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Republic of Zambia ZAMBIA BASIC EDUCATION COURSE BASIC EDUCATION MATHEMATICS SYLLABUS GRADE 8 – 9 Prepared by the Commercial Subjects Curriculum Committee Published by the Curriculum Development Centre P.O. Box 50092 Lusaka ZAMBIA BASIC EDUCATION COURSE BASIC EDUCATION MATHEMATICS SYLLABUS GRADE 8 – 9 A product of the December 1982 February 1983, March 1983 and November 1983 workshops held at the Curriculum Development Centre P.O. Box 50092 Lusaka Compiled by Hibajene M. Monga in collaboration with the Mathematics working Committee (c) All rights are reserved. No part of this syllabus may be reproduced, stored in a retrieval manner, transmitted in any means without the prior consent of the copyright owner. Phototypeset and printed by Printpak (Z) Ltd CONTENTS Page Preface .................................................................................................................. ii Acknowledgements............................................................................................................. iii Introduction........................................................................................................................ iv General Aims..................................................................................................................... v Objectives........................................................................................................................... vi Productive skills ............................................................................................................... vii Individual skills ............................................................................................................... viii Grade 8: Content .............................................................................................................. 19 Terminal objectives ......................................................................................................... 20 Grade 9: Content............................................................................................................... 22 Terminal objectives......................................................................................................... 23 PREFACE The syllabus which follows has been prepared against the background and needs of the Education Reform. In this respect, it is a unique contribution to the Zambian Curricula. Its ultimate goals, however, are the reactions and responses of pupils to it. Even more important will be the pupils’ achievement from it in terms of knowledge, skills and values to be acquired. These are so vital to the development and betterment of not only the pupil himself but to the community both immediate and distant. The content of this syllabus points towards this requirement and expectations. Thus the content of this syllabus reflects the structure of Mathematics, application and contribution to problem solving which do not only relate to the Mathematics and technological pursuits but also to the development of the nation. It is for this reason that the syllabus aims at providing pupils with tools and means to tackle some challenges and problems found in Mathematics and later on in life. Chairman EXAMINATIONS COUNCIL OF ZAMBIA ACKNOWLEDGEMENTS The Mathematics Department of the Curriculum Development Centre gratefully acknowledges the dedicated work put into the production of the syllabus by the following people: Mr. B.M. Ambekar Mathematics Departments, C.D.C. Lusaka Mr. M.M. Mbalo Shikatende Primary School, Shibuyunji. Mr. N.S.J. Hansingo Inspectorate, Lusaka, General Education Mr. S.T. Talilelo Inspectorate, Lusaka, General Education Dr. E.B. Nkwanga University of Zambia, Lusaka. Mr. F.S. M’hango Malcom Moffat T.T. College, Serenje. Ms. H.M. Monga Mathematics Department, C.D.C. Lusaka Mr. H.P. Mulenga NISTICOL, Chalimbana, Lusaka Dr. S. Mukoboto Evaluation Department, C.D.C. Lusaka Mr. A. Mukuyamba Kamwala Secondary School, Lusaka Mrs. R.K. Munkombwe Jacaranda Primary School, Lusaka Mr. O.B. Simukonda Nkrumah Teachers’ College, Kabwe Particular thanks go to UNICEF who sponsored the Workshops at which the above named people completed the draft of this syllabus. Lastly, thanks are also due to all Mathematics teachers, specialists and other individuals whose contributions were sincerely appreciated. INTRODUCTION This syllabus in Mathematics for Basic Education (Grades 8-9) has been produced against the background of the Educational Reforms. When constructing the aims and objectives of this syllabus special consideration was given to the present social needs, and the traditional applications of the subject in addition to the Mathematical requirements for (The emphasis in this syllabus is on essential knowledge and skills leading to self-reliance) In other words the basis Mathematics Curriculum should strengthen the link between schooling and preparation for working life. Taught or treated with this curriculum, pupils should not only acquire Mathematical knowledge and skills enabling them to be productive, but also knowledge and skills that enable them to be self-reliant, by the end of Grade 9. The working committee identified a number of productive skills in Mathematics as shown in the syllabus on page Roman numeral (X). The danger with such a list of skills is that it usually takes only the school context and not the social context into account. It is for this reason that a working definition of a skill is now given. Productive skills. A skill is practical knowledge in combination wit ability. It can also be defined in terms of the following features:i) It can be taught ii) It can be improved with practice and feedback iii) It can be applied with variety of different areas (which are usually) combined together to form a smooth sequence of actions directed towards a particular out-come. In this syllabus skills can be grouped into two main categories namely: i) General and Social skills ii) Individual skills General and Social skills i) ii) iii) iv) Social and life skills – creative and problem solving - successfully community Attitudes to work - Confidence - Commitment - Motivation - Commonsense Basic knowledge of working life - Understanding the role and purpose of work in relation to society. - Understanding the difference between work and employment. - Knowledge of occupation categories. - Understanding basic economic processes at the individual occupation and national level. - Knowledge of basic technological and industrial processes. - Knowledge of self-employment such as cooperatives. Community areas. AIMS OF THE BASIC EDUCATION (GRADES 8 -9) MATHEMATICS CURRICULUM 1. To equip the child to live effectively in this modern age of Science and Technology and enable him/her to contribute to the social and economic development of Zambia. 2. To simulate and encourage creativity and problem solving. 3. To develop the Mathematical abilities of a child to his/her full potential and assist him/her to study Mathematics as a discipline and to use it as a tool in various subject areas. 4. To assist the child to understand mathematical concepts in order that he/she may better comprehend his/her environment. 5. To develop in the child an appreciation of Mathematics in the traditional environment. OBJECTIVES OF BASIC EDUCATION (GRADES 8 -9) MATHEMATICS CURRICULUM 1. To develop interest in mathematics and encourage a spirit of enquiry 2. To build up understanding and appreciation of basic mathematical concepts and computational skills in order to apply them in everyday life. 3. To develop clear mathematical thinking and expression in the child. 4. To develop ability to recognise problems and to solve them with related mathematical knowledge and skills. 5. To develop and foster order speed and accuracy. 6. To provide the child necessary mathematical knowledge and skills in order for him/her to be productive and self-reliant. 7. To develop in the child a positive attitude towards production, self-reliance and entrepreneurship. 8. To provide necessary mathematical pre-requisites for further education. SHORT TERM SKILLS The pupils should be able to:1. Classify objects and numbers according to a given condition. 2. Demonstrate an understanding of number concept and numeration 3. Perform the four basic operations on numbers and measures. 4. Demonstrate skills in measurement in appropriate units 5. Estimate and approximate numbers and measures. 6. Translate verbal data into symbols and vice-versa. 7. Identify plain and solid shapes and acquire an understanding of their basic properties and spatial relationships. 8. Draw and construct geometrical shapes and solids. 9. Collect, classify, tabulate, represent and interpret data. 10. Solve problems involving fractions, ratios and proportions, average and percentages as applied to numbers and measures. 11. Solve problems involving household, social and commercial arithmetic. 12. Solve problems involving measurements (length, area, volume, capacity, mass, money time and speed, time and distance). 13. Identify different types of symmetry and draw symmetrical figures. 14. Read and draw compass bearing and use them in scale drawing and map reading. 15. Use appropriate mathematical language 16. Construct and use graphs. 17. Perform algebraic operations LONG TERM SKILLS 1. Numeracy: (Basic requirements for employment – This forms a basis for the Mathematics curriculum). e.g. – An ability to make use of Mathematical knowledge and skills with ease and confidence in everyday life - An ability to understand and appreciate information which is presented in mathematics terms such as graphs, charts, tables and percentages. These skills are not restricted to a computation skills alone, but to wider aspects of numeracy. A few are listed below: a) b) c) d) e) Read, write, add, subtract, divide and multiply numbers. Read and recognise units for length, area volume and masses Handle and interpret mathematical data. Use simple Algebra identify basic geometric shapes II Communication e.g. - III Practical Work e.g. - Speaking Reading Writing Listening Use of written information sources. Visual discrimination between objects according to shape, colour. Handle and use tools and instruments. Classify objects to given properties Plan activities in sequence The combination of various individual skills with social skills leads to productive work. Skills cannot therefore be applied nor taught in isolation as they are inter-related and inter-dependent. While it may be easy to test for a specific mathematical (individual) skill in a school situation the practical situation in working life would require one to test a combination of motivation, attitudes, knowledge and skills. GRADE 8 CONTENT 1. SETS a) b) c) d) e) Universal set Complement of a set including symbol Equivalent sets including symbol. Single and combined operation on sets. Include use of Venn diagrams to illustrate a, b, and c. 2. Number and Numeration a) A brief history of the Hindu Arabic number system. b) Sets of numbers (odd, even, whole, prime, natural, integers). c) Number patterns. d) Place value and expanded notation e) The ideas of ordering. f) The four operations as applied to numbers and measures. g) Use of brackets. h) The commutative, associative and distributive laws with respect to the four operations. 3. Fractions, Ratios and Percentages. a) b) c) d) 4. Order of operations of addition, subtraction, multiplication and division using fractions. Operations with fractions, decimals, percentages and ratios Relations between fractions, decimals and percentages. Verbal problems. Arithmetic problems a) b) Problems on mass, measures, money and time. Average as applied to numbers and measures. 5. Social and Commercial Arithmetic a) Household arithmetic. i) Shopping bills and simple accounts. ii) Electricity and water bills. iii) Budgeting. b) Social Arithmetic i) Banks and post office services ii) Insurance iii) Pensions schemes. c) Commercial Arithmetic. i) Simple interest. ii) Ready reckoner. 6. Approximations. a) Decimal places. 7. The basic processes of algebra a) Use of letter to represent numbers. b) Index notation. c) Directed numbers. d) e) f) g) Use of brackets when combining the four algebraic operations. Application of the four operations to algebraic expressions. Use of the Laws of commutative, associative and distributive on algebraic expressions. Substitution and evaluation in an algebraic expression. 8. Coordinates. a) The origin, the X – and Y – axes, the XOY plane b) Position fixing, sets of points. 9. Equations and inequations. a) Sequence of ordered pairs resulting in graphs of linear equations. b) Solution of simple linear equations and inequations in one variable. c) Solutions sets of simple linear inequations. Measurement and construction a) Use of Mathematical instruments. b) Geometry arising from measurements and scale drawing. c) Properties of angles at a point and angles made with parallel lines. d) Perpendicular bisector of a straight line. e) Angle bisector. f) Parallel and perpendicular lines. g) Angles of 30°, 60°, and 90°. h) Perpendicular to a given straight line from a given point. Shapes and symmetry a) Recognition and drawing of two dimensional shapes. b) Recognition and drawing of three dimensional shapes. c) Nets of cube and cuboid. Angle properties of triangle. Statistics a) Definition, characteristics and importance of statistics. b) Collection, classification and tabulation of data. c) Pictographs. d) Bar-charts. e) Pie-charts. f) Line graph GRADE 8 TERMINAL OBJECTIVES 10. 11. 12. 13. By the end of Grade 8, the child should be able to:1. Give a brief history of the Hundu – Arabic number system 2. Use appropriate set language and notation including the following symbols < (Equivalent) and ‘A’ Complement. 3. Recognise number patterns. 4. Recognise and use sets of numbers. > 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. Use the Laws of commutative and associative laws and ideas of closure on the binary operations of addition, multiplication, subtraction and division. Use the distributive property of multiplication over addition and subtraction. Order numbers. Show the relationships between fractions, decimals, percentages and ratios. Carry out operations with fractions, decimals, percentages and ratios Use the correct order operations with fractions or mixed numbers Solve verbal problems involving averages, fractions, percentages and ratios. Solve verbal problems involving averages. Keep simple household and business accounts. Make simple house budgets. Solve simple and practical problems in electricity and water bills. Appreciate the value of using savings and current accounts. Use deposit and withdraw slips Solve simple problems on insurance and pension schemes. Calculate simple interest (using formula) Read and make ready reckoners. Express a given number correctly to the required number of decimal places. Use letters to represent numbers. Use Index notation. Apply the four operations to algebraic expressions. Use brackets when combining the four algebraic operations. Use the commutative, associative and distributive laws to simplify working on algebraic expressions. Substitute in, and evaluate algebraic expressions. Plot and read ordered pairs on a cartesion diagram. Plot the graph of a simple linear equations and inequations. Read the graph in order to obtain the solution of simple linear equation. Find solution sets simple linear inequations. Use mathematical instrument to construct the following:a) Perpendicular to a given straight line from a given point b) Angle bisector. c) Angles of 30°, 45°, and 90°. d) Perpendicular bisector of a straight line. Identify properties of angles at a point and angles made with parallel lines. Recognise and draw figures of two and three dimensional shapes. Draw and make notes of cubes and cuboids. Use angle properties of a triangle. Illustrate given date in the form of picture graphs, bar-charts, pie-charts and line graphs. Intepret pictographs, bar-charts, pie-charts, and line graphs. Solve simple and practical problems involving objectives 1 to 38 GRADE 9 1. 2. 3. 4. 5. 6. 7. CONTENT SETS a) Use of Venn diagrams to illustrate equal sets, subsets, intersection of sets, union of sets, complement of a set, equivalent sets, universal sets, membership of a set, empty set. b) relations and mappings. Number and Numeration. a) Numeration system to any base less than ten. b) Denary octal and binary scales. c) Additional and subtraction in base two and eight. d) Multiplication and division in base two and five. e) Conversion from one base to another. Fractions, ratio and proportion. a) Direct proportion: b) Inverse proportion: c) Proportional parts. Arithmetic problems a) Problems involving pound and pence; dollars and cents. b) Time, distance and speed. c) Travel graphs. d) Length, area and volume. Social and Commercial Arithmetic. a) Social Arithmetic i) Wages and salaries ii) Taxes iii) Mathematics in Transport. b) Commercial Arithmetic i) Profit and loss. ii) Commissions and discount. Approximations and Estimations. a) Significant figures. b) Use of standard form or index notation c) Significance of the digit ‘O’ when approximating. d) Estimation. The basic processes of algebra a) Simplification of algebraic expressions. b) 4.C.F. and L.C.M. of algebraic expressions. c) Construction of formulae d) Interpretation, evaluation and easy manipulation of formulae. e) Simple factors. f) Simple fractions. 8. Equations and inequations. a) b) c) 9. Graphical representation of a linear equation in one or two variables. Solution set of simple linear inequalities. Solution of a system of simultaneous linear equations. Shapes and Symmetry a) c) d) e) f) g) h) Recognition and drawing of two dimensional shapes. Properties of two dimensional figures (squares, rectangles, parallelograms, rhombus, kite isosceles and equilateral triangles.) Line symmetry in two dimensions. Rotational symmetry in two dimensions. Symmetrical figures. Symmetrics of regular polygons. Nets of cylinder and pyramid. 10. PYTHAGORAS THEOREM [no formal proof – use perfect squares]. 11. Mensuration. a) Perimeter and areas of square, rectangles, triangles and circles and their composite figures. b) surface area and volume of cuboid and cylinder. 12. Similar Triangles. 13. Statistics a) Simple frequency tables b) Mean, mode and modian from ungrouped data (simple examples only). c) Mean from simple frequency table. GRADE 9 TERMINAL OBJECTIVES By the end of Grade 8, the child should be able to:1. 2. 3. 4. 5. 6. 7. 8. Draw and interpret Venn diagrams involving operations on sets. Solve problems on relations and mapping using Venn diagrams. Count in any base less than 10. Convert numbers in base ten to bases two, eight and five, and vice versa. Add and subtract in base eight, five and two. Multiply and divide in bases two and five. Use the unitary and ratio methods of calculation in solving problems in direct proportion. Use the product and ratio methods of calculation in solving problems in inverse proportion. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. Convert Zambian currency into pounds and pence, dollars and cents and any other required currency. Solve problems on speed, time and distance. Draw, interpret, and use travel graphs. Understand and solve problems involving wages, salaries and taxes. Use Mathematics in transport problems. Find profit and loss as percentage and as amounts of money. Find the cost of articles when percentages discount and commission on selling and buying transactions are given. Round off numbers. Use the standards from A X 10 N where N is a positive or negative interger and where 1 « A » 10. Find H.C.F. and L.C.M. of algebraic expressions (including fractional). Simplify algebraic expressions. Factorise expressions in the form ax = bx; + bx + kay + kby. Construct and interpret formulae. Change the subject of formula. Find the value of the required variable in a given formula. Solve linear equations in one or two variables using graphs. Use graphs to illustrate the solution sets of simple linear inequalities. Find solutions of a system of simultaneous linear equations. Construct: 1. an angle equal to a given angle 2. triangle from given data Use campass bearing and direction Use scale drawings to solve problems involving bearings. Solve problems involving angles of elevation and depression. Identify and draw two and three dimensional figures. Recognise the symmetrical properties of two dimensional figures. Find the number of axes of symmetry in given figures. Find the centre of rotation of figures. Solve problems involving line and rotational symmetry. Draw and make nets of cylinders and pyramids. State and use Pythagoras theorem. Find areas of simple polygons (rectangles, squares, circles, triangles). Calculate perimeter and circumference of simple polygons. Calculate surface area of cuboids and cylinders. Calculate volumes of cubes, cuboids and cylinders Identify and draw similar triangles. Construct simple frequency tables from given data. Construct simple frequency tables using suitable class intervals. Calculate and use the mean, mode and median from ungrouped data. Calculate and use mean from simple frequency tables. Solve simple and practical problems involving objectives 1 to 46......