1. MATHEMATICS CURRICULUM ASSESSMENT POLICY STATEMENT
ORIENTATION WORKSHOP FOR TEACHERS
GR EDWARDS
22 OCTOBER 2011

2. Attendance register Claim forms S & T Claim Form Z43
ADMINISTRATION
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Claim forms
S & T Claim Form
Z43

3. GENERIC TRAINING

4. INTRODUCTION
The Curriculum and Assessment Policy Statement (CAPS) is a revision of the National Curriculum Statement (NCS).
In developing the CAPS, a key aim has been to have just one document providing guidelines for planning, content and assessment for each subject.
The CAPS also continue to support the key principles that underline the NCS, including:
social transformation;
high knowledge and high skills;
integration and applied competence;
progression;
articulation and portability;
human rights, inclusivity, environmental and social justice;
valuing of indigenous knowledge systems (IKS) and credibility,
quality and efficiency.

5. WHAT IS MATHEMATICS?
Mathematics is the study of quantity, structure, space and change.
Mathematicians seek out patterns, formulate new conjectures , and establish axiomatic systems by rigorous deduction from appropriately chosen axioms and definitions.
Axiomatic is one approach to establishing mathematical truth.
Mathematics is distinctly human activity practiced by all cultures.
Mathematical problem solving enables us to understand the world around us, and most of all, to teach us to think creatively.

6. PRINCIPLES APPLY ACROSS ALL GRADES:
No calculators with programmable functions, graphical or symbolic facilities should be allowed. Calculators should only be used to perform standard numeric computations and to verify calculations by hand.
Mathematical modelling is an important focal point of the curriculum. Real life problems should be incorporated into all sections whenever possible. Examples used should be realistic and not contrived.
Investigations provide the opportunity to develop in learners the ability to be methodical, to generalize, make conjectures and try to justify or prove them. Learners need to reflect on the process and not be concerned only with getting the answer(s).
Appropriate approximation and rounding skills should be taught the impression is not gained that all answers which are either irrational numbers or recurring decimals should routinely be given correct to two decimal places.
Teaching should not be limited to “how” but should also feature the “when” and “why” of problem types: Finding the mean and standard deviation of a set of data has little relevance unless learners have a good grasp of why and when such calculations might be useful.

7. PRINCIPLES APPLY ACROSS ALL GRADES:
Mixed ability teaching requires teachers to challenge the most able learners and at the same time provide remedial support for those who are not competent yet. Teachers need to design questions to rectify misconceptions that are exposed by tests and examinations.
Problem solving and cognitive development should be central to all mathematics teaching. Learning procedures and proofs without a good understanding of why they are important will leave learners ill equipped to use their knowledge in later life.

8. GENERIC TRAINING Policy documents Critical outcomes Time allocation
Focus of Content Areas
Weighting of Content Areas
Allocation of Teaching Time
Programme of Assessment

9. Policy Documents
National Curriculum and Assessment Policy Statement (CAPS) for Mathematics.
National Policy pertaining to the Programme and Promotion requirements of the National Curriculum Statements Grades R – 12(NPR).
National Protocol for Assessment Grades R – 12(NPA).

10. Critical Outcomes
The National Curriculum Statement Grades R - 12 aims to produce learners that are able to:
 identify and solve problems and make decisions using critical and creative thinking;
 work effectively as individuals and with others as members of a team;
 organise and manage themselves and their activities responsibly and effectively;

11.  collect, analyse, organise and critically evaluate information;
 communicate effectively using visual, symbolic and/or language skills in various modes;
 use science and technology effectively and critically showing responsibility towards the environment and the health of others; and
 demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.

12. Time Allocation 4½ hours per week. Six(6) periods of 45 minutes each.
Make sure you get the time on your roster.

13. The Main Topics in the FET Mathematics Curriculum
Focus of Content Areas
The Main Topics in the FET Mathematics Curriculum
1. Functions
2. Number Patterns, Sequences, Series
3. Finance, growth and decay
4. Algebra
5. Differential Calculus

14. The Main Topics in the FET Mathematics Curriculum
6. Probability
7. Euclidean Geometry and Measurement
8. Analytical Geometry
9. Trigonometry
10. Statistics

15. The Main Topics in the FET Mathematics Curriculum
OUT :
Linear Programming
Transformations
IN :
Probability
Euclidean Geometry

16. Weighting of Content Areas
CAPS p. 12

17. Content clarification with teaching guidelines
Allocation of Teaching Time
Sequencing and Pacing of Topics
Grade 10
Grade 11
Grade 12

18. Daily Lesson Plan
Example
Voorbeeld

19. Programme of Assessment

20. WHAT IS ASSESSMENT Assessment is a planned process of identifying
(selecting learner response items)
gathering
(learner responses)
interpreting
(marking learner responses)
information about the knowledge and skills demonstrated by learners.

21. ASSESSMENT
INFORMAL
no need to be recorded by teacher, could be marked by learner or peer, usually used to develop skills, demonstrate knowledge and skills and for learners to practice, not used for promotion purposes(solely developmental purpose)
FORMAL
marked and recorded by teacher, 7 tasks in Programme of Assessment, used for promotion purposes (mainly promotion purpose)

22. Why? What? Who? How? When? Where?
ASSESSMENT
Why?
What?
Who?
How?
When?
Where?

23. WHY? PURPOSE Developmental: to assist learner to learn
(i.e. apply knowledge, etc)
Promotion:
to make a summative judgement of the learner’s ability
(e.g. use the marks for any of the tasks in the programme of assessment)

24. WHO Teacher (formal assessment task e.g. project, controlled test)
Learner (informal assessment task e.g. homework, classwork)
Peer (informal assessment task e.g. homework)
SMT (e.g. controlled/standardised test)
External (e.g. controlled test set by district, etc)

25. WHAT What content, skills, values
E.g. ability to collect data, make observations, one-step problem-solving, multi-step problem solving, interpreting and drawing graphs, recalling laws and definitions, converting units, etc
Use taxonomy

26. HOW
FORMAL TASK:
project, investigation, assignment, controlled test, June examination, Final examination
INFORMAL TASK:
homework, classwork, class test

27. When Last 15 minutes of a period (e.g. classwork)
First 5 minutes of a lesson (e.g. oral Q & A)
End of term, week, year (e.g. control test, june exam, class test, final exam, project, etc)
End of unit of work, concept, section (e.g. class test, homework)
Weekly (e.g. assignment)
Daily (homework)

28. Where
Classroom
Home

29. GRADE 10: FORMAL ASSESSMENT
Grades
Formal School-based assessments
End-of –Year examinations
R-3
100%
n/a
4-6
75%
25%
7-9
40%
60%
10 & 11
25% including a midyear examination 12
25% including midyear and trial examinations
External examination: 75%

30. FORMAL ASSESSMENT: GRADE 10
PROGRAMME OF ASSESSMENT FOR GRADES 10
ASSESSMENT TASKS
(25%)
END - OF
YEAR
ASSESSMENT
(75%)
TERM 1
TERM 2
TERM 3
TERM 4
Type %
Final Examination (
2 x 100
marks giving a
total of 200 marks for
papers 1 and 2)
Test 10
Assignment/Test
Project /
investigation 2
Mid
Year
Examination 30
Total: 30
marks
Total: 40 marks
Total: 20
Total: marks
Total = 300 marks
FINAL MARK = 25% (ASSESSMENT TASKS) +75% (FINAL EXAM)=100%
Table 3:
Assessment plan and weighting of tasks in the programme of
assessment for G
rades 10
Test %

31. Cognitive levels(p.55) Knowledge 20% Routine Procedures 35%
Complex Procedures
30%
Problem Solving
15%

32. Knowledge (20%) Straight recall.
Identification of correct formula on the information sheet(no changing of the subject).
Use of mathematical facts.
Appropriate use of mathematical vocabulary.

33. Routine Procedures (35%)
Estimation and appropriate rounding of numbers.
Proofs of prescribed theorems and derivation of formulae.
Identification and direct use of correct formula on the information sheet(no changing of the subjects).
Perform well known procedures.
Simple applications and calculations which might involve few steps.
Derivation from given information may be involved.
Identification and use (after changing the subject) of correct formula.
Generally similar to those encountered in class.

34. Complex Procedures (30%)
Problems involve complex calculations and/or higher order reasoning.
There is often not an obvious route to the solution.
Problems need not be based on a real world context.
Could involve making significant connections between different representations.
Require conceptual understanding.

35. Problem Solving (15%)
Non-routine problems (which are not necessarily difficult).
Higher order reasoning and processes are involved.
Might require the ability to break the problem down into its constituent parts.

36. Number of Assessment Tasks and Weighting
Term 1
Test
Project/Assignment 10 20
Term 2
Assignment/Test
Examination 30
Term 3
Term 4

37. In general
Although the project/investigation is indicated in the first term, it could be scheduled in term 2. Only ONE project/investigation should be set per year.
Tests should be at least ONE hour long and count at least 50 marks.
Project or investigation must contribute 25% of term 1 marks while the test marks contribute 75% of the term 1 marks. The combination (25% and 75%) of the marks must appear in the learner’s report.
None graphic and none programmable calculators are allowed (for example, to factorise a² - b² = (a-b)(a+b), or to find roots of equations) will not be allowed. Calculators should only be used to perform standard numerical computations and to verify calculations by hand.
Formula sheet must not be provided for tests and for final examinations in Grades 10 and 11.

38. Mark distribution for Mathematics NCS end-of-year papers: Grades 10
Description
Grade 10
Statistics
15 ± 3
Algebra and equations
(and inequalities)
30 ± 3
Analytical Geometry
Patterns and sequences
Trigonometry and measurement
50 ± 3
Finance, growth and decay
10 ± 3
Euclidean Geometry
20 ± 3
Functions and graphs
Probability
TOTAL
100
No calculators with programmable functions, facilities or symbolic facilities (for example, to factorise, or to find roots of equations) will be allowed. Calculators should only be used to perform standard numerical computations and to verify calculations by hand.

39. Bookwork Grade 12 Paper 1 – maximum 6 marks
Paper 2 – Theorems and/or trigonometric proofs – maximum 12 marks
Grade 11
Paper 2 - Theorems and/or trigonometric proofs – maximum 12 marks
Grade 10
No bookwork

40. Annual Assessment Plan
Annual Assessment Plan should be given to learners at beginning of year.
Include dates, task, maximum mark

41. Exam and Test templates
End of year exam
Tests

42. The 7 Formal Assessment Tasks
5 tests
1 project / investigation
June examination
Final examination Or
4 tests
1 assignment

43. Moderation Internal and External Internal
HoD (or subject head) if HoD did not specialise in subject
All Programme of Assessment (PoA) tasks: HoD moderates before task is given to learners
HoD moderates 10% of learner responses to Programme of Assessment tasks
External
Moderation by Subject advisors

44. Moderation: What to look for?
Duration, length
Weighting of content
Weighting of cognitive levels
Language – mathematical vs layman
Use of pictures, diagrams, graphs to facilitate language
Level of difficulty

45. CONTENT TRAINING

46. IN GENERAL
Each content area has been broken down into topics. The sequencing of topics within terms gives an idea of how content areas can be spread and re-visited throughout the year.
The examples discussed in the Clarification Column in the annual teaching plan which follows are by no means a complete representation of all the material to be covered in the curriculum. They only serve as an indication of some questions on the topic at different cognitive levels. Text books and other resources should be consulted for a complete treatment of all the material.
The order of topics is not prescriptive, but ensure that in the first two terms, more than six topics are covered/taught so that assessment is balanced between paper 1 and 2.

47. CONTENT TRAINING(p.22) Term 1: Algebraic expressions Exponents
Numbers and Patterns
Equations and Inequalities
Trigonometry

48. ALGEBRAIC EXPRESSIONS (3 WEEKS)
Real numbers
Surds
Appropriate rounding
Multiply a binomial by trinomial
Factorising
Trinomials
Grouping in pairs
Sum and difference of two cubes
Use factorising to simplify algebraic fractions
Add and subtract algebraic fractions

49. Different cognitive levels in factorisation

50. EXPONENTS (2 WEEKS) Revise the laws of exponents
Use the laws of exponents to simplify expressions and solve equations

51. Examples

52. NUMBERS AND PATTERNS (1 WEEK)
Arithmetic sequence is done in Grade 12, hence is not used in Gr. 10
Consider the linear number pattern 3; 5; 7; 9; ....

53. Examples

54. EQUATIONS AND INEQUALITIES (2 WEEKS)
Solve linear equations
Solve quadratic equations
Solve simultaneous equations
Solve literal equations
Solve linear inequalities

55. EXAMPLES

56. TRIGONOMETRY (3 WEEKS) Special angles and reciprocal ratios
θ ε { 0º; 30º; 45º; 60º; 90º} without using a calculator
cosec θ; sec θ ; cot θ (examined only in gr. 10)
Solving right angles triangles
Solving simple trigonometric equations (angles between 0º and 90º )
Defining and plotting trigonometric functions

57. EXAMPLES
Similarity of triangles is fundamental to the trigonometric ratios sinθ; cosθ and tanθ;

59. Triangles for special angles

60. Term 2: Functions Activity Euclidean Geometry Activity (Revision)
CONTENT TRAINING
Term 2:
Functions
Activity
Euclidean Geometry
Activity (Revision)

61. FUNCTIONS (4 WEEKS) The concept of a function
Plot basic graphs defined by:
Investigate the effect of a and q on the graphs defined by
Investigate the effect of a and q on
the trigonometric graphs
Sketch, use and interpret the graphs

62. Functions
Activity

63. Euclidean Geometry(3 weeks)
Activity

64. Euclidean Geometry(3 weeks)
Similar and congruent triangles
Detailed revision of basic geometry
Revision of triangles and parallel lines
Concepts of similarity and congruence
Investigate special polygons
Properties of quadrilaterals
Making conjectures and then proving them

65. CONTENT TRAINING Term 3: Analytical Geometry Finance and growth
Statistics
Euclidean Geometry
Trigonometry
Measurement

66. Analytical geometry(2 weeks)
The distance between two points
The gradient of a line segment
The midpoint of a line segment

67. Examples

68. Examples

69. Finance and Growth(2 weeks)
Simple and compound growth
Foreign exchange rates

70. STATISTICS (2.5 WEEKS) Measures of central tendency
grouped and ungrouped data
Measure of dispersion
Five number summaries and box and whiskers diagram
Analysing and interpreting statistical summaries

71. Euclidean Geometry(1 week)
Solve problems and prove riders using the properties of parallel lines, triangles and quadrilaterals.

72. Problems in two dimensions
Trigonometry(2 weeks)
Problems in two dimensions

73. Example
At the base of an electricity pylon, two poles and the cross wire are positioned as in the diagram:
(a) What angle does each wire make with the ground?
(b) What is the length of each wire?
(c) At what height above the ground do the two wires intersect?
Platinum Mathematics Gr. 10 ,Maskew Miller Longman, J Campbell S McPetrie

74. Example(cont.)

75. Measurement(1 week)
Revise the volume and surface area of right-prisms and cylinders
Study the effect on volume and surface area when multiplying any dimension by a constant factor k
Calculate the volume and surface area of sphere, right pyramids and right cones
(In case of pyramids, bases must either be equilateral triangle or a square.
Problem types must include composite figures)

76. VOLUME AND SURFACE AREA

77. VOLUME AND SURFACE

78. VOLUME AND SURFACE

79. CONTENT TRAINING
Term 4:
Probability

80. Probability(2 weeks) Use of probability models.
Use of Venn diagrams to solve probability problems.

81. TOWARDS GREATER PERFORMANCE IN MATHEMATICS
THAT’S IT
TOWARDS GREATER PERFORMANCE IN MATHEMATICS