Yearlyplan mathF

8/14/2019 Yearlyplan mathF

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1

Yearly Plan Mathematics Form 5 (2009)

Week

No

Learning ObjectivesPupils will be taught

to.....

Learning Outcomes

Pupils will be able to

No of

Periods

Suggested Teaching & Learning

activities/Learning Skills/Values

Points to Note

Learning Area : NUMBER BASES -- 2 weeks

First Term

1

5/1-9/1/09

1. Understand and use

the concept of numberin base two, eight and

five.

(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) fivein expanded notation

1

1

2

Use models such as a clock face or a

counter which uses a particular

number base.

Discuss

- Dicuss digits used- Place valuesin the number system with a

particular number base.

Skill : Interpretation, observe

connection between base two, eightand five.

Use of daily life examples

Values : systematic, careful, patient

Emphasis the ways to read numbers in

variours bases.

Give examples:

Numbers in base two are also know as

binary numbers.

Expanded notation

Give examples

2

12/1-

16/1/09

(iv) Convert a number in base:

a) two

b) eight

c) five

to a number in base ten and

vice versa.

2 Use number base blocks of twos,

eights and fives.

Perform repeated division to convert a

number in base ten to a number in other

bases.

Give examples.


2/22

2

Week

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Learning Outcomes

Pupils will be able toNo of

Periods


activities/Learning Skills/ValuesPoints to Note

(v) Convert a number in a certain

base to a number in another

base.

(vi) Perform computations

involving :

a) addition

b) subtration

of two numbers in base two

3

1

Discuss the special case of

converting a number in base two

directly to a number in base eightand vice versa.

Skill : Interpretation, convertingnumbers to base of two, eight, five

and then.

Use of daily life examples

Values : systematic, careful, patient

Limit conversion of numbers to base two,

eight and five only.

The usage of scientific calculator in

performing the computitations.

Topic 2 : Graphs of Functions II --- 3 weeks

319/1-

23/1/0

9

2.1 Understand

and use theconcept of

graphs of

functions

(i) Draw the graph of a:

a) linear function :y = ax + b, where a

and b are constant;

b) quadratic function

cbxaxy 2 ,where a, b and c are

constans, 0a c) cubic function :

dcxbxaxy 23 ,

where a, b, c and d are

constants, 0a

d) reciprocal function

x

ay , where a is a

constants, 0a

2 Explore graphs of functions using

graphing calculator or the GSP

Compare the characteristic of

graphs of functions with different

values of constants.

Values : Logical thinking

Skills : seeing connection, using

the GSP

Questions for 1..2(b) are given in the

form of 0 bxax ; a and b arenumerical values.

Limit cubic functions.

Refer to CS.


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3

Week

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Learning Outcomes


Periods



426-30/1/09

(ii) Find from the graph

a) the value ofy, given avalue ofx

b) the value(s) ofx,given a value ofy

(iii) Identify:a) the shape of graph

given a type of

function

b) the type of functiongiven a graph

c) the graph given a

function and viceversa

(iv) Sketch the graph of agiven linear, quadratic,

cubic or reciprocalfunction.

CUTI TAHUN BARU CINA

1

2

2

Play a game or quiz

For certain functions and some valuesofy, there could be no corresponding

values ofx.

Limit the cubic and quadraticfunctions.Refer to CS.

Limit cubic functions.

Refer to CS.

5

2/2-6/2/09

2.2 Understandand use the

concept of thesolution of an

equation bygraphicalmethod.

(i) Find the point(s) ofintersection of two graphs

(ii) Obtain the solution of an

equation by finding thepoint(s) of intersection oftwo graphs

(iii) Solve problems involvingsolution of an equation by

1

1

2

Explore using graphing calculatorof GST to relate thex-coordinate of

a point of intersection of twoappropriate graphs to the solution

of a given equation. Makegeneralisation about the point(s) ofintersection of the two graphs.

Use everyday problems.

Use the traditional graph plottingexercise if the graphing calculator or

the GSP is unavailable.

Involve everyday problems.


4/22

4

Week

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Learning Outcomes


Periods



graphical method. Skills : Mental process

6

9/2-13/2/09

( Mid

Semester 1

exam 10/2-13/2/09)

2.3 Understand and

use the concept of the

region representing

inequalities in two

variables.

(i) Determine whether a given

point satisfies

a) baxy or baxy or baxy

(ii) Determine the position of a

given point relative to the

equation baxy

(iii) Identify the region

satisfying baxy orbaxy

(iv) Shade the regions

representing the inequalities

a) baxy or baxy b) baxy or baxy

(v) Determine the region which

satisfy two or more

simultaneous linear

inequalities.

2

2

2

Include situations involving ax ,ax , ax , ax or ax .

Values: Making conclusion,

connection and comparison, careful

Emphasise on the use of dashed and solid

line as well as the concept of region.


5/22

5

WeekNo

Learning ObjectivesPupils will be taughtto.....

Learning OutcomesPupils will be able to

No of

Periods



Points to Note

Topic/Learning Area :

TRANSFORMATIONS III ( 3 weeks )

7

16/2-

20/2/09

3.1 Understandingand use of theconcept of

combination of

twotransformations.

(i) determine the image of anobject under combination oftwo isometric

transformations.

1 using CD-Rom interactiveactivities.

Everyday life example:around the school.

Recall the types oftransformations:

- translation- rotation- reflection- enlargement- isometric

transformation

(ii) determine the image of anobject under combination of:

a. two enlargementsb. an enlargement and and an

isometric transformation.

2 using Geometers Sketchpad. CD-Rom Give variety of examples to

show an enlargement and

isometric transformation.


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Points to Note

(iii) Draw the image of an objectunder combination of two

transformations.(iv) State the coordinates of the

image of a point under

combined transformations.

2 Give examples on theblackboard and students are

asked to draw the imageunder 2 transformations

Tr. will state the coordinatesof the image of a point under

combined transformations.

8

23/2-

27/2/09

(v) Determine whethercombined transformation AB

is equivalent to combined

transformation BA.

3 Using Maths exercise books(grids)

Do exercises from thetextbooks

(vi) specify two successivetransformations in a

combined transformation

given the object and theimage.

2 Outdoor activity studentsare brought to specific site of

the school compound and ask

to identify the two successive

transformations : pictures

should consist of an object

and an image.

9

2/3-

6/3/09

(vii) Specify a transformationwhich is equivalent to the

combination of two

isometric transformations.

(viii) Solve problems involvingtransformations.

5

Classroom activities useGSP and CD-ROM

(Multimedia Gallery)

To specify isometrictransformation

Different examples to begiven

Various problem solvingquestions to be given

- limit to translation, reflation & rotation.


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Points to Note

Topic/Learning Area :

MATRICES ( 4 weeks )

10

9/3-13/3/09

4.1 Understand anduse the concept

of matrix.

(i) Form a matrix from giveninformation.

(ii) Determine:a. the number of rowsb. the number of columnsc. the order of a matrix(iii) Identify a specific element in

a matrix

1 Understanding the concept ofmatrices through daily

examples:

- price of food on a menu- a contingent of altelitic- seating of students in

class

- mark sheet of students Introduce the order (mxn) of

a matrix Class activity students arerequested to identify the

students seating position in

class

Other examples give

* m represents row

* n represents column

10 4.2 Understand anduse the conceptof equal matrices.

(i) Determine whether twomatrices are equal.

(ii) Solve problems involvingequal matrices.

2 Teacher gives examples oftwo equal matrices and

discusses equal matrices in

terms of the corresponding

elements.

Different problems given tosolve equal matrices.


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8

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Points to Note

10

4.3 Perform additionand subtraction

on matrices.

(i) Relate to real life situationssuch as keeping score of

medal tally or points in

sports.

(ii) Find the sum or thedifference of two matrices.

(iii) Perform addition andsubtraction on a fewmatrices.

(iv) Solve matrix equationsinvolving addition and

subtraction.

CUTI PERTENGAHAN

PENGGAL 1 [16/3-20/3/09]

2 Teacher shows the examplesfrom the textbook to

determine how addition orsubtraction can be performed

on 2 given matrices.

Examples given to find theaddition and subtraction of

two matrices.

Examples given to solvematrix equations involving

additions and subtractions

To include finding values ofunknown elements

limit to not more than 3 rowsand 3 columns.

11

23/3-

27/3/09

4.4 PerformMultiplication of

a matrix by a

number.

(i) Multiply a matrix by anumber.

(ii) Express a given matrix as amultiplication of another

matrix by a number.

(iii) Perform calculation onmatrices involving addition,subtraction and scalarmultiplication.

(iv) Solve matrix equationsinvolving addition,

subtraction and scalarmultiplication.

2 Teacher shows examples onscalar multiplication of

matrix:

- give examples of real lifesituations such as in

industrial productions.

examples given on thecalculation of matrices

involving addition,

subtraction, and scalar

multiplication.

Examples given on problemsolving questions.

To include finding values ofunknown elements.


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9

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Points to Note

11 4.5 Performmultiplication of

two matrices.

(i) determine whether twomatrices can be multiplied

and state the order of the

product when the two

matrices can be multiplied.

(ii) Find the product of twomatrices.

(iii) Solve matrix equationsinvolving multiplication of

two matrices.

3 Teacher gives real lifesituations. Examples:-

-

to find the cost ofmeals in the

restaurant

- teacher shows how 2matrices can be

multiplied.

Examples given for theproduct of two matrices.

Examples given on problemsolving involving

multiplication of 2 matrices.

Limit to not more than 3 rowsand 3 columns

Limit to 2 unknown elements

12

30/3-

3/4/09

4.6 Understand anduse the conceptof identifymatrix.

(i) determine whether a givenmatrix is an identity matrixby multiplying it to anothermatrix.

(ii) Write identity matrix of anyorder.

(iii) Perform calculationinvolving identity matrices.

2 Teacher discusses theproperty of the number as an

identity for multiplication of a

number.

Teacher introduces identitymatrix or unit matrix.

Teacher gives examples ofidentity matrix of any order.

Teacher discusses theproperties:

- AI = A- IA = A

Unit matrix is denoted by I.

Limit to 3 rows and 3 columns.


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10

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Points to Note

12

4.7 Understand anduse the concept

of inverse matrix.

(i) Determine whether a

2 X 2 matrix is the

inverse matrix ofanother 2 X 2

matrix.

(iii) Find the inverse matrix of a2 X 2 matrix using:

a. the method of solvingsimultaneous linear

equations

b. a formula

3 teacher introduces theconcept of inverse matrix and

its denotion. Examples given on problemsolving questions involving

matrix:

- using simultaneouslinear equations

- using a formula

-1

AA = I

13

6/4-

10/4/09

4.8 Solvesimultaneouslinear equationsby using

matrices.

(i) Write simultaneous linearequations in matrix form.

(ii) Find the matrix pq

in

a b p h

c d q k

using

the inverse matrix.

(iii) solve simultaneous linearequations by the matrix

method.

(iv) Solve problems involvingmatrices.

5 Teacher shows examples howto write simultaneous linear

equations in matrix form

To solve simultaneous linearequations by using inverse

matrix

Project involving matricesusing electronic spreadsheet

to be given to students.

* limit to 2 unknowns.


11/22

11

Week

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Learning Objectives

Pupils will be taught

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Points to Note

Topic/Learning Area : 5. VARIATIONS

(1 Weeks)

14

13/4-

17/4/09

5.1 Understand and

use the concept of

direct variation

(i) State the changes in aquantity with respect to thechanges in another quantity,

in everyday life situations

involving direct variation.(ii) Determine from given

information whether aquantity.

(iii) Express a direct variation inthe form of equation

involving two variables.

(iv) Find the value of a variablein a direct variation when

sufficient information isgiven.

(v) Solve problems involvingdirect variation for the

following cases:

y x ; y x2

; y x3

;

y x1/2

.

1

1

Discuss the characteristics of the graph

of y agains x when y x.

Relate mathematical variation to

Charless Law or the mation of the

simple pendulum.

Discuss the characteristics of the graphs

of y against xn.

Communicative skills

Coorperation an d systematic

Y varies directly as x , yx.

yxn

, limit n to 2, 3 and

Y = kx where k is the constant of

variation.


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Points to Note

15

20/4-24/4/09

5.2 Understand anduse the concept of

inverse variationi) State the changes in a

quantity with respect tochanges in another

quantity, in everyday

life situations involving

inverse variation.

ii) Determine form giveninformation whether a

quantity vaqries

inversely as another

quantity.

iii) Express an inversevariation in the form of

equation involving twovariables.

iv) Find the value of avariable in an inverse

variation when

sufficient information

is given.

v) Solve problemsinvolving inverse

variation for the

following cases:

y 1/x; y 1/x2

y 1/x3; y 1/x1/2

1

1

Discuss the the form of the graph and

relates it to science, eg. Boyles Law.

For cases y 1/xn , n = 2,3 and ,discuss the characteristics of the graph of

y against 1/xn

Graph drawing skill

Be straight and honest.

Y varies inversely as x if and only if xy

is a constant.

y 1/x

For the cases y 1/xn, limit n to 2,3 and

If y 1/x, then y = k/x, where k is the

constan t of variation.

Use:

Y = k/x or

x1y1=x2 y2to get the solution.


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Points to Note

15


joint variation

(i) Represent a joint

variation by using the

symbol

for thefollowing cases:

a) two direct variations

b) two inverse

variations

c) a direct variation

and an inverse

variation.

(ii) Express a jointvariation in the form of

equation.(iii) Find the value of a

variable in a joint

variation when

sufficient information

is given.

(iv) Solve problemsinvolving joint

variation.

1

1

1

Discuss joint variation for the three cases

in everyday life situations.

Relate to science, eg. Ohms Law.

For the cases y xn zn,Y 1/ xn zn and y xn / zn,

Limit n to 2,3 and .


14/22

14

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Points to Note

Topic/Learning Area 6: GRADIENT & AREA

UNDER A GRAPH --- 3 weeks16

27/4-30/4/09

17

18-20

6.1 Understand and

use the concept ofquantity represented

by the gradient of a

graph

(i) State the quantity represented

by the gradient of a graph

(ii) Draw the distance-time

graph, given:a) a table of distance-time

values

b) a relationship betweendistance and time

(iii) Find and interpret thegradient of a distance-time graph

(iv) Find the speed for a period

of time from a distance-timegraph

(v) Draw a graph to show therelationship between two

variables representing certainmeasurements and state the

meaning of its gradient

ULANGKAJI [4/5-

8/5/09

PEPERIKSAAN

PENGGAL 1

[11/5-29/5/09

1

2

2

2

2

Use examples in various areas such

as technology and social science

Use of daily life examples like

speed of a car, Formula One Grand

Prix, a sprinter

Compare and differentiate between

distance-time graph and speed-time

graph

Use real life situations such as

traveling from one place to anotherby train or by bus.

Use examples in social science and

economy, for example, the

increase in population in certain

years

Limit to graph of a straight line.

The gradient of a graph represents the

rate of change of a quantity on the

vertical axis with respect to the change

of another quantity on the horizontal

axis. The rate of change may have a

specific name for example speed for a

distance-time graph.

Emphasise that:Gradient = change of distance

Time

= speed

Include graphs which consists of a

combination of a few straight lines.

For example,

Time, t

Distance, s


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Points to Note

21-22

15/6-26/6/09

6.2 Understand theconcept of quantity

represented by the area

under a graph

(i) State the quantity representedby the area under a graph

(ii) Find the area under a graph

(iii) Determine the distance by

finding the area under thefollowing of speed-time graphs: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.

1

2

4

2

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 parallel tothe x-axis

A straight lien in the form ofy=kx+ h

A combination of the above.

Include speed-time and acceleration-

time graphs.

Limit to graph of a straight line or a

combination of a few straight lines.

V represents speed, t represents time, h

and k are constants.

For example:

Speed, v

time, t


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16

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Points to Note

Topic/Learning Area : PROBABALITY II

Second Term --- 2 weeks

23

29/6-

3/7/09


probability of an

event.

(i) Determine the sample space

of an experiment withequally likely outcomes.

(ii) Determine the probability of

an event with equiprobablesample space.

(iii)Solve problems involvingprobability of an event.

1

1

1

Discuss equiprobable sample space

through concrete activities and begin

with simple cases such as tossing a

fair coin.

Use tree diagrams to obtain sample

space for tossing a fair coin or

tossing or tossing a fair dice

activities. The Graphing calculator

may also be used to simulate theseactivities.

Discuss events that produce

P(A) = 1 and P(A) = 0

Limit to sample space with equally

likely outcomes.

A sample space in which each outcomes

is equally likely is called equiprobable

sample space.

The probability of an outcome A, with

equiprobable sample space

S, is P(A) = n (A)n (S)

( )n S

Use tree diagram where appropriate.

Include everyday problems and making

predictions.

24

6/7-10/7/09

7.2 Understand andused the concept of

probability of thecomplement of an

event.

(i) State the complement of an

event in :

(a) words(b) set notations

(ii) Find the probability of the

complement of an event.

1

1

Include events in real life

situations such as winning or

losing a game and passing or

failing an exam.

The complement of an event A is the set

of all outcomes in the sample space that

are not included in the outcomes ofevent A.


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Points to Note

24 7.3 Understand usethe concept of

probability of

combined event.

(i) List the outcomes for events:

(a) A or B as elements of set

A B(b) A and B as elements of

set A B

(ii) Find the probability by

listing the outcomes of the

combined events :

(a) A or B

(b) A and B

(iii) Solve problems involving

probability of combinedevents.

2

2

1

Use real life situations to show the

relationship between

A or B and A B A and B and A B.

An example of a situation is being

chosen to be a member of an

exclusive club with restricted

conditions.

Use tree diagram and coordinate

planes to find all the outcomes of

combined events.

Use two-way classification tables of

events from newspaper articles orstatistical data to find probability of

combined events. Ask students to

create tree diagrams from these

tables. Example of a two-way

classification table :

Means of going to work

Officers Car Bus Others

Men 56 25 83

Women 50 42 37

Discuss :

situations where decisionshave to be made onprobability, for example in

business, such as determining

the value for aspecific

insurance policy and time the

slot for TV advertisements

the statement probability isthe underlying language of

statistics

Emphasise that :

knowledge about probability isuseful in making decisions.

prediction based on probabilityis not definite or absolute.


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Points to Note

Topic/Learning Area : BEARING --- 1 week

25

13/7-17/7/09

8.1. Understand anduse the concept ofbearing.

(i) Draw and label the eight maincompass directions:

a) north, south, east, west

b) north east, north west,

south east, south west

ii) State the compass angle ofany compass direction.

(iii) Draw a diagram of a pointwhich shows the direction of

B relative to another point Agiven the bearing of B from

A.

(iv) State the bearing point Afrom point B based on given

information.

(v) Solve problemsinvolving bearing.

1

1

1

2

Carry out the activities or games

involving finding directions using a

compass such as treasure hunt or

scravenger hubt. It can also be about

locating several points on a map,

finding the position of students inclass.

Discuss the use of bearing in real lifesituations. For example, a map

reading and navigation.

Compass angle and bearing are written

in three digit form, from 0000

to 3600.

They are measured in a clockwise

direction from north. Due north is

considered as bearing 0000. For cases

involving degrees up to one decimalpoint.


19/22

19

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No

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Points to Note

Topic 9

Learning Area: EARTH AS SPHERE ( 3 weeks )

26

20/7-24/7/09

9.1 Understand and

use the concept oflongitude

(i) Sketch a great circle through the

north and south poles.(ii) State the longitude of a given

point.

(iii) Sketch and label a meridianwith the longitude given.

(iv) Find the difference betweentwo longitudes

1

1

Model such as globes should be used.

Introduce the meridian through

Greenwich in England as the

Greenwich Meridian with longitude0

Discuss that:

All points on a meridian have thesame longitude

There are two meridians on agreat circle through both poles.

Meridians with longitude xE(orW) and (180- x)W(or E) forma great circle through both poles.

Emphasise that longitude 180E and

longitue 180W refer to the samemeridian.

Express the difference between two

longitudes with an angle in the range

of 0 x 180

27

27/7-31/7/09

9.2 Understand anduse the concept oflatitude

(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.

1

1

Discuss that all the points on a

paralell of latitude have the same

latitude.

Emphasise that

o the latitude of the equator is 0o latitude ranges from 0 to 90N

( or S )

Involve actual places on the earth.

Express the diffrence between two

latitudes with an angle in the range

of 0 x 180.

28

3/8-

7/8/09

9.3 Understand theconcept of

locations of a

place.

Use a globe or a map to find

locations of cities around the world.

Use a globe or map to name a place

given its location.

1

1

i. State the latitude and longitudeof a given place

ii. Mark the location of a place

iii. Sketch and label the latitude andlongitude of a given place.

A place on the surface of the earth is

represented by a point.

The, location of a place A at latitude

xN and longitude yE is written ,as

A(xN, yE).


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Points to Note

Topic 10

Learning Area: PLANS AND ELEVATIONS

2 weeks

29

10/7-

14/8/09


orthogonal projection.

i. Identify orthogonalprojections.

ii. Draw orthogonalprojections, given anobject and a plane.

iii. Determine the differencebetween an object andits orthogonal

projections with respectto edges and angles.

1

2

2

Use models, blocks or plan andelevation kit.

Emphasise the different uses of dashed

lines and solid lines.

Begin wth the simple solid object such as

cube, cuboid, cylinder, cone, prism and

right pyramid.

30

17/8-21/8/09

10.2 Understand anduse the concept of plan

and elevation.

i. Draw the plan of a solidobject.

ii. Draw- the front elevation- side elevation

of a solid object

iii. Draw the plan of asolid object.

1

2

1

Carry out activities in groups where

students combine two or more

different shapes of simple solidobjects into interesting models and

draw plans and elevation for thes

models.

Use models to show that it is

important to have a plan and at least

two side elevation to construct a solid

Limit to full-scale drawings only.

Include drawing plan and elevation in one

diagram showing projection lines.


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Points to Note

iv. Draw

- the front elevation- side elevationof a solid object

CUTI PERTENGAHAN

PENGGAL 2

[24/8-31/8/09]

ULANGKAJI

[1/9-18/9/09]

PEPERIKSAAN

PERCUBAAN SPM

[ ]

1

object.

Carry out group project:

Draw plan and elevations of buildings

or structures, for example students or

teachers 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.


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Points to Note

Yearlyplan mathF

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