Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
OVERVIEW
Term 1
Term 2
Term 3
Term 4
Algebra III (9 wk)
Unit 1: Solutions to Quadratic Equations (E Math) (0.5
wk)
Unit 2: Linear Inequalities (E Math) (0.5 wk)
Unit 3: Equations and Inequalities (A Math) (2 wk)
Unit 4: Indices and Standard Form (E Math) (0.5 wk)
Unit 5: Surds and Indices (A Math) (1 wk)
Unit 6: Logarithms (A Math) (2 wk)
Unit 7: Polynomials and Partial Fractions (A Math) (2
wk)
Unit 8: Matrices (E Math) (0.5 wk)
Coordinate Geometry III (2 wk)
Unit 1: Coordinate Geometry (E Math)
(0.5 wk)
Unit 2: Points, Lines and Slopes (A Math)
(1.5 wk)
Functions I (5 wk)
Unit 1: Direct and Inverse Proportions (E
Math) (1 wk)
Unit 2: Applications of Straight Line
Graphs (A Math) (1 wk)
Unit 3: The Modulus and Power
Functions (A Math) (2 wk)
Unit 4: Parabolas and Circles (A Math) (1
wk)
Revision (2 wk)
Geometry III (1.5 wk)
Unit 1: Congruent and Similar Triangles
(E Math) (0.5 wk)
Unit 2: Area and Volume of Similar
Figures and Solids (E Math) (1 wk)
Trigonometry III (5.5 wk)
Unit 1: Trigonometric Ratios (E Math) (1
wk)
Unit 2: Further Trigonometry (E Math)
(1.5 wk)
Unit 3: Trigonometric Functions (A Math)
(2 wk)
Unit 4: Simple Trigonometric Identities
and Equations (A Math) (1 wk)
4 Class Tests (10% for E Math, 10% for A Math)
E Math Class Test 1: Week 2
A Math Class Test 1: Week 3
E Math Class Test 2: Week 6
A Math Class Test 2: Week 7
4 Class Tests (10% for E Math, 10% for A
Math)
E Math Class Test 3: Week 3
A Math Class Test 3: Week 4
E Math Class Test 4: Week 6
A Math Class Test 4: Week 7
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Arithmetic III (2 wk)
Unit 1: Applications of Mathematics in
Practical Situations (E Math) (1 wk)
Unit 2: Linear Graphs and their
Applications (E Math) (1 wk)
Geometry III (2 wk)
Unit 3: Mensuration – Arc Length, Sector
Area, Radian Measure (E Math) (1 wk)
Unit 4: Geometrical Properties of Circles
(E Math) (1 wk)
4 Class Tests (10% for E Math, 10% for A
Math)
E Math Class Test 5: Week 3
A Math Class Test 5: Week 4
E Math Class Test 6: Week 6
A Math Class Test 6: Week 7
EOY E Math Exam (70%)
EOY A Math Exam (70%)
1
Hwa Chong Institution
Scheme of Work 2014
Time Allocated
In Weeks/hrs
0.5 week
Time frame
Term 1 Week 1
Subject/Programme : Mathematics
Level : Secondary 3 SIP
Content/Learning Outcomes
Content(topic/theme/concept)
Algebra III (Unit 1/Solutions to Quadratic
Equations)
Suggested Curriculum of Parallels
Core:
Students to understand the concept
of equality
At the end of the topic, students will be able
to:
1. Solve quadratic equations by
factorisation (revision).
2. Form a quadratic equation when the
roots are given
3. Complete a given expression of the
form ( x 2  kx) to obtain a perfect
square.
4. Solve a quadratic equation by
‘completing the square’ method.
5. Solve a quadratic equation by using the
Students to be able to identify
patterns
 b  b 2  4ac
.
2a
Solve a non-quadratic equation by
reducing it to a quadratic equation.
Solve problems involving quadratic
equations.
Manipulate algebraic
formulae:
formula x 
6.
7.
8.
Connection:
Students to make connections to
previous formulae learnt in Sec 2
Learning Activities
Suggestions:
- Blended/Cooperative
Learning:
Students to be organized in
expert groups, each group
to watch one of the
suggested videos and share
with rest of group on what
they learnt about the
algebraic identities
a 2  b2  (a  b)(a  b)
a 2  2ab  b2  (a  b)2
Assessment/Feedback
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Students to present
on what they have
learnt from the
videos to the rest of
the class
- Summative
assessment: Class
Test: Topics for E
Math Test 1
(a) Solutions to
Quadratic
Equations
(b) Linear
Inequalities
a 2  2ab  b2  (a  b)2
Students to link the concept of
equality to different contexts (e.g.
politics)
Resources
Online Resources:
Special Factoring
http://www.purplemath.c
om/modules/specfact2.
htm
Geometrical
Interpretation of
a 3  b3
http://www.youtube.com
/watch?v=5x4gJPchSiY
Geometrical
Interpretation of
a 3  b3
http://www.youtube.com
/watch?v=9RHJt0GXLc
Y
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 1
a3  b3  (a  b)(a 2  ab  b2 )
a3  b3  (a  b)(a 2  ab  b 2 )
In Weeks/hrs
0.5 week
Content(topic/theme/concept)
Algebra III (Unit 2/Linear Inequalities)
Time frame
Term 1 Week 1
At the end of the topic, students will be able
to:
1. State the properties of inequalities:
(a) if x  y and y  z , then
Core:
Students to understand the concept
of inequality
x  z.
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Blended/Cooperative
Learning:
Students to be organized in
expert groups, each group
to watch one of the
suggested videos and share
with rest of group on what
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Students to present
Online Resources:
Solving Inequalities
http://www.youtube.com
/watch?v=wYEYeFGxH
kI
Absolute value
inequality
http://www.youtube.co
2
Hwa Chong Institution
Scheme of Work 2014
(b) if x  y , then x  z
and x  z  y  z ,
Subject/Programme : Mathematics
Level : Secondary 3 SIP
 yz
they learnt about the
inequalities
(c) if x  y and z  0, then
x y
xz  yz and  ,
z z
(d) if x  y and z  0, then
x y
xz  yz and  ,
z z
2.
3.
4.
- Summative
assessment: Class
Test: Topics for E
Math Test 1
(a) Solutions to
Quadratic
Equations
(b) Linear
Inequalities
and use them to solve simple
inequalities.
Distinguish the difference between <
and  and use a number to represent
them.
Solve problems involving inequalities.
Solve linear inequalities involving one
variable.
In Weeks/hrs
2 week
Content(topic/theme/concept)
Algebra III (Unit 3/Equations and Inequalities)
Time frame
Term 1 Week 2 to
3
At the end of the topic, students will be able
to:
1. Solve linear and non-linear
simultaneous equations
2. Discuss the geometrical significance of
the algebraic solution of simultaneous
equations with the use of suitable IT
tools,
3. Discuss the number of solutions of a
pair of simultaneous linear and nonlinear equations (i.e. there may be 2
solutions, 1 solution or no solution),
4. Solve word problems involving linear
and non-linear equations.
on what they have
learnt from the
videos to the rest of
the class
Core:
Students to understand that they can
solve a system of equations by using
equivalent systems, in order to find
the value of one of the variables.
Students to understand that they can
represent and solve a system of
equations in more than one way,
Students to understand that quadratic
function can be expressed in many
forms. The values of a, b, and c or h
and k or p and q gives different
information about the quadratic
function.
Students to understand that
completing a perfect square trinomial
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Experiential Learning:
Use a spreadsheet or
graphing software to
(a) investigate the
relationship between
the number of points
of intersection and
the nature of
solutions of a pair of
simultaneous
equations, one linear
and one quadratic.
(b) explain how the roots
of the equation
ax 2  bx  c  0
are related to the
sign of
b 2  4ac
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Mathematical
Modelling Task on
Marshall Cavendish
Pg 33
- Alternative formative
assessment: Open
Ended Tasks on
Quadratics (One
Equals to Zero and
Other Mathematical
Surprises Pg 8 – 11,
m/watch?v=BoIxUeGe
k_g
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 3
Online Resources:
Simultaneous Equations
http://www.youtube.com
/watch?v=SZ4x-HzhaKo
Simultaneous Equations
and Intersections of
Graphs
http://www.purplemath.c
om/modules/syseqgen.
htm
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 1
- Math Through the
Ages
3
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
5. Relationships between the roots and
coefficients of a quadratic equation
6. Conditions for a quadratic equation to
have:
(a) two real roots
(b) two equal roots
(c) no real roots
and related conditions for a given line to:
(a) intersect a given curve
(b) be a tangent to a given curve
(c) not intersect a given curve
ax 2  bx  c to the form
a( x  h)2  k and use it to (i)
7. Transform
sketch the graph; and (ii) deduce the
quadratic formula or by using
completing the square method
ax  bx  c to the form
a ( x  p )( x  q ) and use it to (i)
8. Transform
2
sketch the graph
2
9. Conditions for ax  bx  c to be
always positive (or always negative)
10. Solving quadratic inequalities, and
representing the solution on the
number line
allows them to factor the completed
trinomial as well as the square of the
binomial
(c) show graphically why
there are no real
solutions to a
quadratic equation
Students to understand that they can
derive the quadratic formula from the
quadratic equation form by
completing the square method
ax 2  bx  c  0
2
when b  4ac is
Students to understand that the
different discriminant give rise to
different types of solutions
negative.
(d) investigate how the
positions of the
graph
y  ax 2  bx  c
31 - 35)
- Performance Task –
Paper Helicopter
ASMS
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 1
- Summative
assessment: Class
Test: Topics for A
Math Test 1
(a) Equations and
Inequalities
vary with the sign of
Connections:
Students to make connections with
applications in physics, decision
making (linear algebra), business
problems
Discuss with students situations that
relates to quadratic function include
the stopping distance of a car and
throwing an object into the air.
Throwing a stone, for example,
follows a trajectory path, which can be
modelled by a quadratic equation.
Discuss the difference between the
parabola vs catenary
b 2  4ac , and
describe the graph
when
b 2  4ac  0
(e) Examine the solution
of a quadratic
equation and that of
its related quadratic
inequality (e.g.
4 x2  x  5  0
and
4 x 2  x  5  0 ),
and describe both
solutions and their
relationship.
Practice:
Students to assume the role as a
mathematician involved in operation
research to use systems of equations
to optimize resources.
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
4
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
Derivation of quadratic formula –
expose students to algebraic
manipulation experienced by
practitioner.
Identity:
Explore biographies of
Mathematicians such as Diophantus,
Al-Kharizmi, Abu Kamil Babylonian
tablets
In Weeks/hrs
0.5 week
Time frame
Term 1 Week 4
Content(topic/theme/concept)
Algebra III (Unit 4/Indices and Standard
Form)
At the end of the topic, students will be able
to:
1. Use the Multiplication Law of Indices to
simplify terms that involve positive
indices.
2. Use the Division Law of Indices to
simplify terms that involve positive
indices.
3. Use the Power Law of Indices to simplify
terms that involve positive indices.
4. Use the various Laws of Indices to
simplify terms that involve positive
indices.
5. State the Laws of Indices involving zero
and negative indices and use them to
evaluate numerical expressions with
zero and negative indices.
6. State the Law of Indices involving
fractional indices and use it to evaluate
and simplify expressions involving them.
7. Solve equations involving indices.
Core:
Simplify/evaluate and solve
expressions/equations by applying
the laws of indices
Connection:
- Represent product of any
expression that is used repeatedly
as a factor using exponential
notation
-
-
Describe and compare numbers
written in index form, e.g. “Which
is greater, 210 or 102?”
Understand the significance and
the meaning of negative and
fractional exponents and how
these might be different from
positive integer exponents
Suggestions:
- Blended Learning:
engage in homebased
learning, followed by
classroom discussion.
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment: projects
or/and oral
presentations:
The use of indices
and the real-life
applications
Online resources:
Index Notation Quizzes:
http://quiz.econ.usyd.ed
u.au/mathquiz/indices/in
dex.php
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 2
- Summative
assessment: Class
Test: Topics for E
Math Test 2
(a) Indices and
Standard
Form
(b) Matrices
Practice:
- Application of standard
form/Indices in the area of
(a) Microbiology (size of atom in
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
5
Hwa Chong Institution
Scheme of Work 2014
8.
9.
Use the standard form to express very
large or very small numbers.
Use the calculator to evaluate numbers
involving standard form and power of a
number.
In Weeks/hrs
1 week
Content(topic/theme/concept)
Algebra III (Unit 5/Surds and Indices)
Time frame
Term 1 Week 5
At the end of the topic, students will be able
to:
1. Recognise surds and state the rules of
surds
2. Perform arithmetical operations
(addition, subtraction, and multiplication)
on expressions involving simple surds in
the numerator
3. Rationalise fractions involving surds in
the denominator
4. Solve problem sums involving surds
5. Solve equations involving surds.
6. Solve equations involving indices
7. Sketch graphs of exponential functions
8. Solve challenging equations involving
surds
Subject/Programme : Mathematics
Level : Secondary 3 SIP
nanometers, 10-9)
(b) Astronomy OR Social
Science (world population in
billions, 109)
(c) Financial Mathematics
(Compound Interest)
and the make sense of the figures
Core:
Students to understand that they can
combine surds using properties of
real numbers
Students to understand that they can
write a surd using different ways (in
index form, or with radical signs)
Suggestions:
- Collaborative Learning
Students to
(a) investigate how
squaring an equation
would lead to
extraneous solutions
Students to understand that by
squaring an equation involving surds,
they may introduce extraneous
solutions and the solutions need to be
check to ensure they still fulfil the
original equation
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment: Open
Ended Tasks on
Surds (One Equals
to Zero and Other
Mathematical
Surprises Pg 12-13,
18 - 22)
- Summative
assessment: Class
Test: Class Test:
Topics for A Math
Test 2
(a) Surds and
Indices
(b) Logarithms
Students to make sense of numbers
in surd form and recognise that the
quadratic formula gives the real roots
of quadratic equations in various
forms (integer, rational number and
conjugate surds).
Online Resources:
History of Surds
http://www.mathsisgood
foryou.com/AS/surds.ht
m
Hotel Infinity
http://www.mathsisgood
foryou.com/artefacts/hil
berthotel.htm
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 2
Connections:
Students to make use of scientific
notation for real life data.
In Weeks/hrs
2 week
Content(topic/theme/concept)
Algebra III (Unit 6/Logarithms)
Core:
Students to understand that
logarithms and exponents have
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Experiential Learning:
Use a spreadsheet or
Suggestions:
- Formative
assessment: Pop
Online Resources:
Richter Scale
http://www.khanacade
6
Hwa Chong Institution
Scheme of Work 2014
Time frame
Term 1 Week 6 to
Week 7
At the end of the topic, students will be able
to:
1. Know functions a x , e x , log a x, ln x
2.
3.
4.
5.
6.
and their graphs
Know equivalence of
Subject/Programme : Mathematics
Level : Secondary 3 SIP
corresponding properties
Students to understand that they can
use logarithms to solve exponential
equations and vice versa
y  a x  x  log a y
Students to understand that
log a a  1 and
log a 1  0 for any a  0 and
a 1
y  a x  x  log a y are
Show that
Understand and apply Laws of
logarithms:
(1) product (2) quotient (3) power (4)
change-of-base laws
Solve equations involving logarithmic
functions
Solve challenging equations involving
exponential and logarithmic functions
inverse functions
Connections:
Students to relate the solution of the
equation f ( x)  0 to the graph
y  f ( x) to verify the existence of
the solutions or to justify that the
solution does not exist.
Students to relate the exponential and
logarithmic functions to sciences (e.g.
pH value, Richter scale of
earthquakes, decibel scale for sound
intensity, radioactive decay,
population growth).
Practice:
Students to model real-life problems
using exponential functions, such as
the half-life function and heat and
cooling function.
Identity:
Students to trace the history of
logarithms and the invention of log
tables, and logarithms by assuming
the role of mathematician
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
graphing software to
(a) investigate the
characteristics of an
exponential and
logarithmic graphs
(b) display real-world
data graphically and
match it with an
appropriate
exponential or
logarithmic function.
Quiz
- Alternative formative
assessment: Open
Ended Tasks on
Logarithmic
Functions (One
Equals to Zero and
Other Mathematical
Surprises Pg 23 –
24, 27 - 30)
- Alternative formative
assessment:
Mathematical
Modeling on
Marshall Cavendish
Pg 57, 189
my.org/math/algebra/l
ogarithmstutorial/logarithm_pro
perties/v/richter-scale
Logarithms in the Real
World
http://www.youtube.co
m/watch?hl=enGB&v=3oZPPIVC8MU
&gl=SG
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 2
- Performance Task:
Students to
investigate the cause
and effect
earthquakes that
happened in the last
5 years for e.g.
Sichuan Earthquake
2008, China, Tohoko
Earthquake 2011,
Japan, Christchurch
Earthquake, New
Zealand. Students to
reflect on how they
could help in the face
of such natural
disasters.
- Performance Task:
7
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
Students to
investigate the
impact of Indonesian
Tremors to
Singapore
- Summative
assessment: Class
Test: Class Test:
Topics for A Math
Test 2
(a) Surds and
Indices
(b) Logarithms
In Weeks/hrs
2 week
Time frame
Term 1 Week 8 to
Week 9
Content(topic/theme/concept)
Algebra III (Unit 4/Polynomials and Partial
Fractions)
At the end of the topic, students will be able
to:
1. Definition of polynomial.
2. Multiplication and division of polynomial.
3. Types of equations – identity vs
conditional equation.
4. Equating two equivalent polynomials
and then comparing
coefficients
f ( x )  Q( x ) D( x )  R ( x )
5.
6.
7.
8.
9.
Able to recognize quotient & remainder
from a given identity.
Know the Division Algorithm (long
division)
Define remainder theorem and know its
limitation.
Apply reminder theorem to solve for
unknowns in polynomial.
Able to revert back to the division
Core:
Students to understand that the
properties of integers apply to
polynomials
Students to relate to Fundamental
theorem of algebra
Students to understand that the
degree of a polynomial equation tells
them about the number of roots that
the equation has
Students to understand that they
could divide polynomials by long
division using steps similar to dividing
whole numbers
Students to understand that when (x a) is a factor of the polynomial, then
the graph of the polynomial has an xintercept.
Students express a proper algebraic
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Experiential Learning:
Use a spreadsheet or
graphing software to
(a) investigate the graph
of a cubic polynomial
and discuss
(i) the linear factors
of the polynomial
and the number of
real roots; and
(ii) the number of real
roots of the related
cubic equation,
with reference to the
points of intersection
with the x-axis
Flipped classroom :
 Students view this
video on teachertube
[Long division of
Suggestions:
- Formative
assessment: Pop
Quiz
Online resources:
 Partial Fractions
 Online quiz on
Partial fraction
- Alternative formative
assessment:
Concept Map on the
behavior of roots for
Quadratic vs Cubic
functions
- Alternative formative
assessment:
Mathematical
Modeling on
Marshall Cavendish
Pg 89
- Research on Oliver
Heaviside
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 3
- Summative
assessment: Class
Test: Class Test:
8
Hwa Chong Institution
Scheme of Work 2014
10.
11.
12.
13.
14.
15.
16.
algorithm to find the quotient and the
remainder when the divisor is non-linear
Define factor theorem
Use factor theorem to solve for
unknowns in polynomial.
Apply factor theorem to factorise cubic
expressions and solve cubic equations.
decompose a rational expression into
partial fractions,
perform long division on improper
rational expressions before expressing
the proper rational expressions as
partial fractions,
using “cover-up” rule to determine the
unknown constants
include cases where denominator is of
the form ( ax  b)(cx  d ) ,
(ax  b)(cx  d )2 and
(ax  b)( x 2  c 2 )
Subject/Programme : Mathematics
Level : Secondary 3 SIP
fraction in its partial form.
Students identify whether an
algebraic fraction is a proper or an
improper fractions.
Connections:
Make connections between division of
polynomial and division of whole
number, and express the division
algorithm as
P( x)  ( x  a)Q( x)  R .
Students perform long division on an
improper fraction and express it as
the sum of a polynomial and a proper
fraction before expressing it as partial
fractions
Practice:
Relate cubic equations to design of
roller coasters (consideration of max
allowed speed) and link to integrated
resorts.
Polynomial] on
improper fraction on
express it as the sum
of a polynomial and a
proper fraction before
expressing it as partial
fractions.
Topics for A Math
Test 3
(a) Polynomials
and Partial
Fractions
(b) Points, Lines
and Slopes
Blended Learning :
Students discuss on
applications of partial
fractions in real life
application eg.
electrical or
mechanical
engineering where
partial fractions is
used not only for
finding integrals, but
also for analyzing
linear differential
systems like resonant
circuits and
feedback-control
systems.
Students research on Oliver
Heaviside to discover that he was first
person to use partial fractions to
analyze linear differential systems
Identity:
Explore biographies of
Mathematicians Tartaglia Vs Cardano
and their quest in solving of cubic
equations.
Relate to Arithmetic in Nine Sections,
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
9
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
Relate to ancient questions on
1. Trisecting an angle
2. Doubling the cube
3. Constructing a regular heptagon
In Weeks/hrs
0.5 week
Content(topic/theme/concept)
Algebra III (Unit 8/Matrices)
Time frame
Term 1 Week 9
At the end of the topic, students will be able
to:
1. Present information in the form of a
matrix of any order,
2. Define equal, zero, identity matrices.
3. Find unknowns in equal matrices.
4. Perform addition and subtraction on
matrices of same order, perform scalar
multiplication.
5. Perform matrix multiplication on small
order matrices.
Core:
Students to represent and understand
information displayed in matrix form
Students to understand that they can
make use of properties of equality
and inverse operations to solve
equations.
Connections:
Students to discuss some
applications of matrix multiplication,
e.g. decoding messages and
transformation matrices for movie
making.
Practice:
Students to assume the role as a
mathematician involved in
cryptography to encrypt or decrypt
messages using matrices
Suggestions:
- Experiential Learning:
Use a graphing
calculator
(a) to input matrices
and to compute
inverse matrices –
simplify decoding
process.
- Collaborative Learning
Students to get into
groups and justify if two
matrices can be
multiplied by checking
the orders of the
matrices.
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Students to encode
and decode using
shift transformations
(refer to NSA lesson
plan) and present
their work in an oral
presentation
- Summative
assessment: Class
Test: Topics for E
Math Test 2
(c) Indices and
Standard
Form
(d) Matrices
Online Resources:
Matrices Khan
Academy
http://www.khanacadem
y.org/math/algebra/alge
bra-matrices
NSA lesson plan on
encoding and decoding
http://www.nsa.gov/aca
demia/_files/collected_l
earning/high_school/alg
ebra/matrices_secret_w
eapon.pdf
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 5
Students to assume the role as a
mathematician involved in operation
research to use matrices to optimize
resources.
Identity:
Students to discuss how the idea of
matrices is being used in
spreadsheets and how these
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
10
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
programs are useful in their everyday
lives.
Time Allocated
In Weeks/hrs
0.5 week
Time frame
Term 2 Week 1
In Weeks/hrs
1.5 week
Time frame
Term 2 Week 1 to
Week 2
Content/Learning Outcomes
Content(topic/theme/concept)
Coordinate Geometry III (Unit 1/Coordinate
Geometry)
At the end of the topic, students will be able
to:
1.
Locate the position of a coordinate
point on a graph and find the length of
a line segment.
2.
Find the gradient of a line joining two
given points.
3.
Find the equation of a straight line
given its gradient m and one point on
the line.
4.
Find the equation of a straight line
joining two given points.
5.
Solve related problems involving
equations of straight lines.
Content(topic/theme/concept)
Coordinate Geometry III (Unit 2/Points, Lines
and Slopes)
At the end of the topic, students will be able
to:
1. Given coordinates of two points
calculate, revise
(a) mid-point
(b) distance
(c) gradient
2. Prove squares, rectangles,
Suggested Curriculum of Parallels
Core:
Students to understand that a line can
be graphed and its equation can be
written such its characteristics like
slope and point on line can be shown
Learning Activities
Suggestions:
- Collaborative Learning:
Students to explore and
discuss ways of finding
the equation of line
Connections:
Relate to gradient in Geography
Core:
Students to understand that a line can
be graphed and its equation can be
written such its characteristics like
slope and point on line can be shown
Students to understand that they can
compare the slopes of two lines and
determine if the lines are parallel or
perpendicular
Students to understand that the
distance between two points and the
angle stays the same regardless of
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Collaborative Learning:
Students to explore and
discuss ways of finding
the area of a triangle (or
polygon) with given
vertices.
- Students to discuss
other ways of finding
area of rectilinear
figures.
Assessment/Feedback
Suggestions:
- Formative
assessment: Pop
Quiz
- Summative
assessment: Class
Test: Class Test:
Topics for E Math
Test 3
(a) Coordinate
Geometry
(b) Congruent
and Similar
Triangles
(c) Area and
Volume of
Similar
Figures and
Solids
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Concept Map of
properties of lines in
Coordinate
Geometry
Resources
Online Resources:
Descartes and
Coordinate System
http://www.bookrags.co
m/research/descartesand-his-coordinatesystem-mmat-02/
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 4
Online Resources:
Descartes and
Coordinate System
http://www.bookrags.co
m/research/descartesand-his-coordinatesystem-mmat-02/
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
11
Hwa Chong Institution
Scheme of Work 2014
3.
4.
5.
6.
7.
8.
parallelograms and other standard
polygons
Understand and solve problems
involving collinear points
Understand gradient of a perpendicular
line using the relationship m1m2  1
Identify equations of parallel or
perpendicular lines
Formulate equations of lines passing
through a given point and parallel or
perpendicular to another given line
Find equation of perpendicular bisector
between two points
Find the area of rectilinear figure given
its vertices(Shoelace Formula)
Subject/Programme : Mathematics
Level : Secondary 3 SIP
location and orientation change.
- Alternative formative
assessment:
Mathematical
Modeling on
Marshall Cavendish
Pg 162
Students to discuss how to solve
geometry problems involving finding
(i) the equation of a line perpendicular
or parallel to a given line, (ii) the
coordinates of the midpoint of a line
segment (horizontal, vertical and
oblique), and (iii) equation of the
perpendicular bisector of a line
segment.
Chapter 6
- Summative
assessment: Class
Test: Class Test:
Topics for A Math
Test 3
(a) Polynomials
and Partial
Fractions
(b) Points, Lines
and Slopes
Connections:
Relate gradient to tangent of the
angle of inclination between the line
and the positive direction of the x-axis
and deduce the relationship between
the gradient of (a) two parallel lines,
(b) two perpendicular lines
Relate to gradient in Geography
Time Allocated
In Weeks/hrs
1 week
Time frame
Term 2 Week 3
Content/Learning Outcomes
Content(topic/theme/concept)
Geometry III (Unit 1/Congruent and Similar
Triangles)
At the end of the topic, students will be able
to:
1. Identify congruent triangles.
2. State and use the congruency tests:
SSS, SAS, AAS and RHS to test if two
triangles are congruent.
3. Apply the congruency tests to solve
given triangles.
Suggested Curriculum of Parallels
Learning Activities
Core:
- Construct proofs (using appropriate
language, definitions and theorems)
on certain geometrical shapes by
making use of the geometrical
properties
Suggestions:
- Blended learning:
students to engage in
homebased learning,
followed by classroom
discussion.
- Connect and relate non-similar
triangles with common base/height
- Inquiry Learning: (Group
work) Use GSP/
Geogebra/ Geometrical
software or any other
methods to investigate
Connection:
- Know the converse is true (i.e. if 2
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Assessment/Feedbac
k
Suggestions:
- Formative
assessment: Pop
Quiz
- Summative
assessment: Class
Test: Class Test:
Topics for E Math
Test 3
(a) Coordinate
Geometry
Resources
Online resources:
Geometry – proofs:
http://mathflix.luc.edu/N
CTM_cat/Geometry/Pro
ofs/nctm-geometryproofs-math-videos.html
Teoalida’s Website –
Architecture and
Housing around the
world and AutoCAD 2D
and 3D design services:
12
Hwa Chong Institution
Scheme of Work 2014
4. Identify similar triangles.
5. State the tests for similarity between two
triangles.
6. Use the rules for similarity between two
triangles to solve problems involving
similar triangles.
Subject/Programme : Mathematics
Level : Secondary 3 SIP
triangles are congruent, both will
follow SSS, SAS and AAS or RHS
(if it is a right-angled triangle))
- Apply Congruency and Similarity in
real-world contexts
the properties relating
the sides and angles of
triangles
- Alternative formative
assessment: Construct
geometrical questions
and demonstrate a good
understanding of the
proofs and apply the
concepts
(b) Congruent
and Similar
Triangles
(c) Area and
Volume of
Similar
Figures and
Solids
- Enrichment activity:
Work in Groups and
(a) apply Congruency
and Similarity in
real life (e.g. scale
model and maps)
(b) use Similarity to
explain
photographic
principles and
dimension of a
photo given the
pixel count
In Weeks/hrs
1 week
Time frame
Term 2 Week 3 to
Week 4
Content(topic/theme/concept)
Geometry III (Unit 2/Area and Volume of
Similar Figures and Solids)
At the end of the topic, students will be able
to:
1. State that the ratio of the areas of any
two similar figures is equal to the
square of the ratio of any two
corresponding lengths of the figures.
2. Use the above rule to solve problems
Core:
- Understand and apply the concept
of scale factor; how it will affect the
size/area/volume of figures/objects
Connection:
- Connect ratio with scale factor
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Blended learning:
students to engage in
homebased learning,
followed by classroom
discussion.
- Alternative formative
assessment: Construct
geometrical questions
and demonstrate a good
Suggestions:
- Formative
assessment: Pop
Quiz
- Summative
assessment: Class
Test: Class Test:
Topics for E Math
Test 3
(a) Coordinate
http://www.teoalida.com
/
Print Resources:
- Elementary
Geometry by
Alexander and
Koeberlein (3rd
Edition, Houghton
Mifflin)
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 8
Online resources:
Geometry – proofs:
http://mathflix.luc.edu/N
CTM_cat/Geometry/Pro
ofs/nctm-geometryproofs-math-videos.html
Teoalida’s Website –
Architecture and
Housing around the
world and AutoCAD 2D
13
Hwa Chong Institution
Scheme of Work 2014
3.
4.
Time Allocated
Subject/Programme : Mathematics
Level : Secondary 3 SIP
involving the area and lengths of two
similar figures.
State that the ratio of the volumes of
any two similar solids is equal to the
cube of the ratio of any two
corresponding lengths of the solids.
Use the above rule to solve problems
involving the volumes, areas and
lengths of two similar solids.
understanding of the
proofs and apply the
concepts
Content/Learning Outcomes
Suggested Curriculum of Parallels
Learning Activities
In Weeks/hrs
1 week
Content(topic/theme/concept)
Trigonometry III (Unit 1/Trigonometric Ratios)
Time frame
Term 2 Week 4 to
Week 5
At the end of the topic, students will be able
to:
1. Define the three basic trigonometrical
ratios in terms of the lengths of the
hypotenuse side, opposite side and
adjacent side with respect to an acute
angle of a right-angled triangle.
2. Find the value of a trigonometrical ratio
using a calculator.
3. Find the length of a side of a right-angled
triangle using trigonometrical ratios.
4. Find the value of an angle of a rightangled triangle using trigonometrical
ratios.
5. Solve problems involving angles and
Core:
- Develop an understanding of size,
shape, relative position of plane
objects in space by demonstrating
an understanding of the conditions
needed to form the 3 basic
trigonometric ratios
Suggestions:
- Blended learning:
students to engage in
homebased learning,
followed by classroom
discussion.
- Represent the problems by
modeling and select and use
appropriate trigonometric ratios to
process information in problem
solving.
Connection:
- Apply their algebraic manipulation
skills to solve for triangles.
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
- Use geometrical
software to investigate
the 3 basic trigo
functions
- Hands-on activity:
“Tigonometric Ratios –
Complete the Puzzle”
(Maths Rm Resource)
Geometry
(b) Congruent
and Similar
Triangles
(c) Area and
Volume of
Similar
Figures and
Solids
Assessment/Feedbac
k
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment: Using
geometrical software
to do projects or/and
oral presentations on
Application in
navigation and
architecture. (LO5,
LO7)
and 3D design services:
http://www.teoalida.com
/
Print Resources:
- Elementary
Geometry by
Alexander and
Koeberlein (3rd
Edition, Houghton
Mifflin)
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 9
Resources
Online resources:
FAQs about
Trigonometry:
http://catcode.com/trig/i
ndex.html
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 10
- Summative
assessment: Class
Test: Class Test:
14
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
lengths of a right-angled triangle.
6. Solve practical everyday life problems
using trigonometrical ratios.
7. Solve more complicated problems with
the use of trigonometry.
- Connect gradient with
opposite
.
tan  
adjacent
In Weeks/hrs
1.5 week
Content(topic/theme/concept)
Trigonometry III (Unit 2/Further Trigonometry)
Time frame
Term 2 Week 5 to
Week 6
At the end of the topic, students will be able
to:
1. Solve triangles through Sine Rule &
Cosine rule
2. Formula for area of triangle
3. know the concept of bearings
4. Solve 2D, 3D problems
5. Compue angles of elevation and
depression, shortest distance, maximum
angle elevation.
Core:
Students to use the sine and cosine
rules to articulate the relationships
between the sides and angles of a
triangle, e.g. the lengths of the sides
are proportional to sine of the
corresponding angles, Pythagoras
theorem is a special case of the
cosine rule, etc
Students to understand that the
angles of elevation and depression
are acute angles of right triangles
formed by horizontal distance and a
vertical height; and that shortest
horizontal distance would give
maximum angle of elevation or
depression
Students to visualise height, north
direction, right-angled triangle, etc.
from 2D drawings of 3D situations.
Connections:
Students to relate to applications of
Trigonometry to different fields like
geography and astronomy, physics
and engineering
Topics for E Math
Test 4
(a) Trigonometric
Ratios
(b) Further
Trigonometry
Suggestions:
- Experiential Learning:
Use Clinometer app on
iPhone or Android phone
to find the angle of
elevation or depression
of particular buildings
- Experiential Learning:
To organise a treasure
hunt where treasures are
located at different spots
as a result of ambiguous
case of sine rule.
Students to use Bearing
app on iPhone or
Android phone to locate
the treasures.
Suggestions:
- Formative
assessment: Pop
Quiz
Online Resources:
Leaning tower of Pisa
http://www.clarku.edu/~
djoyce/trig/apps.html
- Alternative formative
assessment:
Concept Map on
connecting the areas
of triangles from
various topics for
different types of
triangles
Applications of
Trigonometry
http://www.youtube.com
/watch?v=wvmU7XKdt3
w
Suggestions:
- Formative
assessment: Pop
Quiz
- Summative
assessment: Class
Test: Class Test:
Topics for E Math
Test 4
(c) Trigonometric
Ratios
(d) Further
Trigonometry
Trigonometry in Real
Life
http://www.youtube.com
/watch?v=n1A2HqSXtG
I
Print Resources:
- New Syllabus
Mathematics 3 6th
Edition by Shinglee
Chapter 11
Practice:
Student to assume the role of a pilot
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
15
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
to find out the actual flight distance
using cosine rule.
In Weeks/hrs
2 week
Time frame
Term 2 Week 6 to
Week 8
Content(topic/theme/concept)
Trigonometry III (Unit 3/Trigonometric
Functions)
At the end of the topic, students will be able
to:
1. Know the concept of unit circle
2. Know the six trigonometric functions for
angles of any magnitude (in degrees)
3. Know principal values of
sin 1 x,cos1 x, tan 1 x
4.
5.
6.
Know the exact values of the
trigonometric functions for special
angles (0, 30, 45, 60, 90, 180,…)
amplitude, periodicity and symmetries
related to sine and cosine functions
graphs of
Core:
Students to understand that angles
are the domain elements of the
trigonometric functions
Students to understand that the
properties of inverse functions
expand to trigonometric functions
Students to understand that periodic
behaviour is behaviour that repeats
over intervals of equal length.
Students to understand that they can
translate periodic functions in the
same way as they translate other
functions
y  a sin  bx   c, y  a cos bx   Students
c
to understand that
trigonometric functions, and their
 x
 x  compositions gain significance when
y  a sin    c, y  a cos    they
c are used to model waves and
b
 b  periodic behaviour
y  a tan  bx 
Connections:
Students to discuss the relationships
between sin A, cos A and tan A, with
respect to the line segments related
to a unit circle.
Students to relate
sin 1 x, cos1 x, tan 1 x to the
sine, cosine and tangent functions
Suggestions:
- Experiential Learning:
Use a Geogebra or GSP
to
(a) investigate the
relationship of sin
A, cos A and tan A
with respect to the
unit circle.
(b) display the graphs
of trigonometric
functions and
discuss their
behaviour, and
investigate how a
graph (e.g.
y  a sin bx  c
) changes when a,
b or c varies.
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Mathematical
Modeling on
Marshall Cavendish
Pg 307
- Performance Task:
Students to get into
groups to find out the
different ferris
wheels for e.g.
Singapore Flyer
around the world and
to use sine or cosine
to its function
Online Resources:
Trigonometric Functions
and Unit Circle
http://www.youtube.com
/watch?v=rrXLl2WTKEc
Applications of
Trigonometry –
geography and
astronomy, physics and
Engineering
http://www.clarku.edu/~
djoyce/trig/apps.html
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 11
- Summative
assessment: Class
Test: Topics for A
Math Test 4
(a) Trigonometric
Functions
(b) Simple
Trigonometric
Identities and
Equations
1
respectively (e.g. sin x is an
angle whose sine is x, and the
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
16
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
 1
 is  2
principal value of sin 1  
 

 6
30° or  
Students to relate the sine and cosine
functions to sciences (e.g. tides,
Ferris wheel and sound waves).
Practice:
Students to assume the role of
mathematician to trace the historical
development of trigonometry – from
circle trigonometry to triangle
trigonometry in astronomy
Students to model natural
phenomena –tides, heartbeat, music
etc. using graphs of
y  f ( x) sin x
y  a sin(f ( x))
where
f ( x) can be
1 2
, x , x,
x
e x and relate to real life examples of
sound waves with such patterns.
In Weeks/hrs
1 week
Time frame
Term 2 Week 9
Content(topic/theme/concept)
Trigonometry III (Unit 4/Trigonometric
Identities and Equations)
At the end of the topic, students will be able
to:
sin A
1. Use of
 tan A ,
cos A
Core:
Students to understand that the
interrelationships amongst the six
basic trigonometric functions make it
possible to write trigonometric
expressions in various equivalent
forms
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Blended learning:
students to engage in
homebased learning,
followed by classroom
discussion.
- Hands-on activity:
“Tigonometric Identities
Suggestions:
- Formative
assessment: Pop
Quiz
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 12
- Alternative formative
assessment:
Mathematical
Modeling on
17
Hwa Chong Institution
Scheme of Work 2014
cos A
 cot A ,
sin A
cos 2 x  sin 2 x  1 ,
1  tan 2 A  sec 2 A ,
1  cot 2 A  cosec2 A
2.
3.
4.
Time Allocated
In Weeks/hrs
1 week
Time frame
Term 3 Week 1
Subject/Programme : Mathematics
Level : Secondary 3 SIP
Connections:
Students to relate
– Complete the Puzzle”
(Maths Rm Resource)
cos 2 x  sin 2 x  1 to Pythagoras
- Summative
assessment: Class
Test: Topics for A
Math Test 4
(a) Trigonometric
Functions
(b) Simple
Trigonometric
Identities and
Equations
theorem.
Solve simple trigonometric equations
Prove simple trigonometric identities
Simplify trigonometric expressions
Content/Learning Outcomes
Content(topic/theme/concept)
Functions I (Unit 1/Direct and Inverse
Proportions)
At the end of the topic, students will be able
to:
1. Understand and apply direct
variation
2. Sketch straight line graphs
illustrating direct variations
3. Understand and apply inverse
variation in word problems
4. Sketch reciprocal graphs illustrating
inverse variations
5. Understand and apply part variation
in word problems
6. Sketch graphs to show part
Suggested Curriculum of Parallels
Learning Activities
Core:
- Find the ratio and constant
connecting the variables and use
these to form equation
- Explain the concept of variations
using equations and graphs
Suggestions:
- Blended Learning:
engage in homebased
learning, followed by
classroom discussion.
Connection:
- Understand the meaning of ratio,
i.e. if the variables are related (i.e.
same kind), the ratio represent the
rate and will not change
- Represent variations graphically
Practice:
Students assumed the role of
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Marshall Cavendish
Pg 323
- Inquiry Learning: Work in
groups and design real
life problems involving
variation(s).
Assessment/Feedbac
k
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment: Using
the existing Science
experiments and
demonstrate the use
of variation(s)
- Summative
assessment: Class
Test: Topics for E
Math Test 5
(a) Direct and
Resources
Online resources:
Graphs and Proportion
– Higher:
http://www.bbc.co.uk/sc
hools/gcsebitesize/math
s/algebra/proportionhire
v1.shtml
Proportions/Variations:
http://www.onlinemathle
arning.com/proportions.
html
Variation:
http://www.themathpage
.com/alg/variation.htm
18
Hwa Chong Institution
Scheme of Work 2014
7.
8.
9.
In Weeks/hrs
1 week
Time frame
Term 3 Week 2
Subject/Programme : Mathematics
Level : Secondary 3 SIP
variations
Investigate effect of different
proportionality constants in the
graphs,
Understand and formulate joint
variation in word problems
Solve challenging problems
involving different types of
variations.
researcher and explore variations in
science experiments (e.g. Hooke’s
Law, Boyle’s Law and etc)
Content(topic/theme/concept)
Functions I (Unit 1/Applications of Straight
Line Graphs)
Core:
Students to know what linear and
non-linear relationships are.
At the end of the topic, students will be able
to:
1.
Determine a linear relation based on
experimental results of two non-linearly
related quantities
2.
Convert non-linear equations into linear
form
3.
Derive the relationship between two
variables given the straight line graphs
4.
Determine unknowns in relations using
experimental data by applying linear
law to obtain straight line graphs
5.
Understand independent and
dependent variables
6.
Understand and identify outliers or
incorrect readings
7.
Expected to plot linear graph given set
of experimental data. (with no scale
given)
Students to understand that it is
possible to transform a given nonlinear equation into a linear equation
Students know how to transform nonlinear relationships to linear form.
Students know how to determine the
unknown constants from a straight
line graph.
Students know how to apply linear
law to analyse experimental data.
Connections:
Students to relate the use of straight
line graph to the experience in
science experiment and explain why
they do it (e.g. oscillation of a
pendulum (Hooke’s Law), relationship
between resistance in circuit (Ohm’s
Law)
Students to relate to concepts learnt
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Inverse
Proportion
(b) Applications
of
Mathematics
in Practical
Situations
(c) Linear Graphs
and their
Applications
Suggestions:
- Maths Journal: The way
to transform a given nonlinear equation into a
linear equation depends
on the form of the
equation given. Use a
table to explore some
typical transformations.
- Inquiry Learning: To
engage in simple
Science experiments to
collect data and analyse
data using a straight line
graph.
- Exploratory Activity: To
predict population growth
using suitable linear
function. (Textbook: Pg.
213)
- Collaborative Learning:
To explore alternative
water sources for
Singapore in 2060.
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment:
Mathematical
Modeling on
Marshall Cavendish
Pg 213
- Summative
assessment: Class
Test: Topics for A
Math Test 5
(a) Applications
of Straight
Line Graphs
(b) The Modulus
and Power
Functions
Print Resources:
- New Syllabus
Mathematics 2 7th
Edition by Shinglee
Chapter 1
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 8
Online resources:
- Singapore data
(http://data.gov.sg/hom
e.aspx)
- To convert non-linear
relationships to linear
form.
(http://www.youtube.co
m/watch?v=pX6WlxP2
eok)
- Applications of linear
law
(http://www.youtube.co
m/watch?v=Gvb6MLB_
x6I)
19
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
in coordinate geometry.
Practice:
Students understand that some
phenomena in Science or in real
world can be modelled using an
equation. For example, students can
conduct simple Science experiments
to collect data. Part (a) to find a
formula (V = RI) for the resistance of
a resistor. Part (b) to find a formula
(Win-Win, Innovation)
(LO8: Reflect on and
respond to community,
national and global
issues, as an informed
and responsible
citizen.)
( T = 2 L ) for the period of a
pendulum.
Identity:
Students will be working in groups.
Based on the data on water
consumption per capita in Singapore
for the past 10 years, students will
plot graphs to estimate future water
consumption and to identify and
explain abnormal or inconsistent data.
Using the results, students are to
explore new water sources for
Singapore.
Linear law can only be applied when
there are only two unknown constants
in the original non-linear equation.
What happens if the non-linear
equation has more than two unknown
constants? Using suitable software,
plot the curve of best fit to fit a given
set of data directly to decide the
relationship between x and y.
In Weeks/hrs
2 week
Content(topic/theme/concept)
Functions I (Unit 3/The Modulus and Power
Core:
Students to understand that a pairing
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
- Experiential Learning:
Use a spreadsheet or
Suggestions:
- Formative
Print Resources:
- Additional
20
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
Functions)
Time frame
Term 3 Week 3 to
Week 4
At the end of the topic, students will be able
to:
1.
Know
x and the graph of
f ( x) where f ( x) is linear,
2.
3.
quadratic or trigonometric
Solve equations involving modulus
functions.
accurately sketch the standard graphs
(a) power
y  ax n for
2  n  3
function
(b) exponential function
y  ka x growth,
y  ka  x decay
of items from two sets is special if
each item from one set pairs with
exactly one item from the second set
Students to understand that
sometimes it is possible to model
data from a real world situation with a
linear equation
Students to understand that an
absolute value of x is its distance
from 0 and the absolute of f(x) is its
distance from the line y = 0.
Students to understand that they can
add or subtract functions based on
the operations of real numbers,
however, they must consider the
domain of each function.
Students to relate the graph of
exponential function with logarithmic
function and that they are inverse
functions of each other
Connections:
Students to relate the functions to real
life data.
Students to relate the graph of
exponential function with logarithmic
functions
Students to relate exponential graphs
with population growth, growth of
bacteria, microorganisms, radioactive
decay etc
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
graphing software to
(a) explore the
characteristics of the
various functions
(b) display real-world
data and match it
with appropriate
functions
(regression)
- Collaborative Learning:
Work in groups to match
and justify sketches of
graphs with their respective
functions.
assessment: Pop
Quiz
Mathematics 360 by
Marshall Cavendish
Chapter 4
- Alternative formative
assessment:
Mathematical
Modeling on
Marshall Cavendish
Pg 236
- Alternative formative
assessment: Using
the existing Science
experiments and
demonstrate the use
of exponential and
logarithmic functions
(e.g. rates of cooling
and heating)
- Performance Task:
Students examine
the problem of
space-pollution
caused by humanmade debris in orbit
to develop an
understanding for
functions and
modeling at
http://illuminations.nc
tm.org/lessonplans/9
-12/debris/index.html
- Performance Task:
Students develop
and analyse
exponential model
21
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
for the behaviour of
light passing through
water at
http://illuminations.nc
tm.org/lessonplans/9
-12/light/index.html
- Summative
assessment: Class
Test: Topics for A
Math Test 5
(a) Applications
of Straight
Line Graphs
(b) The Modulus
and Power
Functions
In Weeks/hrs
1 week
Content(topic/theme/concept)
Functions I (Unit 4/Parabolas and Circles)
Time frame
Term 3 Week 5
At the end of the topic, students will be able
to:
1. accurately sketch the standard graphs
y  kx
2
(a) parabolic
(b) ( x  a)  ( y  b)  r
Perform simple transformation of
standard graphs
Estimation of the gradient of a curve by
drawing a tangent
Derive the equation of a circle with
centre (a, b) and radius r using the
Pythagoras theorem, and the special
case when the centre is at the origin.
2
2.
3.
4.
2
2
Core:
Students to relate the graph of

y 2  x to y  x2
y  f ( x) to x  f ( y )

and that they are inverse functions of
each other
Students to understand that the
information in the equation of a circle
allows the circle to be graphed.
Students to understand that the
equation of a circle can be written if
its centre and radius are known.
Connections:
Students to find centre of a broken
circular wheel in archaeological
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
- Experiential Learning:
Use a spreadsheet or
graphing software to
(a) explore the
characteristics of the
various functions
(b) investigate the graph
of
y 2  kx when
k varies.
(c) display real-world
data and match it
with appropriate
functions
(regression)
Suggestions:
- Formative
assessment: Pop
Quiz
Print Resources:
- Additional
Mathematics 360 by
Marshall Cavendish
Chapter 9
- Summative
assessment: Class
Test: Topics for A
Math Test 6
(a) Parabolas
and Circles
- Collaborative Learning:
(a) Work in groups to
match and justify
sketches of graphs
22
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
studies or to find epicentre by solving
3 circle equations, detected from 3
satellite stations.
with their respective
functions.
Students to relate parabolas to
examples in sciences and in the real
world.
Students to discuss how to solve
geometry problems involving
intersection of a parabola/circle and a
straight line.
Time Allocated
In Weeks/hrs
1 week
Time frame
Term 3 Week 6
Content/Learning Outcomes
Content(topic/theme/concept)
Arithmetic III (Unit 1/Applications of
Mathematics in Practical Situations)
Suggested Curriculum of Parallels
Learning Activities
Core:
Students to understand the financial
terms such as profit, loss, interest,
taxes, currency
Suggestions:
- Enrichment activity:
Work in Groups and
(a) Find out the
different types of
interest rates
offered by
housing loans,
car loans, etc,
and determine
which of these
loans would be
suitable for the
different income
groups.
At the end of the topic, students will be able
to:
Connections:
1. Solve problems involving profit and Compare and contrast the traditional
loss.
and modern views and perspectives
2. Solve problems involving further
on use of loans and credit
examples of percentages.
3. Solve problems involving simple
The 2008 financial sub-prime loans
interest.
which spiral into a global crisis;
4. Solve problems involving
question on affordability of commodity
compound interest.
5. Solve problems involving hire
Practice:
purchase.
Students to assume the role of a bank
6. Convert one currency to another.
officer offering different types of loan
7. Calculate simple taxation problems. packages for different income groups
8. Solve problems involving personal
for car loans or housing loans
and household finances.
9. Interpret and use tables and charts Identity:
in solving problems.
Students to understand the
10. Use different problem solving
importance of saving (household
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Assessment/Feedbac
k
Suggestions:
- Formative
assessment: Pop
Quiz
- Alternative formative
assessment: Oral
Presentation of the
different types of
loan packages by
different financial
institutions
- Summative
assessment: Class
Test: Topics for E
Math Test 5
(a) Direct and
Inverse
Proportion
(b) Applications
of
Mathematics
Resources
Online resources:
Various banks’ websites
HDB website
Print Resources:
- Arithmetic of Life
Insurance (Unit 24,
Teaching Sec Math
by Alfred S.
Posamentier)
- New Syllabus
Mathematics 2 7th
Edition by Shinglee
Chapter 6
23
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
strategies to solve everyday life
problems.
In Weeks/hrs
1 week
Time frame
Term 3 Week 7
Time Allocated
In Weeks/hrs
1 week
Time frame
Term 3 Week 8
budgeting, long term financial
planning) and develop good habits of
using money (preventing bankruptcy,
taking calculated risks in investments)
Content(topic/theme/concept)
Arithmetic III (Unit 2/Linear Graphs and their
Applications)
Core:
Students to understand how to draw
travel graphs
At the end of the topic, students will be able
to:
1. Interpret and use conversion
graphs.
2. Interpret and use travel graphs.
3. Draw graphs to represent practical
problems.
4. Solve problems involving linear
graphs such as travel graphs and
graphs in practical situations.
Content/Learning Outcomes
Content(topic/theme/concept)
Geometry III (Unit 1/Mensuration – Arc
Length, Sector and Area, Radian Measure)
At the end of the topic, students will be able
to:
1. Find the area and circumference of
a circle, a quadrant and a semi-
in Practical
Situations
(c) Linear Graphs
and their
Applications
Suggestions:
- Formative
assessment: Pop
Quiz
Connections:
Students to learn how to interpret the
travel graphs and relate them to the
speed travelled.
Suggestions:
- Enrichment activity:
Work in Groups and
(a) Find out the
different types of
travel graphs by
different kinds of
vehicles or motion
Suggested Curriculum of Parallels
Learning Activities
Assessment/Feedbac
k
Suggestions:
Core:
 Students understand the
definition of angles in radian.
 Students apply the generalize
formulae of arc length and area
of sector/segment to provide
solution to problem sums.
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
Suggestions:
Inquiry Learning :

Students establish the
realationship between
- Summative
assessment: Class
Test: Topics for E
Math Test 5
(a) Direct and
Inverse
Proportion
(b) Applications
of
Mathematics
in Practical
Situations
(c) Linear Graphs
and their
Applications
Formative
Asssessment :
 Quizlet flash cards
on conversions of
angles from
degree to radian
Print Resources:
New Syllabus
Mathematics 3 7th
Edition by Shinglee
Chapter 7
Resources
Online resources:
 ivle package
 Real life
Application of
circular Measure
 What is 1 radian?
 Who Wants to be
a Millionaire?
24
Hwa Chong Institution
Scheme of Work 2014
2.
3.
4.
Subject/Programme : Mathematics
Level : Secondary 3 SIP
circle.
Find the arc length and area of a
sector.
Define a radian and to convert an
angle in radian to degree and vice
versa.
Use the formula s  r and
A
1 2
r  to solve problems
2
involving arcs and sectors with
angles expressed in radians.
In Weeks/hrs
1 week
Time frame
Term 3 Week 9
Content(topic/theme/concept)
Geometry III (Unit 2/Geometrical Properties
of Circles)
At the end of the topic, students will be able
to:
1. State the symmetric properties of a
circle,
(i) a straight line drawn from the centre
of a circle to bisect a chord is perpendicular
to the chord,
(ii) equal chords are equidistant from the
centre of a circle or centres of equal circles.
2. Calculate the perpendicular
distance between the centre of a
circle and a chord and solve related
problems.
3. State the angle properties of a
Connection:

Students apply fractions of the
circumference and the area of
circle respectively to find the arc
length and area of a sector.

Students synthesis concepts of
area of a sector and area of
triangle to dervive the
generalize the formula for area
of segment .
Practice:

Application of Circular Measure
real life. [Article from
MatheMatics teacher | Vol. 104,
No. 5 • December 2010/January
2011

Fields in which radian are
applied.
Core:
Classify angles inside, on and outside
the circle, define line and line
segments related to the circle and
apply these concepts in problem
solving (using appropriate language,
definitions and theorems for effective
communication)
angles in degree and
radian in a unit
circle.[ Refer to Java
Applet and Activity
Worksheet 1]
Blended Learning:
Students explore ivle
resource package to equip
them with the concepts
required for mastery of this
unit followed by room
dicussions on any
misconception/s arise from
the assigned assignment.
Suggestions:
- Blended learning:
students to engage in
homebased learning,
followed by classroom
discussion.
Connection:
Understand circle properties are
logical consequences of the
principles/theorems developed in the
previous units.
- Inquiry Learning: Work in
groups and use
GSP/Geogebra/Geometr
ical software or any
other methods to
discover various circle
theorems
Practice:
Students assumed the role of a
mechanical engineer and study the
- Enrichment activities
(a) Archaelogy studies
in broken wheels
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT

and vice versa.
Who Wants to be
a Millionaire?
Circula Measure
- Summative
assessment: Class
Test: Topics for E
Math Test 6
(a) Mensuration –
Arc Length,
Sector Area,
Radian
Measure
(b) Geometrical
Properties
Direct and
Inverse
Proportion
Circular Measure
Print Resources:
- New Syllabus
Mathematics 3 7th
Edition by Shinglee
Chapter 12
Suggestions:
- Formative
assessment: Pop
Quiz
Online resources:
GSP resources in
S:\Maths\Resources\IP
Ma S2\Geometry II
- Alternative formative
assessment:
(a) Construct
geometrical
questions and
demonstrate a
good
understanding
of the proofs
and apply the
concepts
(b) projects or/and
oral
Print Resources:
- Elementary Geometry
by Alexander and
Koeberlein (3rd
Edition, Houghton
Mifflin)
- New Syllabus
Mathematics 3 7th
Edition by Shinglee
Chapter 13
25
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
circle,
(i) an angle at the centre of a circle is
twice any angle at the circumference
subtended by the same arc,
(ii) a triangle in a semicircle with the
diameter as one of its sides, has a
right angle at the circumference,
(iii) angles in the same segment of a
circle are equal, and use the above
properties to solve related problems.
4.
State that angles in opposite
segments of a circle are
supplementary and use the
property to solve problems
involving angles of a quadrilateral
on a circle and related problems on
the property.
5.
Use all the above properties to
prove mathematical statements
involving angle properties of circles.
6.
State the property that a tangent to
a circle is perpendicular to the
radius drawn to the point of contact.
conveyor belt where the chain belt
represents common external tangents
to 2 circular gears.
and arc
(b) The use of paper
folding to visualize
symmetric
properties of circles,
e.g. “the
perpendicular
bisector of a chord
passes through the
centre”
(c) Generalisation of
two-secant theorem
to tangent from
external point and
vice versa
(d) Study of scope of
satellite
Constructions of Plane
diagrams involving loci,
lines (parallel/
perpendicular), angle and
line bisectors and circles
presentations
on real-life
applications
involving
geometrical
properties of
circles
- Summative
assessment: Class
Test: Topics for E
Math Test 6
(a) Mensuration –
Arc Length,
Sector Area,
Radian
Measure
(b) Geometrical
Properties
Direct and
Inverse
Proportion
7.
State the properties regarding
tangents drawn from an external
point,
(i) tangents drawn to a circle from an
external point are equal in length,
(ii) tangents subtend equal angles at
the centre,
(iii) the line joining the external point to
the centre of the circle bisects the angle
between the tangents,
and use the above properties to solve
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
26
Hwa Chong Institution
Scheme of Work 2014
Subject/Programme : Mathematics
Level : Secondary 3 SIP
problems involving tangents to a circle.
Note: (SIP) for SIP, Italic & underlined for SBGE, bold & underlined for SSMT
27