Download work schedule for grade 10

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
Number and Number
relationships
LO 1
Grade 10
Rational and irrational numbers
(integral) Exponents, surds
Number patterns (general term linear)
Grade 11
Real and non-real numbers (intuitive)
(rational) Exponents and surds
Number patterns (general term quadratic)
Grade 12
Simple and compound growth
Simple and compound decay
Different periods of compounding
Compound growth and decay – calculating the period
(n)
Application to annuities, bond repayments and sinking
funds
Investment and loan options
Foreign exchange
Logarithms (laws and use in real life situation)
Using number patterns to solve problems geometric and
arithmetic sequences
Functions and Algebra
LO 2
Grade 10
Exploring various types of functions,
generalizing the effects of various parameters
Grade 12
Exploring inverses of functions
Use characteristic of various functions to draw
their graphs
Grade 11
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 product and
factors; algebraic fractions (monomial
denominators)
Algebraic manipulations including algebraic
fractions (binomial denominators); completing
the square
Factorise 3rd degree polynomials – including
examples requiring the factor theorem
Solving equations:
 Linear
 Quadratic (by factorization)
 Exponential
Solving equations:
 Quadratic (factorization/completing the
square/formula)
Use characteristic of various functions to draw
their graphs
Solving linear inequalities
Simultaneous equations (both linear)
Simultaneous equations (one linear and one
quadratic)
Mathematical modelling
Mathematical modelling
Average rate of change
Average gradient; gradient at a point
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 – determining the coordinates of the feasible region to solve
optimisation problems
Linear programming – the “search line” method
to solve optimization problems
LO 3
Grade 10
Grade 11
Volume and surface area of prisms and
cylinders
Volume and surface areas of pyramids, cones
and spheres
Geometry of triangles and quadrilaterals
Similarity of triangles
Analytical (co-ordinate) geometry
 Distance formula
 Gradient
 Midpoint
Analytical (co-ordinate) geometry
 Equations of straight lines
 Inclination
Analytical (co-ordinate) geometry

Circles

Tangents to circles
Transformation geometry
 Horizontal and vertical translations
 Reflections in the x and y-axes, the line
y=x
Transformation geometry
 Rotations through an angle of 90° or 180°
 Enlargements
Transformation geometry
 Rotation about the origin
 Preservation properties of transformation
Trigonometry
 Special angle functions
 Fundamental identities
 Reduction formulae
 General solution of trig equations
 Sine-, cosine- and area rules
 Problems in two dimensions
Trigonometry
 Compound angle identities
 Problems in two and three dimensions
Historical development of geometry and
trigonometry
Historical development of geometry and
trigonometry
Familiarity with other geometries e.g. spherical , “taxi cab” - and fractal geometry
Space, Shape and Measurement
Grade 12
Trigonometry
 Definition of the basic functions
 Solving triangles and problems in two
dimensions in context
Historical development of geometry and
trigonometry
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
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
Data analysis (descriptive statistics)
 Measures of central tendencies and spread
 Representation of data
 Sampling
 Regression function
 Correlation coefficients
Probability models and relative frequency
Using Venn diagrams as an aid to solve
probability problems
Dependant and independent events
Using Venn and tree diagrams as an aid to
solve probability problems
Generalise the fundamental counting principle
Sources of bias; uses and misuses of data
Making predictions from data analysis
Investigative project
Sources of bias; uses and misuses of data
Making predictions from data analysis
Skewed and symmetric data
Investigative project
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
Resources
Describe the local context in which the school is
situated
Indicate in broad strokes available resources, e.g.
Khanya laboratory, library, LTSM and how they will
be utilised (see notes below)
Policy issues
Principles of the NCS
Managing diversity
Describe the implication of supporting policies
and legislation e.g. White paper 6 and 7 on
Inclusive education and e-education respectively
Indicate in broad strokes how the principles of the
NCS will be infused
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 3
PRODUCTS –
Binomial by
WEEK 4
FACTORS –
trinomials ;
(linear
general term)
trinomial
grouping
10.1.3
10.2.4
10.2.4
WEEK 1
WEEK 2
RATIONAL
NUMBERS,
NUMBER
PATTERNS
SURDS &
EXPONENTS
10.1.1 & 10.1.2
Daily informal assessment/class work
INVESTIGATION/ ASSIGNMENT(PoA) [10%]
WEEK 12
WEEK 13
CO-ORDINATE GEOMETRY
Distance between two points
Gradient of line-segment
Midpoint of line-segment
10.3.3
WEEK 14
WEEK 15
PROPERTIES OF POLYGONS
Conjectures and
generalisations
Disprove conjectures
10.3.2
WEEK 5
ALGEBRAIC
FRACTIONS
Simplification
of fractions –
monomial
denominator
10.2.4
WEEK 6
LINEAR
EQUATIONS
&
INEQUALITIE
S
10.2.5
WEEK 7
Systems of
linear
equations
WEEK 8
Quadratic &
Exponential
Equations
WEEK 9
REVISION & TEST
WEEK 10+ 11
SCHOOL
HOLIDAYS
10.2.5
Daily informal assessment/class
Daily informal assessment/class
work
work
TERM 2
WEEK 16
WEEK 17
WEEK 18
WEEK 19
Investigating characteristics & sketching the GRAPHS OF
VARIOUS FUNCTIONS (linear; quadratic; hyperbolic;
exponential)
Investigate average rate of change
10.2.1 – 10.2.3 & 10.2.7
Daily informal assessment/class work
CONTROLLED TEST(PoA) [10%]
WEEK 20
WEEK 21
WEEK 22
MID-YEAR EXAMINATION(PoA) [30%]
Daily informal assessment/class work
Daily informal assessment/class work
ASSIGNMENT/ INVESTIGATION(PoA) [10%]
TERM 3
WEEK 25
WEEK 26
WEEK 27
WEEK 28
WEEK 29
WEEK 30
WEEK 31
WEEK 23
WEEK 24
Trigonometric functions
SIMPLE & COMPOUND
DATA HANDLING
DATA HANDLING
VOLUME &
(definitions & applications)
GROWTH FORMULAE:
Represent data effectively
SURFACE
Collects, organises and
Interest, hire purchase,
Bar/ compound bar;
AREA
interprets univariate numerical
Graphical representations of
inflation, population growth, etc.
histograms;freguency
data
trig. functions
polygons;pie charts;line/broken
Measures of central tendency
line graph
Measures of dispersion
10.1.4 – 10.1.5
10.4.1
10.3.1
10.3.5, 10.2.1 – 10.2.3
CONTROLLED TEST(PoA)[10%]
Daily informal assessment/class work
Daily informal assessment/class work
PROJECT(PoA) [20%]
TERM 4
WEEK 35
WEEK 36
WEEK 37
WEEK 38
WEEK 39
WEEK 40
WEEK 41

WEEK 33
WEEK 34
TRANSFORMATION
SOLVING 2D PROBLEMS
FINAL EXAMINATION
GEOMETRY
USING TRIG RATIOS
Admin, Reflection & Planning
(translation & reflection)
(scale drawing, maps &
for the coming year.

building plans)
10.3.4
10.3.6
Daily informal assessment/class work

ASSIGNMENT(PoA) [10%]
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
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
AS 11.1.1
AS 11.1.4 – 11.1.5
11.1.3
ALGEBRA
REVISION & TEST
SCHOOL HOLIDAYS
AS 11.2.4 – 11.2.5(a) and (b)
AS 11.3.3
Daily informal assessment/class work
Daily informal
assessment/class work
TEST (PoA) [10%]
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
Daily informal assessment/class work
INVESTIGATION/ASSIGNMENT(PoA) [10%]
TERM 2
WEEK 12
WEEK 13
CO-ORDINATE
GEOMETRY
Equation of the
straight line,
inclination of a line
WEEK 14
WEEK 15
TRIGONOMETRY
Identities; Special Angles; Reduction formulae;
negative angles
Equations including specific and general
solutions
WEEK 16
WEEK 17
WEEK 18
TRANSFORMATIONS
enlargement by a constant factor k
rotating around the origin through an
angle of 90 and 180
AS 11.3.3 (a) – (c)
AS 11.3.4
Daily informal assessment/class work
WEEK 19
WEEK 20
STATISTICS
measures of central tendency &
dispersion
differentiate between symmetric and
skewed data and make relevant
deductions
Bias and misuse of statistics
AS 11.4.1 (a) ;
WEEK 21
WEEK 22
MID-YEAR EXAMINATION
Daily informal assessment/ class work/
INVESTIGATION/ASSIGNMENT (PoA) [10%]
TERM 3
WEEK 23
WEEK 24
WEEK 25
WEEK 26
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
WEEK 27
WEEK 28
SINE, AREA & COSINE RULES
Solves problems in 2 - dimensions by
constructing and interpreting geometrical and
trigonometric models
AS 11.3.5 (a – d)
Daily informal assessment/ class work / PROJECT(PoA) [20%]
WEEK 29
WEEK 30
WEEK 31
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
11.4.1 (b)
AS 11.2.8
TEST[10%]
Daily informal assessment/class work
WEEK 32
TERM 4
WEEK 33
WEEK 34
WEEK 35
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
WEEK 36
WEEK 37
REVISION OF BOTH PAPER 1 AND
PAPER 2 WORK
WEEK 38
WEEK 39
WEEK 40
FINAL EXAMINATION
WEEK 41
Admin, Reflection
& Planning for
the year ahead




Daily informal assessment/class work
AS 11.4.2
REVISION ASSIGNMENT of all
LO’s (PoA) [10%]
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
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
FINANCIAL MATHEMATICS
Calculates the value of n in the formula A=P(1  i)
Formal definition of a function ;
graphs of the inverse relations of functions, in particular
the inverses of: y  ax  q ; y  ax 2 ; y  a x ; a  0 ;
F
WEEK 15
x[(1  i)n  1] and
i
WEEK 16
WEEK 17
CALCULUS
AS 12.3.5 - 12.3.6
x[1  (1  i)n ]
i
AS 12.1.4 – 12.1.5
ASSIGNMENT (10%)
TERM 2
;
WEEK 18
AS 12.3.3
CONTROLLED TEST (10%)
WEEK 19
WEEK 20
WEEK 21
MID-YEAR EXAMINATION
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
Compound Angle Identities
P
analyses investment and loan options ; (including pyramid and microlenders’ schemes)
AS 12.1.2 ; 12.2.1 – 12.2.3
Daily informal assessment/class work /INVESTIGATION/PROJECT (20%) ;
WEEK 12
WEEK 13
WEEK 14
TRIGONOMETRY:
Equation of a circle (any centre)
Equation of a tangent to a circle
given a point on the circle
Applies knowledge of geometric series to solving annuity, bond
repayment and sinking fund problems, with or without the use of the
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
AS 12.1.3
CO-ORDINATE GEOMETRY
n
WEEK 22
SEMESTER
FINALISATION
OF PORTFOLIOS
(15%)
AS 12.2.4 ; 12.2.7
Daily informal assessment/class work /ASSIGNMENT (10%)
TERM 3
WEEK 23
WEEK 24
TRIGONOMETRY:
Solves problems in 2 and 3
dimensions
WEEK 25
WEEK 26
TRANSFORMATIONS
WEEK 27
LINEAR PROGRAMMING
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
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
AS 12.3.4
AS 12.2.8
AS 12.3.6
WEEK 28
WEEK 29
WEEK 30
REVIEW
WEEK 31
TRIAL EXAMINATION
(25%)
WEEK 32
TERM
FINALISATION
OF PORTFOLIOS
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
REVIEW
REVISION ASSIGNMENT of all LO’s
FINAL EXAMINATION
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
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:
Resources:
LINEAR PROGRAMMING
List Textbooks, papers, internet, e
learning, multimedia
Prior knowledge: straight lines; linear
inequalities; representing lines/inequalities;
simultaneous solutions.
(New) Terminology: constraints; feasible
region; objective function; optimisation;
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
Reflection and feedback:
Forms of assessment:
homework/ classwork, short
tests, assignment
How did learners find LP? What worked well? How can I improve lesson/ material/ presentation/
learner participation? Was time allocation enough/ too much? Etc.