Study & Master Mathematical Literacy Teacher’s Guide Grade 12

[Pages:250]Study & Master

Mathematical Literacy

CAPS

Karen Morrison ? Karen Press

Teacher's Guide

Grade

12

Study & Master

Mathematical Literacy

Grade 12

Teacher's Guide

Karen Morrison ? Karen Press

cambridge university press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S?o Paulo, Delhi, Mexico City

Cambridge University Press The Water Club, Beach Road, Granger Bay, Cape Town 8005, South Africa

cup.co.za

? Cambridge University Press 2013

This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

First published 2013

ISBN 978-1-107-38128-5

Editor: Clarice Smuts Typesetters: Karlie Hadingham, Maryke Garifallou, Anne Evans Illustrators: Sue Beattie, Karlie Hadingham, Anne Evans, Maryke Garifallou Photographs: Mike van der Wolk pp. 213, 221 Cover image: aaifotostock ........................................................................................................................... Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables and other factual information given in this work are correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter. ...........................................................................................................................

notice to teachers

The photocopy masters in this publication may be photocopied or distributed [electronically] free of charge for classroom use within the school or institution which purchases the publication. Worksheets and copies of them remain in the copyright of Cambridge University Press and such copies may not be distributed or used in any way outside the purchasing institution. ........................................................................................................................... If you want to know more about this book or any other Cambridge University Press publication, phone us at +27 21 4127800, fax us at +27 21 419-8418 or send an e-mail to capetown@

Contents

Section 1 Introduction

5

Section 2 Planning

17

Section 3 Unit-by-unit

29

Section 4 Resources

193

APhotocopiable additional activities

195

(Measurement and Finance assignments

and investigations)

B Additional activities: solutions

233

C Multiplication tables

238

DTransparencies

241

Section 5 Documents247

Section 1 Introduction

Study & Master Mathematical Literacy Grade 12 is based on the Curriculum and Assessment Policy Statement (CAPS) issued by the Department of Basic Education in December 2011. The CAPS is an amended version of the National Curriculum Statement Grades R?12, and replaces the 2002 National Curriculum Statement Grades R?9 and the 2004 National Curriculum Statement Grades 10?12.

The general aims of the South African curriculum as stated

in the CAPS:

a. T he Curriculum and Assessment Policy Statement gives expression to what are regarded to be knowledge, skills and values worth learning. It will ensure that learners acquire and apply knowledge and skills in ways that are meaningful to their lives. In this regard, the curriculum promotes the idea of grounding knowledge in local contexts, while being sensitive to global imperatives.

b. The Curriculum and Assessment Policy Statement serves the purposes of: ? equipping learners, irrespective of their socio-economic background, gender, physical ability or intellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningful participation in society as citizens of a free country ? providing access to higher education ? facilitating the transition of learners from education institutions to the workplace ? providing employers with a sufficient profile of a learner's competences.

c. The Curriculum and Assessment Policy Statement is based on the following principles: ? social transformation: ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of our population ? active and critical learning: encouraging an active and critical approach to learning, rather than rote and uncritical learning of given truths ? high knowledge and high skills: the minimum standards of knowledge and skills to be achieved at each grade are specified and they set high, achievable standards in all subjects ? progression: the content and context of each grade show progression from simple to complex ? human rights, inclusivity, environmental and social justice: the principles and practices of social and environmental justice and human rights as defined in the Constitution of the Republic of South Africa are included.

d.The Curriculum and Assessment Policy Statement (General) is sensitive to issues of diversity such as poverty, inequality, race, gender, language, age, disability and other factors: ? valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country as important contributors to nurturing the values contained in the constitution

Section 1 ? Introduction

5

? credibility, quality and efficiency: providing an education that is comparable in quality, breadth and depth to those of other countries.

e.The Curriculum and Assessment Policy Statement aims to produce learners who are able to: ? identify and solve problems and make decisions using critical and creative thinking ? work effectively as individuals and with others as members of a team ? organise and manage themselves and their activities responsibly and effectively ? collect, analyse, organise and critically evaluate information ? communicate effectively using visual, symbolic and/or language skills in various modes ? use science and technology effectively and critically showing responsibility towards the environment and the health of others ? demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation.

f.Inclusivity should become a central part of the organisation, planning and teaching at each school. This can only happen if all teachers have a sound understanding of how to recognise and address barriers to learning, and how to plan for diversity.

Time allocation: Grades 10?12 The instructional time allocation in Grades 10?12 is set out in the table below.

Subject I. Home Language II. First Additional Language III. Mathematics and Mathematical Literacy IV. Life Orientation V. Three electives

Time allocation per week (hours) 4,5 4,5 4,5 2

12 (3 ? 4 h)

The CAPS states that `the allocated time per week may be utilised only for the minimum required NCS subjects as specified above, and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wish to offer additional subjects, additional time must be allocated for the offering of these subjects.'

What is Mathematical Literacy?

Mathematical literacy can be defined as `an individual's capacity to use mathematics as a fully functioning member of a society' (Ball and Stacey, University of Melbourne).

The CAPS document identifies the following five key elements of the subject Mathematical Literacy: ? the use of elementary mathematical content ? real-life contexts ? solving familiar and unfamiliar problems ? decision-making and communication ? the use of integrated content and/or skills in solving problems.

6

Section 1 ? Introduction

In other words, the subject Mathematical Literacy aims to produce learners who have: ? a sense of self-worth and who are able to control aspects of their life

related to mathematical understanding ? the skills and understanding to play a responsible role in our society ? the ability to calculate, estimate and use measuring instruments ? developed strategies and decision-making skills that allow them to be

innovative and flexible in their approach to solving problems ? the ability to communicate results and explanations and the skills to work

effectively and collaboratively with others ? the ability to draw sensible conclusions from information presented

graphically and apply skills in data-handling and interpretation.

What does it mean to be mathematically literate? Mathematical literacy is more than the ability to do basic arithmetic. It also includes: ? working confidently and competently with numbers, measures and

diagrams in a range of real and realistic contexts ? choosing and applying a range of techniques and skills, including the use

of technology (calculators and computers) ? understanding how numbers and measurements are collected, organised

and displayed in tables, graphs and other forms ? developing and using decision-making and problem-solving strategies that

suit both the problem and the context ? communicating results and solutions in appropriate ways.

The flow diagram below breaks down the steps that a mathematically numerate person will follow and details what is involved in each step.

A mathematically literate person is able to ...

Solve problems in real contexts

? daily life ? decisions ? school ? home

? community ? finance

? money

by deciding how to respond

? find information ?interpret

information ?act on given

information ?communicate

information

to information involving

mathematical ideas

? number ? shape and space ? patterns ? data ? probability ? measurement

represented in different ways

?numbers and symbols

? pictures ? shapes ? formulae ? tables ? graphs ? maps ? words/text

Mathematics and Mathematical Literacy are not the same Mathematics is an abstract subject that is often theoretical and that requires specific language, skills and methods to deal with subject-specific problems.

Mathematical Literacy takes mathematical knowledge and skills and applies them to everyday situations and problems. Mathematical Literacy is contextual and useful. When learners take processes and ideas from mathematics and apply them in contexts that are specific to their lives (such as choosing a cellphone contract), they are mathematically literate. The following table shows differences between Mathematics and Mathematical Literacy. It also shows how the content and context are interconnected when you are developing mathematical literacy.

Section 1 ? Introduction

7

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