Gr12 Mathematics JikaImfundo Tracker Term3 2018

education Department: Education PROVINCE OF KWAZULU-NATAL MATHEMATICSMATHEMA 12 MATHEMATICSMATHE MATHEMATICSMATHT MATHEMATICSMATH MATHEMATICSMATHE MATHEMATICSMATH GRADE MATHEMATICSMATHT MATHEMATICSMATA MATHEMATICS MATHEMATICSMATH TEACHER TOOLKIT MATHEMATICSMATA CAPS Planner and Tracker MATHEMATICSMATHT Jik’iMfundo is a programme to improve learning outcomes, funded by the National Education Collaboration Trust, the KwaZulu-Natal Department of Education and others. MATHEMATICSMATH 2018 TERM 3 THE PROGRAMME TO IMPROVE LEARNING OUTCOMES MATHEMATICSMATHE The Stables Hollard Campus ENDORSED BY 22 Oxford Road Tel: +27 11 351 2430/2457 Parktown 2193 Email: admin@pilo.co.za ISBN: 978-1-928320-83-8 Grade 12 Maths Tracker 2018 Term 3 cover 92 KZN.indd 1 3/7/2018 3:27:15 PM

GRADE 12 Mathematics Teacher Toolkit: CAPS Planner and Tracker 2018 TERM 3

Published in 2016, and revised in 2017 and 2018, by Jika iMfundo. Jik’iMfundo is a programme to improve learning outcomes, funded by the National Education Collaboration Trust, the KwaZulu-Natal Department of Education and others. The Programme to Improve Learning Outcomes (PILO) The Stables, Hollard Campus, 22 Oxford Road, Parktown, 2193 Tel: +27 11 351 2430/2457 Email: admin@pilo.co.za © The National Education Collaboration Trust (NECT) A partnership involving business, civil society, government and labour that strives to improve education outcomes. The National Education Collaboration Trust Ground Floor, Block D, Lakefield Office Park, 272 West Avenue, Centurion, 0163 Tel: +27 12 752 6200 Email: info@nect.org.za Web: www.nect.org.za No part of this publication may be reproduced without prior permission from the NECT. These materials are currently being evaluated and will be improved on the basis of the evaluation. ISBN: 978-1-928320-83-8 Materials development by the PILO team along with representatives from the districts and province. Publishing management by The Word Horse, www.wordhorse.co.za Design and typesetting by COMPRESS.dsl, www.compressdsl.com

CONTENTS A. About the Tracker and Resources____________________________________ 2 B. Lesson Preparation Key Steps_______________________________________ 6 C. Planning for Assessment____________________________________________ 8 D. Trackers for Each Set of Approved LTSMs___________________________ 12 1. Classroom Mathematics_ ____________________________________ 12 2. Clever: Keeping Maths Simple________________________________ 22 3. Maths Handbook and Study Guide____________________________ 32 4. Mind Action Series Mathematics______________________________ 42 5. Platinum Mathematics_______________________________________ 52 6. Via Afrika Mathematics_ _____________________________________ 62 7. Siyavula Everything Maths____________________________________ 72 E. Assessment Resources_____________________________________________ 82 1. Grade 12 Mathematics Test Term 3____________________________ 82 2. Grade 12 Mathematics Test Term 3: Memorandum and    Cognitive Levels of Questions_ _____________________________ 84_ 3. Information Sheet: Mathematics_ _____________________________ 87_ 4. Grade 12 Mathematics Suggested Assessment Record Term 3______ 88

A. ABOUT THE PLANNER AND TRACKER I have looked at the planner and tracker. It goes too fast! 1. Your quick guide to using this planner and tracker What is Jika iMfundo and where do I fit in? The CAPS planner and tracker is an expanded ATP. It helps you pace yourself as if you were able to cover everything in the ATP/CAPS. When you fall behind because time has been lost, or because the learners are progressing slowly, you need to confidently discuss this with your teaching What you do matters! What you do every day as a teacher team without feeling blamed. The pace of coverage will be can change the life-chances of every child that you teach. determined by the pace of learning. That is why coverage Jika iMfundo is a campaign that supports teachers by must be tracked by the teacher and the SMT. providing CAPS planners and trackers so that teachers can plan to cover the curriculum, track progress, and seek help when they are falling behind. How do I use the planner and tracker? But who will help me? See the "Quick 5-step Guide to Using the CAPS Planners and Trackers" on the opposite page. Jika iMfundo will work with your school management team (SMT) and assist them to have supportive and professional conversations with you about curriculum coverage that will be orientated to identifying and solving problems. 2 Grade 12 Mathematics

QUICK 5-STEP GUIDE TO USING THE CAPS PLANNERS AND TRACKERS If this is a campaign, who is part of it? 1. Find the textbook that YOU are using. 2. Use the planning page each week to plan your teaching for the week. It will help you link the CAPS content and skills to relevant material in the textbook, the teacher's guide, and other materials such as the All teacher unions in KwaZulu-Natal support Jika iMfundo DBE workbook. because they believe it will help teachers in their work. The district director, circuit managers and subject advisers are leading Jika iMfundo in your district because they believe that we can improve learning if we improve curriculum 3. Keep a record of the date when you were able to complete the topic. coverage. You, as a teacher, and your colleagues on the It may be different from the date you planned, and for different staff and the SMT of the school are invited to join Jika classes. Write this date in the column on the right for your records. iMfundo. Because what you do matters. 4. At the end of the week, reflect and check if you are up to date. Make notes in the blank space. 5. Be ready to have a professional and supportive curriculum coverage If you see mistakes in the planners and trackers, please send details of these to conversation with your HoD (or subject or phase head). admin@pilo.co.za. If you would like to be kept informed about developments in Jika iMfundo, send the following information to admin@pilo.co.za: • your cell phone number The CAPS planners and trackers also provide guidelines for • the grade/s you teach assessment with samples, and may also have enrichment • the subject/s you teach. and remedial suggestions. Read the introduction pages We will add you to a WhatsApp group that will operate in your circuit. carefully for a full explanation. Look for Jika iMfundo on Facebook. Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 3

2. Purpose of the tracker 4. Links to the approved sets of Learner’s Books and The Grade 12 Mathematics Curriculum and Assessment Planner and Tracker is a tool Teacher’s Guides and the Siyavula Everything Maths books to support you in your role as a professional teacher. Its main purpose is to help you There is a tracker for each of the six sets of approved Learning and Teaching Support to keep pace with the time requirements and the content coverage of the CAPS. The Materials (LTSMs) as well as for the Siyavula Everything Maths books. Each tracker tracker provides a programme of work which should be covered each day of the term coordinates the CAPS requirements with the content set out in the Learner’s Book and a space for reflection on work done. By following the programme in the tracker, you and Teacher’s Guide for that set of LTSMs. You must therefore refer to the tracker for should cover the curriculum in the allocated time, have time for informal assessments the book that is used by learners at your school. If you have copies of other Learner’s and consolidation, and complete and go over the formal assessment programme with Books, you can of course refer to these too, for ideas for teaching the same content in the learners. By noting the date when each lesson is completed, you can see whether or different ways – but you must be sure to cover the content systematically. For each set not you are on track and, if not, you can strategise with your head of department (HOD) of LTSMs in the tracker, links are given to the relevant pages in both the Learner’s Book and peers as to how best to make up time to ensure that all the work for the term is and Teacher’s Guide to make it easier for you to access the correct resources. completed. In addition, the tracker encourages you to reflect on what in your lessons is effective, and where content coverage could be strengthened. These reflections can be In addition, the tracker for each of the sets of LTSMs on the national catalogue also shared with colleagues. In this way, the tracker encourages continuous improvement in gives links to content provided in the Siyavula Everything Maths Learner’s Book and practice. This tracker should be kept and filed at the end of the term. Teacher’s Guide. The exercises in the Siyavula Everything Maths books are referred to by exercise and page number. If you are using these as an additional resource 3. Links to the CAPS you should review them before each lesson, and decide how best to use them – for teaching, revision, extension or for consolidation, either in class or for homework. The Mathematics tracker for Grade 12 is based on the requirements prescribed by the Department of Basic Education’s Curriculum and Assessment Policy Statement In a few instances, when necessary, we recommend that you use only selected activities (CAPS) for Mathematics in the FET (Further Education and Training) Phase. The work from the Learner’s Book. This is when the recommended exercises have more work set out for each day is linked directly to the topics and subtopics given in the CAPS, than can be done in the time allocated to the lesson. (The * symbol indicates that you and the specified amount of time is allocated to each topic. The tracker gives the should Select questions.) In other instances, the Learner’s Books do not have adequate page number in the CAPS document of the topics and subtopics being addressed in activities for learners to consolidate work done on a topic. (The # symbol indicates that each session to help you refer to the curriculum document directly should you wish you should Supplement the work.) You could also use other Learner’s Books from the to do so. In each tracker, some lessons are set aside for revision or consolidation. In catalogue of LTSMs, material in the Siyavula Everything Maths Learner’s Book, or other these lessons, no new content is specified, allowing the time to be used to review resources which you have, to supplement the content coverage as needed. concepts learners might have found difficult in the preceding lessons or for revision in preparation for the trial examinations. Each tracker is based on the latest print editions of the approved sets of LTSMs. It is important to note that page numbers may differ slightly from other print runs of the Please note: The sequence of topics in this tracker does not follow the order given in the CAPS, but rather the provincial teaching plan of the KwaZulu-Natal Department of same Learner’s Book. If the page numbers in your edition are not exactly the same as Education. This means that one of the Term 3 topics in the CAPS, Euclidean Geometry, those given in the tracker, you should use the activity/exercise numbers given in the which was done during Term 2, has been replaced by Finance, growth and decay tracker to guide you to the correct pages. These should only differ by a page or two (a CAPS Term 1 topic). The other two CAPS Term 3 topics – Statistics (Regression and from those given in the tracker. correlation) and Counting and probability – are included in the KwaZulu-Natal Term 3 work schedule. 4 Grade 12 Mathematics

5. Managing time allocated in the tracker indicates when in the series of lessons the formal assessments are to be done and when feedback should be given. We have provided an exemplar test for you in Section E The CAPS prescribes four and a half hours of Mathematics per week in Grade 12. The Assessment Resources of this document. Also provided are a marking memorandum tracker for each Learner’s Book provides a suggested plan for five 55-minute lessons a for the test and an analysis according to the weighting of cognitive levels specified in week, making up 4,6 hours. As each school organises its timetable differently, you may the CAPS. You can use this exemplar test instead of the term test which you may find have to divide the sessions in the programme slightly differently to accommodate the in the LTSMs used by your class. length of the lessons at your school in a way that ensures that the full amount of time for Mathematics is used constructively. It is suggested that you discuss testing times with your colleagues teaching other subjects in order to avoid the learners having to write several tests on the same day. Where your This tracker is based on a third term of 11 weeks. Three weeks have been allocated lessons are less than one-hour in duration, you will also need to make appropriate to the trial examination period. If you use this tracker in a third term of a different arrangements for your learners to have sufficient time to write a one hour test. length, you should adjust the pace of work to accommodate the longer or shorter time which you have available. It is important that you take note of this at the start The province provides a common trial examination for your learners. A list of trial of the term. As Term 3 is an examination term, you may want to set learners weekly examination exemplars (or in some cases, end-of-year exemplars) provided in the revision of Grade 11 and 12 topics. Areas of concern found in the weekly revision LTSMs has been provided in Table 2 in Section C Planning for Assessment. This is to could be discussed in consolidation lessons or in lessons allocated to examination help with revision and consolidation before the trial examination. revision in the tracker. A suggested assessment record sheet is provided for you in Section E Assessment Resources. You may copy and complete it for the learners in your class(es). This records 6. Sequence adherence the marks of the formal assessments that you carry out in the term. You may prefer to The content in each tracker has been carefully sequenced, and it is therefore important use your own mark sheet created using your class list where you might like to record that lessons are not skipped. Should you miss a Mathematics lesson for any reason or some informal assessment marks that are awarded or key comments for your own should you be going at a slower pace, you should continue the next day from where interest. you last left off. Do not leave a lesson out to get back on track. You may need to speed The CAPS (as well as good practice) require informal assessment as well as formal up the pace of delivery to catch up to the lesson schedule – by covering the lesson assessment of learners. However, no links are made to informal assessment in the concept content of two consecutive days in one day. To do this, you could cut out or tracker so that you can assess your learners informally in ways and at times that seem cut back on some of the routine activities, like homework reflection, to save time, until best for them. Section C Planning for Assessment of this document, does, however, you are back on track for curriculum coverage. Where practical, you could also use the offer you some support in planning for informal assessment (and of course, the formal time allocated for revision or consolidation to complete work not yet done. assessments provided by the sets of LTSMs may be used for informal assessment if they have not been used as formal assessment). 7. Links to assessment In Term 3 of Grade 12, the formal assessment programme specified in the CAPS 8. Resources requires, as a minimum, that learners complete one test and write the trial examination. Each learner must have access to a scientific calculator and a geometry set for both Some of the approved Learner’s Books and Teacher’s Guides provide exemplar tests school and home use. which you can use with your class. The Formal Assessment Plan for Each Set of LTSMs, provided in Section C of this tracker, lists the suggested assessments, and on which There are a number of readily accessible resources to assist you and your learners, pages in the Learner’s Books or Teacher’s Guides they can be found. The tracker also which you might like to look at as you prepare for each topic, including: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 5

• The Grade 12 Examination Guidelines available from the DBE website: to the CAPS content focus for the year and the term. It is important that you www.education.gov.za, provides useful information. For example, are clear about the content focus as this will frame everything you do in your recommended ways of abbreviating reasons in proofs or calculations in Mathematics lessons during the term. The time allocation per term is given in Euclidean Geometry and the Information Sheet, which the Grade 12s may the CAPS document on page 17. This indicates how many hours are to be spent refer to when doing assessment activities, are supplied. on each topic. Note that where the term length is different to the total number of • Useful glossaries can be found at the back of the Learner’s Books of Classroom weeks specified in the CAPS, you will have to adjust the pace at which you work on Mathematics, Maths Handbook and Study Guide Mathematics and Mind each topic. Action Series Mathematics. 2. Prepare resources: It is very important that you check what is required for each • Summaries of each topic can be found in the Learner’s Books of Maths lesson ahead of time so that you have all your resources available and ready Handbook and Study Guide Mathematics, Mind Action Series Mathematics, for use. Platinum Mathematics, Via Afrika Mathematics and Siyavula Everything Maths. • The Mindset Learn website: http://learn.mindset.co.za, has useful resources, 3. Prepare the content: Think carefully about what it is that you will teach your learners including videos and worksheets. in each lesson. Think about the prior knowledge of the content that learners should • The Khan Academy website: www.khanacademy.org provides YouTube videos have learned in earlier grades that will be built on in the lesson. You should refer of teachers giving detailed explanations on many topics. to the CAPS content and skills clarification column for further guidance while you • The Maths and Science Marketing website http://mathsandscience.com/ prepare. provides a number of resources, including tests and examinations. • Prepare a short introduction to the topic so that you can explain it in simple • Many other websites are available which provide teacher support. These can terms to your learners. The Learner’s Book and Teacher’s Guide will assist be found by searching the topics on the internet. you. Also think about how learners will develop an understanding of the main • Section C Planning for Assessment in this document, gives references to tests concepts of the lesson topic. You need to think about how to explain new in various LTSMs. It may be worth your while to look at these before you teach Mathematics content and skills to your learners. a topic. • Make sure you have prepared for teaching concepts before you teach. Prepare yourself to assist learners with any questions they might have during B. LESSON PREPARATION KEY STEPS the lesson. Look at the activities in the Learner’s Book and in the Siyavula Everything Maths Learner’s Book and think about how best to help your learners engage with them. Consider what will be done in class and at home. The tracker provides a detailed programme to guide you through the daily content Be sure to have some extension and remediation activities ready to use as you need to teach your class, and when to do formal assessments. You are still required needed. It is a good idea to do your own answers to the exercises/activities to draw up your own lesson plans and will still make the final professional choices you will be giving your learners so that you are aware of where learners may about which examples and explanations to give, which activities to set for your class have difficulties. Also identify any common misconceptions, and plan how you and how to manage your class on a daily basis. It is a good idea that you and your will address these. Mathematics colleagues agree on a day that you can get together to plan your lessons • Consider the needs of any learners with barriers to learning in your class as a group and submit your plans to your HOD for quality assurance. To deliver the and how best you can support them. The DBE has published some excellent lessons successfully you must do the necessary preparation yourself. Bear in mind materials to support you in working with learners with learning barriers. that your lessons will not succeed if you have not prepared properly for them. This Two such publications, which are available from both the Department of entails a number of key steps, such as those noted below. Education’s website (www.education.gov.za) and Thutong portal 1. Review the term focus: Start by looking at the CAPS and orientating yourself (www.thutong.doe.gov.za/InclusiveEducation) are: 6 Grade 12 Mathematics

−− Directorate Inclusive Education, Department of Basic Education (2011) Siyavula Everything Maths Learner’s Book. These activities allow learners to Guidelines for Responding to Learner Diversity in the Classroom Through practise their mathematical and problem solving skills. It is important that Curriculum and Assessment Policy Statements. Pretoria. you prepare yourself for the classwork activity because you need to assist −− Directorate Inclusive Education, Department of Basic Education. (2010). learners as they do the classwork. You may also need to select particular Guidelines for Inclusive Teaching and Learning. Education White Paper 6. questions from each activity for the classwork in advance. This will ensure that Special Needs Education: Building an Inclusive Education and Training all activity types and concepts are covered each day and enable you to give System. Pretoria. quick and clear instructions to your learners about which exercise they should do, which is necessary as the exercises given in the various Learner’s Books 4. Plan the steps in your lesson, and think carefully about how much time to vary greatly in length. allocate to different learner activities. Also think about how to organise the learners when they work. Most lessons should include the steps below and we Depending on your learners and the activities, you could discuss one or two of have suggested the time to be spent on each (for a 55-minute lesson) – but you the classwork activities with the whole class before allowing the learners to work might find that you need to work differently in some lessons, such as when a test is independently. Give the learners an opportunity to complete these activities being written. alone, in pairs, and in groups, so that they experience working alone as well as • Homework review/reflection (10 minutes): This is the first activity of the with their peers. Encourage learners, where appropriate, to write the questions lesson. During this part of the lesson you may reflect on the previous day’s with their answers and to show their working neatly and systematically in their work. We recommend that you use these 10 minutes to remediate and correct workbooks. Plan the timing of the lesson so that you and the learners can go the previous day’s homework and do spot testing. Learners should have over some of the classwork together and they can do corrections in the lesson. marked their work from the answers provided at the back of their Learner’s If you require your learners to work in groups, carefully assign learners in such Book. Choose one or two activities that you noted were problematic, to go a way that there are learners with mixed abilities who can assist each other in over more thoroughly. Allow learners the opportunity to write corrections as each group. needed. If peer or individual marking has been done, you should regularly sample some learners’ books to moderate this marking and to see what errors This is also the part of the lesson where you can assist learners who need extra are being made so you can remediate these. support and extend those who need enrichment. Throughout the lesson, try to • Lesson content – introduction and concept development (15 minutes): identify learners who need additional support or extension by paying attention This is the second activity of the lesson. We recommend that you are actively to how well they managed the homework, how they respond when you develop involved with your class for 15 minutes – going through examples interactively the new content, and how they cope with the class activities. While the rest of with your learners or assisting them with introductory investigations. There are the class is busy working through the classwork activities, you should spend worked examples, suggested explanations and introductory investigations some time with the learners that need extra support and help them to work in the Learner’s Book or Teacher’s Guide that you should go through with through the remediation activities. If learners successfully complete the daily your class as a whole. The CAPS content clarification column would also classwork activities ahead of the rest of the class, be prepared to give them be a useful reference should you need further examples or ideas to enrich extension activities to do. Most of the LTSMs provide activities and ideas for your explanations. You should elaborate on these explanations and provide remediation and extension. additional examples if necessary. • Allocate homework (5 minutes): This is the fourth and final activity of the • Classwork activity (25 minutes): This is the third activity of the lesson. This lesson. In this step you should tell the learners about the homework for the part of the lesson provides an opportunity for learners to consolidate new day and make sure they know what is expected of them and understand what concepts by doing activities or exercises from the Learner’s Book or the it is that they have to do. It is a good idea to get learners into the habit of Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 7

regular daily homework such as completing unfinished classwork, revising C. PLANNING FOR ASSESSMENT what was done in class and noting what they did not understand. Once they have done this they should complete any additional work that you have set Note: All assessments should be done under controlled conditions. Teachers should them to do for homework such as specific questions you have chosen from the invigilate and there should be no talking among the learners. classwork to be done as homework, or some of the remediation or extension activities given in the LTSMs you are using. 1. Formal assessment Homework enables the learners to consolidate the Mathematics that you Table 1 below shows the minimum requirement for formal assessment in Grade 12 have taught them in class. It also promotes learner writing, development of given by the CAPS (p. 54). mathematical knowledge and language and the development of regular study habits. Encourage your learners to show their parent(s) or their guardian(s) the work they have done. Table 1: NUMBER OF ASSESSMENT TASKS AND WEIGHTING WEIGHT 5. After each lesson, reflect on how it went: Each week there is a reminder to you TASKS (%) that you should note your thoughts about the week’s lessons. You will use these notes as you plan and prepare for your teaching and in discussions with your HOD Term 1 Test 10 Project/Investigation 20 and peers. School-based Assignment 10 Term 2 Test 10 Mid-year examination 15 assessment Term 3 Test 10 Trial examination 25 Term 4 School-based assessment mark 100 School-based assessment mark (as a % of the promotion mark) 25% End-of-year examination 75% Promotion mark 100% Note: • Tests should be at least ONE hour long and count at least 50 marks. • Mid-year examinations consist of two papers: Paper I and Paper II. Each examination is normally three hours long. • Graphic and programmable calculators (for example, to factorise (a2 – b2) = (a – b)(a + b), or to find roots of equations) are not allowed (CAPS Errata May 2013). Calculators should only be used to perform standard numerical computations and to verify calculations by hand. • A formula sheet may be provided for tests and for final examinations. 8 Grade 12 Mathematics

Table 2 gives an overview of how the minimum requirements of the formal assessment accordingly. The tracker and this assessment plan indicate when the test could be programme fit into the weekly planned lessons in the tracker. done. Some of the LTSMs provide more than one test; in such cases you would need to choose one to use for formal assessment purposes, and could use the other for an Note that the exemplar test is 60 minutes long. Therefore, five minutes more should be informal assessment/practice activity. Alternatives have been shown in Table 2 below. arranged beforehand, as the lessons are 55 minutes each. Other tests and assessments The last column also gives the page references of trial examination exemplars (or end- found in the LTSMs are listed below the exemplar test in the second column. Should of-year exemplars) in the LTSMs. These can be used for revision and consolidation in you wish to use one of these tests (other than one which may be found in the Learner’s preparation for the trial examinations. Book) instead of the exemplar provided at a different time, you may of course do so. If you set a test at a different time, you will need to adjust the programme in the tracker Table 2: TERM 3 FORMAL ASSESSMENT PLAN FOR EACH SET OF LTSMs Trial examination LTSMs Test In last three weeks of term Classroom Week 5 – Lesson 22 Exemplar end-of-year examinations Mathematics Exemplar test: Section E of tracker Paper 1: LB pp. 407–409 Other possible tests Memorandum: TG pp. 525–529 Test: Financial mathematics TG p. 167 Paper 2: LB pp. 410–413 Memorandum: TG pp. 168–169 Memorandum: TG pp. 530–535 Test: Counting and probability TG pp. 479–480 Memorandum: TG pp. 481–482 Test: Statistics (Regression and correlation) TG p. 465 Memorandum: TG pp. 466–467 Other assessments Project: Finance LB pp. 126–127, TG pp. 164–166 Clever: Keeping Week 5 – Lesson 22 End-of-year sample papers Maths Simple Exemplar test: Section E of tracker Paper 1: LB pp. 423–426 Other tests Memorandum: LB pp. 442–449 Practice test: Financial mathematics TG p. 95 Paper 2: LB pp. 427–432 Memorandum: TG p. 96 Memorandum: LB pp. 450–455 Practice test: Counting and probability TG p. 328 Additional sample papers Memorandum: TG p. 329 Paper 1: Paper One TG pp. 348–350 Practice test: Statistics (Regression and correlation) Memorandum: TG pp. 366–371 TG pp. 303–304 Paper 2: Paper Two TG pp. 351–356 Memorandum: TG pp. 305–306 Memorandum: TG pp. 372–376 Other assessments Paper 3: Paper One TG pp. 357–360 Project: Finance TG pp. 341–342 Memorandum: TG pp. 377–381 Rubric: TG pp. 343–344 Paper 4: Paper Two TG pp. 361–365 Memorandum notes: TG pp. 345–346 Memorandum: TG pp. 382–385 Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 9

Trial examination LTSMs Test In last three weeks of term Maths Handbook Week 5 – Lesson 22 Exemplar preliminary examinations and Study Guide Exemplar test: Section E of tracker Paper 1: LB pp. 312–318 Other assessments Memorandum: TG pp. 121–126 Grade 11 Revision of statistics assignment Paper 2: LB pp. 318–324 LB pp. 381–382 Memorandum: TG pp. 126–130 Memorandum: TG pp. 134–136 Mind Action Series Week 5 – Lesson 22 End of year examination exemplars Mathematics Exemplar test: Section E of tracker Paper 1: TG pp. 339–343 Other assessments Memorandum: TG pp. 344–352 Project: Legal and illegal investment schemes Paper 2: TG pp. 353–359 LB pp. 105–109, TG pp. 95–97 Memorandum: TG pp. 360–367 Rubric: TG pp. 98–99 Memorandum: TG pp. 100–102 Platinum Week 5 – Lesson 22 Preliminary exams (exemplars) Mathematics Exemplar test: Section E of tracker Paper 1: TG pp. 362–365 Other assessments Memorandum: TG pp. 280–282 Project: Financial maths Paper 2: TG pp. 366–370 LB p. 114, TG p. 87 Memorandum: TG pp. 283–285 Project: Pyramid schemes Exam practice: Preliminary TG pp. 343–345 Paper 1: LB pp. 283–285 Rubric: p. 266 Memorandum: LB pp. 387–388 Control test book Paper 2: LB pp. 286–289 Relevant questions can be selected from the three tests provided. Memorandum: LB pp. 389–390 More examination practice papers have been included in the Learner’s Book. Via Afrika Week 5 – Lesson 22 End-of-year exemplar papers Mathematics Exemplar test: Section E of tracker Paper 1: LB pp. 318–321 Note: The Term 3 tests provided in the TG (pp. 370–375) cover Memorandum: TG pp. 412–418 Euclidean geometry, regression and the counting principle, so are not Paper 2: LB pp. 322–325 suitable for KZN use unless selected questions are used. Memorandum: TG pp. 419–423 Other assessments Additional exemplars Assignment: Financial mathematics Paper 1: TG pp. 424–427 LB p. 99, TG pp. 118–119 Memorandum: TG pp. 428–435 Paper 2: TG pp. 436–438 Memorandum: TG pp. 439–443 Siyavula Week 5 – Lesson 22 Everything Maths Exemplar test: Section E of tracker Topics in exemplar test Finance, growth and decay Counting and probability 10 Grade 12 Mathematics

Please note: The DBE occasionally makes changes to the assessment requirements • Classroom Mathematics offers Check your skills and Extend your skills. published in the CAPS. If any changes are made after this document is printed, you • Clever: Keeping Maths Simple gives comprehensive revision worksheets in the will need to adjust the assessment programme provided here and in the trackers Teacher’s Guide at the end of every chapter. accordingly. • Mind Action Series Mathematics offers Some challenges after each revision exercise. 2. Informal assessment • Platinum Mathematics provides Basic Target and Advanced Target worksheets at the back of the Teacher’s Guide. Extensive revision tests are also provided In addition to the prescribed formal assessment, you should include some informal at the end of each section. assessments to help you and the learners gain insight into how they are progressing. • Via Afrika gives Questions at the beginning (revision) and end (consolidation) Much informal assessment is integrated into teaching and learning – in class discussions, of each section. responses to questions, and as classwork is done and homework reviewed. It is also • In the Siyavula Everything Maths books, extra questions on the Intelligence a good idea, however, to set some written informal written assessment tasks that Practice Service may be found online on www.everythingmaths.co.za or on simulate more formal assessment activities, such as examination or test questions, as your cell phone (m.everythingmaths.co.za). they allow learners to develop important examination techniques such as keeping to time limits and first answering what they know best. The table above lists assessment The trackers do not specify when such informal assessments should be done as you material in the LTSMs which can be used for informal assessment. will use your professional judgement in this regard. Although marks do not have to be recorded for informal assessment, you might like to keep a record of these in order to In addition, each set of LTSMs provides revision exercises as well as remediation and monitor your learners’ progress. extension exercises, all of which may be used for informal assessment: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 11

D. TRACKERS FOR EACH SET OF APPROVED LTSMs 1. Classroom Mathematics This section maps out how you should use the Classroom Mathematics Learner’s Book • Did the purpose of the lesson succeed? For instance, did the learners reach and Teacher’s Guide in a way that enables you to cover the curriculum sequentially, a good understanding of the key concepts and skills for the day? Could they aligning with the CAPS, for well-paced and meaningful teaching. use the language expected of them? Could they write what was expected of them? The following components are provided in the columns of the tracker table: • Did the learners cope with the work set for the day? For instance, did they 1. Lesson number. finish the classwork? Was their classwork done adequately? Did you assign 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page the homework? numbers are given at the start of each CAPS topic. • Are your learners’ books up to date? 3. Page reference in the Learner’s Book (LB pp.). • Does what the learners have done in their books correlate with the tracked 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). comments in the tracker? Where an exercise has been recommended for more than one day, it has been divided into two parts. Briefly write down your reflection weekly, following the prompts in the tracker. 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What went well? 6. Links to related content in the Siyavula Everything Maths Learner’s Book • What did not go well? (examples, exercises and page numbers are referenced) and to the • What did the learners find difficult or easy to understand or do? Siyavula Everything Maths Teacher’s Guide. • What will you do to support or extend learners? 7. Date completed. • Did you complete all the work set for the week? • If not, how will you get back on track? Weekly reflection • What will you change for next time? Why? The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. The reflection should be based on the daily lessons you have taught each week. It will You can share this reflection with your HOD and peers, and together think of ways of provide you with a record for the next time you implement the same lesson and also improving on the daily work that the learners in your class are doing. When you reflect forms the basis for collegial conversations with your HOD and peers. you could think about things such as: • Was your preparation for the lesson adequate? For instance, did you have all the necessary resources? Had you thought through the content so that you understood it fully and so could teach it effectively? 12 Grade 12 Mathematics

Classroom Mathematics Week 1 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 1 FINANCE, GROWTH AND DECAY 83–87 4.1* 125–127 CAPS p. 42 Revise Grade 11 financial mathematics 2 Solve problems for future value annuities using the sum of a 88–92 4.2* 127–130 3-2 150–154 geometric series (pp. 109–115) 3 Derive the formula and solve problems involving future value 93–98 4.3* 131–133 3-3 155–157 annuities (pp. 115–117) 4 Solve problems for present value annuities (loan repayments) 98–104 4.4* 134–138 using the formula for a geometric series; Solve problems involving deferred payments; Determine the balance on a loan 5 Derive the formula and solve problems involving present value 104–109 4.5 138–139 3-4 157–161 annuities no. 1–3 (pp. 118–124) Note: If preferred, the present value annuity formula (Lesson 5) may be developed in Lesson 4 before doing Exercise 4.4. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 13

Classroom Mathematics Week 2 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 6 Solve problems involving present value annuities 109–111 4.5 139–144 3-5 162–164 no. 4–10* (pp. 125–131) 7 Use logarithms to calculate the value of n, the time period in 112–116 4.7–4.8* 145–149 3-1 146–150 simple formulae and in annuities formulae (pp. 106–109) 8 Calculate the final payment of a loan; Critically analyse 116–122 4.9–4.11* 150–155 Note investment and loan options such as pyramid schemes (pp. 131–133) 9 Revise finance, growth and decay (Check your skills ex.) 123–124 4.12 156–158 3-6 164–170 no. 1–5 (pp. 134–135) 10 Revise finance, growth and decay (cont.) (Check your skills ex.) 124 4.12 158–160 no. 6–9 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 14 Grade 12 Mathematics

Classroom Mathematics Week 3 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 11 Revise finance, growth and decay (cont.) (Extend your skills ex.) 125 4.13 160–163 12 COUNTING AND PROBABILITY CAPS p. 49 355–356 13.1 468–471 10-1 474–482 Revise Grade 11 probability (dependent/independent events, (pp. 402–413) mutually exclusive events, complementary events, etc.) 13 Revise contingency tables and whether events are independent 357–358 Example – 10-2–10-3 482–493 or not; 1# (pp. 413–424) Revise Venn diagrams and tree diagrams (use Siyavula Everything Maths) 14 Learn about and apply the fundamental counting principle to 359–361 13.2–13.3 471–472 10-4 494–495 number of arrangements no. 1–4 (pp. 425–428) 15 Apply the fundamental counting principle to number of 362 13.3 472 arrangements (cont.) no. 5–10 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 15

Classroom Mathematics Week 4 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 16 Learn about applying the fundamental counting principle to 363–365 13.4–13.5 472–473 10-5 495–497 permutations; (pp. 329–431) Work with factorial notation 17 Apply the fundamental counting principle to permutations 366–369 13.6 474 10-6 497–499 (cont.) (pp. 431–433) 18 Solve problems involving different letter arrangements 369–373 13.7–13.8 474 10-7 500–502 (pp. 433–436) 19 Apply the fundamental counting principle to solve probability 374–378 13.9 475–476 10-8 502–506 problems no. 1–3 (pp. 436–440) 20 Apply the fundamental counting principle to solve probability 379 13.9 476 problems (cont.) no. 4–8 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 16 Grade 12 Mathematics

Classroom Mathematics Week 5 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 21 Revise counting and probability 380–381 13.10 477–478 10-9 506–512 (use Check your skills) (pp. 440–443) 22 Formal assessment: Test 23 STATISTICS 317–323 12.1 438–441 9-1 430–439 Regression and Correlation CAPS p. 48 no. 1–4 (pp. 360–372) Revise measures of central tendency, measures of dispersion, symmetrical and skewed data and cumulative frequency 24 Revise Grade 11 work (cont.) 323 12.1 441–442 no. 5–8 25 Draw scatter plots of bivariate data and discuss correlation 325–328 12.2 443–446 Note: Refer to Lesson 21: If learners do not have time to complete Exercise 13.10 (Check your skills) (LB pp. 380–381, TG pp. 477–478), they may complete the exercise at home. They can also do Exercise 13.11 (Extend your skills) (LB p. 382, TG p. 478) for enrichment at home. Full solutions can then be photocopied. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 17

Classroom Mathematics Week 6 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 25 Calculate and analyse the correlation coefficient, r 329–334 12.3 446–448 9-4 453–461 (pp. 387–393) 26 Find the line of best fit intuitively and make predictions using 334–340 12.4 449–451 9-2 439–445 interpolation and extrapolation (pp. 372–379) 27 Calculate the least squares regression line using formulae and 340–346 12.5 451–453 9-3 445–453 then the calculator, draw a scatter plot and the regression line; no. 1–2 (pp. 380–386) Make predictions 28 Calculate the least squares regression line, draw a scatter plot 346–348 12.5 453–457 and the regression line and make predictions (cont.); no. 3–5 Review test done in previous week 29 Revise statistics: regression and correlation 349–352 12.6 458–460 9-5 461–472 (pp. 394–399) Note: Refer to Lesson 29: The revision exercise Check your skills: Exercise 12.6 (LB pp. 349–352, TG pp. 458–460) may be completed by learners at home. Extend your skills: Exercise 12.7 (LB pp. 353–354, TG pp. 461–464) for enrichment (optional) should be done by learners at home. Full solutions for learners can be photocopied from the Teacher’s Guide. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 18 Grade 12 Mathematics

Classroom Mathematics Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 30 31 32 33 34 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 19

Classroom Mathematics Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 40 41 42 43 44 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 20 Grade 12 Mathematics

Classroom Mathematics Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 21

2. Clever: Keeping Maths Simple This section maps out how you should use the Clever: Keeping Maths Simple Learner’s • Did the purpose of the lesson succeed? For instance, did the learners reach Book and Teacher’s Guide in a way that enables you to cover the curriculum sequentially, a good understanding of the key concepts and skills for the day? Could they aligning with the CAPS, for well-paced and meaningful teaching. use the language expected of them? Could they write what was expected of them? The following components are provided in the columns of the tracker table: • Did the learners cope with the work set for the day? For instance, did they 1. Lesson number. finish the classwork? Was their classwork done adequately? Did you assign 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page the homework? numbers are given at the start of each CAPS topic. • Are your learners’ books up to date? 3. Page reference in the Learner’s Book (LB pp.). • Does what the learners have done in their books correlate with the tracked 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). comments in the tracker? Where an exercise has been recommended for more than one day, it has been divided into two parts. Briefly write down your reflection weekly, following the prompts in the tracker. 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What went well? 6. Links to related content in the Siyavula Everything Maths Learner’s Book • What did not go well? (examples, exercises and page numbers are referenced) and to the • What did the learners find difficult or easy to understand or do? Siyavula Everything Maths Teacher’s Guide. • What will you do to support or extend learners? 7. Date completed. • Did you complete all the work set for the week? • If not, how will you get back on track? Weekly reflection • What will you change for next time? Why? The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. The reflection should be based on the daily lessons you have taught each week. It will You can share this reflection with your HOD and peers, and together think of ways of provide you with a record for the next time you implement the same lesson and also improving on the daily work that the learners in your class are doing. When you reflect forms the basis for collegial conversations with your HOD and peers. you could think about things such as: • Was your preparation for the lesson adequate? For instance, did you have all the necessary resources? Had you thought through the content so that you understood it fully and so could teach it effectively? 22 Grade 12 Mathematics

Clever: Keeping Maths Simple Week 1 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 1 FINANCE, GROWTH AND DECAY CAPS p. 42 81–85 4.1* 76–78 Revise Grade 11 financial mathematics 2 Solve problems for future value annuities using the sum of a 86–88 4.2* 78–79 3-2 150–154 geometric series (pp. 109–115) 3 Derive the formula and solve problems involving future value 89–92 4.3 79–80 3-3 155–157 annuities; no. 1–4 (pp. 115–117) Compare investments 4 Solve problems involving future value annuities (cont.) 92–93 4.3 80 no. 5–8 5 Derive the formula and solve problems involving present value 93–97 4.4 80–81 annuities (loans and loan repayments) no. 1–3 Note: Refer to Lesson 2: Teach learners the modified future value formula for investments which start immediately (Example 2 LB p. 86). Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 23

Clever: Keeping Maths Simple Week 2 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 6 Solve problems involving present value annuities; 98 4.4 81–82 3-4 157–161 Determine the outstanding balance on a loan (no. 4–9) (pp. 118–124) 7 Calculate repayments for deferred annuities 98–101 4.5 82–84 3-5 162–164 (pp. 125–131) 8 Use logarithms to calculate the value of n, the time period in 101–103 4.6* 85–86 3-1 146–150 simple formulae (pp. 106–109) 9 Use logarithms to calculate the value of n, the time period in 104–106 4.7 86–88 Note annuities formulae and in radioactive decay; (pp. 131–133) Read note on pyramid schemes 10 Revise finance, growth and decay 106– 107 Rev. ex. 88 3-6 164–170 no. 1–5 (pp. 134–135) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 24 Grade 12 Mathematics

Clever: Keeping Maths Simple Week 3 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 11 Revise finance, growth and decay (cont.) 107 Rev. ex. 89 no. 6–9 12 COUNTING AND PROBABILITY 348–359 13.1 307–312 10-1 474–482 CAPS p. 49 no. 1–5 (pp. 402–413) Revise Grade 11 probability (dependent/ independent events, mutually exclusive events, complementary events, Venn diagrams, tree diagrams and contingency tables) 13 Revise Grade 11 probability (cont.) 359–360 13.1 312–313 10-2–10-3 482–493 no. 6–12 (pp. 413–424) 14 Learn about and apply the fundamental counting principle to 360–362 13.2 313–314 10-4 494–495 number of arrangements (pp. 425–428) 15 Apply the fundamental counting principle to number of 362–366 13.3 314–315 arrangements (cont.) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 25

Clever: Keeping Maths Simple Week 4 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 16 Work with factorial notation; 366–371 13.4–13.5 315–317 10-5 495–497 Solve problems involving different letter arrangements (pp. 329–431) 500–502 10-7 (pp. 433–436) 17 Apply the fundamental counting principle to permutations and 371–373 13.6 317–318 10-6 497–499 combinations (pp. 431–433) 18 Apply the fundamental counting principle to solve probability 374–376 Rev. ex. 318–319 10-8 502–506 problems no. 1–5 (pp. 436–440) 19 Apply the fundamental counting principle to solve probability 377–378 Rev. ex. 319–321 problems (cont.) no. 6–13 20 Apply the fundamental counting principle to solve probability 378–379 Rev. ex. 321–323 problems (cont.) no. 14–23 Notes: 1. Refer to Lesson 17: Combinations may be done for enrichment purposes – they are not stipulated in the CAPS. 2. There is a good summary of Grade 12 concepts in the Learner’s Book (pp. 379–-380). Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 26 Grade 12 Mathematics

Clever: Keeping Maths Simple Week 5 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 21 Revise counting and probability (use Revision worksheet 1 and – – 324–327 10-9 506–512 Revision worksheet 2 in TG) (pp. 440–443) 22 Formal assessment: Test 23 STATISTICS 315–324 12.1 279–282 9-1 430–439 Regression and Correlation CAPS p. 48 no. 1–3 (pp. 360–372) Revise measures of central tendency, measures of dispersion, symmetrical and skewed data and cumulative frequency 24 Revise Grade 11 work (cont.) 324–325 12.1 282–284 no. 4–8 25 Draw scatter plots of bivariate data and discuss correlation; 325–329 12.2 284–285 9-2 439–445 Draw in the line of best fit intuitively (pp. 372–379) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 27

Clever: Keeping Maths Simple Week 6 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 26 Calculate and analyse the correlation coefficient, r; 329–336 12.3 285–287 9-4 453–461 Calculate the least squares regression line, draw a scatter plot (pp. 387–393) and the regression line; Make predictions using interpolation and extrapolation 27 Calculate the least squares regression line and the correlation 336–340 Rev. ex. 287–288 9-3 445–453 coefficient, draw a scatter plot and the regression line and make no. 1–3 (pp. 380–386) predictions (cont.) 28 Revise statistics: regression and correlation 340–342 Rev. ex. 288–290 no. 4–7 29 Revise statistics: regression and correlation (cont.); 342–347 Rev. ex. 290–292 9-5 461–472 Review test done in previous week no. 8–11 (pp. 394–399) 30 Revise statistics: regression and correlation (use Revision – – 293–302 worksheet 1 and Revision worksheet 2 in TG) Note: Refer to Lesson 30: Learners may complete these revision worksheets at home. Full solutions can then be photocopied (Revision worksheet 1 TG pp. 297–299; Revision worksheet 2: TG pp. 301–302). Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 28 Grade 12 Mathematics

Clever: Keeping Maths Simple Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 31 32 33 34 35 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 29

Clever: Keeping Maths Simple Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 36 37 38 39 40 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 30 Grade 12 Mathematics

Clever: Keeping Maths Simple Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 31

3. Maths Handbook and Study Guide This section maps out how you should use the Maths Handbook and Study Guide • Did the purpose of the lesson succeed? For instance, did the learners reach Mathematics Learner’s Book and Teacher’s Guide in a way that enables you to cover a good understanding of the key concepts and skills for the day? Could they the curriculum sequentially, aligning with the CAPS, for well-paced and meaningful use the language expected of them? Could they write what was expected teaching. of them? • Did the learners cope with the work set for the day? For instance, did they The following components are provided in the columns of the tracker table: finish the classwork? Was their classwork done adequately? Did you assign 1. Lesson number. the homework? 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page • Are your learners’ books up to date? numbers are given at the start of each CAPS topic. • Does what the learners have done in their books correlate with the tracked 3. Page reference in the Learner’s Book (LB pp.). comments in the tracker? 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). Where an exercise has been recommended for more than one day, it has been Briefly write down your reflection weekly, following the prompts in the tracker. divided into two parts. • What went well? 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What did not go well? 6. Links to related content in the Siyavula Everything Maths Learner’s Book • What did the learners find difficult or easy to understand or do? (examples, exercises and page numbers are referenced) and to the • What will you do to support or extend learners? Siyavula Everything Maths Teacher’s Guide. • Did you complete all the work set for the week? 7. Date completed. • If not, how will you get back on track? • What will you change for next time? Why? Weekly reflection The reflection should be based on the daily lessons you have taught each week. It will The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. provide you with a record for the next time you implement the same lesson and also You can share this reflection with your HOD and peers, and together think of ways of forms the basis for collegial conversations with your HOD and peers. improving on the daily work that the learners in your class are doing. When you reflect you could think about things such as: • Was your preparation for the lesson adequate? For instance, did you have all the necessary resources? Had you thought through the content so that you understood it fully and so could teach it effectively? 32 Grade 12 Mathematics

Maths Handbook and Study Guide Week 1 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 1 FINANCE, GROWTH AND DECAY 50–54 Notes 3-1 146–150 CAPS p. 42 (pp. 106–109) Revise Grade 11 financial mathematics; Use logarithms to determine n, the time period (use Siyavula Everything Maths) 2 Solve problems for future value annuities using the sum of a 55–62 1 23–24 3-2 150–154 geometric series; 85 no. 1 (pp. 109–115) Derive the formula and solve problems involving future value annuities 3 Solve problems involving future value annuities 85 1 23–25 3-3 155–157 no. 2–5# (pp. 115–117) 4 Solve problems involving future value annuities made at the 63–65 2 25–26 beginning of the time periods 85–86 5 Develop and solve problems involving present value annuities 66–72 3# 26 3-4 157–161 (loans and loan repayments); 86 (pp. 118–124) Determine the outstanding balance on a loan Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 33

Maths Handbook and Study Guide Week 2 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 6 Determine repayments involving deferred payments 73–74 4 26–27 86 7 Determine final payments with reduced values 75–80 5 27–28 8 Critically analyse investment and loan options such as pyramid 81–84 Mixed ex. 28–29 3-5; 162–164 schemes; 87 no. 1–5 Note Apply finance formula to growth and decay (pp. 125–133) 9 Critically analyse investment and loan options such as pyramid 87–88 Mixed ex. 29–32 schemes (cont.); no. 6–10 Apply finance formula to growth and decay (cont.) 10 Revise finance, growth and decay (use Siyavula Everything 3-6 164–166 Maths) no. 1–5 (p. 134) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 34 Grade 12 Mathematics

Maths Handbook and Study Guide Week 3 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 11 Revise finance, growth and decay (cont.) (use Siyavula 3-6 167–170 Everything Maths) no. 6–11 (p. 134–135) 12 COUNTING AND PROBABILITY 294–296 1 116–117 10-1 474–482 CAPS p. 49 308 no. 1–3# (pp. 402–413) Revise Grade 11 probability (dependent/independent events, mutually exclusive events, complementary events etc.) 13 Revise Venn diagrams and tree diagrams; 297–301 1 117–118 10-2–10-3 482–493 Revise contingency tables and whether events are independent 308–309 no. 4–6# (pp. 413–424) or not 14 Learn about and apply the fundamental counting principle to 302 2# 118 10-4 494–495 number of arrangements 309 (pp. 425–428) 15 Work with factorial notation; 303–306 3# 119 10-5–10-6 495–498 Apply the fundamental counting principle to different 310 no. 1–5 arrangements and probability (pp. 329–432) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 35

Maths Handbook and Study Guide Week 4 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 16 Learn about applying the fundamental counting principle to 307 4# 119 10-6 498–499 permutations 310 no. 6–12 (pp. 432–433) 17 Apply the fundamental counting principle to solve probability 311 Mixed ex. 119–120 problems 18 Apply the fundamental counting principle to solve problems 10-7 500–502 involving number of arrangements (use Siyavula Everything (pp. 433–436) Maths) 19 Apply the fundamental counting principle to solve probability 10-8 502–506 problems (pp. 436–440) (use Siyavula Everything Maths) 20 Apply the fundamental counting principle to solve probability 10-9 506–509 problems (cont.) (use Siyavula Everything Maths) no. 1–6 (pp. 440–442) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 36 Grade 12 Mathematics

Maths Handbook and Study Guide Week 5 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 21 Revise counting and probability (use Siyavula Everything Maths) 10-9 509–512 no. 7–14 (p. 443) 22 Formal assessment: Test 23 STATISTICS 275–282 1 110–111 9-1 430–439 Regression and Correlation CAPS p. 48 289 no. 1–2# (pp. 360–372) Revise measures of central tendency, measures of dispersion, symmetrical and skewed data and cumulative frequency 24 Revise Grade 11 work (cont.) 290 1 111–113 no. 3–6 25 Find the line of best fit intuitively and make predictions using 9-2 439–445 interpolation and extrapolation (use Siyavula Everything Maths) (pp. 372–379) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 37

Maths Handbook and Study Guide Week 6 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 26 Calculate the least squares regression line, draw a scatter plot 283–285 2 113–114 9-3 445–453 and the regression line; 291 (pp. 380–386) Make predictions 27 Calculate the least squares regression line using formulae and 286–288 Mixed ex.# 114–115 9-4 453–456 then the calculator, draw a scatter plot and the regression line 292 no. 1–3 and make predictions (cont.); (pp. 387–391) Calculate and analyse the correlation coefficient, r 28 Calculate and analyse the correlation coefficient, r (cont.) 9-4 456–461 (use Siyavula Everything Maths) no. 4–8 (pp. 392–393) 29 Revise statistics: regression and correlation 9-5 461–464 (use Siyavula Everything Maths); no. 1–5 Review test done in previous week (pp. 394–396) 30 Revise statistics: regression and correlation (cont.) 9-5 464–472 (use Siyavula Everything Maths) no. 6–11 (pp. 396–399) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 38 Grade 12 Mathematics

Maths Handbook and Study Guide Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 31 32 33 34 35 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 39

Maths Handbook and Study Guide Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 36 37 38 39 40 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 40 Grade 12 Mathematics

Maths Handbook and Study Guide Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 41

4. Mind Action Series Mathematics This section maps out how you should use the Mind Action Series Mathematics • Did the purpose of the lesson succeed? For instance, did the learners reach Learner’s Book and Teacher’s Guide in a way that enables you to cover the curriculum a good understanding of the key concepts and skills for the day? Could they sequentially, aligning with the CAPS, for well-paced and meaningful teaching. use the language expected of them? Could they write what was expected of them? The following components are provided in the columns of the tracker table: • Did the learners cope with the work set for the day? For instance, did they 1. Lesson number. finish the classwork? Was their classwork done adequately? Did you assign 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page the homework? numbers are given at the start of each CAPS topic. • Are your learners’ books up to date? 3. Page reference in the Learner’s Book (LB pp.). • Does what the learners have done in their books correlate with the tracked 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). comments in the tracker? Where an exercise has been recommended for more than one day, it has been divided into two parts. Briefly write down your reflection weekly, following the prompts in the tracker. 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What went well? 6. Links to related content in the Siyavula Everything Maths Learner’s Book • What did not go well? (examples, exercises and page numbers are referenced) and to the • What did the learners find difficult or easy to understand or do? Siyavula Everything Maths Teacher’s Guide. • What will you do to support or extend learners? 7. Date completed. • Did you complete all the work set for the week? • If not, how will you get back on track? Weekly reflection • What will you change for next time? Why? The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. The reflection should be based on the daily lessons you have taught each week. It will You can share this reflection with your HOD and peers, and together think of ways of provide you with a record for the next time you implement the same lesson and also improving on the daily work that the learners in your class are doing. When you reflect forms the basis for collegial conversations with your HOD and peers. you could think about things such as: • Was your preparation for the lesson adequate? For instance, did you have all the necessary resources? Had you thought through the content so that you understood it fully and so could teach it effectively? 42 Grade 12 Mathematics

Mind Action Series Mathematics Week 1 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 1 FINANCE, GROWTH AND DECAY 62 Rev. 63 CAPS p. 42 Revise Grade 11 financial mathematics 2 Use logarithms to calculate the value of n, the time period in 63–65 1* 63–65 3-1 146–150 simple formulae (pp. 106–109) 3 Use the sum of a geometric series or the future value annuity 65–75 2 57–63 3-2 150–154 formula to solve problems no. 1* 65 (pp. 109–115) 4 Use the sum of a geometric series or the future value annuity 75–76 2 65–67 formula to solve problems (cont.) no. 2–10* 5 Solve problems involving future value annuities; 76–80 3* 67–69 Use logarithms to calculate the value of n, the time period Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 43

Mind Action Series Mathematics Week 2 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 6 Solve problems involving loans or loan repayments using the 81–88 4 70 sum of a geometric series or the present value annuity formula no. 1–4 7 Solve problems involving present value annuities 89 4 70–73 3-4 157–161 no. 5–11 (pp. 118–124) 8 Solve problems involving deferred payments; 89–92 5* 73–76 Determine the final payment of an annuity 9 Critically analyse and compare investments and loans; 92–96 6–7 76–79 3-5 162–164 Determine the outstanding balance on a loan (pp. 125–131) 10 Solve problems involving sinking funds; 96–99 8 79–80 3-3 155–157 Read about pyramid schemes (use Siyavula Everything Maths) (pp. 115–117) Note (pp. 131–133) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 44 Grade 12 Mathematics

Mind Action Series Mathematics Week 3 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 11 Revise finance, growth and decay 100–102 Rev. ex. 80-84 3-6 164–170 (pp. 134–135) 12 COUNTING AND PROBABILITY 305–306 Rev. ex. 323 10-1 474–482 CAPS p. 49 no. 1–2# (pp. 402–413) Revise Grade 11 probability (dependent/independent events, mutually exclusive events, complementary events, etc.) 13 Revise Venn diagrams and tree diagrams; 306–307 Rev. ex. 323–325 10-2–10-3 482–493 Revise contingency tables (use Siyavula Everything Maths) no. 3–8 (pp. 413–424) 14 Learn about and apply the fundamental counting principle to 308–310 1 325–326 10-4 494–495 number of arrangements (pp. 425–428) 15 Work with factorial notation (use Siyavula Everything Maths); 310–313 2 326–327 10-5 495–497 Learn about applying the fundamental counting principle to (pp. 329–431) permutations Notes: 1. Refer to Lesson 11: The Revision Exercise (LB pp. 100–102, TG pp. 80–84) as well as Some Challenges (LB pp. 102–104, TG pp. 85–94) may be completed by learners at home. Full solutions can then be photocopied for them. 2. Refer to Lesson 12: A very good summary of Grade 10 and 11 definitions is provided (LB p. 305). 3. Refer to Lesson 12: An approach to teaching probability (TG pp. 321–322) is worthwhile reading. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 45

Mind Action Series Mathematics Week 4 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 16 Apply the fundamental counting principle arrangements of 313–316 3 327–329 10-6 497–499 objects in a row (pp. 431–433) 17 Apply the fundamental counting principle to solve problems 317–320 4 329–331 10-7 500–502 involving different letter arrangements (pp. 433–436) 18 Apply the fundamental counting principle to solve probability 321–324 5 331–332 10-8 502–506 problems no. 1–4 (pp. 436–440) 19 Apply the fundamental counting principle to solve probability 324 5 332–334 problems (cont.) no. 5–9 20 Revise counting and probability 325–326 Rev. ex. 335 10-9 506–512 no. 1–5 (pp. 440–443) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 46 Grade 12 Mathematics

Mind Action Series Mathematics Week 5 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 21 Revise counting and probability (cont.) 326–327 Rev. ex. 335–338 no. 6–7 Some challenges 22 Formal assessment: Test 23 STATISTICS 288–289 Rev. ex. 307 9-1 430–439 Regression and Correlation CAPS p. 48 no. 1–2 313–314 (pp. 360–372) Revise measures of central tendency, measures of dispersion, symmetrical and skewed data and cumulative frequency 24 Revise Grade 11 work (cont.) 289–291 Rev. ex. 314–316 no. 3–6 25 Draw scatter plots of bivariate data and an intuitive line of best 9-2 439–445 fit (use Siyavula Everything Maths) (pp. 372–379) Notes: 1. Refer to Lesson 21: There is an error in the solution to Revision exercise Question 6(d) (TG p. 336). The answer should be: 1 x 5 x 12 x 4 + 1 x 5 x 13 x 1 = 305. 2. Refer to Lesson 23: Revision notes and Worked Examples on these subtopics can be found in Siyavula Everything Maths (LB pp. 360–369). 3. Blank, labelled grids have been supplied for exercises (TG pp. 308–312). Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 47

Mind Action Series Mathematics Week 6 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 26 Calculate the least squares regression line, draw a scatter plot 292–296 1 317–318 9-3 445–453 and the regression line and make predictions (interpolation and no. 1–3 (pp. 380–386) extrapolation) 27 Calculate the least squares regression line, draw a scatter plot 296–300 1 319–320 and the regression line and make predictions cont. no. 4–7 28 Calculate and analyse the correlation coefficient, r 300–303 2 320 9-4 453–461 (pp. 387–393) 29 Revise statistics: regression and correlation; 304 Rev. ex.# 320 9-5 461–464 Review test done in previous week no. 1–5 (pp. 394–396) 30 Revise statistics: regression and correlation (cont.) (use Siyavula 9-5 464–472 Everything Maths) no. 6–11 (pp. 396–399) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 48 Grade 12 Mathematics

Mind Action Series Mathematics Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 31 32 33 34 35 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 49

Mind Action Series Mathematics Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 36 37 38 39 40 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 50 Grade 12 Mathematics

Mind Action Series Mathematics Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 51

5. Platinum Mathematics This section maps out how you should use the Platinum Mathematics Learner’s Book • Did the purpose of the lesson succeed? For instance, did the learners reach and Teacher’s Guide in a way that enables you to cover the curriculum sequentially, a good understanding of the key concepts and skills for the day? Could they aligning with the CAPS, for well-paced and meaningful teaching. use the language expected of them? Could they write what was expected of them? The following components are provided in the columns of the tracker table: • Did the learners cope with the work set for the day? For instance, did they 1. Lesson number. finish the classwork? Was their classwork done adequately? Did you assign 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page the homework? numbers are given at the start of each CAPS topic. • Are your learners’ books up to date? 3. Page reference in the Learner’s Book (LB pp.). • Does what the learners have done in their books correlate with the tracked 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). comments in the tracker? Where an exercise has been recommended for more than one day, it has been divided into two parts. Briefly write down your reflection weekly, following the prompts in the tracker. 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What went well? 6. Links to related content in the Siyavula Everything Maths Learner’s Book • What did not go well? (examples, exercises and page numbers are referenced) and to the • What did the learners find difficult or easy to understand or do? Siyavula Everything Maths Teacher’s Guide. • What will you do to support or extend learners? 7. Date completed. • Did you complete all the work set for the week? • If not, how will you get back on track? Weekly reflection • What will you change for next time? Why? The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. The reflection should be based on the daily lessons you have taught each week. It will You can share this reflection with your HOD and peers, and together think of ways of provide you with a record for the next time you implement the same lesson and also improving on the daily work that the learners in your class are doing. When you reflect forms the basis for collegial conversations with your HOD and peers. you could think about things such as: • Was your preparation for the lesson adequate? For instance, did you have all the necessary resources? Had you thought through the content so that you understood it fully and so could teach it effectively? 52 Grade 12 Mathematics

Platinum Mathematics Week 1 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 1 FINANCE, GROWTH AND DECAY 60–61 1 44–45 CAPS p. 42 Revise Grade 11 financial mathematics 2 Derive the future value annuities formula and solve problems 62–65 2 46 3-2 150–154 no. 1 (pp. 109–115) 3 Solve problems involving future value annuities 65–66 2 46 no. 2–6 4 Derive the present value annuities formula and solve problems 66–70 3 46 3-4 157–161 no. 1–2 (pp. 118–124) 5 Solve problems involve present value annuities 70 3 47 no. 3–7 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 53

Platinum Mathematics Week 2 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 6 Solve problems involving sinking funds and future value 71–75 4–5* 47–48 3-3 155–157 annuities that end early (pp. 115–117) 7 Calculate the outstanding balance on a loan; 75–78 6–7 49–50 Solve problems involving deferred payments 8 Use logarithms to calculate the value of n, the time period 79–81 8 51 3-1 146–150 (pp. 106–109) 162–164 3-5 (pp. 125–131) 9 Analyse investment and loan options such as pyramid schemes 82–87 9 52 10 Revise finance, growth and decay 88 Rev. test 52–53 3-6 164–170 no. 1–6 (pp. 134–135) Note: Refer to Lesson 8: Read note on pyramid schemes in Siyavula Everything Maths (pp. 131–133). Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 54 Grade 12 Mathematics

Platinum Mathematics Week 3 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 11 Revise finance, growth and decay (cont.) 89 Rev. test 53–54 no. 7–11 12 COUNTING AND PROBABILITY 256–260 1 225–227 10-1 474–482 CAPS p. 49 (pp. 402–413) Revise Grade 11 probability (dependent/independent events, mutually exclusive events, complementary events etc.) 13 Revise the use of Venn diagrams, tree diagrams and 261–266 2 227–230 10-2–10-3 482–493 contingency tables to solve problems (pp. 413–424) 14 Learn about and apply the fundamental counting principle to 267–269 3 230 10-4 494–495 number of arrangements; 273 no. 1–5 (pp. 425–428) 495–497 Learn about factorial notation (use Siyavula Everything Maths) 10-5 (pp. 329–431) 15 Apply the fundamental counting principle to number of 269–274 3 230 10-6 497–499 arrangements and to permutations no. 6–11 (pp. 431–433) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 55

Platinum Mathematics Week 4 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 16 Apply the fundamental counting principle to permutations 274 3 230 10-7 500–502 (cont.) no. 12–17 (pp. 433–436) 17 Apply the fundamental counting principle to solve probability 275–279 4 231 10-8 502–506 problems no. 1–2 (pp. 436–440) 18 Apply the fundamental counting principle to solve probability 279 4 231–232 problems (cont.) no. 3–7 19 Revise counting and probability 280–281 Rev. test 232 no. 1–5 20 Revise counting and probability (cont.) 281 Rev. test 232 no. 6–11 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 56 Grade 12 Mathematics

Platinum Mathematics Week 5 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 21 Revise counting and probability (cont.) 282 Rev. test 233 10-9 506–512 no. 12–16 (pp. 440–443) 22 Formal assessment: Test 23 STATISTICS 240–242 1# 215–217 9-1 430–437 Regression and Correlation CAPS p. 48 no. 1–4 Revise measures of central tendency, measures of dispersion, (pp. 360–371) symmetrical and skewed data and cumulative frequency 24 Revise Grade 11 work (cont.) (use Siyavula Everything Maths) 9-1 437–439 no. 5–10 (pp. 371–372) 25 Discuss scatter plots; 9-2 439–445 Find the line of best fit intuitively and make predictions using (pp. 372–379) interpolation and extrapolation (use Siyavula Everything Maths) Note: Refer to Lesson 21: If more material is required for revision, then select questions from Exercise 10-9 in Siyavula Everything Maths. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 57

Platinum Mathematics Week 6 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 26 Calculate the least squares regression line first by using a 9-3 445–453 formula then by using a calculator (use Siyavula Everything (pp. 380–386) Maths) 27 Calculate and analyse the correlation coefficient, r; 243–250 2 217–219 Calculate the least squares regression line, draw a scatter plot no. 1–2 and the regression line; Make predictions 28 Calculate the least squares regression line, draw a scatter plot 251–252 2 219–221 9-4 453–461 and the regression line; no. 3–5# (pp. 387–393) Make predictions (cont.) 29 Revise statistics: regression and correlation; 253–254 Rev. test 222–223 Review test done in previous week no. 1–4 30 Revise statistics: regression and correlation (cont.) 254–255 Rev. test 223–224 9-5 461–472 no. 5–8 (pp. 394–399) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 58 Grade 12 Mathematics

Platinum Mathematics Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 31 32 33 34 35 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 59

Platinum Mathematics Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 36 37 38 39 40 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 60 Grade 12 Mathematics

Platinum Mathematics Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 61

6. Via Afrika Mathematics This section maps out how you should use the Via Afrika Mathematics Learner’s Book • Did the purpose of the lesson succeed? For instance, did the learners reach and Teacher’s Guide in a way that enables you to cover the curriculum sequentially, a good understanding of the key concepts and skills for the day? Could they aligning with the CAPS, for well-paced and meaningful teaching. use the language expected of them? Could they write what was expected of them? The following components are provided in the columns of the tracker table: • Did the learners cope with the work set for the day? For instance, did they 1. Lesson number. finish the classwork? Was their classwork done adequately? Did you assign 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page the homework? numbers are given at the start of each CAPS topic. • Are your learners’ books up to date? 3. Page reference in the Learner’s Book (LB pp.). • Does what the learners have done in their books correlate with the tracked 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). comments in the tracker? Where an exercise has been recommended for more than one day, it has been divided into two parts. Briefly write down your reflection weekly, following the prompts in the tracker. 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What went well? 6. Links to related content in the Siyavula Everything Maths Learner’s Book • What did not go well? (examples, exercises and page numbers are referenced) and to the • What did the learners find difficult or easy to understand or do? Siyavula Everything Maths Teacher’s Guide. • What will you do to support or extend learners? 7. Date completed. • Did you complete all the work set for the week? • If not, how will you get back on track? Weekly reflection • What will you change for next time? Why? The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. The reflection should be based on the daily lessons you have taught each week. It will You can share this reflection with your HOD and peers, and together think of ways of provide you with a record for the next time you implement the same lesson and also improving on the daily work that the learners in your class are doing. When you reflect forms the basis for collegial conversations with your HOD and peers. you could think about things such as: • Was your preparation for the lesson adequate? For instance, did you have all the necessary resources? Had you thought through the content so that you understood it fully and so could teach it effectively? 62 Grade 12 Mathematics

Via Afrika Mathematics Week 1 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 1 FINANCE, GROWTH AND DECAY CAPS p. 42 76–77 Questions 102–104 Revise Grade 11 financial mathematics * 2 Derive the formula and solve problems involving future value 78–81 1 105–107 3-2 150–154 annuities no. 1 (pp. 109–115) 3 Solve problems involving future value annuities 81 1 107 no. 2–6 4 Derive the formula and solve problems involving present value 82–85 2 108–109 3-4 157–161 annuities (pp. 118–124) 5 Use logarithms to calculate the value of n, the time period in 86–87 3 110–111 3-1 146–150 simple formulae (pp. 106–109) Note: Read the Teacher’s Guide for good advice (TG p. 122) on this topic. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 63

Via Afrika Mathematics Week 2 *Select Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 6 Analyse investments and loans; Determine the outstanding 88–92 4* 112–116 3-5 162–164 balance on a loan 5 (pp. 125–131) 7 Solve problems involving sinking funds 92–93 6 116 3-3 155–157 (pp. 115–117) 8 Solve problems involving deferred payments 94–95 7 116–117 Note (pp. 131–133) 9 Determine the value of the final payment and use logarithms to 96–97 8 117 determine the time periods 10 Read about pyramid schemes; 100–101 Questions 120 3-6 164–170 Revise finance, growth and decay no. 1–6 (pp. 134–135) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 64 Grade 12 Mathematics

Via Afrika Mathematics Week 3 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 11 Revise finance, growth and decay (cont.) 101 Questions 120–121 no. 6–11 12 COUNTING AND PROBABILITY CAPS p. 49 280–281 Questions 345–347 10-1 474–482 Revise Grade 11 probability (dependent/independent events, (pp. 402–413) mutually exclusive events, complementary events etc.) 13 Revise solving probability problems using Venn diagrams 282–283 1 348–351 10-2–10-3 482–493 (pp. 413–424) 14 Revise solving probability problems using tree diagrams and 284–287 2–3 351–352 contingency tables 15 Learn about and apply the fundamental counting principle 288–289 4 345–355 10-4 494–495 different arrangements; (pp. 425–428) 495–497 Work with factorial notation (use Siyavula Everything Maths) 10-5 (pp. 329–431) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 65

Via Afrika Mathematics Week 4 #Supplement Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 16 Apply the fundamental counting principle to number of 289–291 5# 355 10-7 500–502 arrangements (cont.) (pp. 433–436) 17 Learn about applying the fundamental counting principle to 10-6 497–499 permutations (use Siyavula Everything Maths) (pp. 431–433) 18 Apply the fundamental counting principle to solve probability 292–293 6 356–357 10-8 502–506 problems no. 1–5 (pp. 436–440) 19 Apply the fundamental counting principle to solve probability 294 6 357–358 problems (cont.) no. 6–11 20 Apply the fundamental counting principle to solve probability 295 6 358–359 problems (cont.) no. 12–19 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 66 Grade 12 Mathematics

Via Afrika Mathematics Week 5 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 21 Revise counting and probability 296–297 Questions 359–361 10-9 506–512 (pp. 440–443) 22 Formal assessment: Test 23 STATISTICS 262–265 Questions 326–329 9-1 430–439 Regression and Correlation CAPS p. 48 (pp. 360–372) Revise measures of central tendency, measures of dispersion and cumulative frequency 24 Revise symmetrical and skewed data 266–269 1 330–332 25 Discuss scatter plots; 9-2 439–445 Find the line of best fit intuitively and make predictions using (pp. 372–379) interpolation and extrapolation (use Siyavula Everything Maths) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 67

Via Afrika Mathematics Week 6 Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 26 Calculate and analyse the correlation coefficient, r; 270–276 2 333–337 9-4 453–461 Calculate the least squares regression line, draw a scatter plot no. 1–2 (pp. 387–393) and the regression line; Make predictions 27 Calculate the least squares regression line, the correlation 276–277 2 337–340 9-3 445–453 coefficient, draw a scatter plot and the regression line and make no. 3–8 (pp. 380–386) predictions (cont.) 28 Revise statistics: regression and correlation 278–279 Questions 341–344 29 Revise statistics: regression and correlation (cont.) (use Siyavula 9-5 461–464 Everything Maths); no. 1–5) Review test done in previous week (pp. 394–396) 30 Revise statistics: regression and correlation (use Siyavula 9-5 464–472 Everything Maths) no. 6–11 (pp. 396–399) Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 68 Grade 12 Mathematics

Via Afrika Mathematics Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 31 32 33 34 35 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 69

Via Afrika Mathematics Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Siyavula Everything Class pp. ex. pp. Maths LB ex. TG pp. Date completed 36 37 38 39 40 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 70 Grade 12 Mathematics

Via Afrika Mathematics Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 71

7. Siyavula Everything Maths This section maps out how you should use the Siyavula Everything Maths Learner’s Book • Did the purpose of the lesson succeed? For instance, did the learners reach and Teacher’s Guide in a way that enables you to cover the curriculum sequentially, a good understanding of the key concepts and skills for the day? Could they aligning with the CAPS, for well-paced and meaningful teaching. use the language expected of them? Could they write what was expected of them? The following components are provided in the columns of the tracker table: • Did the learners cope with the work set for the day? For instance, did they 1. Lesson number. finish the classwork? Was their classwork done adequately? Did you assign 2. CAPS concepts and skills linked to Learner’s Book content. CAPS page the homework? numbers are given at the start of each CAPS topic. • Are your learners’ books up to date? 3. Page reference in the Learner’s Book (LB pp.). • Does what the learners have done in their books correlate with the tracked 4. Learner’s Book exercises that cover the CAPS content for the day (LB ex.). comments in the tracker? Where an exercise has been recommended for more than one day, it has been divided into two parts. Briefly write down your reflection weekly, following the prompts in the tracker. 5. Page reference in your Teacher’s Guide for the day’s activities (TG pp.). • What went well? 6. Date completed. • What did not go well? • What did the learners find difficult or easy to understand or do? Weekly reflection • What will you do to support or extend learners? The tracker gives you space to reflect on your Mathematics lessons on a weekly basis. • Did you complete all the work set for the week? You can share this reflection with your HOD and peers, and together think of ways of • If not, how will you get back on track? improving on the daily work that the learners in your class are doing. When you reflect • What will you change for next time? Why? you could think about things such as: The reflection should be based on the daily lessons you have taught each week. It will • Was your preparation for the lesson adequate? For instance, did you have all provide you with a record for the next time you implement the same lesson and also the necessary resources? Had you thought through the content so that you forms the basis for collegial conversations with your HOD and peers. understood it fully and so could teach it effectively? 72 Grade 12 Mathematics

Siyavula Everything Maths Week 1 Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 1 FINANCE, GROWTH AND DECAY 106–109 3-1 146–150 CAPS p. 42 Use logarithms to calculate the value of n, the period of an investment 2 Derive the formula and solve problems involving future value annuities 109–115 3-2 150–154 3 Solve problems involving sinking funds 115–117 3-3 155–157 4 Derive the formula and solve problems involving present value annuities 118–122 3-4 157–159 124 no. 1–4 5 Solve problems involving deferred payments; 122–124 3-4 159–161 Determine the balance on a loan no. 5–8 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 73

Siyavula Everything Maths Week 2 Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 6 Analyse investment and loan options; Read note on pyramid schemes 125–133 3-5 162–164 7 Revise finance, growth and decay 134 3-6 164–166 no. 1–5 8 Revise finance, growth and decay (cont.) 134–135 3-6 167–170 no. 6–11 9 Revise finance, growth and decay (cont.) – – – 10 Revise finance, growth and decay (cont.) – – – Note: There is a shortage of material for this topic. More material may be sourced from other sets of LTSMs or from past trial (preliminary) or final examination papers. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 74 Grade 12 Mathematics

Siyavula Everything Maths Week 3 Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 11 Revise finance, growth and decay (cont.) – – – 12 COUNTING AND PROBABILITY 402–413 10-1 474–482 CAPS p. 49 Revise Grade 11 probability (dependent/independent events, mutually exclusive events, complementary events, etc.) 13 Revise Venn diagrams and tree diagrams 413–421 10-2 482–489 14 Revise contingency tables and whether events are independent or not 421–424 10-3 489–493 15 Learn about and apply the fundamental counting principle to number of 425–428 10-4 494–495 arrangements Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 75

Siyavula Everything Maths Week 4 Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 16 Work with factorial notation 329–431 10-5 495–497 17 Apply the fundamental counting principle to counting problems and 431–433 10-6 497–499 permutations 18 Solve problems involving different letter arrangements 433–436 10-7 500–502 19 Apply the fundamental counting principle to solve probability problems 436–440 10-8 502–506 20 Revise counting and probability 440–442 10-9 506–509 no. 1–6 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 76 Grade 12 Mathematics

Siyavula Everything Maths Week 5 Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 21 Revise counting and probability (cont.) 443 10-9 509–512 no. 7–14 22 Formal assessment: Test 23 STATISTICS 360–370 9-1 430–434 Regression and Correlation CAPS p. 48 no. 1–2 Revise measures of central tendency, measures of dispersion, five number summary, symmetrical and skewed data and cumulative frequency 24 Revise Grade 11 work (cont.) 371–372 9-1 434–439 no. 3–10 25 Discuss scatter plots, find the line of best fit intuitively and make predictions 372–379 9-2 439–445 using inter-polation and extrapolation Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 77

Siyavula Everything Maths Week 6 Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 26 Calculate the least squares regression line using formulae and then the 380–386 9-3 445–453 calculator, draw a scatter plot and the regression line; Make predictions 27 Calculate and analyse the correlation coefficient, r 387–391 9-4 453–456 no. 1–3 28 Calculate and analyse the correlation coefficient, r (cont.) 392–393 9-4 456–461 no. 4–8 29 Revise statistics: regression and correlation; 394–396 9-5 461–464 Review test done in previous week no. 1–5 30 Revise statistics: regression and correlation 396–399 9-5 464–472 no. 6–11 Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 78 Grade 12 Mathematics

Siyavula Everything Maths Week 7 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 31 32 33 34 35 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 79

Siyavula Everything Maths Week 8 Catch up, consolidation and revision; Plan your week Lesson CAPS concepts and skills LB LB TG Class pp. ex. pp. Date completed 36 37 38 39 40 Note: Work in class on matric past paper questions (based on the CAPS) is advised during this week. Reflection Think about and make a note of: What went well? What did not go well? What did What will you change next time? Why? the learners find difficult or easy to understand or do? What will you do to support or extend learners? Did you complete all the work set for the week? If not, how will you get back on track? HOD: Date: 80 Grade 12 Mathematics

Siyavula Everything Maths Week 9–11 Trial examinations End-of-term reflection Think about and make a note of: 3. What ONE change should you make to your teaching practice to help you teach 1. Was the learners’ performance during the term what you had expected and hoped more effectively next term? for? Which learners need particular support with Mathematics in the next term? What strategy can you put in place for them to catch up with the class? Which learners would benefit from extension activities? What can you do to help them? 2. With which specific topics did the learners struggle the most? How can you adjust 4. Did you cover all the content as prescribed by the CAPS for the term? If not, what your teaching to improve their understanding of this section of the curriculum in are the implications for your work on these topics in the future? What plan will you the future? make to get back on track? HOD: Date: Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 81

E. ASSESSMENT RESOURCES 1. Grade 12 Mathematics Test Term 3 Time: 65 minutes Total: 55 marks INSTRUCTIONS TO LEARNERS: 82 Grade 12 Mathematics 1. There are five questions. Answer all questions. 2. Show all your calculations where necessary. Full marks will not be awarded where working out should be shown but is not. 3. Scientific non-programmable calculators may be used. 4. Answer questions to two decimal places where appropriate. 5. Write neatly and legibly. QUESTION 1 1.1 What is the nominal interest rate per annum, compounded semi-annually, of an annual effective interest rate of 8,25%? (3) 1.2 The value of a car depreciates at a reducing balance rate of 11,5% per annum. Determine how many years and months it will take for the car to halve in value. (4) 1.3 Mr Phosa plans to buy a house for two million rand. He has to pay a deposit of 15% and take a loan from the bank for the balance owing. Investor Bank offers him an interest rate of 9,5% per annum compounded monthly. 1.3.1 If he pays off the loan over 20 years, what are his monthly payments? (5) 1.3.2 What is the balance of the loan after 10 years? (4)  [16] QUESTION 2 Mrs Gabela has bought a new tractor for R800 000 for her farm. She has decided to replace this tractor in five years’ time, when its trade-in value will be R200 000. The replacement cost of the tractor is expected to increase by    8% per annum. 2.1 Show that Mrs Gabela will have to pay a cash amount of R975 462,46 when she replaces the tractor in five years’ time. (3) 2.2 One month after purchasing her present tractor, she starts to put money into a sinking fund to replace this tractor. For five years, she deposits the same amount, every month into an account which pays interest at a rate of 12% per annum compounded monthly. At the end of five years, she has exactly R975 462,46, the amount needed to purchase the new tractor, after she trades in her present tractor. Calculate the monthly deposit.  (5) 2.3 Suppose that 12 months after the purchase of the present tractor and every 12 months thereafter, Mrs Gabela withdraws R5 000 from her account, to pay for the maintenance of the present tractor. If she makes five such withdrawals, what will the new monthly deposit be? (4) [12]

QUESTION 3 Mr Panache wants to start organising next year’s matric dance. He asked 150 of the current Grade 11s to indicate their preferred venue. They had to choose either the school hall (S), a restaurant (R) or an hotel (H). The information collected is shown in the Venn Diagram below: S R 23 4 41 1 8 11 41 21 H    3.1 Are the events S and H mutually exclusive? Justify your answer. (2) 3.2 Calculate: 3.2.1 P(S ∪ R)' (2) 3.2.2 The probability of the Grade 11s preferring only TWO of the given venue choices. (2) 3.3 Show, with all working, whether the events preferring the school hall (S) and preferring a restaurant (R) are independent or not.  (4) [10] QUESTION 4 A soccer star is suffering from an injury. The probability that the player will be fit to play in the upcoming 1 3 1 match is 3 . When he plays, the probability that his team will win is 4 but otherwise it is only 2 . 4.1 Set up a tree diagram to illustrate all the possible outcomes. (3) 4.2 Hence (or otherwise) calculate the probability that his team will win the next game. (3) [6] QUESTION 5 5.1 In how many different ways can Johnny dress for a party if he has three jackets, four pairs of jeans, two pairs of shoes and five shirts? (2) 5.2 If there are 24 Grade 12s in your class and there is only first and second place for class representative and vice-class representative, in how many ways can this selection be made? (3) 5.3 The word I N D E F I N I T E is given. 5.3.1 If the letters are not repeated, calculate the total number of arrangements of these letters that can be made. (3) 5.3.2 Determine the probability that an arrangement will have the E’s together. (3) [11] Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 83

2. Grade 12 Mathematics Test Term 3: SOLUTIONS MARKS COGNITIVE Memorandum and Cognitive Levels of Questions LEVELS Note: The last column in the memorandum shows the cognitive level for each question 1.2 Let the value of the car be Rx in the test. The levels are: A = P(1 – i)n variables and formula 1 2 x = x(1 – 0,115) n variables and formula K Knowledge – straight recall of facts. 1 177 n R Routine procedures – well-known, simple applications and calculations. 2 = (200) 1 C Complex procedures – procedures involving complex calculations and/or n = log ( 2 ) 177 200 log form higher reasoning. or P Problem solving – solving problems for which higher order reasoning and 1 n = log0,885( 2 ) (decimal) processes are involved. n = 5.67 years More information about these levels can be found in the CAPS (p. 53). n = 5 years 8 months years & months (4) C A suggestion for test and exam marking 1.3 1.3.1 LOAN: 85% x 2 000 000 = 1 700 000 amount Underline errors committed by learners and apply Consistent Accuracy (CA) marking. OR This means the learner loses the mark for each mistake made and you mark the rest of the answer according to their mistake(s). However, if the learner shows a lack of 15% x 2 000 000 understanding of the concept, no marks are given. Also, if the learner has made the = 300 000 question easier, no marks are given from that part onwards. ∴ LOAN: 2 000 000 – 300 000 = 1 700 000 x(1 – (1 + i)–n) SOLUTIONS MARKS COGNITIVE P = i 0,095 –240 x(1 – (1 + 12 ) ) LEVELS time & interest rate 1 700 000 = 0,095 QUESTION 1     12 principal amount P i 1.1 1 + ieff = (1 + nom m ) m formula ∴ x = R15 846,23 answer (5) R i 1 + 8,25% = (1 + 2 )2 15 846,23(1 – (1 + 0,095 )–120) 1.3.2 B = 12 formula i 0,095 1,0825 = 1 + 2 working out time & other values 12    ∴ i = 0,08086…   = R1 224 615,85 answer rate = 8,09% rate (3) R OR 0,095 120 15 846,23(1 + 0,095 12 )120 – 1) B = 1 700 000(1 + 12 ) – 0,095 12   = R1 224 615,90 (4) C 84 Grade 12 Mathematics

SOLUTIONS MARKS COGNITIVE SOLUTIONS MARKS COGNITIVE LEVELS LEVELS QUESTION 2 QUESTION 3 2.1 A = P(1 + i) n 3.1 S and H are not mutually exclusive because 800 000(1 + 0,08) 5 correct formula & substitution n(S ∩ H) ≠ 0 (2) K 62 3.2 3.2.1 P(S u R)' = 150 = 0,41 answer R1 175 462,46 answer OR Cash needed to replace tractor: 150 – 88 62 P(S u R)' = 150 = 150 = 0,41 (2) R 1 175 462,46 – 200 000 8 + 4 + 11 R975462,46 subtracting 200 000 (3) R 3.2.2 P(only 2) = 150 3 values x((1 + i)n –1) 23 2.2 F= correct formula   = 150 i x((1 + 0,12 12 )60 – 1) 975 462,46 = 0,12 substitution & time period   = 0,15 answer (2) R 12 ∴ x = R11944,00 answer (5) R 3.3 36 P(S) = 150 P(R) = 150 57 2.3 Monthly rate must be converted to an effective rate: 36 57 0,12 P(S) x P(R) = 150 x 150 product 1 + ieff = (r + 12 )12    = 0,09 answer   ieff = 0,12682 5 And P(S ∩ R) = 150 rate = 12,68% (to 2 dec. places) answer Total value of money withdrawn:    = 0,03 answer 5 000((1 + 0,1268)5 – 1) P(S) x P(R) ≠ P(S ∩ R) = 0,1268 ∴ These events are not independent. conclusion (4) R = R32 196,17 answer New monthly deposit: x((1 + 0,12 12 )60 – 1) 975 462,46 + 32 196,17 = 0,12 adding the 12 2 values (4) P ∴ x = R12 338,22 answer Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 85

SOLUTIONS MARKS COGNITIVE ANALYSIS OF COGNITIVE LEVELS FOR TERM 3 TEST LEVELS Table 3 below shows the weighting of marks across the cognitive levels in the exemplar QUESTION 4 test provided above. As can be seen, this differs slightly from the suggested weightings 4.1 3 W in the CAPS. This is acceptable, provided the two lower cognitive levels add up to 4 approximately 55%, while the two higher levels add up to approximately 45%. In this 1 F one mark exemplar test, the two lower levels together account for 55% of the marks, and the two 3 for each 1 higher for 45%. W’ correct pair 4 of branches 1 Table 3: ANALYSIS OF COGNITIVE LEVELS OF THE TEST W 2 Cognitive levels Mark out of Percentage of Percentage of 2 55 marks in the marks at each level 3 F’ test prescribed by the 1 W’ CAPS (p. 53) 2 (3) P Knowledge 2 4% ≈ 20% 1 3 2 1 4.2 P(W) = 3 x 4 + 3 x 2 correct two terms Routine procedures 28 51% ≈ 35% 1 1   = 4 + 3 Complex procedures 11 20% ≈ 30% 3+4 7   = = 12 = 0,58 answer (3) R Problem solving 14 25% ≈ 15% 12 QUESTION 5 5.1 3 x 4 x 2 x 5 = 120 different ways product & answer (2) R 24! 5.2 P OR 24 x 23 OR (24 – 2)! 24 2 any of these formats = 522 ways answer (3) P 5.3.1 Number of arrangements: 10! 3!2!2! numerator & denominator = 151 200 answer (3) C 5.3.2 P(E’s together) 9! 3! x 2! 1 = 151200 = 5   numerator & denominator answer (3) P 86 Grade 12 Mathematics

3. Information Sheet: Mathematics –b± b2 – 4ac x= 2a A = P(1 + ni) A = P(1 – ni) A = P(1 – i) n A = P(1 + i) n Tn = a + (n – 1)d n Sn = 2 (2a + (n – 1)d) Tn = ar n – 1 a(r n – 1) a Sn = r–1 ;r≠1 S∞ = 1 – r ; –1 < r < 1 x[(1 + i)n – 1] x[1 – (1 + i)–n] F= i P= i f (x + h) – f (x) h 0 f '(x) = lim h 2 2 x1 + x2 y1 + y2 d = (x2 – x1) + (y2 – y1) M ( 2 ; 2 ) y2 – y1 y = mx + c y – y1 = m(x – x1) m = x2 – x1 m = tan θ (x – a)2 + (y – b)2 = r2 a b c a2 = b2 + c2 –2bc.cos A In △ABC: sin A = sin B = sin C 1 area △ABC = 2 ab.sin C sin(α + β) = sin α.cos β + cos α.sin β sin(α – β) = sin α.cos β – cos α.sin β cos(α + β) = cos α.cos β – sin α.sin β cos(α – β) = cos α.cos β + sin α.sin β cos2 α – sin2 α cos 2α = 1 – 2 sin2 α sin 2α = 2 sin α.cos α 2 cos2 α – 1 n Σf (x) (xi – x–)2 i=1 x– = n σ2 = n n(A) Teacher Toolkit: CAPS Planner and Tracker 2018 Term 3 P(A) = n(S) P(A or B) = P(A) + P(B) – P(A and B) 87

4. Grade 12 Mathematics Suggested Assessment Record Term 3 Grade 12 Mathematics Suggested Assessment Record Term 3 Exam Exam Test Paper Paper Exam Total Total Term 3 1 2 SBA Weighting SBA Weighting /10 /25 Term 3 % Rating (1–7) /50 /150 /150 /300 Total Date of assessment: NAME AND SURNAME 88 Grade 12 Mathematics

education Department: Education PROVINCE OF KWAZULU-NATAL MATHEMATICSMATHEMA 12 MATHEMATICSMATHE MATHEMATICSMATHT MATHEMATICSMATH MATHEMATICSMATHE MATHEMATICSMATH GRADE MATHEMATICSMATHT MATHEMATICSMATA MATHEMATICS MATHEMATICSMATH TEACHER TOOLKIT MATHEMATICSMATA CAPS Planner and Tracker MATHEMATICSMATHT Jik’iMfundo is a programme to improve learning outcomes, funded by the National Education Collaboration Trust, the KwaZulu-Natal Department of Education and others. MATHEMATICSMATH 2018 TERM 3 THE PROGRAMME TO IMPROVE LEARNING OUTCOMES MATHEMATICSMATHE The Stables Hollard Campus ENDORSED BY 22 Oxford Road Tel: +27 11 351 2430/2457 Parktown 2193 Email: admin@pilo.co.za ISBN: 978-1-928320-83-8 Grade 12 Maths Tracker 2018 Term 3 cover 92 KZN.indd 1 3/7/2018 3:27:15 PM