RPT Math F5 2018 SMK Methodist

LEARNING
AREA/WEEKS
1. Number Bases
(Week 1 – Week 3)

LEARNING
OBJECTIVES
1.1 Understand and use the
concept of number in
base two, eight and five

LEARNING OUTCOME
(i)

State zero, one, two, three, …,
as a number in base:
a)
two
b)
eight
c)

five

(ii)

State the value of a digit of a
number in base:
a)
two
b)
eight
c)
five

(iii)

Write a number in base:
a)
two
b)
eight

c)
five
in expanded number.

(iv)

Convert a number in base:
a)
two
b)
eight
c)
five
to a number in base ten and vice
versa.

(v)

Convert a number in a certain
base to a number in another

base.

(vi)

Perform computations
involving:
a) addition
b) subtraction
of two numbers in base two.

TEACHING AND LEARNING
ACTIVITIES
Use models such as a clock face or a
counter which uses a particular
number base.
Number base blocks of twos, eights
and fives can be used to demonstrate
the value of a number in the respective
number bases.
For example:

2435 is

STRATEGIES
Thinking Skills
-working out
mentally
-identifying
relationship
Teaching Strategies
-Contextual
learning
- Constructivism
- Mastery
learning
- Exploratory
Vocabulary
-expand notation
Teaching Aids
- model (clock face)

2
4
3
Discuss
 digits used
 place values
in the number system with a particular
number bases.
Number base blocks of twos, eights
and fives can also be used here. For
example, to convert 1010 to a number
in base two, use the concept of least
number of blocks (23), tiles (22),
rectangles (21) and squares (20). In this
case, the least number of objects
needed here are one block, zero tiles,
one rectangle and zero squares. So,
1010 = 10102.

Moral Values

Cooperation, rational
Thinking Skills
-working out
mentally
-identifying
relationship
- problem solving
Teaching Strategies
-Contextual
learning
- Constructivism
- Mastery
learning
- Exploratory

1

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

LEARNING OUTCOME

TEACHING AND LEARNING
ACTIVITIES
Discuss the special case of converting
a number in base two directly to a
number in base eight and vice versa.
For example, convert a number in
base two directly to a number in base
eight through grouping of three
consecutive digits.
Perform addition and subtraction in
the conventional manner.
For example:
1010
+ 110
____________

____________

STRATEGIES
Vocabulary
-convert
Teaching Aids
- models
- reference book
Moral Values
Cooperation, honesty,
courage.

2

2. Graph of
functions II
(Week 4 –6)

LEARNING
AREA/WEEKS

2.1 Understand and use the
concept of graph of
functions.

LEARNING
OBJECTIVES

(i) Draw the graph of a :
(a) linear function:
y = ax + b,
a,b are constants.
(b) quadratic function :
y = ax2 + bx + c,
a, b, c are constants, a ≠ 0.
(c) cubic function :
y = ax3 + bx2 + cx + d,
a, b, c, d are constant,
a ≠ 0.
(d) reciprocal function :

y = a/x,
a constant, a ≠ 0.
(ii) Find from a graph :
(a) value of y given value of x
(b) the value (s) of x, given a
value of y.
(iii) Identify :
(a) the shape of graph given a
type of function.
(b) the type of function given
of graph.
(c) the graph given a function
and vice versa.
LEARNING OUTCOME

Explore graph of functions using
graphing calculator or the Geometer’s
Sketchpad.

Thinking Skills

working out mentally
identify relationship

Compare the characteristics of graph
of functions with different values of
constants.
For example :

Teaching Strategies
-Contextual
learning
- Constructivism
-Mastery learning
- Exploratory

A

B

Vocabulary
- Linear function
- Quadratic function
- Cubic function
- Reciprocal function
Graph B is broader than graph A and
intersects the vertical axis above the
horizontal axis.

TEACHING AND LEARNING
ACTIVITIES

\

Teaching Aids
Graph box
Scientific Calculator
CDROM

STRATEGIES

3

2. Graph of
functions II
(Week 4 –6)

2.1 Understand and use the
concept of graph of
functions.

2.2 Understand and use the
concept of the solution
of an equation by
graphical method

1

2.3 Understand and use
the concept of the
region representing
inequalities in two
variables

(i) Draw the graph of a :
(a) linear function:
y = ax + b,
a,b are constants.
(b) quadratic function :
y = ax2 + bx + c,
a, b, c are constants, a ≠ 0.
(c) cubic function :
y = ax3 + bx2 + cx + d,
a, b, c, d are constant,
a ≠ 0.
(d) reciprocal function :
y = a/x,
a constant, a ≠ 0.
(ii) Find from a graph :
(a) value of y given value of x
(b) the value (s) of x, given a
value of y.
(iii) Identify :
(a) the shape of graph given a
type of function.
(b) the type of function given
of graph.
(c) the graph given a function
and vice versa.
(iv) Sketch the graph of a given
linear, quadratic, cubic or
reciprocal function.
(i)
Find the point(s) of
intersection of two graphs.
(ii)
Obtain the solution of an
equation by finding the
(iii)
Point(s) of intersection of
two graphs.
(iv)
Solve problems involving
(v)
solution of an equation by
graphical method.
(i) Determine whether a given points
satisfies:
y = ax + b or y > ax + b or
y < ax + b.

Explore graph of functions using
graphing calculator or the Geometer’s
Sketchpad.

Thinking Skills
working out mentally
identify relationship

Compare the characteristics of graph
of functions with different values of
constants.
For example :

Teaching Strategies
-Contextual
learning
- Constructivism
-Mastery learning
- Exploratory

A

B

Vocabulary
- Linear function
- Quadratic function
- Cubic function
- Reciprocal function
Graph B is broader than graph A and
intersects the vertical axis above the
horizontal axis.

As reinforcement, let students play a
game; for example matching cards of
graphs with their respective functions.
When the students have their
matching partners, ask them to group
themselves into four groups of types
of functions. Finally, ask each group
to name the type of function that is
depicted on the cards.
Explore using graphing calculator or
the Geometer’s Sketchpad to relate the
x-coordinate of a point of intersection
of two appropriate graphs to the
solution of a given equation. Make
generalization about the point(s) of
intersection of the two graphs.

\

Teaching Aids
Graph box
Scientific Calculator
CDROM

Moral Values
Cooperation, rational
CCTS:
Thinking skills
-Evaluating
-Constructing
-Problem solving
Teaching Strategies:
-Constructivism
-graphing
-cooperative learning
- Mastery
learning
- Exploratory
- Problem solving
Vocabulary:

4

LEARNING
AREA/WEEKS
LEARNING
AREA/WEEKS
4. Matrices
(Week 7 – 9)

LEARNING OBJECTIVS

LEARNING OUTCOMES

LEARNING
OBJECTIVES
4.1 Understand and use the
concept of matrix.

LEARNING OUTCOME
Student will be able to…
(i) Form a matrix from given information.
(ii) Determine :
i.
The number of rows
ii.
the number of columns
iii.
The order of a matrix
(iii) Identify a specify element in a matrix.

4.2 Understand and use the
concept of equal
matrices.
4.3 Related to real life
situations such as in
industrial productions.

(i). Determine whether two matrices are equal.
(ii). Solve problem involving equal matrices.
(i)

Determine whether addition or
subtraction can be performed on two
given matrices.
Find the sum or the difference of two
matrices.
Perform addition and subtraction on a
few matrices.
Solve matrix equations involving
addition and subtraction.

(ii)
(iii)
(iv)

4.4 Perform multiplication
of a matrix by a
number.

(i)
(ii)

Multiply a matrix by a number.
Express a given matrix as a
multiplication of another matrix by a
number.
Perform calculation on matrices
involving addition, subtraction and
scalar multiplication.
Sole matrix equations involving
addition, subtraction and scalar
multiplication.

(iii)

15.2.2018 – 19.2.2018
CUTI TAHUN BARU CINA
4.5 Perform multiplication
of two matrices

(iv)

(i)

Determine whether two matrices
can be multiplied and state the
order of the product when two
matrices can be multiplied

TEACHING AND LEARNING
ACTIVITIES
TEACHING AND LEARNING
ACTIVITIES
Represent data in real life situations,
for example, the price of food on a
menu, in table form and then in
matrix form.
Use student seating positions in the
classroom by rows and columns to
identify a student who is sitting in a
particular row and in particular
column as a concrete example.
Discuss equal matrices in term of :
 The order
 The corresponding
elements.
Related to real life situations such s
keeping score of medal tally or
point in sports.
Related to real life situations such as
in industrial productions.
Related to real life situations such as
finding the cost of a meal in the
restaurant
For matrices A and B, discuss the
relationship between AB and BA
Begin with discussing the property
of the number 1 as an identity for
multiplication of numbers.
Discuss:
 an identity matrix is a square
 there is only one identity matrix
for each order
Discuss the properties:
 AI=A
 IA=A
Relate to the property of
multiplicative inverse of numbers.
Example:

STRATEGIES
STRATEGIES
Thinking Skills
-working out
mentally
-identifying
relationship
Teaching Strategies
-Contextual
learning
- Constructivism
- Mastery
learning
- Exploratory
Vocabulary
-standard form
-single number
-scientific
notation
Teaching Aids
-flash card
-scientific Calculator
Moral Values
Cooperation, rational
Thinking Skills
-working out
mentally
-identifying
relationship
Vocabulary
-standard form
-single number

5

LEARNING
AREA/WEEKS

LEARNING OBJECTIVS

4.6 Understand and use the
concept of identity
matrix.

LEARNING OUTCOMES
(ii)
(iii)

Find the product of two matrices
Solve matrix equations involving
multiplication of two matrices

(i)

Determine whether a given
matrix is an identity matrix by
multiplying it to another matrix.
Write identity matrix of any
order
Perform calculation involving
identity matrices

(ii)
(iii)
4.7 Understand and use the
concept of inverse matrix

4.8 solve simultaneous
linear equations by using
matrices

(i)

Determine whether a 2 x 2
matrix is the inverse matrix of
another 2 x 2 matrix.
(ii)
Find the inverse matrix of a 2 x 2
matrix using:
(a) the method of solving simultaneous
linear equations
(b) a formula

(i)

Write simultaneous linear
equations in matrix form

(ii)

Find the matrix   in
q

 p

a b   p  h
 c d   q    k  using the

   
inverse matrix
(iii)

TEACHING AND LEARNING
ACTIVITIES
2 x 2-1=2-1x 2= 1
Use the method of solving
simultaneous linear equations to
show that not all square matrices
have inverse matrices.
Using matrices and their respective
inverse matrices in the previous
method to relate to the formula.
Express each inverse matrix as a
multiplication of a matrix by a
number. Compare the scalar
multiplication to the original matrix
and discuss how the determinant is
obtained.
Discuss the condition for the
existence of inverse matrix.
Related to equal matrices by writing
down the simultaneous equations as
equal matrices first.
Discuss why:
 The use of inverse matrix is
necessary. Relate to solving linear
equations of type ax = b
 It is important to place the
inverse matrix at the right place on
both sides of the equation.
Relate the use of matrices to other
areas such as in business or
economy, science etc.
Carry
out
projects(electronic
spreadsheet)

STRATEGIES
-product
-identity matrix
-unit matrix
Vocabulary
-standard form
-single number
-inverse matrix
Vocabulary
-standard form
-single number
-scientific
notation
- matrix method
Teaching Aids
-flash card
-scientific Calculator
Moral Values
Cooperation, rational

Solve simultaneous linear
equations by the matrix method

6

LEARNING
AREA/WEEKS

LEARNING OBJECTIVS
(iv)

LEARNING
AREA/WEEKS
5. Variations
(Week 10 - 11)

LEARNING
OBJECTIVES
5.1 Understand and use the
concept of direct
variations

TEACHING AND LEARNING

LEARNING OUTCOMES

ACTIVITIES

Solve problems involving
matrices

LEARNING OUTCOME
(i) State the changes in a quantity with
respect to the changes in another
quantity, in everyday life situations
involving direct variation.
(ii) Determine from given information
whether a quantity varies directly as
another quantity.

TEACHING AND LEARNING
ACTIVITIES
Discuss the characteristics of the
graph of y against x when y �x.
Relate mathematical variation to other
area such as science and technology.
For example, the Charles Law or
motion of the simple pendulum.

(iv) Find the value of a variable in a
direct variations when sufficient
informations is given.
(v) Solve problems involving direct
variations for the followinf cases :
2

y �x; y �x ; y �x

3

STRATEGIES
Thinking Skills
-working out
mentally
-identifying
Relationship
- making inference
Teaching Strategies
-Contextual
learning
- Constructivism
- Mastery
learning
- Exploratory

(iii) Express a direct variations in the
form of equation involving two variables

For the cases

y �x n , n = 2,3,

1 Vocabulary
, - Direct variations
2 - quantity

discuss the characteristics of the graph
of y against x n .

1

- constant of variations
- variable
Teaching Aids
-flash card
-scientific
calculator

y �x 2
5.2 Understand and use the
concept of inverse
variation.

STRATEGIES

(i) State the changes in a quantity with
respect to changes in another quantity, in
everyday life situations involving
inverse variation.

Discuss the form of the graph of y

(ii) Determine from given information
whether a quantity varies inversely as

Relate to other areas like science and
technology. For example, Boyle’ Law.

against

1
1
when y � .
x
x

Moral Values
Rationality, courage
Thinking Skills
-working out
mentally

7

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

LEARNING OUTCOME
another quantity
(iii) Express as inverse variation in form
of equation involving two variables.
(iv) Find the value of a variable in an
inverse variation when sufficient
information in given
(v) Solve problems involving inverse
variations for the following cases :

1
1
y� ;y� 2;
x
x
1
1
y� 3;y� 1
x
x2

5. Variations
(Week 10 - 11)

5.3 Understand and use the
concept of joint
variation.

(i) Represent a joint variation by using
the symbol �for the following cases :
a) two direct variations
b) two inverse variations
c) a direct variations and an inverse
variation.
(ii) Express a joint variation in the form
of equation.
(iii) Find the value of a variable in joint
variations when sufficient information is
given.
(iv) Solve problems involving joint
variation

(19.3.2018 – 25.3.2018)
FIRST TERM HOLIDAY

TEACHING AND LEARNING
ACTIVITIES
For the cases y �

1
1
, n  2,3 and ,
xn
2

discuss characteristics of graph y
against

1
.
xn

Discuss joint variation for the three
cases in everyday life situations.
Relate to other areas like science and
technology.
For example:

STRATEGIES
-identifying
Relationship
- problem solving
Vocabulary
- inverse variation
Teaching Aids
-scientific
calculator
Moral Values
Diligence, moderation

V
I � means the current I varies Thinking Skills
-working out
R
directly as the voltage V and varies
inversely as the resistance R.

mentally
-identifying
Relationship
- problem solving
- decision making
Teaching Strategies
-Contextual
learning
- Constructivism
- Mastery
learning
- Exploratory
Vocabulary
- joint variation
Teaching Aids
-scientific
calculator
Moral Values
Patience, diligence

8

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

LEARNING OUTCOME

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES
6.1 Understand and use the
concept of quantity
represented by the
gradient of a graph.

LEARNING OUTCOME

6. Gradient and
area under a
graph.
( Week 12 - 13 )

(i) State the quantity represented
by the gradient of graph.
(ii) Draw the distance-time
graph, given:
a. a table of distance-time
values.
b. a relationship between distance
and time.
(iii) Find and interpret the
gradient of a distance-time
graph.
(iv) Find the speed for a period of
time from a distance-time
graph.
(v) Draw a graph to show the
relationship between two
variable representing certain
measurement and state the
meaning of its gradient.

6.2 Understand the concept
of quantity represent
any meaningful
quantity.

(i) State the quantity represented
by the area under a graph.
(ii) Find the area under a graph.
(iii) Determine the distance by
finding the area under the
following types of speed-time
graphs:

TEACHING AND LEARNING
ACTIVITIES

TEACHING AND LEARNING
ACTIVITIES
Use examples in various areas such
as technology and social science.
Compare and differentiate between
distance-time graph and speed-time
graph.

STRATEGIES

STRATEGIES
CCTS
i)Thinking skills :
- interpreting
- generalization
-drawing diagram.
ii) Teaching strategies:
- discussion

Use real life situations such as
travelling from one place to another
by train or by bus.
Use examples in social science and
economy.

Vocabulary:
- gradient
- distance-time
-speed-time
-acceleration
-deceleration
-constant speed
-distance
-average speed
-uniform speed
Moral value:
- Cooperation
- rationality

Discuss that in certain cases, the area
under a graph may not represent any
meaningful quantity.
For example :
The area under the distance-time
graph.
Discuss the formula for finding the
area under a graph involving:
 a straight line which is

Teaching aids:
- CD courseware

9

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

LEARNING OUTCOME
a) v = k (uniform speed)
b) v = kt
c) v = kt + h
d) a combination of the above.
(iv) Solve problems involving
gradient and area under a graph.

LEARNING
AREA/WEEKS
7. Probability

LEARNING
OBJECTIVES
7.1 Understand and use the
concept of probability
of an event

LEARNING OUTCOME
(i)

Determine the sample
space of an experiment
with equally likely
outcomes.

(ii)

Determine the probability
of an event with
equiprobable sample
space.

(iii)

Solve problems involving
probability of an event

(i)

State the complement of an
event in :
a) words
b) set notation

( Week 14-15 )

7.2 Understand and use the
concept of probability of
combined event

7.3 Understand and use the
concept of probability of
combined event

(ii)

Find the probability of the
complement of an event

(i)

List the outcomes for
events:
a) A or B as element of
set A  B
b) A and B as elements
of set
A ∩ B.

(ii)

Find the probability by

TEACHING AND LEARNING
ACTIVITIES
parallel to the x-axis.
 a straight line in the form of
y = kx + h.
 a combination of the above.

STRATEGIES

TEACHING AND LEARNING
ACTIVITIES
Discuss equiprobable sample space
through concrete activities, begin
with simple cases ( tossing fair coin)
Use tree diagrams to obtain sample
space for tossing a fair coin or tossing
a fair die activity.
Produce P(A) = 1 and P(A) = 0.
Include events in real life situations
such as winning or losing a game and
passing or failing an exam.
Use real life situations to show the
relationship between
 A or B and A  B
 A and B and A ∩ B.

STRATEGIES

An example of situation being chosen
to be a member of an exclusive club
with restricted conditions.
Use tree diagrams& coordinate planes
to find outcomes of combined events.
Use two-way classification tables of
events from newspaper articles or
statistical data to find probability of
combined events. Ask students to
create tree diagram from these tables.
Example(two-wayclassification table)
Means of going to work
Officers car
bus
Others
Men
56
25
83
Women 50
42
37

Thinking Skills
-working out
mentally
-identifying
relationship
Teaching Strategies
- Constructivism
- Exploratory
Vocabulary
-equally likely
-equiprobably sample
space
-tree diagram
- complement of an
event
Teaching Aids
-coins
-dice
Moral Values
Cooperation, rational
Thinking Skills
-working out
mentally
-making inference
Teaching Strategies
- Constructivism
- Contextual Learning

10

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

LEARNING OUTCOME
listing the outcomes of the
combined event:
a) A or B
b) A and B
(iii) Solve problems involving
probability of combined event.

LEARNING
AREA/WEEKS
8.Bearing
(Week 16 - 17)

LEARNING
OBJECTIVES
8.1 Understand and use the
concept of bearing

LEARNING OUTCOME
(i) Draw and label the eight main
compass direction:
b. North,South,East,West
c. North-East, North-West
d.
South –East, South-West.
e.
(ii) State the compass angle of any
compass direction.
(iii) Draw a diagram of a point which
shows the direction of B relative to
another point A given the bearing of
B from A.
(iv) State the bearing of point A from
point B based on given information.

1.5.2017 – LABOUR DAY

(v) Solve problems involving bearing.

TEACHING AND LEARNING
ACTIVITIES
Discuss:
Situation where decisions to be made
based on probability, example in
business, as determining the value for
a specific insurance policy and time
the slot for TV advertisements.
The statement “ probability is the
underlying language of statistics”.
TEACHING AND LEARNING
ACTIVITIES
Carry out activities or games
involving finding direction using a
compass, such as treasure hunt or
scavenger hunt. It can also be about
locating several points on a map.
Discuss the use of bearing in real life
situation. For example, in map reading
and navigation.

STRATEGIES
Vocabulary
- combined event
Teaching Aids
- CD-ROM
- worksheets
STRATEGIES
Thinking Skills
-describing
-interpreting
-drawing diagram
-problem solving
Teaching Strategies
-Contextual
learning
- Constructivism
- Mastery learning
Vocabulary
-north-east
-south-east
-north-west
-south-west
-compass angle
-bearing
Teaching Aids
-compass. Map, scientific
calculator, geometry set,
worksheets.
Moral Values
Cooperation, rational

11

9. Earth as a sphere
(Week 18 – 19)

9.1 Understand and use the
concept of longitude.

i) Sketch a great circle through the north
and south poles.
ii) State the longitude of a given point.

MID YEAR EXAMINATION
(Week 20 – 22)
(9.6.2018 – 24.6.2018 )
MID YEAR HOLIDAY
LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

Models such as globes should be used.
Introduce the meridian through
Greenwich in England as the
Greenwich Meridian with longitude
0˚.

iii) Sketch and label the a meridian with
the longitude given.

Thinking Skills
-working out
Mentally
-classifying
-categorizing
Teaching Strategies
- Constructivism
- Exploratory
Teaching Aids
-globe or map

LEARNING OUTCOME

TEACHING AND LEARNING
ACTIVITIES

STRATEGIES

12

9. Earth as a sphere
(Week 18 – 19)

9.1 Understand and use the
concept of longitude.

i) Sketch a great circle through the north
and south poles.
ii) State the longitude of a given point.

MID YEAR EXAMINATION
(Week 20 – 22)
(9.6.2018 – 24.6.2018 )
MID YEAR HOLIDAY

9. Earth as a sphere
(Week 23 – 24)

2
3
4
5
9.2 Understand and use the
concept of latitude.

Models such as globes should be used.
Introduce the meridian through
Greenwich in England as the
Greenwich Meridian with longitude
0˚.

iii) Sketch and label the a meridian with
the longitude given.

Teaching Strategies
- Constructivism
- Exploratory
Teaching Aids
-globe or map

iv) Find the difference between two
longitudes.
i) Sketch a circle parallel to the equator.
ii) State the latitude of a given point.
iii) Sketch and label a parallel of
latitude.
iv) Find the difference between two
latitudes

Discus that:
 All points on a meridian have
the same longitude
 There are two meridians on a
great circle through both
poles
 Meridians with longitudes
x˚E (0r W) and 180˚ - x˚)W
(or E) form a great circle
through both poles.
Emphasize that
 The latitude of the equator is
0˚
 Latitude ranges from 0˚ to
90˚ ( or S )
Involve actual places on the earth.
Express the difference between two
latitudes with an angle in the range of
0˚ < x < 180˚.

9.3 Understand the concept
of location of a place

Thinking Skills
-working out
Mentally
-classifying
-categorizing

i) State the latitude and longitude of a
given place
ii) Mark the location of a place

Moral Values
Cooperation, rational
Thinking Skills
-compare and contrast
-constructing
Teaching Strategies
- Constructivism
- Exploratory
Teaching Aids
-globe or map
Moral Values
Cooperation, rational

Use a globe or a map to find locations
of cities around the world

Thinking Skills
-working out
Mentally
-describing
-giving opinion

Use a globe or a map to name a place
given its location.

Teaching Strategies
- Constructivism

13

LEARNING
AREA/WEEKS
9. Earth as a sphere
(Week 23 – 24)

LEARNING
OBJECTIVES
9.4 Understand and use the
concept of distance on
the surface of the earth
to solve problems

LEARNING OUTCOME
i) Find the length of an arc of a great
circle in nautical mile, given the
subtended angle at the centre of the earth
and vice versa
ii) Find the distance between two points
measured along a meridian, given the
latitudes of both points.
iii) Find latitude of point given latitude
of another point and distance between
two points along same meridian.
iv) Find the distance between two points
measured along the equator, given the
longitudes of both points
v) Find the longitude of a point given the
longitude of another point and the
distance between the two points along
the equator.
vi) State relation between radius of earth
and the radius of a parallel of latitude.
vii) State the relation between the length
of an arc on the equator between two
meridians and length of corresponding
arc on a parallel of latitude.
viii) Find distance between two points
measured along a parallel of latitude
ix) Find the longitude of a point given
the longitude of another point and the
distance between the two points along a
parallel of latitude.
x) Find the shortest distance between
two points on the surface of the earth.
xi) Solve problems involving:
a) distance between two points
b) traveling on surface of earth

TEACHING AND LEARNING
ACTIVITIES
Use a globe to find the distance
between two cities or towns on the
same meridians.

STRATEGIES
Thinking Skills
-working out
Mentally
-giving opinion
Teaching Strategies
- Constructivism
- Exploratory

Sketch the angle at the centre of the
earth that is subtended by the arc
between two given points along the
equator. Discuss how to find the value
of this angle.

Vocabulary
Nautical mile
Teaching Aids
-globe or map

Use models such as the globe to find
relationships between the radius of the
earth and radii parallel of latitudes

Find the distance between two cities
or towns on the same parallel of
latitude as a group project.

Moral Values
Cooperation, rational
Thinking Skills
-working out
Mentally
-constructing
-problem solving
Teaching Strategies
- Constructivism
- Exploratory

Use the globe and a few pieces of
string to show how to determine the
shortest distance between two points
on the surface of the earth.

Teaching Aids
-globe or map
Moral Values
Cooperation, rational

14

LEARNING
AREA/WEEKS

LEARNING
OBJECTIVES

LEARNING OUTCOME

TEACHING AND LEARNING
ACTIVITIES

STRATEGIES

15

LEARNING
AREA/WEEKS
10. Plans and
elevations
(Week 25 - 26)

LEARNING OBJECTIVES

LEARNING OUTCOME

10.1 Understand and use the
concept of orthogonal
projection

(i)

Identify orthogonal projection.

(ii)

Draw orthogonal projection,
given an object and a plan.

(iii)

10.2 Understand and use the
concept of plan and
elevation

(i)

Draw the plan of a solid
object.

(ii)

Draw
a) the front elevation
b) side elevation of a solid
object.

(iii)

(iv)

3.
Transformation III
(Week 27 – 28)

3.1 Understand and use the
concept of combination of two
transformations.

I.

Determine the difference
between an object and its
orthogonal projection with
respect to edges and angles.

Draw
a) the plan
b) the front elevation
c) the side elevation
of a solid object to scale.
Solve problems involving plan
and elevation.

Determine the image of an object
under combination of two isometric
transformations.
II.
Determine the image of an object
under combination of:
a) two enlargements
b) an enlargement and an
isometric transformation.
III. Draw the image of an object under

TEACHING AND LEARNING
ACTIVITIES
Use models, blocks or plan and
elevation kit.
Carry out activities in groups where
students combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevations for these
models.
Use models to show that it is
important to have a plan and at least
two side elevations to construct a
solid object.
Carry out group project:
Draw plan and elevations of
buildings or structures, for example
students’ or teacher’s dream home
and construct a scale model based
on the drawings. Involve real life
situations such as in building
prototypes and using actual home
plans.

STRATEGIES
Thinking Skills
- identifying
relationship
- describing
- problem solving
- drawing diagrams
Teaching Strategies
- Contextual
learning
- Constructivism
- Mastery
learning
Vocabulary
Orthogonal
Projection
Plan
Front elevation
Side elevation
Teaching Aids
models
blocks
plan and
elevation kit
Moral Values
Cooperation, rational,
justice, freedom, courage

Relate to transformations in real life
situation such as tessellation
patterns on walls, ceiling or floors.
Explore combined transformation
using the graphing calculator, the
Geometer’s Sketchpad, or the
overhead projector and
transparencies.

Thinking Skill
Working out mentally
Identify relationship
Translating
Problem solving
Drawing diagram
Teaching Strategies
Contextual learning

16

LEARNING
AREA/WEEKS
10. Plans and
elevations
(Week 25 - 26)

LEARNING OBJECTIVES
10.1 Understand and use the
concept of orthogonal
projection

LEARNING OUTCOME
(i)

Identify orthogonal projection.

(ii)

Draw orthogonal projection,
given an object and a plan.

(iii)

10.2 Understand and use the
concept of plan and
elevation

(i)

Draw the plan of a solid
object.

(ii)

Draw
a) the front elevation
b) side elevation of a solid
object.

(iii)

(iv)

LEARNING
AREA/WEEKS

LEARNING OBJECTIVES
3.2 Understand and use the
concept of combination of two
transformations.

Determine the difference
between an object and its
orthogonal projection with
respect to edges and angles.

Draw
a) the plan
b) the front elevation
c) the side elevation
of a solid object to scale.
Solve problems involving plan
and elevation.

combination of two transformations.
LEARNING OUTCOME
III. State the coordinates of the image of a
point under combined transformation
IV. Determine whether combined
transformation AB is equivalent to
combined transformation BA.
V. Specify two successive

TEACHING AND LEARNING
ACTIVITIES
Use models, blocks or plan and
elevation kit.
Carry out activities in groups where
students combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevations for these
models.
Use models to show that it is
important to have a plan and at least
two side elevations to construct a
solid object.
Carry out group project:
Draw plan and elevations of
buildings or structures, for example
students’ or teacher’s dream home
and construct a scale model based
on the drawings. Involve real life
situations such as in building
prototypes and using actual home
plans.

STRATEGIES
Thinking Skills
- identifying
relationship
- describing
- problem solving
- drawing diagrams
Teaching Strategies
- Contextual
learning
- Constructivism
- Mastery
learning
Vocabulary
Orthogonal
Projection
Plan
Front elevation
Side elevation
Teaching Aids
models
blocks
plan and
elevation kit
Moral Values
Cooperation, rational,
justice, freedom, courage

TEACHING AND LEARNING
ACTIVITIES
Investigate the characteristics of an
object and its image under
combined transformation.
Carry out projects to design patterns
using combined transformations that

Mastery learning
STRATEGIES
Conceptual Learning
Constructivism
Cooperative Learning
Enquiry
Vocabulary

17

LEARNING
AREA/WEEKS
10. Plans and
elevations
(Week 25 - 26)

LEARNING OBJECTIVES
10.1 Understand and use the
concept of orthogonal
projection

LEARNING OUTCOME
(i)

Identify orthogonal projection.

(ii)

Draw orthogonal projection,
given an object and a plan.

(iii)

10.2 Understand and use the
concept of plan and
elevation

Determine the difference
between an object and its
orthogonal projection with
respect to edges and angles.

(i)

Draw the plan of a solid
object.

(ii)

Draw
a) the front elevation
b) side elevation of a solid
object.

(iii)

(iv)

Draw
a) the plan
b) the front elevation
c) the side elevation
of a solid object to scale.
Solve problems involving plan
and elevation.

transformations in a combined
transformation given the object and
the image.
VI. Specify a transformation which is
equivalent to the combination of two
isometric transformations.
Solve problems involving transformation

TEACHING AND LEARNING
ACTIVITIES
Use models, blocks or plan and
elevation kit.
Carry out activities in groups where
students combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevations for these
models.
Use models to show that it is
important to have a plan and at least
two side elevations to construct a
solid object.
Carry out group project:
Draw plan and elevations of
buildings or structures, for example
students’ or teacher’s dream home
and construct a scale model based
on the drawings. Involve real life
situations such as in building
prototypes and using actual home
plans.

STRATEGIES
Thinking Skills
- identifying
relationship
- describing
- problem solving
- drawing diagrams
Teaching Strategies
- Contextual
learning
- Constructivism
- Mastery
learning
Vocabulary
Orthogonal
Projection
Plan
Front elevation
Side elevation
Teaching Aids
models
blocks
plan and
elevation kit
Moral Values
Cooperation, rational,
justice, freedom, courage

can be used as decorative purposes.
These projects can then be presented
in classroom with the students
describing or specifying the
transformations involved.
Use the Sketchpad to prove the
single transformation which is
equivalent to the combination of

-Combined transformation
-equivalent
-reflection
-translation
-enlargement
-rotation
Teaching aids
- Geometer’s

18

LEARNING
AREA/WEEKS
10. Plans and
elevations
(Week 25 - 26)

LEARNING OBJECTIVES
10.1 Understand and use the
concept of orthogonal
projection

LEARNING OUTCOME
(i)

Identify orthogonal projection.

(ii)

Draw orthogonal projection,
given an object and a plan.

(iii)

10.2 Understand and use the
concept of plan and
elevation

Determine the difference
between an object and its
orthogonal projection with
respect to edges and angles.

(i)

Draw the plan of a solid
object.

(ii)

Draw
a) the front elevation
b) side elevation of a solid
object.

(iii)

(iv)

Draw
a) the plan
b) the front elevation
c) the side elevation
of a solid object to scale.
Solve problems involving plan
and elevation.

TEACHING AND LEARNING
ACTIVITIES
Use models, blocks or plan and
elevation kit.
Carry out activities in groups where
students combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevations for these
models.
Use models to show that it is
important to have a plan and at least
two side elevations to construct a
solid object.
Carry out group project:
Draw plan and elevations of
buildings or structures, for example
students’ or teacher’s dream home
and construct a scale model based
on the drawings. Involve real life
situations such as in building
prototypes and using actual home
plans.

STRATEGIES
Thinking Skills
- identifying
relationship
- describing
- problem solving
- drawing diagrams
Teaching Strategies
- Contextual
learning
- Constructivism
- Mastery
learning
Vocabulary
Orthogonal
Projection
Plan
Front elevation
Side elevation
Teaching Aids
models
blocks
plan and
elevation kit
Moral Values
Cooperation, rational,
justice, freedom, courage

two isometric transformations.

Sketchpad
- graphing calculator
-graph paper
-a pair of compass
-ruler
Moral Values
Cooperation, Courage,
Rational Mental &

19

LEARNING
AREA/WEEKS
10. Plans and
elevations
(Week 25 - 26)

LEARNING OBJECTIVES
10.1 Understand and use the
concept of orthogonal
projection

LEARNING OUTCOME
(i)

Identify orthogonal projection.

(ii)

Draw orthogonal projection,
given an object and a plan.

(iii)

10.2 Understand and use the
concept of plan and
elevation

Determine the difference
between an object and its
orthogonal projection with
respect to edges and angles.

(i)

Draw the plan of a solid
object.

(ii)

Draw
a) the front elevation
b) side elevation of a solid
object.

(iii)

(iv)

Draw
a) the plan
b) the front elevation
c) the side elevation
of a solid object to scale.
Solve problems involving plan
and elevation.

TEACHING AND LEARNING
ACTIVITIES
Use models, blocks or plan and
elevation kit.
Carry out activities in groups where
students combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevations for these
models.
Use models to show that it is
important to have a plan and at least
two side elevations to construct a
solid object.
Carry out group project:
Draw plan and elevations of
buildings or structures, for example
students’ or teacher’s dream home
and construct a scale model based
on the drawings. Involve real life
situations such as in building
prototypes and using actual home
plans.

STRATEGIES
Thinking Skills
- identifying
relationship
- describing
- problem solving
- drawing diagrams
Teaching Strategies
- Contextual
learning
- Constructivism
- Mastery
learning
Vocabulary
Orthogonal
Projection
Plan
Front elevation
Side elevation
Teaching Aids
models
blocks
plan and
elevation kit
Moral Values
Cooperation, rational,
justice, freedom, courage
Physical Cleanliness

20

LEARNING
AREA/WEEKS
10. Plans and
elevations
(Week 25 - 26)

LEARNING OBJECTIVES
10.1 Understand and use the
concept of orthogonal
projection

LEARNING OUTCOME
(i)

Identify orthogonal projection.

(ii)

Draw orthogonal projection,
given an object and a plan.

(iii)

10.2 Understand and use the
concept of plan and
elevation

(i)

Draw the plan of a solid
object.

(ii)

Draw
a) the front elevation
b) side elevation of a solid
object.

(iii)

(iv)

(18.8.2018 – 26.8.2018)
SECOND TERM HOLIDAY
31.8.2018 – NATIONAL DAY
SPM TRIAL EXAMINATION

Determine the difference
between an object and its
orthogonal projection with
respect to edges and angles.

Draw
a) the plan
b) the front elevation
c) the side elevation
of a solid object to scale.
Solve problems involving plan
and elevation.

TEACHING AND LEARNING
ACTIVITIES
Use models, blocks or plan and
elevation kit.
Carry out activities in groups where
students combine two or more
different shapes of simple solid
objects into interesting models and
draw plans and elevations for these
models.
Use models to show that it is
important to have a plan and at least
two side elevations to construct a
solid object.
Carry out group project:
Draw plan and elevations of
buildings or structures, for example
students’ or teacher’s dream home
and construct a scale model based
on the drawings. Involve real life
situations such as in building
prototypes and using actual home
plans.

STRATEGIES
Thinking Skills
- identifying
relationship
- describing
- problem solving
- drawing diagrams
Teaching Strategies
- Contextual
learning
- Constructivism
- Mastery
learning
Vocabulary
Orthogonal
Projection
Plan
Front elevation
Side elevation
Teaching Aids
models
blocks
plan and
elevation kit
Moral Values
Cooperation, rational,
justice, freedom, courage

REVISION SPM TRIAL WEEK 29
REVISION FOR SPM 2018
UNTIL WEEK 40

SPM EXAMINATION 2018
5.11.2018 – 4.12.2018

13.8.2018 (WEEK 30)
21

SMK METHODIST ACS (M) JALAN LINTANG 70000 SEREMBAN NEGERI
SEMBILAN

RANCANGAN PENGAJARAN TAHUNAN
YEARLY LESSON PLAN
MATEMATIK TINGKATAN 5
TAHUN 2018

22