTION 4
assessment
4.1 introduction
Assessment is a continuous planned process of identifying, gathering and interpreting information about the performance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence RI�DFKLHYHPHQW��HYDOXDWLQJ�WKLV�HYLGHQFH��UHFRUGLQJ�WKH�¿QGLQJV�DQG�XVLQJ�WKLV�LQIRUPDWLRQ�WR�XQGHUVWDQG�DQG�WKHUHE\�DVVLVW�WKH�OHDUQHU¶V�GHYHORSPHQW�LQ�RUGHU�WR�LPSURYH�WKH�SURFHVV�RI�OHDUQLQJ�DQG�WHDFKLQJ��
Assessment should be both informal (Assessment for Learning) and formal (Assessment of Learning). In both cases regular feedback should be provided to learners to enhance the learning experience.
Assessment of Mathematical Literacy
In accordance with the aims of the subject Mathematical Literacy assessment in Mathematical Literacy must measure the extent to which learners are able to make sense of scenarios based on authentic and realistic, familiar and unfamiliar real-life contexts by drawing on both mathematical and non-mathematical techniques and/or considerations.
As such, assessment tasks should:
%� be based on authentic real-life contexts and use real-life data;
%� require learners to select and use appropriate mathematical content in order to explore contexts;
%� require learners to take into account possible non-mathematical considerations that may have a bearing on the desired outcome to a problem.
Some assessment tasks might more explicitly give learners the opportunity to demonstrate their understanding RI� VSHFL¿F�PDWKHPDWLFDO� FRQWHQW� DQG�RU� VNLOOV� �H�J�� the ability to ‘solve equations’ or ‘calculate statistics such as mean, median and mode for different sets of data’���ZKLOH�RWKHU�DVVHVVPHQW�WDVNV�PLJKW�EH�OHVV�IRFXVHG�RQ�VSHFL¿F�mathematical content and rather draw on a range of content and/or skills from a variety of content topics to explore and make sense of an authentic context.
Teachers need to design assessment tasks that provide learners with the opportunity to demonstrate both competence in mathematical content and the ability to use a variety of both mathematical and non-mathematical techniques and/or considerations to make sense of real-life, everyday, meaningful problems.
Areas/topics of focus
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MATHEMATICAL LITERACY GRADES 10-12
97CAPS
DVVHVVLQJ�WKH�OHDUQHUV¶�DELOLW\�WR�VROYH�SUREOHPV�DQG�H[SORUH�FRQWH[WV�UHODWLQJ�WR�WKH�WRSLFV�RI�)LQDQFH��0HDVXUHPHQW��Maps, plans and other representations of the physical world, Data handling and Probability, and their ability to use number concepts and equations, tables and graphs in an integrated way in order to make sense of those contexts.
4.2 informal or daily assessment
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Self-assessment and peer assessment actively involves learners in assessment. This is important as it allows OHDUQHUV�WR�OHDUQ�IURP�DQG�UHÀHFW�RQ�WKHLU�RZQ�SHUIRUPDQFH��7KH�UHVXOWV�RI�WKH�LQIRUPDO�GDLO\�DVVHVVPHQW�WDVNV�DUH�not formally recorded unless the teacher wishes to do so. The results of daily assessment tasks are not taken into DFFRXQW�IRU�SURPRWLRQ�DQG�FHUWL¿FDWLRQ�SXUSRVHV��
4.3 Formal assessment
All assessment tasks that make up a formal programme of assessment for the year are regarded as Formal Assessment. Formal assessment tasks are marked and formally recorded by the teacher for progression and FHUWL¿FDWLRQ�SXUSRVHV��$OO�)RUPDO�$VVHVVPHQW�WDVNV�DUH�VXEMHFW�WR�PRGHUDWLRQ�IRU�WKH�SXUSRVH�RI�TXDOLW\�DVVXUDQFH�and to ensure that appropriate standards are maintained.
Formal assessment provides teachers with a systematic way of evaluating how well learners are progressing in a grade and in a particular subject. Examples of formal assessments include tests, examinations, assignments, investigations, practical tasks, demonstrations, etc. Formal assessment tasks form part of a year-long formal Programme of Assessment in each grade and subject.
6SHFL¿F�GHWDLOV�UHJDUGLQJ�WKH�IRUPDO�DVVHVVPHQW�UHTXLUHPHQWV�LQ�0DWKHPDWLFDO�/LWHUDF\�DUH�JLYHQ�LQ�WKH�VHFWLRQ�WLWOHG�Programme of assessment below.
The forms of assessment used should be age and development level appropriate. The design of these tasks should cover the content of the subject and include a variety of tasks designed to achieve the objectives of the subject.
Formal assessments must cater for a range of cognitive levels and abilities of learners. The levels appropriate to Mathematical Literacy are described below.
Mathematical Literacy assessment taxonomy
Assessment can be pitched at different levels of cognitive demand. At one end of the spectrum are tasks that require the simple reproduction of facts, while at the other end of the spectrum tasks require detailed analysis and the use of varied and complex methods and approaches.
MATHEMATICAL LITERACY GRADES 10-12
98 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Complexity in Mathematical Literacy is structured around the following assessment taxonomy framework:
%� Level 1: Knowing
%� Level 2: Applying routine procedures in familiar contexts
%� Level 3: Applying multi-step procedures in a variety of contexts
%� /HYHO����5HDVRQLQJ�DQG�UHÀHFWLQJ��
The levels of this taxonomy are described in Appendix 1 and are illustrated by means of references to an assessment task (Responsible use of paracetamol) provided in Appendix 2.
When designing assignments, investigations, and especially tests and examinations, teachers should use the following guideline for deciding on the number of marks to be allocated to questions at each of the levels of the taxonomy.
table 1: distribution of marks according to the levels of the mathematical literacy taxonomy in Formal assessment tasks
levels of the mathematical literacy assessment taxonomy Percentage of marks allocated to each level in an assessment
Level 1: Knowing 30% (± 5%)
Level 2: Applying routine procedures in familiar contexts 30% (± 5%)
Level 3: Applying multi-step procedures in a variety of contexts 20% (± 5%)
/HYHO����5HDVRQLQJ�DQG�UHÀHFWLQJ 20% (± 5%)
It is important to point out that in order to promote the vision that Mathematical Literacy involves the use of both mathematical and non-mathematical techniques and considerations in exploring and understanding of authentic real-life scenarios, this taxonomy should not be seen as being associated exclusively with different levels of mathematical calculations and/or complexity. In determining the level of complexity and cognitive demand of a task, consideration should also be given to the extent to which the task requires the use of integrated content and skills drawn from GLIIHUHQW� WRSLFV�� WKH� FRPSOH[LW\� RI� WKH� FRQWH[W� LQ�ZKLFK� WKH� SUREOHP� LV� SRVHG�� WKH� LQÀXHQFH�RI� QRQ�PDWKHPDWLFDO�considerations on the problem, and the extent to which the learner is required to make sense of the problem without guidance or assistance.
4.4 Programme of assessment
4.4.1 Programme of assessment in Mathematical Literacy
The Programme of Assessment is designed to spread formal assessment tasks in all subjects in a school throughout a term.
Programme of Assessment for Mathematical Literacy in Grades 10 and 11
The Programme of Assessment for Mathematical Literacy in Grades 10 and 11 consists of HLJKW� WDVNV�which are internally assessed:
%� Seven of the eight tasks are completed during the school year and make up 25% of the total mark for Mathematical Literacy.
MATHEMATICAL LITERACY GRADES 10-12
99CAPS
%� The end-of-year examination is the eighth task and makes up the remaining 75%.
Table 2a illustrates one possible Programme of Assessment for Mathematical Literacy for Grades 10 and 11.
table 2a: example of a Programme of assessment for Grades 10 and 11 showing the weighting of assessment tasks
Continuous assessment (25%) eXamination(75%)
term 1 term 2 term 3 term 4
Grade 10
Assignment/
Investigation*
(10%)
Assignment/
Investigation*
(10%)
Assignment/
Investigation*
(10%)
Assignment/
Investigation*
(10%) Examination
Control Test
(15%)
Examination
(30%)
Control Test
(15%)
Grade 11
Assignment/
Investigation*
(10%)
Assignment/
Investigation*
(10%)
Assignment/
Investigation*
(10%)
Assignment/
Investigation*
(10%) Examination
Control Test
(15%)
Examination
(30%)
Control Test
(15%)
* Teachers can choose to evaluate either an assignment or an investigation completed by the learners during each term. By the end of the year learners should have completed two assignments and two investigations.
The suggested Programme of Assessment assumes that:
%� all the topics and sections are addressed throughout the year;
%� the topics are weighted in accordance with the suggested minimum weightings for each topic outlined in Chapter 2 of this document;
%� content and/or skills are integrated across a variety of topics throughout teaching and learning, and in the assessment activities.
Programme of Assessment for Mathematical Literacy in Grade 12
The Programme of Assessment for Mathematical Literacy in Grade 12 consists of HLJKW�WDVNV:
%� Seven tasks are internally assessed and completed during the school year making up 25% of the total mark for Mathematical Literacy;
%� The eighth task is an externally assessed end-of-year examination and makes up the remaining 75%.
MATHEMATICAL LITERACY GRADES 10-12
100 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Table 2b illustrates one possible Programme of Assessment for Mathematical Literacy for Grade 12.
table 2b: example of a Programme of assessment for Grade 12 showing the weighting of assessment tasks
Continuous assessment (25%) eXamination(75%)
term 1 term 2 term 3 term 4
Grade 12
Assignment
(10%)
+
Investigation
(10%)
Assignment/
Investigation
(10%)
Control Test
(10%)Examination
Control Test
(10%)
Examination*
(25%)
Examination*
(25%)
* In Grade 12, one of the tasks in Term 2 and/or Term 3 must be an internal examination.
In instances where only one of the two internal examinations is written in Grade 12, the other examination should be replaced by a control test at the end of the term.
The suggested Programme of Assessment assumes that:
%� all the topics and sections are addressed throughout the year;
%� the topics are weighted in accordance with the suggested minimum weightings for each topic outlined in Chapter 2 of this document;
%� content and/or skills are integrated across a variety of topics throughout teaching and learning, and in the assessment activities.
Description of assessment tasks in Mathematical Literacy
The different tasks listed in the Programme of Assessment are described as follows:
MATHEMATICAL LITERACY GRADES 10-12
101CAPS
Control test
Control tests assess content under controlled examination or test conditions. Control tests are essential to prepare learners for examinations and, as such, should resemble the examinations in terms of structure and the conditions under which they are administered. Learners are expected to prepare for these tests and the content that will be tested is explicitly communicated to learners timeously, well before the test.. All information required in the test, including any real-life resources around which questions have been posed, will be provided by the teacher.
Example: Having studied how taxation is determined using tax bracket tables and tax deduction tables, learners could be set a test on determining taxation for an individual based on the salary information provided. The salary slip and any other information that is required for answering the questions in the test are provided by the teacher.
Assignment
,Q� WKH� FRQWH[W� RI�0DWKHPDWLFDO� /LWHUDF\�� DQ� DVVLJQPHQW� LV� D� ZHOO�VWUXFWXUHG� WDVN� ZLWK� FOHDU� JXLGHOLQHV� DQG� D� ZHOO�GH¿QHG�outcome. An assignment could provide learners with the opportunity to consolidate a topic or section that has been covered in class, or to apply an approach or method studied in class to a new context, or to revise for tests and/or examinations. Both the content and contexts of the assignment are likely to be familiar to the learner. While the teacher may allocate classroom time to an assignment and supervise the completion, parts of an assignment should also be completed by the learner in his or her own time and/or with the assistance of other learners.
Example: If learners have determined the bank fees for a given bank statement based on the fee structure for a savings bank account for a particular month, an assignment could ask the learners to calculate the bank fees for the same bank statement but based on the fee structure for a different kind of bank account.
Investigation
In the context of Mathematical Literacy, an investigation involves a guided discovery, where learners are led through a process of discovering a particular concept or idea through leading questions. This guided discovery may include the collection of data and/or information to solve a problem.
Example: Learners are presented with two adverts showing different cell phone contract options. Questions are provided to guide them through various calculations that expose the costs involved in each contract. At the conclusion of the investigation, learners are in a position to be able to make a decision about which cell phone option is the most cost-effective for a given condition.
MATHEMATICAL LITERACY GRADES 10-12
102 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Summary of the formal assessment tasks listed in the CAPS document
The tables below provide a summary of the various suggested assessment tasks included in this document.
table 3: summary of suggested assessments listed in the CaPs document for Grades 10-12
Grade 10
topic section assessment type and title Page reference
Numbers and calculations with numbers
Rounding Assignment: Exploring the impact of rounding 31
Proportion Investigation: Comparing direct and indirect proportion 32
Rates Assignment: Comparing prices 33
Percentages Assignment: Comparing actual and relative size 34
Patterns, relationships and representations
Representations of relationships in tables, graphs and equations
Investigation: Identifying and representing a relationship in daily life 42
Assignment: Representing electricity costs graphically 42
Finance
Financial documents Assignment: 0DNLQJ�VHQVH�RI�D�KRXVHKROG�ELOO 49
Income, H[SHQGLWXUH��SUR¿W�loss, income-and-expenditure statements and budgets
Assignment: Developing a household budget 51
Measurement
Measuring length and distance Assignment: Measuring accurately 63
Perimeter, area and volume Assignment: Designing and costing a small vegetable garden 69
Time Assignment: %DNLQJ�D�FDNH 71
Maps, plans and other representations of the physical world
Scale Investigation: What happens if you resize a map or plan? 73
Maps Assignment: )LQGLQJ�\RXU�ZD\ 75
PlansAssignment: Writing instructions 76
Assignment: Assembling an object 76
Data handling All sections Assignment: Electricity usage 88
Probability All sections Assignment: Unfair play 94
MATHEMATICAL LITERACY GRADES 10-12
103CAPS
Grade 11
topic section assessment type and title Page reference
Patterns, relationships and representations
Representations of relationships in tables, graphs and equations
Assignment: Representing cell phone costs graphically 42
Working with two or more relationships
Investigation: Comparing costs on different cell phone systems 45
Finance
Tariff systems Investigation: :KLFK�FHOO�SKRQH" 50
Break-even analysis Assignment: Running a home industry business 52
Interest Investigation: Comparing simple and compound interest graphically 53
Banking, loans and investments Assignment: :KLFK�EDQN" 54
,QÀDWLRQ Investigation: 7UDFLQJ�LQÀDWLRQ�LQ�WKH�UHDO�ZRUOG 57
Taxation Assignment: Understanding UIF 59
Measurement
Measuring mass (weight) Investigation: ,QYHVWLJDWLQJ�WKH��PDVV��ZHLJKW�VWDWXV�RI�DGXOWV 65
Measuring volume Assignment: 0DNLQJ�DQG�FDOLEUDWLQJ�D�UDLQ�JDXJH�WR�PRQLWRU�rainfall 66
Perimeter, area and volume Assignment: Household ZDWHU�FRQVXPSWLRQ 69
Time Assignment: Mini-Olympics 71
Maps, plans and other representations of the physical world
Plans, conversions, DUHD��¿QDQFH Assignment: Painting a classroom 78
Models, surface area, volume Investigation: :KLFK�ER[�VKRXOG�\RX�XVH" 80
Data handling All sections Investigation: Healthy living for adults 88
Probability All sectionsInvestigation: Tossing coins
Investigation: Pregnancy tests94
MATHEMATICAL LITERACY GRADES 10-12
104 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Grade 12
topic section assessment type and title Page reference
Patterns, relationships and representations
Working with two or more relationships
Investigation: Comparing costs on different electricity systems 45
Finance
Financial documents Assignment: 8QGHUVWDQGLQJ�WKH�³7D[�3RFNHW�*XLGH´ 49
Banking, loans and investments Assignment: Modelling a loan 56
Taxation Assignment: Calculating personal income tax 59
Exchange rates Assignment: Planning a holiday in another country 59
Measurement
Measuring mass (weight) Investigation: ,QYHVWLJDWLQJ�WKH�ZHLJKW�VWDWXV�RI�FKLOGUHQ 65
Perimeter, area and volume
Investigation: 7LOLQJ�D�ÀRRU
Investigation: Housing density69
7LPH��PDSV��¿QDQFH Assignment: Planning a trip 71
Maps, plans and other representations of the physical world
0DSV��¿QDQFH��timetables Assignment: Planning a trip 75
Plans, models, perimeter, area, YROXPH��¿QDQFH
Assignment: Building a house 78
Models Assignment: Building a model of a school hall 80
Data handling All sections Assignment: 5LVN\�EHKDYLRXU 88
Probability All sections Investigation:�3UREDELOLW\�LQ�WKH�ZRUOG 94
4.4.2 Examinations for Grades 10, 11 and 12
Overview
%� Examination papers for Grades 10 and 11 will be internally set, marked and moderated, unless otherwise instructed by provincial departments of education.
%� 7KH�*UDGH����¿QDO�HQG�RI�\HDU�H[DPLQDWLRQ�LV�QDWLRQDOO\�VHW��PDUNHG�DQG�PRGHUDWHG�
Time and mark allocation
Table 4 shows the number of and stipulated mark and time allocations for examination papers (and control tests) for Grades 10-12:
MATHEMATICAL LITERACY GRADES 10-12
105CAPS
table 4: number of examination papers and control tests with marks and duration for Grades 10-12
Grade 10 Grade 11 Grade 12
term 1 Control Test Control Test Control Test
term 2Paper 1
1 hour
(50 marks)
Paper 2:
1 hour
(50 marks)
Paper 1:
1½ hours
(75 marks)
Paper 2:
1½ hours
(75 marks)
Paper 1:
2 hours
(100 marks)
Paper 2:
2 hours
(100 marks)
term 3 Control Test Control Test
Control Test Control Test
Paper 1:
3 hours
(150 marks)
Paper 2:
3 hours
(150 marks)
term 4Paper 1
1½ hours
(75 marks)
Paper 2
1½ hours
(75 marks)
Paper 1:
2 hours
(100 marks)
Paper 2:
2 hours
(100 marks)
Nationally set examination
Paper 1:
3 hours
(150 marks)
Paper 2:
3 hours
(150 marks)
Additional information regarding examination papers
For each examination in Grades 10, 11 and 12 there are two examination papers. These papers assess the same content but are differentiated according to intention, cognitive demand and the nature of contexts included in the examinations.
Paper 1: A “skills” paper working with familiar contexts
2YHUYLHZ�
This examination paper assesses basic mathematical skills and competency, and primarily contains questions at the NQRZLQJ (Level 1) and routine procedures (Level 2) levels. The examination also contains a small number of multi-step procedures (Level 3) questions, which will allow for more in-depth analysis of contexts and/or problems. The FRQWH[WV�LQFOXGHG�LQ�WKLV�SDSHU�DUH�OLPLWHG�WR�WKRVH�VSHFL¿HG�LQ�WKH�FXUULFXOXP�RXWOLQH�VHFWLRQ�RI�WKLV�&$36�GRFXPHQW��
,QWHQWLRQ�
The intention of this paper is to assess understanding of the core content and/or skills outlined in the CAPS document in the context of authentic real-life problems. Although questions will be contextualised, the focus is primarily on DVVHVVLQJ�SUR¿FLHQF\�LQ�D�UDQJH�RI�FRQWHQW�WRSLFV��WHFKQLTXHV�DQG�RU�VNLOOV��
6WUXFWXUH�DQG�VFRSH�RI�FRQWHQW�
$�0DWKHPDWLFDO�/LWHUDF\�3DSHU���H[DPLQDWLRQ�ZLOO�W\SLFDOO\�FRQVLVW�RI�¿YH�TXHVWLRQV��
%� Each question will be contextualised and may focus on more than one context.
%� Each question will contain sub-questions.
%� 7KH�¿UVW�IRXU�TXHVWLRQV�ZLOO�EH�IRFXVHG�RQ�HDFK�RI�WKH�WRSLFV�
- Finance
- Measurement
MATHEMATICAL LITERACY GRADES 10-12
106 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
- Maps, plans and other representations of the physical world
- Data handling
with the content and/or skills outlined in the following topics integrated throughout each question:
�- Interpreting and communicating answers and calculations
�- Numbers and operations with numbers
�- Patterns, relationships and representations.
%� 7KH�¿IWK�TXHVWLRQ�ZLOO�LQWHJUDWH�FRQFHSWV�DQG�RU�VNLOOV�IURP�DFURVV�DOO�WKH�WRSLFV�LQ�WKH�FXUULFXOXP�
%� The topic of Probability will be assessed in the context of one or more of these questions rather than as a question on its own.
6FRSH�RI�FRQWH[WV�
&RQWH[WV�XVHG�LQ�WKH�3DSHU���H[DPLQDWLRQ�ZLOO�EH�OLPLWHG�WR�WKRVH�VSHFL¿HG�LQ�WKH�&XUULFXOXP�2XWOLQH�VHFWLRQ�RI�WKH�CAPS document thus the contexts used in this examination will be familiar to the learners.
'LVWULEXWLRQ�RI�PDUNV�DFFRUGLQJ�WR�WKH�WD[RQRP\�OHYHOV�
A Paper 1 examination should include questions at the different levels of the taxonomy according to the following mark distribution:
%� 60% (±5%) of the marks at Level 1 (NQRZLQJ);
%� 35% (±5%) of the marks at Level 2 (applying routine procedures in familiar contexts);
%� 5% (minimum) of the marks at Level 3 (applying multi-step procedures in a variety of contexts).
&RPPHQWV�RQ�PDUN�DOORFDWLRQ�
Given the nature of this subject where there is very little recall and/or emphasis on the memorisation of facts, it is not anticipated that one-mark questions will be included in the examination. Even in situations where all that is required is for information to be read straight from a table, the information in the table has to be interpreted and the appropriate LQIRUPDWLRQ� ORFDWHG�DQG� LGHQWL¿HG��7KLV�SURFHVV� LQYROYHV� WZR�VWHSV�DQG�VKRXOG�EH�DZDUGHG� WZR�PDUNV�� ,W� LV�DOVR�envisioned that a mark will be allocated for each step of working required in a calculation.
Paper 2: An “applications” paper, using both familiar and unfamiliar contexts
7KLV� H[DPLQDWLRQ� SDSHU� LV� DQ� ³DSSOLFDWLRQV´� SDSHU� DQG� SULPDULO\� FRQWDLQV� multi-step procedures (Level 3) and UHDVRQLQJ�DQG�UHÀHFWLQJ (Level 4) questions, and a small number of routine procedures (Level 2) questions. The purpose of the Level 2 questions in this paper is to provide learners with greater access to the contexts in which problems are situated.
MATHEMATICAL LITERACY GRADES 10-12
107CAPS
,QWHQWLRQ�
The intention of this examination paper is to assess the ability to identify and use a variety of mathematical and non-mathematical techniques and/or considerations to understand and explore both familiar and unfamiliar authentic contexts.
6WUXFWXUH�DQG�VFRSH�RI�FRQWHQW�
$�0DWKHPDWLFDO�/LWHUDF\�3DSHU���H[DPLQDWLRQ�ZLOO�W\SLFDOO\�FRQVLVW�RI�IRXU�RU�¿YH�TXHVWLRQV��
%� Each question will contain sub-questions.
%� Each question will explore one or more contexts, drawing on content and/skills from two or more of the following topics:
�- Finance
�- Measurement
�- Maps, plans and other representations of the physical world
�- Data handling
with the content and/or skills outlined in the following topics integrated throughout each question:
�- Interpreting and communicating answers and calculations
�- Numbers and operations with numbers
�- Patterns, relationships and representations.
%� The topic of Probability will be assessed in the context of one or more of these questions and not as a question on its own.
%� Each question will include sub-questions consisting of a small number of questions at the routine procedures (Level 2) levels, and a greater number at the multi-step procedures (Level 3) and� UHDVRQLQJ�DQG�UHÀHFWLQJ�(Level 4) levels.
%� The focus of each question will be on assessing the ability to explore and understand a context(s) rather than RQ�PDWKHPDWLFDO�SUR¿FLHQF\�
6FRSH�RI�FRQWH[WV�
Contexts used in a Paper 2 examination will include both familiar and unfamiliar contexts and are not limited to WKRVH�VSHFL¿HG�LQ�WKH�&XUULFXOXP�2XWOLQH�VHFWLRQ�RI�WKH�&$36�GRFXPHQW�
'LVWULEXWLRQ�RI�PDUNV�DFFRUGLQJ�WR�WKH�WD[RQRP\�OHYHOV�
A Paper 2 examination should include questions at the different levels of the taxonomy according to the following mark distribution:
%� 25% of the marks at Level 2 (applying routine procedures in familiar contexts);
MATHEMATICAL LITERACY GRADES 10-12
108 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
%� 35% of the marks at Level 3 (applying multi-step procedures in a variety of contexts);
%� 40% of the marks at Level 4 (UHDVRQLQJ�DQG�UHÀHFWLQJ).
Paper 1 and Paper 2 compared
Table 5 shows a summary of the differences between Paper 1 and Paper 2 examinations.
table 5: summary of the differences between Paper 1 and Paper 2
Paper 1 Paper 2
intention³%DVLF�VNLOOV´�SDSHU�ĺ�DVVHVVHV�SUR¿FLHQF\�RI�content and/or skills
³$SSOLFDWLRQV´�SDSHU�ĺ�DVVHVVHV�DELOLW\�WR�XVH�both mathematical and non-mathematical techniques/considerations to explore familiar and unfamiliar contexts.
structure and scope of content and/or skills
5 questions.
First four questions deal with contexts relating to each of these topics:
%� Finance
%� Measurement
%� Maps, plans and other representations of the physical world
%� Data handling
Fifth question integrates content from across all of these topics.
Probability will be examined in the context or one or more of the other questions.
7KH�³%DVLF�6NLOOV´�WRSLFV�Numbers and operations ZLWK�QXPEHUV and Patterns, relationships and representations will be integrated throughout all other questions.
Each question can contain more than one context.
4 or 5 questions.
Each question deals with contexts drawing integrated content from across all of these topics:
%� Finance
%� Measurement
%� Maps, plans and other representations of the physical world
%� Data handling
Probability will be examined in the context of one or more of the other questions.
7KH�³%DVLF�6NLOOV´�WRSLFV�Numbers and operations ZLWK�QXPEHUV and Patterns, relationships and representations will be integrated throughout all other questions.
Each question can contain more than one context.
taxo
n om
y le
vels
level 1 60% (±5%) ---
level 2 35% (±5%) 25% (±5%)
level 3 5% (minimum) 35% (±5%)
level 4 --- 40% (±5%)
Contexts ³)DPLOLDU´��WKDW�LV��OLPLWHG�WR�WKH�FRQWH[WV�OLVWHG�LQ�the CAPS document.
%RWK�³IDPLOLDU´�DQG�³XQIDPLOLDU´��WKDW�LV��QRW�OLPLWHG�to the contexts listed in the CAPS document.
Contexts
In order to achieve the aim of Mathematical Literacy to help learners develop the ability to use a variety of mathematical and non-mathematical techniques and/or considerations to explore and understand both familiar and unfamiliar real-life contexts, it is essential that assessment items and examinations draw on realistic and authentic contexts. Learners should be asked to interpret newspaper articles, real bank statements, real plans and other authentic resources, rather than contrived problems containing only a semblance of reality.
MATHEMATICAL LITERACY GRADES 10-12
109CAPS
Weightings of topics
The following weightings are stipulated for each topic in examinations:
table 6: Weighting per topic
Topic Weighting (%)
Basic Skills Topics
Interpreting and communicating answers and calculations No weighting is provided for these topics.
Rather, they will be assessed in an integrated way in the Application Topics.Numbers and calculations with numbers
Patterns, relationships and representations
Application Topics
Finance 35% (±5%)
Measurement 20% (±5%)
Maps, plans and other representations of the physical world 15% (±5%)
Data handling 25% (±5%)
Probability Minimum of 5%
Distribution of marks according to the taxonomy levels
Table 7 illustrates the percentage of marks to be allocated to the different taxonomy levels for Grades 10, 11 and 12.
table 7: Percentage of marks to be allocated to the different assessment taxonomy levels in examinations in Grades 10, 11 and 12
the four levels of the mathematical literacy assessment taxonomyGrades 10, 11 and 12
Paper 1 Paper 2 overall allocation
Level 1: Knowing 60% (±5%) 30% (±5%)
Level 2: Applying routine procedures in familiar contexts 35%(±5%) 25% (±5%) 30% (±5%)
Level 3: Applying multi-step procedures in a variety of contexts 5% (minimum) 35% (±5%) 20% (±5%)
/HYHO����5HDVRQLQJ�DQG�UHÀHFWLQJ 40% (±5%) 20% (±5%)
Additional information on the mid-year examainations
Much of the information relating to the structure of the examinations provided above relies on the whole curriculum having been covered and so relates primarily to examinations that take place at the end of the year. Clearly this will not be the case for the mid-year examinations, which will focus on assessing content covered in Terms 1 and 2.
It is not the intention of this document to prescribe the contents and the weighting of the various topics covered in these mid-year examinaitions. However, the following guidelines are suggested:
%� Two examinations papers: Paper 1 (Basic Skills Paper) and Paper 2 (Applications Paper).
%� The structure of the questions in these papers should follow the structure suggested above for Paper 1 and Paper 2 examinations (see Table 5 on page 99 above).
MATHEMATICAL LITERACY GRADES 10-12
110 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
%� The examinations should include questions on all of the topics covered in Terms 1 and 2:
�- This means that in Grade 10 teachers can choose to include questions that assess the content, skills and contexts covered in the Basic Skills topics of Numbers and calculations with numbers and Patterns, relationships and representations (both of which designated to be taught in Term 1 in the work schedule provided at the beginning of this document).
�- In Grade 11 teachers can choose to include questions that assess the content, skills and contexts covered in the Basic Skills topic of Patterns, relationships and representations (which is designated to be taught in Term 1 according to the work schedule provided at the beginning of this document).
%� Teachers can decide on an appropriate weighting of the topics assessed in the examination, possibly as determined by the amount of content included in a topic or section and the amount of time taken to teach the topic or section. The table below shows an example of a possible weighting of topics for a Grade 10 mid-year examination (across both Paper 1 and Paper 2).
table 8: example of weightings per topic in the mid-year examinations
term topic / sectionWeeks allocated in suggested
work schedule (on page 14 above)
Weighting (% of combined
Paper 1 & Paper 2)
1
Numbers and calculations with numbers 5 10%
Patterns relationships and representations 3 10%
Contexts focussing on Measurement (Conversions and Time) 1 10%
2
Contexts focussing on Measurement (Measuring length/distance, mass, volume and temperature) 2 15%
Contexts focussing on Finance (Financial docuyments and Tariff systems) 2 20%
Contexts focussing on Maps, plans and other representations of the physical world (Scale and Maps)
2 20%
Contexts focussing on Probability 2 15%
4.5 recording and reporting
5HFRUGLQJ�LV�D�SURFHVV�LQ�ZKLFK�WKH�WHDFKHU�GRFXPHQWV�WKH�OHYHO�RI�D�OHDUQHU¶V�SHUIRUPDQFH�LQ�D�VSHFL¿F�DVVHVVPHQW�task. It indicates learner progress towards the achievement of the knowledge as prescribed in the Curriculum and Assessment Policy Statements��5HFRUGV�RI�OHDUQHU�SHUIRUPDQFH�VKRXOG�SURYLGH�HYLGHQFH�RI�WKH�OHDUQHU¶V�FRQFHSWXDO�progression within a grade and her / his readiness to progress or to be promoted to the next grade. Records of learner performance should also be used to verify the progress made by teachers and learners in the teaching and learning process.
Reporting is a process of communicating learner performance to learners, parents, schools, and other stakeholders. /HDUQHU�SHUIRUPDQFH�FDQ�EH�UHSRUWHG�LQ�D�QXPEHU�RI�ZD\V�ZKLFK�LQFOXGH�UHSRUW�FDUGV��SDUHQWV¶�PHHWLQJV��VFKRRO�visitation days, parent-teacher conferences, phone calls, letters, class or school newsletters, etc. Teachers in all grades report in percentages against the subject. Seven levels of competence have been described for each subject listed for Grades R-12. The various achievement levels and their corresponding percentage bands are as shown in the Table below.
MATHEMATICAL LITERACY GRADES 10-12
111CAPS
Codes and PerCentaGes For reCordinG and rePortinG
ratinG Code desCriPtion oF ComPetenCe PerCentaGe
7 Outstanding achievement 80 - 100%
6 Meritorious achievement 70 - 79%
5 Substantial achievement 60 - 69%
4 Adequate achievement 50 - 59%
3 Moderate achievement 40 - 49%
2 Elementary achievement 30 - 39%
1 Not achieved 0 - 29%
Note: The seven point scale should have clear descriptors that give detailed information for each level.
Teachers will record actual marks against the task by using a record sheet; and report percentages against the VXEMHFW�RQ�WKH�OHDUQHUV¶�UHSRUW�FDUGV�
4.6 moderation of assessment
Moderation refers to the process which ensures that the assessment tasks are fair, valid and reliable. Moderation should be implemented at school, district, provincial and national levels. Comprehensive and appropriate moderation practices must be in place for the quality assurance of all subject assessments.
In Mathematical Literacy:
%� Grade 10 and 11 tasks are internally moderated. The subject advisor will moderate a sample of these tasks during school visits to verify the standard of the internal moderation.
%� Grade 12 tasks are moderated by the provincial subject advisor. This process will be managed by the provincial education department.
MATHEMATICAL LITERACY GRADES 10-12
112 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
4. 7 appendices
aPPendiX 1
desCriPtion oF tHe leVels in tHe matHematiCal literaCy assessment taXonomy
Complexity in Mathematical Literacy is structured around the following assessment taxonomy framework:
%� Level 1: Knowing
%� Level 2: Applying routine procedures in familiar contexts
%� Level 3: Applying multi-step procedures in a variety of contexts
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It is important to recognise that this taxonomy should not be seen as associated exclusively with different levels of mathematical calculations and/or complexity. In determining the level of complexity and cognitive demand of a task, consideration should also be given to the extent to which the task requires the use of integrated content DQG�VNLOOV�GUDZQ�IURP�GLIIHUHQW�WRSLFV��WKH�FRPSOH[LW\�RI�WKH�FRQWH[W�LQ�ZKLFK�WKH�SUREOHP�LV�SRVHG��WKH�LQÀXHQFH�RI�non-mathematical considerations on the problem, and the extent to which the learner is required to understand the problem without guidance or assistance.
level 1: knowing
/HYHO����.QRZLQJ questions serve two functions:
%� To familiarise learners with the context in which problems are posed by asking them questions about the context;
%� To test ability to interpret contextualised information, to use familiar techniques to perform basic calculations and to explain common terms.
%� Examples of the types of tasks at the NQRZLQJ�level of the Mathematical Literacy taxonomy include:
%� reading information directly from a table (e.g. WKH�GDWH�RQ�D�EDQN�VWDWHPHQW��WKH�WLPH�WKDW�D�EXV�OHDYHV�WKH bus terminal);
%� performing basic operations on numbers (e.g. subtracting income and expenditure values to determine the SUR¿W�ORVV�IRU�D�EXVLQHVV��DGGLQJ�YDOXHV�WR�VKRZ�KRZ�WKH�³$PRXQW�GXH´�YDOXH�RQ�DQ�HOHFWULFLW\�ELOO�KDV�EHHQ determined);
%� measuring accurately (e.g. measuring the dimensions of a room on a given plan accurately using a ruler).
%� rounding answers appropriately as per a given instruction (e.g. URXQGLQJ�RII�DQ�DQVZHU�WR�RQH�GHFLPDO place ZKHQ�LQVWUXFWHG�WR�GR�VR);
%� identifying the appropriate formula to be used in a given calculation (e.g. identifying the formula for the area of D�FLUFOH�DV�DUHD� �ʌ�î�UDGLXV��IURP�D�JLYHQ�OLVW�RI�DUHD�IRUPXODH);
MATHEMATICAL LITERACY GRADES 10-12
113CAPS
%� recognising and explaining vocabulary appropriate to a particular scenario (e.g. “discrete” and “continuous” in the context of data; “event” and “outcome” in the context of Probability; “dependent” and “independent” YDULDEOHV��³GHELW´�DQG�³FUHGLW´�LQ�WKH�FRQWH[W�RI�¿QDQFH);
%� reading values directly from the values provided on a graph or table (e.g. UHDGLQJ�RII�WKH�FRVW�RI�WDONLQJ�IRU 60 PLQXWHV�RQ�D�FHOO�SKRQH�FRQWUDFW�IURP�D�JUDSK�VKRZLQJ�WKH�FRVW�RI�FDOOV�RYHU�WLPH);
%� performing conversions within the metric system (e.g. IURP�PP�WR�FP�WR�P�WR�NP��IURP�PO�WR�Ɛ��IURP�J�WR�NJ; from seconds to minutes to hours).
Example:In the responsible use of paracetamol task in appendix 2 below, Questions 1.1, 2.1.1, 3.1.1, 1.2 and 1.3 are at the NQRZLQJ level of the taxonomy. %� Questions 1.1, 2.1.1 and 3.1.1 require the learner to interpret the given information and read information directly
from the tables in the text. None of these questions require a calculation. The intention of these questions is to force learners to read the information provided in the tables and, hopefully, to help them to become more familiar and comfortable with the context.
%� Questions 1.2 and 1.3 both require a basic calculation.�- Question 1.2 requires the learner to determine the relationship between body weight and dosage of
paracetamol from the information given at the start of the task and to use this relationship to determine the dosage for children of a given weight . The task requires the use of a basic operation (multiplication) and all the information is given.
�- Question 1.3 requires the learner to use the same information and operation as in Question 2 to complete a table of values.
level 2: applying routine procedures in familiar contexts
Tasks at the applying routine procedures in familiar contexts level of the Mathematical Literacy taxonomy require learners to perform well-known procedures and complete common tasks in familiar contexts. Learners know which procedure/task is required from the way the problem is posed and all the necessary information to solve the problem is immediately available to the learner. Routine procedures questions commonly involve single-step calculations, repeating the same calculation several times, or the completion of a task with which learners are familiar (e.g. FRQVWUXFWLQJ�DQ�LQFRPH�DQG�H[SHQGLWXUH�VWDWHPHQW�WR�UHÀHFW�DQ�LQGLYLGXDO¶V�¿QDQFHV).
Examples of routine procedures tasks include:
%� substituting values into given equations (e.g. GHWHUPLQLQJ�WKH�EDQN�FKDUJH�IRU�GHSRVLWLQJ�PRQH\�LQWR�DQ account using a given formula);
%� solving equations by means of trial and improvement or algebraic processes;
%� drawing graphs from given tables of values (e.g. GUDZLQJ�D�JUDSK�WR�VKRZ�WKH�FRVW�RI�D�FDOO�RQ�D�FHOO�SKRQH contract over time from a given table of time and cost values);
%� constructing a budget for a small household project;
%� XVLQJ�WD[�GHGXFWLRQ�WDEOHV�WR�GHWHUPLQH�WKH�DPRXQW�RI�WD[�WR�EH�GHGXFWHG�IURP�DQ�HPSOR\HH¶V�VDODU\�
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MATHEMATICAL LITERACY GRADES 10-12
114 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
%� calculating the mean, median and/or modal averages of a set of data;
%� increasing or decreasing an amount by a percentage (e.g. GHWHUPLQLQJ�KRZ�PXFK�D�SHUVRQ�ZLOO� SD\� IRU�D television set if a 5% discount is given);
%� estimating values from the values provided on a graph or in a table (e.g. RQ�D�JUDSK� VKRZLQJ�SRSXODWLRQ VWDWLVWLFV�LQ�PLOOLRQV�IRU�WKH�GLIIHUHQW�SURYLQFHV�LQ�6RXWK�$IULFD��HVWLPDWH�WKH�SRSXODWLRQ�RI�.ZD=XOX�1DWDO);
%� converting units of measurement between different systems of measurement using given conversion tables and/or factors (e.g��XVLQJ�D�EDNLQJ�FRQYHUVLRQ�WDEOH�WR�FRQYHUW�IURP�J�WR�PO�ZKHQ�EDNLQJ�D�FDNH);
%� using a given scale to determine actual length or distance (e.g. XVLQJ�D�VFDOH�RI�������RQ�D�SODQ�WR determine WKH�DFWXDO�OHQJWK�DQG�ZLGWK�RI�WKH�ZDOOV�RI�D�URRP).
In the responsible use of paracetamol task in appendix 2 below, Questions 1.4 and 1.5 are at the applying routine procedures in familiar contexts level of the taxonomy.
%� Question 1.4 requires the learner to describe the relationship between input and output values in a table of data by means of an equation. Since the relationship is linear and learners from Grade 9 upwards should be familiar with this relationship, the task is one that requires the application of routine procedures.
%� Question 1.5 requires the learner to draw a graph of a linear function based on a table of values and/or an equation. The knowledge and skills required to draw this graph have been developed in Grades 8 and 9 and nurtured from Grade 10 upwards in Mathematical Literacy, and hence is considered to be the application of a routine procedure.
%� Since it is expected that learners will deal with a large number of contexts in which the relationship between the variables is linear, it is reasonable to suggest that the nature of the context is familiar, even if the learner has not expressly dealt with medicine as a context before.
%� Notice that in Questions 1.4 and 1.5, the number of steps in every calculation is limited to one or two, or a repetition of the same calculation several times. Also notice that it is obvious from the way in which the questions are posed precisely what is required in order to complete the question.
level 3: applying multi-step procedures in a variety of contexts
Tasks at the applying multi-step procedures in a variety of contexts level of the Mathematical Literacy taxonomy require learners to solve problems or complete tasks using well-known procedures and methods, but where the procedure or method is not immediately obvious from the way the problem is posed. As such, learners may have to GHFLGH�RQ�WKH�PRVW�DSSURSULDWH�SURFHGXUH�RU�PHWKRG�WR�¿QG�WKH�VROXWLRQ�WR�WKH�TXHVWLRQ�RU�WR�FRPSOHWH�D�WDVN��DQG�they may have to perform one or more preliminary calculations or complete one or more preliminary tasks before determining a solution.
Situations in which a variety of mathematical and non-mathematical content, skills and/or considerations should be utilised from different topics in the curriculum in order to make sense of a problem, are also at the multi-step procedures level of the taxonomy.
Tasks at the multi-step procedures level contain far less direction or guidance than tasks at the routine procedures level and require that learners make decisions regarding the appropriate content, methods and non-mathematical considerations needed to solve problems and complete tasks.
Examples of multi-step procedures tasks include:
%� deciding on the most appropriate graph and an appropriate means of constructing that graph to represent a
MATHEMATICAL LITERACY GRADES 10-12
115CAPS
particular scenario (e.g. constructing a table of values to represent a tariff structure for a particular electricity V\VWHP�DQG�WKHQ�XVLQJ�WKH�WDEOH�RI�YDOXHV�WR�GUDZ�D�JUDSK�WR�UHSUHVHQW�WKDW�WDULII�VWUXFWXUH);
%� determining the most appropriate scale in which to draw a plan, determining dimensions according to that scale, and then drawing the plan according to those scaled dimensions;
%� determining the quantity of paint needed to paint the walls of a building by determining the surface area of the walls of a building, using a conversion ratio to convert the surface area value from m2 to litres, rounding the litres value up to the nearest whole litre and then making a decision about the most appropriate quantity of paint to be bought based on available tin sizes;
%� using maps, a distance chart, weather report information and other travel resources to plan a trip, giving consideration to where to stop for petrol, estimated travelling distance and time, and estimated travel costs;
%� researching the costs involved in a fund-raising activity and preparing a budget for the activity;
%� XVLQJ�JLYHQ�LQÀDWLRQ�UDWHV�WR�LQYHVWLJDWH�WKH�HVWLPDWHG�YDOXH�RI�DQ�LWHP�RYHU�D�PXOWLSOH�WLPH�SHULRG���(�J��if a car LV�FXUUHQWO\�ZRUWK�5��������ZKDW�ZRXOG�WKH�FDU�EH�ZRUWK�LQ�WZR�\HDUV¶�WLPH�LI�WKH�YDOXH�RI�WKH�FDU depreciated E\�DSSUR[LPDWHO\�����LQ�WKH�¿UVW�\HDU�DQG�����LQ�WKH�VHFRQG�\HDU"�
In the responsible use of paracetamol task in appendix 2 below, Questions 2.1.2 and 3.2 are at the applying multi-step procedures in a variety of contexts level of the taxonomy.
%� 4XHVWLRQ�������UHTXLUHV�WKH�OHDUQHU�WR�¿UVW�GHWHUPLQH�KRZ�PDQ\�PJ�RI�SDUDFHWDPRO�LV�VDIH�IRU�D�SDUWLFXODU�FKLOG�and then the number of measures of the medicine to be given to this child. This is a multi-step procedure and, though not complex, the procedure is not obvious from the way the question is posed.
%� 4XHVWLRQ�����UHTXLUHV�OHDUQHUV�¿UVWO\�WR�FKRRVH�EHWZHHQ�WZR�JUDSKV�²�RQH�IRU�ER\V�DQG�RQH�IRU�JLUOV�²�DQG�secondly to select the appropriate line on each graph to answer the question. In this sense, the procedure is multi-step in nature. While the learner may not have seen this exact graph before, it is expected that a learner LQ�*UDGH����ZLOO�EH�VXI¿FLHQWO\�FRPSHWHQW�DQG�H[SHULHQFHG�ZLWK�JUDSKV�WR�XQGHUVWDQG�WKH�LQIRUPDWLRQ�SUHVHQWHG�in this one.
%� Notice that in both Questions 2.1.2 and 3.2 it is not immediately obvious from the way the questions are posed what calculations are required to answer the questions. Also notice that multiple steps are required in these questions.
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Tasks at the UHDVRQLQJ�DQG�UHÀHFWLQJ level of the Mathematical Literacy taxonomy can be divided into two groups of questions:
%� Questions that require a decision, opinion or prediction about a particular scenario based on calculations in a previous question or on given information (e.g. analysing calculations performed in a previous question on WZR GLIIHUHQW�HOHFWULFLW\�FRVWLQJ�RSWLRQV�DQG�PDNLQJ�D�GHFLVLRQ�DERXW�WKH�PRVW�VXLWDEOH�RSWLRQ�IRU�D�SHUVRQ�ZLWK�SDUWLFXODU�QHHGV��RU�FULWLTXLQJ�D�VWDWHPHQW�UHJDUGLQJ�FULPH�VWDWLVWLFV�UHSRUWHG�LQ�D�QHZVSDSHU DUWLFOH��RU�PDNLQJ�D�SUHGLFWLRQ�DERXW�WKH�SURMHFWHG�LQFRPH�IRU�D�EXVLQHVV�EDVHG�RQ�FXUUHQW�¿QDQFLDO�GDWD).
Examples of these types of UHDVRQLQJ�DQG�UHÀHFWLQJ questions include:
%� comparing provided data on the performance of two groups of learners in an examination and explaining which group performed better based on the available data;
MATHEMATICAL LITERACY GRADES 10-12
116 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
%� providing an opinion on how a particular government minister might react to a particular set of statistics;
%� analysing a completed income-and-expenditure statement for a household and making suggestions on how WKH�PHPEHUV�RI�WKH�KRXVHKROG�FRXOG�FKDQJH�WKHLU�H[SHQGLWXUH�WR�LPSURYH�WKHLU�¿QDQFLDO�SRVLWLRQ�
%� Questions that require learners to pose and answer questions about which mathematics they require to solve a problem, select and use that mathematical content, recognise the limitations of using mathematics to solve WKH�SUREOHP��DQG�FRQVLGHU�RWKHU�QRQ�PDWKHPDWLFDO� WHFKQLTXHV�DQG� IDFWRUV� WKDW�PD\�GH¿QH�RU�GHWHUPLQH�D�solution to the problem. (E.g. ZKHQ�SUHVHQWHG�ZLWK�DGYHUWV�IRU�WZR�GLIIHUHQW�FHOO�SKRQH contracts, learners have WR�GHFLGH�ZKLFK�PHWKRG�ZLOO�EH�WKH�PRVW�DSSURSULDWH�WR�FRPSDUH�WKH�FRVWV�LQYROYHG in the contracts. They may decide to construct tables of values, or draw graphs, or use equations. Having chosen a suitable method, they will need to perform the necessary calculations and then make sense of their calculations in order to make a decision regarding the most affordable contract for an individual with particular needs. They will also need to recognise that irrespective of the mathematical solution to the problem, the individual may choose a cell phone based on personal preference, e.g. colour or cell phone model).
Examples of these types of UHDVRQLQJ�DQG�UHÀHFWLRQ questions include:
%� using calculations to compare income and expenditure values for a business in order to determine whether the EXVLQHVV�LV�LQ�D�KHDOWK\�¿QDQFLDO�SRVLWLRQ�
%� comparing bank charges on two different types of accounts for various transactions and making a decision about the most suitable account for an individual with particular needs;
%� constructing a table to model a loan scenario, taking into account the interest calculated on the loan, the monthly repayment and the closing balance on the loan every month;
%� using the model of the loan scenario to investigate the effect of changes in the interest rate on the loan and the impact of increasing the monthly repayment on the real cost of the loan;
%� designing two different types of boxes for packaging an item, comparing the boxes in terms of wasted space (volume) and materials (surface area), and making a decision about the most cost-effective box for packaging the item.
In the responsible use of paracetamol task in appendix 2 below, Questions 3.1.2 and 3.3 are at the reasoning DQG�UHÀHFWLRQ level of the taxonomy. %� Question 3.1.2 requires the learner to make inferences. Learners are expected to draw on what they have
learnt about the safe use of paracetamol in the questions so far to make deductions or inferences. The answer that the learner provides will be within a range of possible values and the quality of the answer will be based on the reasoning that is evident in determining the answer.
%� In Question 3.3 the learner is expected to evaluate the dosage recommended by the manufacturer. Firstly, the learner should make inferences about why the manufacturer made these recommendations. Secondly, the learner should critique the decision. In critiquing the dosage recommended by the manufacturer, the learner has to draw not only on mathematical content, but also on his or her own experiences of the world. Therefore, this question is at the highest level of the Mathematical Literacy taxonomy.
MATHEMATICAL LITERACY GRADES 10-12
117CAPS
aPPendiX 2
assessment task eXamPle:
RESPONSIBLE USE OF PARACETAMOL
assessment task eXamPle: responsible use of paracetamol
INFORMATION:
Paracetamol is a drug with analgesic (painkilling) properties.
Paracetamol is the active ingredient in the well-known medicine Panado that can be bought over the counter in supermarkets and pharmacies.
Paracetamol is, however, involved in many incidents of accidental poisoning through overdose.
Paracetamol dosage is based on body weight. A healthy single dose of paracetamol for children is considered to be 10 mg per kilogram of body weight, with up to four doses per day.
Question 11.1.
1.1.1. According to the information given above, what is considered to be a healthy dose of paracetamol for children? (1)
1.1.2. How many doses of paracetamol can be administered per day? (1)
[2]
1.2. Calculate how many mg of paracetamol each of the following children can safely take per dose.
1.2.1. Gabriella, weight 12 kg (1)
1.2.2. Ricardo, weight 20½ kg (1)
[2]
1.3. Copy and complete the table below:
Weight of patient 6 kg 7 kg 8 kg 9 kg 15 kg 25 kg 35 kg
Safe dose of paracetamol in mg
[4]
1.4. Write an equation that can be used to determine how many mg of paracetamol is a safe dose for a child of a given weight. [2]
1.5. Based on your answers to 1.2 and/or 1.3, draw a graph that can be used to determine how many mg of paracetamol is a safe dose for a child of a given weight. [3]
Question 2
FURTHER INFORMATION:Paracetamol is sold in supermarkets and pharmacies in the following concentrations:%� Infant drops: 60 mg per drop (0,6 ml)%� Syrup: 120 mg per medicine measure (medicine spoon) (5 ml)%� Tablets: 120 mg per tablet
Page 1 of 3
MATHEMATICAL LITERACY GRADES 10-12
118 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
2.1.
2.1.1. What concentration of paracetamol is found in syrup? [1]
2.1.2. Determine the following:
a. The number of infant drops in a safe dose for a child who weighs 7 kg. (2)
b. The number of medicine measures in a safe dose of syrup for a child who weighs 9½ kg. (2)
c. The number of tablets in a safe dose for a child who weighs 12,25 kg. (2)
[6]
Question 3
FURTHER INFORMATION:
The directions for use on the paracetamol syrup (120 mg/5 ml) packaging state:
%� 3-12 months old: 2,5 to 5 ml per dose
%� 1-5 years old: 5 to 10 ml per dose
%� 6-12 years old: 10 to 20 ml per dose
%� A maximum of 4 doses per day
3.1.
3.1.1. What is the maximum dosage of paracetamol that should be given to a 7-year-old child? (1)
3.1.2. According to these directions, what does the manufacturer consider the weight of a child who is 6-12 years old to be? (4)
[5]
3.2. Refer to the CDC weight-for-age percentile charts on the next page to answer the following questions:
3.2.1. According to the chart, how heavy is a 6 year-old girl whose weight is at the 25th percentile? (1)
3.2.2. According to the chart, how heavy is a 12 year-old girl whose weight is at the 75th percentile?(1)
3.2.3. According to the chart, how heavy is a 6 year-old boy whose weight is at the 75th percentile? (1)
3.2.4 According to the chart, how heavy is a 12 year-old boy whose weight is at the 25th percentile? (1)
[4]
3.3. Based on the information provided in this question (including the weight-for-age charts) discuss the following, giving reasons:
3.3.1. How the recommended dosage for paracetamol syrup has been determined (4)
3.3.2. Whether or not you think this is the most appropriate dosage to recommend (4)
[8]
37
Page 2 of 3
MATHEMATICAL LITERACY GRADES 10-12
119CAPS
responsible use of paracetamol (continued)
Page 3 of 3
MATHEMATICAL LITERACY GRADES 10-12
120 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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121CAPS
aPP
end
iX 3
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to th
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Mat
hem
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MATHEMATICAL LITERACY GRADES 10-12
126 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
toPi
C: d
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127CAPS
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Bil
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sect
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leve
l 1: k
now
ing
leve
l 2: a
pply
ing
rout
ine
proc
edur
es in
fam
iliar
con
text
sle
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MATHEMATICAL LITERACY GRADES 10-12
128 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
4.8 General
This document should be read in conjunction with:
4.8.1 National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
4.8.2 The policy document, National Protocol for Assessment Grades R-12.
