5.1 Subject Framework

5.1 Subject Framework

  1. PLANNING: The Subject Framework, Work Schedule and the Lesson Plan

Below are examples of documents that constitute the three levels of planning. Schools that already have these documents are not compelled to change to these. They may use these documents to modify theirs if there are any major differences, or may simply continue with what they already have. It is important to note the relationship between a work schedule and a lesson plan. A lesson plan must be drawn from a work schedule.

5.1 SUBJECT FRAMEWORK

Example of a Subject Framework for Mathematics

LO 1 / Grade 10 / Grade 11 / Grade 12
Number and Number relationships / Rational and irrational numbers
(integral) Exponents, surds
Number patterns (general term linear)
Simple and compound growth
Foreign exchange / Real and non-real numbers (intuitive)
(rational) Exponents and surds
Number patterns (general term quadratic)
Simple and compound decay
Different periods of compounding / Logarithms (laws and use in real life situation)
Using number patterns to solve problems geometric and arithmetic sequences
Compound growth and decay – calculating the period (n)
Application to annuities, bond repayments and sinking funds
Investment and loan options
LO 2 / Grade 10 / Grade 11 / Grade 12
Functions and Algebra / Exploring various types of functions, generalizing the effects of various parameters
Use characteristic of various functions to draw their graphs
Algebraic manipulations including product and factors; algebraic fractions (monomial denominators)
Solving equations:
  • Linear
  • Quadratic (by factorization)
  • Exponential
Solving linear inequalities
Simultaneous equations (both linear)
Mathematical modelling
Average rate of change / Exploring various types of functions, generalizing the effects of various parameters – extending the types and the range of parameters
Use characteristic of various functions to draw their graphs
Algebraic manipulations including algebraic fractions (binomial denominators); completing the square
Solving equations:
  • Quadratic (factorization/completing the square/formula)
Simultaneous equations (one linear and one quadratic)
Mathematical modelling
Average gradient; gradient at a point
Linear programming – determining the co-ordinates of the feasible region to solve optimisation problems / Exploring inverses of functions
Use characteristic of various functions to draw their graphs
Factorise 3rd degree polynomials – including examples requiring the factor theorem
Differential Calculus:
  • Instantaneous rate of change
  • Limits concept (intuitive)
  • Derivatives from 1st principles
  • Rules for differentiation
  • Tangents to graphs
  • Curve sketching
  • Optimisation problems in context
Linear programming – the “search line” method to solve optimization problems
LO 3 / Grade 10 / Grade 11 /

Grade 12

Space, Shape and Measurement / Volume and surface area of prisms and cylinders
Geometry of triangles and quadrilaterals
Analytical (co-ordinate) geometry
  • Distance formula
  • Gradient
  • Midpoint
Transformation geometry
  • Horizontal and vertical translations
  • Reflections in the x and y-axes, the line
y = x
Trigonometry
  • Definition of the basic functions
  • Solving triangles and problems in two dimensions in context
Historical development of geometry and trigonometry / Volume and surface areas of pyramids, cones and spheres
Similarity of triangles
Analytical (co-ordinate) geometry
  • Equations of straight lines
  • Inclination
Transformation geometry
  • Rotations through an angle of 90° or 180°
  • Enlargements
Trigonometry
  • Special angle functions
  • Fundamental identities
  • Reduction formulae
  • General solution of trig equations
  • Sine-, cosine- and area rules
  • Problems in two dimensions
Historical development of geometry and trigonometry / Analytical (co-ordinate) geometry
  • Circles
  • Tangents to circles
Transformation geometry
  • Rotation about the origin
  • Preservation properties of transformation
Trigonometry
  • Compound angle identities
  • Problems in two and three dimensions
Historical development of geometry and trigonometry
Familiarity with other geometries e.g. spherical -, “taxi cab” - and fractal geometry
LO 4 / Grade 10 / Grade 11 / Grade 12
Data Handling and Probability / Data analysis (descriptive statistics)
  • Measures of central tendencies and spread (percentiles and quartiles)
  • Representation of data
Probability models and relative frequency
Using Venn diagrams as an aid to solve probability problems
Sources of bias; uses and misuses of data
Making predictions from data analysis
Investigative project / Data analysis (descriptive statistics)
  • Measures of central tendencies and spread
  • Five number summary
  • Representation of data
  • Box and whisker plots
  • Ogives
  • Variance and standard deviation
  • Scatter plots
Dependant and independent events
Using Venn and tree diagrams as an aid to solve probability problems
Sources of bias; uses and misuses of data
Making predictions from data analysis
Skewed and symmetric data
Investigative project / Data analysis (descriptive statistics)
  • Measures of central tendencies and spread
  • Representation of data
  • Sampling
  • Regression function
  • Correlation coefficients
Generalise the fundamental counting principle
Sources of bias; uses and misuses of data
Making predictions from data analysis
Normal distributions
Investigative project

Issues impacting on the subject framework

Weighting

/

Context

Describe the local context in which the school is situated /

Resources

Indicate in broad strokes available resources, e.g. Khanya laboratory, library, LTSM and how they will be utilised (see notes below)

Policy issues

Describe the implication of supporting policies and legislation e.g. White paper 6 and 7 on Inclusive education and e-education respectively /

Principles of the NCS

Indicate in broad strokes how the principles of the NCS will be infused /

Managing diversity

Indicate broad strategies to accommodate the differential needs of learners

WORK SCHEDULES

Western Cape Education Department

DIRECTORATE: CURRICULUM DEVELOPMENT

FET NCS

WORK SCHEDULE FOR GRADE 10

2009

SUBJECT: MATHEMATICS

This work schedule is aligned to and must be read in conjunction with the Subject Statement and Subject Assessment Guideline

MATHEMATICS: GRADE 10 (CORE ASSESSMENT STANDARDS ONLY): WORK SCHEDULE: 2009

TERM 1
WEEK 1 / WEEK 2 / WEEK 3 / WEEK 4 / WEEK 5 / WEEK 6 / WEEK 7 / WEEK 8 / WEEK 9 / WEEK 10+ 11
RATIONAL NUMBERS,
SURDS & EXPONENTS / NUMBER PATTERNS
(linear general term) / PRODUCTS – Binomial by
trinomial / FACTORS – trinomials ;
grouping / ALGEBRAIC FRACTIONS
Simplification of fractions – monomial denominator / LINEAR EQUATIONS & INEQUALITIES / Systems of linear equations / Quadratic & Exponential Equations / REVISION & TEST / SCHOOL HOLIDAYS
10.1.1 & 10.1.2 / 10.1.3 / 10.2.4 / 10.2.4 / 10.2.4 / 10.2.5 / 10.2.5
Daily informal assessment/class work
INVESTIGATION/ ASSIGNMENT(PoA) [10%] / Daily informal assessment/class work / Daily informal assessment/class work / Daily informal assessment/class work CONTROLLED TEST(PoA) [10%]
TERM 2
WEEK 12 / WEEK 13 / WEEK 14 / WEEK 15 / WEEK 16 / WEEK 17 / WEEK 18 / WEEK 19 / WEEK 20 / WEEK 21 / WEEK 22
CO-ORDINATE GEOMETRY
Distance between two points
Gradient of line-segment
Midpoint of line-segment / PROPERTIES OF POLYGONS
Conjectures and generalisations
Disprove conjectures / Investigating characteristics & sketching the GRAPHS OF VARIOUS FUNCTIONS (linear; quadratic; hyperbolic; exponential)
Investigate average rate of change / MID-YEAR EXAMINATION(PoA) [30%]
10.3.3 / 10.3.2 / 10.2.1 – 10.2.3 & 10.2.7
Daily informal assessment/class work / Daily informal assessment/class work
ASSIGNMENT/ INVESTIGATION(PoA) [10%]
TERM 3
WEEK 23 / WEEK 24 / WEEK 25 / WEEK 26 / WEEK 27 / WEEK 28 / WEEK 29 / WEEK 30 / WEEK 31
Trigonometric functions (definitions & applications)
Graphical representations of trig. functions / SIMPLE & COMPOUND GROWTH FORMULAE:
Interest, hire purchase, inflation, population growth, etc. / DATA HANDLING
Collects, organises and interprets univariate numerical data
Measures of central tendency
Measures of dispersion / DATA HANDLING
Represent data effectively
Bar/ compound bar; histograms;freguency polygons;pie charts;line/broken line graph / VOLUME & SURFACE AREA
10.3.5, 10.2.1 – 10.2.3 / 10.1.4 – 10.1.5 / 10.4.1 / 10.3.1
Daily informal assessment/class work
PROJECT(PoA) [20%] / Daily informal assessment/class work / CONTROLLED TEST(PoA)[10%]
TERM 4
WEEK 33 / WEEK 34 / WEEK 35 / WEEK 36 / WEEK 37 / WEEK 38 / WEEK 39 / WEEK 40 / WEEK 41 /
  • Non-routine problems should be included in both informal and formal assessment tasks
  • Modelling as a process should be embedded across all LO’s
  • Revision should be integrated throughout

TRANSFORMATION GEOMETRY
(translation & reflection) / SOLVING 2D PROBLEMS USING TRIG RATIOS
(scale drawing, maps & building plans) / FINAL EXAMINATION / Admin, Reflection & Planning for the coming year.
10.3.4 / 10.3.6
Daily informal assessment/class work
ASSIGNMENT(PoA) [10%]
Western Cape Education Department

DIRECTORATE: CURRICULUM DEVELOPMENT

FET NCS

WORK SCHEDULE FOR GRADE 11

2009

SUBJECT: MATHEMATICS

This work schedule is aligned to and must be read in conjunction with the Subject Statement and Subject Assessment Guideline

MATHEMATICS: GRADE 11 CORE ONLY: WORK SCHEDULE: 2009

TERM 1
WEEK 1 / WEEK 2 / WEEK 3 / WEEK 4 / WEEK 5 / WEEK 6 / WEEK 7 / WEEK 8 / WEEK 9 / WEEK 10 & 11
Real & non-real numbers
Exponents and Surds / FINANCIAL MATHEMATICS
Simple and compound decay
straight line depreciation and depreciation on a reducing balance
different periods of compounding growth and decay (including effective and nominal interest rates) / NUMBER PATTERNS
Quadratic general term / ALGEBRA
Manipulate algebraic expressions ; completing the square
Solve quadratic equations by factorisation ; completing the square & formula
Solve quadratic inequalities,
Simultaneous equations in two unknowns, one of which is linear and one which is quadratic, algebraically and/or graphically / REVISION & TEST / SCHOOL HOLIDAYS
AS 11.1.1 / AS 11.1.4 – 11.1.5 / 11.1.3 / AS 11.2.4 – 11.2.5(a) and (b) / AS 11.3.3
Daily informal assessment/class work
INVESTIGATION/ASSIGNMENT(PoA) [10%] / Daily informal assessment/class work / Daily informal assessment/class work
TEST (PoA) [10%]
TERM 2
WEEK 12 / WEEK 13 / WEEK 14 / WEEK 15 / WEEK 16 / WEEK 17 / WEEK 18 / WEEK 19 / WEEK 20 / WEEK 21 / WEEK 22
CO-ORDINATE GEOMETRY
Equation of the straight line, inclination of a line / TRIGONOMETRY
Identities; Special Angles; Reduction formulae; negative angles
Equations including specific and general solutions / TRANSFORMATIONS
enlargement by a constant factor k
rotating around the origin through an angle of 90 and 180 / STATISTICS
measures of central tendency & dispersion
differentiate between symmetric and skewed data and make relevant deductions
Bias and misuse of statistics / MID-YEAR EXAMINATION
AS 11.3.3 (a) – (c) / AS 11.3.4 / AS 11.4.1 (a) ;
Daily informal assessment/class work / Daily informal assessment/ class work/
INVESTIGATION/ASSIGNMENT (PoA) [10%]
TERM 3
WEEK 23 / WEEK 24 / WEEK 25 / WEEK 26 / WEEK 27 / WEEK 28 / WEEK 29 / WEEK 30 / WEEK 31 / WEEK 32
FUNCTIONS
Recognises relationships between variables
Generates as many graphs
Identifies characteristics
Average gradient between two points on a curve ; intuitive understanding of the concept of the gradient of a curve at a point / SINE, AREA & COSINE RULES
Solves problems in 2 - dimensions by constructing and interpreting geometrical and trigonometric models / STATISTICS
bivariate numerical data
Scatter plots and intuitive lines of best fit.
Bias and misuse of statistics / VOLUME & SURFACE AREA
Right pyramids, spheres, right cones & combinations of these
AS 11.3.5 (a – d) / 11.4.1 (b) / AS 11.2.8
Daily informal assessment/ class work / PROJECT(PoA) [20%] / Daily informal assessment/class work / TEST[10%]
TERM 4
WEEK 33 / WEEK 34 / WEEK 35 / WEEK 36 / WEEK 37 / WEEK 38 / WEEK 39 / WEEK 40 / WEEK 41 /
  • Non-routine problems should be included in both informal and formal assessment tasks
  • Modelling as a process should be embedded across all LO’s
  • Revision should be integrated throughout
  • AS 11.4.3 – 11.4.4 must be integrated into lessons on statistics where appropriate

LINEAR PROGRAMMING
Optimise a function in two variables subject to one or more linear constraint
Determine the coordinates of the vertices of the feasible region / REVISION OF BOTH PAPER 1 AND PAPER 2 WORK / FINAL EXAMINATION / Admin, Reflection & Planning for the year ahead
AS 11.4.2
Daily informal assessment/class work / REVISION ASSIGNMENT of all LO’s (PoA) [10%]
Western Cape Education Department

DIRECTORATE: CURRICULUM DEVELOPMENT

FET NCS

WORK SCHEDULE FOR GRADE 12

2009

SUBJECT: MATHEMATICS

This work schedule is aligned to and must be read in conjunction with the Subject Statement and Subject Assessment Guideline

MATHEMATICS: GRADE 12 CORE: WORK SCHEDULE: 2009

TERM 1
WEEK 1 / WEEK 2 / WEEK 3 / WEEK 4 / WEEK 5 / WEEK 6 / WEEK 7 / WEEK 8 / WEEK 9 / WEEK 10 / WEEK 11
NUMBER PATTERNS: SEQUENCES AND SERIES
Solves problems involving number patterns, including arithmetic and geometric sequences and series ;
Correctly interprets sigma notation ;
Proves and correctly selects the formula for and calculates the sum of series / FUNCTIONS, INVERSES AND LOGARITHMS
Formal definition of a function ;
graphs of the inverse relations of functions, in particular the inverses of: ;
Determines which inverses are functions and how the domain of the original function needs to be restricted so that the inverse is also a function / FINANCIAL MATHEMATICS
Calculates the value of n in the formula A=P(1
Applies knowledge of geometric series to solving annuity, bond repayment and sinking fund problems, with or without the use of the formulae:  and analyses investment and loan options ; (including pyramid and micro-lenders’ schemes) / CO-ORDINATE GEOMETRY
Equation of a circle (any centre)
Equation of a tangent to a circle given a point on the circle
AS 12.1.3 / AS 12.1.2 ; 12.2.1 – 12.2.3 / AS 12.1.4 – 12.1.5 / AS 12.3.3
Daily informal assessment/class work /INVESTIGATION/PROJECT (20%) ; ASSIGNMENT (10%) ; CONTROLLED TEST (10%)
TERM 2
WEEK 12 / WEEK 13 / WEEK 14 / WEEK 15 / WEEK 16 / WEEK 17 / WEEK 18 / WEEK 19 / WEEK 20 / WEEK 21 / WEEK 22
TRIGONOMETRY:
Compound Angle Identities / CALCULUS
Factorise third degree polynomials
Intuitive understanding of the limit ; Instantaneous rate of change ;
Derivatives from first principles and rules: equations of tangents to graphs ;
Sketch graphs of cubic functions ; (maxima, minima and points of inflection) ;
Solves practical problems involving optimisation and rates of change / MID-YEAR EXAMINATION
(15%) / SEMESTER FINALISATION OF PORTFOLIOS
AS 12.3.5 - 12.3.6 / AS 12.2.4 ; 12.2.7
Daily informal assessment/class work /ASSIGNMENT (10%)
TERM 3
WEEK 23 / WEEK 24 / WEEK 25 / WEEK 26 / WEEK 27 / WEEK 28 / WEEK 29 / WEEK 30 / WEEK 31 / WEEK 32
TRIGONOMETRY:
Solves problems in 2 and 3 dimensions / TRANSFORMATIONS
uses the compound angle identities to generalise the effect on the co-ordinates of the point after rotation about the origin through an angle
Rigid transformations (translations, reflections, rotations and glide reflections) preserve shape and size, enlargement preserves shape, but not size / LINEAR PROGRAMMING
solves design and planning problems by optimising a function in two variables, subject to linear constraints, establishing optima by means of a search line and further comparing the gradients of the objective function and linear constraint boundary lines / REVIEW / TRIAL EXAMINATION
(25%) / TERM
FINALISATION OF PORTFOLIOS
AS 12.3.6 / AS 12.3.4 / AS 12.2.8
Daily informal assessment/class work /CONTROLLED TEST (10%)
TERM 4
WEEK 33 / WEEK 34 / WEEK 35 / WEEK 36 / WEEK 37 / WEEK 38 / WEEK 39 / WEEK 40 / WEEK 41 / WEEK 42 /
  • Non-routine problems should be included in both informal and formal assessment tasks
  • Modelling as a process should be embedded
across all LO’s
  • Revision should be integrated throughout
  • informal assessment must take place continuously

REVIEW
REVISION ASSIGNMENT of all LO’s / FINAL EXAMINATION

5.1 LESSON PLANS

LESSON PLAN
Grade:11
Subject: MATHEMATICS
Duration: 3 weeks( week 33 – week 35)
Educator: M. Bali (Mrs.)
Assessment standard(s): 11.2.8
Content/context:
LINEAR PROGRAMMING
Prior knowledge: straight lines; linear inequalities; representing lines/inequalities; simultaneous solutions.
(New) Terminology: constraints; feasible region; objective function; optimisation; / Resources:
List Textbooks, papers, internet, e learning, multimedia
Teaching and learning activities (provide examples):
examples of: drawing straight lines, presenting linear inequalities, words to inequalities, systems of linear inequalities, calc. vertices of feasible region(algebraically/ graphically), problems using tables, problems in words,
problems from exemplar papers / Forms of assessment:
homework/ classwork, short tests, assignment
Reflection and feedback:
How did learners find LP? What worked well? How can I improve lesson/ material/ presentation/ learner participation? Was time allocation enough/ too much? Etc.
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