annualplanningformathematicsform42011 110215023402 phpapp01.doc

7/29/2019 Annualplanningformathematicsform42011 110215023402 Phpapp01.Doc

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ANNUAL PLANNING FORMATHEMATICS FORM 4 /

2013

WEEK TOPICS/LEARNING

AREA

LEARNING OUTCOMES POINTS TO NOTE

7 Jan

9

Jan

Registration

Day

Orientation

Week

1

WEEK

(10

Jan

18

Jan)

CHAPTER 1 :

STANDARD FORM

Students will be

taught to understand

and use the concept

of significant figure

Students will be able to:

i. Round off positive

numbers to a given

number of significant

figures when the

numbers are

a. greater than 1

b. less than 1

ii. Perform operations of

addition, subtraction,

multiplication and

division involving a few

numbers and state the

answer in specific

significant figures.

iii. solve problems

involving significant

figures.

Discuss the significance

of zero in a number.

Discuss the use of

significant figures in

everyday life and other

areas


2/29

Students will be


and use the concept

of standard form to

solve problems


i. State positive numbers

in standard form when

the numbers are

a) greater than or

equal to 10

b) less than 1

ii. convert numbers in

standard form to single

numbers

iii. perform operations of

addition, subtraction,

multiplication and

division involving any

two numbers and state

the answers in standard

form

iv. solve problems

involving numbers instandard form

Use everyday life

situations such as in

health, technology,

industry, construction

and business involving

numbers in standard

form

Use the scientific

calculator to explore

numbers in standard

form


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2

WEEKS

(21

Jan 1 Jan)

CHAPTER 2 :

QUADRATIC

EXPRESSIONS AND

EQUATIONS

Students will be


the concept of

quadratic expressions

Students will be able to :i. Identify quadratic

expressions

ii. Form quadratic

expressions by

multiplying any two

linear expressions

iii. Form quadratic

expressions based on

specific situations

Discuss the characteristicsof quadratic expressions

of the form ax2 + bx +

c = 0 where a, b and are

constants, a 0 and x is

an unknown

Students will be

taught how to

factorise quadratic

expressions

Students will be able to :

i. Factorise quadratic

expressions of the form

ax2+bx+c =0or c=0;ii. Factorise quadratic


px2-q, pand qare

perfect squares;

iii. Factorise quadratic


ax2+bx+c, where a, b

and c not equal to

zero;

iv. Factorise quadratic

expressions containing

coefficients with

Discuss the various

methods to obtain the

desired product.

Begin with the case a=1.

Explore the use of

graphing calculator to

factorise quadratic

expressions


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common factors;

Students will be

taught to

understand the

concept of quadratic

equation


i. Identify quadratic

equations with one

unknown;

ii. write quadratic

equations in general

form i.e.

ax2+ bx + c = 0 ;

iii. form quadratic

equations based on

specific situations ;

Discuss the characteristics

of quadratic equations.

Students will be

taught to

understand and use

the concept of roots

of quadraticequations to solve

problems.


i. Determine whether a

given value is a root of

a specific quadratic

equationii. Determine the solutions

for quadratic equations

by:

a) trial and error method

Discuss the number of

roots of a quadratic

equation.


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;

b) factorization ;

iii. solve the problems

involving quadraticequations

Use everyday life

situations.

3

WEEKS

(31

Jan

18

Feb)

CHAPTER 3 : SETS

Students will be

taught to

understand the

concept of set


i. sort given objects into

group

ii. define set by :

a. descriptions;

b. using set notation;

iii. identify whether a

given object is

anelement of a set

and use the symbol

or ;iv. represent sets by

using Venn diagrams;

v. list the element and

state the number of

element of a set;

vi. determine whether a

set is an empty set;

vii. determine whether

two sets are equal;

Use everyday life

examples to introduce

the concept of set.

Discuss the difference

between the

representation of

element and the number

of element in Venn

diagrams.

Discuss why { 0 } and {

} are not empty sets.

Students will be Students will be able to : Begin with everyday life


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taught to

understand and use

the concept of

subset, universal setand the complement

of a set

i. determine whether a

given set is a subset of

a specific set and use

the symbol

or

;ii. represent subset using

Venn diagram;

iii. list the subsets for a

specific set;

iv. illustrate the

relationship between

set and universal set

using Venn diagram;

v. determine the

complement of a given

set ;

vi. determine the


set, subset, universal set

and the complement ofa set;

situations.

Discuss the relationship

between sets and

universal sets.

Students will be

taught to perform

operations on sets:

the intersection

of sets;

the union of sets


i. determine the

intersection of:

a) two sets;

b) three sets;

and use the symbol

;

ii. represent the

intersection of sets

Discuss cases when:

BA =


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using Venn diagram;

iii. state the relationship

between

i.

BA

andA

,ii. BA and B ;

iv. determine the

complement of the

intersection of sets;

v. solve problems

involving the

intersection of sets;

vi. determine the union of

a) two sets;

b) three sets;

and use the symbol

;

vii. represent the union of

sets using

Venn diagram;viii. state the relationship

between

a) BA and A ,

b) BA and B ;

ix. determine the

complement of the

union of sets

x. solve problems

involving the union of

sets

xi. determine the outcome

of combined operations

BA


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on sets

xii solve problems

involving combined

operations on sets2

WEEKS

(21

Feb

4

March)

CHAPTER 4 :

MATHEMATICAL

REASONING

Students will be


the concept ofstatement;


i. determine whether a

given sentence is a

statement;

ii. determine whether a

given statement is true

or false;

iii. construct true or false

statement using given

numbers and

mathematical symbols;

Introduce this topic using

everyday life situations

Focus on mathematical

sentences

Discuss sentences

consisting of:

words only;

numbers and words;

numbers and

mathematical symbols;.

Students will be

taught understand

the concept of

quantifiers all and

some;


i. construct statements

using the quantifier:

a)all;

b)some;

ii. determine whether a

Start with everyday life

situations.


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statement that contains

the quantifier all is

true or false;

iii. determine whether astatement can be

generalised to cover all

cases by using the

quantifier all;

iv. construct a true

statement using the

quantifier all or

some, given an object

and a property.

TEST 1

(7 Mac 11 Mac)

Will be prepared by:

PN. SURIANI

2

WEEKS

(21

Mar

1 Apr)

Students will be

taught to perform

operations involving

the words not or

no, and and or

on statements;


i.

change the truth valueof a given statement by

placing the word not

into the original

statement;

ii. identify two statements

from a compound

statement that contains

the word and;

iii. form a compound

statement by combining

two given statements

Begin with everyday life

situations.


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using the word and;

iv. identify two statement

from a compound

statement that containsthe word or ;

v. form a compound

statement by combining

two given statements

using the word or;

vi. determine the truth

value of a compoundstatement which is the

combination of two

statements with the

word and;

vii. determine the truth

value of a compound

statement which is the

combination of two

statements with the

word or.

Students will be


the concept of

implication;

Students will be able to;

i.

identify the antecedentand consequent of an

implication ifp, then

q;

ii. write two implications


situations.


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from a compound

statement containing if

and only if

iii. construct mathematicalstatements in the form

of implication

a) Ifp, then q;

b) pif and only ifq

v. determine the converse

of a given implication;

vi. determine whether the

converse of an

implication is true or

false

Students will betaught to understand

the concept of

argument;


i. identify the premise

and conclusion of a

given simple argument;

ii. make a conclusion

based on two given

premises for

a) Argument Form I;

b) Argument Form II;

c) Argument Form III;

iii. complete an argument

given a premise and the


situations.

Encourage students to

produce arguments


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conclusion. based on previous

knowledge.

Students will be


and use the concept

of deduction and

induction to solve

problems.

Students will be able to:i. determine whether a

conclusion is made

through:

a) reasoning by

deduction;

b) reasoning by

induction;

ii. make a conclusion for a

specific case based on a

given general

statement, by

deduction;

iii. make a generalization

based on the pattern of

a numerical sequence,

by induction;

iv. use deduction and

induction in problem

solving.

Use specific

examples/activities to

introduce the concept.

3

WEEKS

(4 Apr

-22

Apr)

CHAPTER 5 : THE

STRAIGHT LINE

Students will be

taught to

understand the


i. determine the vertical

and horizontal distances

between two given

Use technology such as

the Geometer's

Sketchpad , graphing

calculators, graph boards,


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concept of gradient

of a straight line

points on a straight line

ii.

determine the ratio ofvertical distance to

horizontal distance

magnetic boards, topo

maps as teaching aid

where appropriate.

Begin with concrete

examples /daily situations

to introduce the concept

of gradient.

Horizontal distance

Discuss:

the relationship

between gradient

and tan

the steepness of th

straight line with

different values of

gradient

Carry out activities to

find the ratios of vertical

distance to horizontal

distance for several pairs

of points on a straight

Vertical

distance


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line to conclude that the

ratio is constant.

Students will be


the concept of

gradient of a straight

line in Cartesian

coordinates


i. derive the formula for

the gradient of a

straight line

ii. calculate the gradient

of a straight linepassing through two

points;

iii. determine the


the value of the

gradient and the :

a) steepness;

b) direction of

inclination, of a straight

line

Discuss the value of

gradient if

P is chosen as (x1

,y1 ) and Q is (x2

,y2 ) ;

P is chosen as (x2,y2 ) and Q is (x1

,y1 )

Students will be

taught to

understand the

concept of intercept;


i. determine the x-

intercept and the y-

intercept of a straight

line

ii. derive the formula for

Students will be taught

to understand the

concept of intercept;


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the gradient of a

straight line in terms of

the x-intercept and the

y-interceptiii. perform calculations

involving gradient, x-

intercept and y-

intercept

Students will be

taught to

understand and use

equation of a straight

line;

i. Find the equation of the

straight line which:

a. is parallel to the x-axis;

b. is parallel to the y-axis;

c. passes through a given

point

and has a specific

gradient;

d. passes through two givenpoints;

ii. find the point of

intersection of two

straight lines by;

a) drawing the two

straight lines;

b) solving simultaneous

equations

Discuss and concludethat the point of

intersection is the only

point that satisfies both

equations

Use the graphing

calculator and

Geometer's Sketchpad or

other teaching aids to

find the point of

intersection


16/29

2

WEEKS

(25

Apr

6 May

Students will be

taught to

understand and usethe concept of

parallel lines


i. verify that two parallel

lines have the samegradient and vice versa;

ii. determine from the

given equation whether

two straight lines are

parallel;

iii. find the equation of the

straight line which

passes through a given

point and is parallel to

another straight line;

iv. solve problems

involving equations of

straight lines

Explore properties of

parallel lines using thegraphing calculator and

Geometer's Sketchpad or

other teaching aids.

CHAPTER 6 :

STATISTICS III

Students will be


the concept of class

interval.


i. Complete the class

interval for a set of data

given one of the class

intervals;

ii. Determine

a) the upper limit and

lower limit;

b) the upper boundary

and lower boundary

Use data obtained from

activities and other

sources such as research

studies to introduce the

concept of class interval .


17/29

of a class in a

grouped data;

iii. Calculate the size of a

class interval;iv. Determine the class

interval, given a set of

data and the number of

classes;

v. Determine a suitable

class interval for a given

set of data ;

vi. Construct a frequency

table for a given set of

data

Discuss criteria for

suitable class intervals

Students will be


and use the

concept of mode andmean of grouped

data ;


i. Determine the modal

class from the

frequency table ofgrouped data ;

ii. Calculate the midpoint

of a class;

iii. Verify the formula for

the mean of grouped

data ;

iv. Calculate the mean

from the frequency

table of grouped data

v. Discuss the effect of the

size of class interval on

the accuracy of the


18/29

mean for a specific set

of grouped data

Students will be

taught to represent

and interpret

data in histogramswith

class intervals of the

same

size to solve

problems ;


i. Draw a histogram

based on the frequency

table of a grouped dataii. Interpret information

from a given histogram;

iii. Solve problems

involving histograms.

Discuss the difference

between histogram and

bar chart.

Use graphing calculator

to explore the effect of

different class interval on

histogram.

Students will be

taught to represent

and interpret data in

frequency polygons

to solve

problems.


i. Draw the frequency

polygon based on

a) a histogram ;

b) a frequency table ;

ii. Interpret information

from a given frequency

polygon ;

iii. Solve problems

involving frequency

polygon.


19/29

Students will be


the concept ofcumulative frequency


i. Construct the

cumulative frequencytable for

a) ungrouped data

b) grouped data

ii. Draw the ogive for :

a) ungrouped data

b) grouped data

Students will be


and use the concept

of measures of

dispersion to solve

problems


i. Determine the range of

a set of data

ii. Determine

a) the median ;

b) the first quartile;

c) the third quartile ;

d) the interquartile

range ;

from the ogive .

iii. interpret information

Discuss the meaning of

dispersion by comparing

a few sets of data.

Graphing calculator can

be used for this purpose

.


20/29

from an ogive

iv. solve problems

involving data

representations andmeasures of dispersion

Carry out a project

/research and analyse as

well as interpret the data

.Present the findings ofthe project/research.

Emphasise the

importance of honesty

and accuracy in

managing statistical

research .

MID YEAR EXAM

(9 MAY 27 MAY)


PN. SURIANI & PN.

SAIDANORLAILI

2

WEEKS

(13

June

24

June)

CHAPTER 7 :

PROBABILITY

Students will be


the concept o

sample space.


i. Determine whether

an outcome is a

possible outcome of

an experiment;

ii. List all the possible

outcomes of an

experiment ;

a) from activities;

b) by reasoning;

iii. Determine the sample

space of an

experiment;

iv. Write the sample

space by using set

notations.

Use concrete examples

such as drawing a die

and tossing a coin.


21/29

Students will be

taught tounderstand the

concept of

events.


i.

identify the elementsof a sample space

which satisfy given

conditions;

ii. list all the element of

a sample space which

satisfy certain condition

using set notations.

iii. determine whether an

event is

possible for a

sample space.

Discuss that an event

is a subset of thesample space

Discuss also impossible

events for a sample

space.

Discuss that the

sample space itself is

an event.

Students will be


and use the

concept of

probability of an

event to solve

problems


i. find the ratio of the

number of

times an event

occurs to the number

of trials.

ii. find the probability of

an event from a big

enough number of

trials;

iii. calculate the

expected number of

times an event will

occur given the

probability of the

Carry out activities to

introduce the concept

of probability . The

graphing calculator can

be used to simulate

such activities.

Discuss situation which

results in:


22/29

event an number of

trials;

iv. solve problems

involving probability;v. predict the

occurrence of an

outcome and make a

decision based on

known information.

probability of

event = 1

probability of

event = 0

Emphasise that the value

of probability is

between 0 and 1.

Predict possible events

which might occur in

daily situations

2

WEEKS

(27

June

8 July)

CHAPTER 8 :

CIRCLES III

Students will be


and use the concept

of tangent to a circle.


i. identify tangent to a

circle;

ii. make inference that

the tangent to a circle

is a straight lineperpendicular to the

radius that passes

through the contact

point;

iii. construct the tangent

to a circle passing

through a point:

a) on the

circumference of

the circle;

b) outside the circle;

iv. determine the

Develop concepts and

abilities through activities

using technology such as

the Geometer`s

Sketchpad and graphing

calculator.


23/29

properties related to

two tangent to a circle

from a given point

outside the circle;v. solve problems

involving tangent to a

circle.

Students will be

taught understand

and use theproperties of angle

between tangent and

chord to solve

problems.


i. identify the angle in

the alternate segmentwhich is subtended by

the chord through the

contact point of the

tangent;

ii. verify the relationship

between the angle

formed by the tangent

and the chord with the

angle in the alternate

segment which is

subtended by the

chord;

Explore the properties of

angle in alternatesegment using

Geometer`s Sketchpad or

other teaching aids.


24/29

iii. perform calculations

involving the angle in

alternate segment;

iv.

solve problemsinvolving tangent to a

circle and angle in

alternate segment.

Students will taught

to understand and

use the properties of

common tangents to

solve problems


i. determine the number of

common tangents which

can be drawn to two

circles which:

a) intersect at two

points;

b) intersect only at one

point;

c) do not intersect;

ii. determine the propertiesrelated the common

tangent to two circles

which:

a) intersect at two

points;

b) intersect only at one

point;

c) do not intersect;

iii. solve problems involving

common tangents to two

circles;

iv. solve problems involving

Discuss the maximum

number of common

tangents for the three

cases.

Include daily situations.


25/29

tangents and common

tangents.

Students will be

taught to

understand and use

the concept of the

values of sin ,

kos , and tan

(0 360) to

solve problems.

i. find the values of sine,

cosine and tangent of

the angles between

90 and 360

ii. find the angles

between 0 and 360,

given the values of

sine, cosine or

tangent

iii. solve problems

involving sine, cosine

and tangent

Relate the daily situation

Students will be

taught to draw and

use the graphs of

sine, cosine and

tangent.


i. Draw the graphs of

sine, cosine and

tangent for angles

between 0o and 360o;

ii. Compare the graphs of

sine, cosine and

tangent for angles

between 0o and 360o;

iii. Solve problems

involving graphs of

sine, cosine and

tangent.

Use the graphing

calculator and

Geometers Sketchpad to

explore the feature of the

graphs of

tan,cos,sin yyy

Discuss the feature of the

graphs of

tan,cos,sin yyy

Discuss the examples of


26/29

these graphs in other

area.

3

WEEKS

(11

July -

29

July)

CHAPTER 10 :

ANGLES OF

ELEVATION AND

DEPRESSIONS

Students will be


and use the concept

of angle of elevation

and angle of

depression to solve

problems


i. identify

a) the horizontal line

b) the angle of

elevation

c) the angle of

depression

for a particular

situation

ii. Represent a particular

situation involving

a)the angle ofelevation

b) the angle of

depression,

using diagrams

iii. Solve problems

involving the angle of

elevation and the

angle of depression

Use daily situations to

introduce the concept

(1 Aug

5

Aug)

REVISION


27/29

TEST 2

(8 AUG 12 AUG)


PN. SAIDANORLAILI

2

WEEKS(15

Aug

26

Aug)

CHAPTER 11 :

LINES AND PLANESIN 3 DIMENSIONS

Students will be


and use the concept

of angle between

lines and planes to

solve problems

Students will be able to

i. identify planes

ii. identify horizontal

planes and inclined

planes

iii. sketch a three

dimensional shape and

identify the specific

planes.

iv. Identify :

a) lines that lies on a

plane.

b) Lines that intersectwith a plane,

v. Identify normals to a

given plane,

vi. Determine the

orthogonal projection

of a line on a plane

vii. Draw and the name

the orthogonal

projection of a line on

a plane

viii. Determine the angle

between a line and a

Carry out activities using

daily situation and 3-

dimensional models.

Differentiate between 2-

dimensional an d 3-

dimensional shapes.

Involve planes found in

natural surroundings.

Begin with 3-dimensional

models.

Use 3-dimensional

models to give clearer

pictures.


28/29

plane

ix. Solve problems

involving the angle

between a line and aplane.

Students will be

taught to

understand and

use the conceptof angle between

two planes to

solve problems


i. identify the line

intersection between

two planes,ii. draw a line on each

plane which is

perpendicular to the

line of intersection of

the two planes at a

point on the line of

intersection

iii. determine the angle

between two planes on

a model and a given

diagram.

iv. Solve problems

involving lines and

planes in 3-

dimensional shapes.

Use 3-dimensional

models to give clearer

pictures.

(5

Sept

14

REVISION


29/29

Oct)

FINAL EXAM

(17 OKT 4

NOV)


PN. SURIANI & PN.

SUNITA

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