RPT_F4_2012

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SMK YAACOB LATIF KUALA LUMPUR

YEARLY LESSON PLAN FORM 4 2012

LEARNING

AREA/ WEEK

LEARNING

OBJECTIVESLEARNING OUTCOMES

SUGGESTED

TEACHING AND

LEARNING

GENERICS CCTSMORAL

VALUES

POINTS TO NOTE/

VOCABULARY

1.0

STANDARD

FORM

WEEK 1

4/1 6/1/12

Student will be

taught to:1.1 understand

and use the

concept of

significant figure;

Student will be able to:

(i) round off positive numbers to a

given numbers to a given number

of significant figures when the

numbers are:

a) greater than 1;b) less than 1;

(ii) perform operations ofaddition, subtraction,

multiplication and division,

involving a few numbers and state

the answer in specific significant

figures;

(iii) solve problems involvingsignificant figure

Discuss the

significance of zero

in a number.

Discuss the use of

significant figuresin everyday life

and other areas.

Cooperative

learning

ICT

Mastery

Learning

Identifying

patterns

Using algorithm

and relationship

Finding allpossible

solutions

Systematic

Rationale

Consistent

Rounded numbers are

only approximates.

Limit to positive

numbers only.

Generally rounding isdone on the final

answer.

Significance

Significant figure

RelevantRound off

Accuracy

WEEK 2

9/1 13/1/12

1.2 understand

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 involvingnumbers in standard form.

Use everyday life

situations such as

in health,

technology,

industry,

construction and

business involving

numbers instandard form.

Use the scientific

calculator to

explore numbers in

standard form.

Cooperative

learning

ICT

Mastery

Learning

Comparing and

differentiating

Identifying

relations

Using algorithm

and relationship

Finding all

possiblesolutions

Systematic

Rationale

Consistent

Another term for

standard form is

scientific notation.

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SUGGESTEDTEACHING AND

LEARNING

GENERICS CCTSMORAL

VALUES

POINTS TO NOTE/

VOCABULARY

2.0

QUADRATIC

EXPRES-

SIONS ANDEQUATIONS

WEEK 3

16/1 20/1/12

2.1 understand

the concept of

quadratic

expression,

i) identify quadratic expressions,

ii) form quadratic expression by

multiplying any two linear

expressions

iii) form quadratic expression

based on specific situation

Discuss the

characteristics of

quadratic

expressions of the

form ax + bx + c,where a, b and c

are constants, a 0

and x is an

unknown.

cooperative

learning

constructivism

i) identifying

patterns

ii) identifying

relations

iii) recognizing

and representing

- rationale

- diligence

Include the case when

b=0 and / or c=0

Emphasize that for the

terms x and x, thecoefficients are

understood to be one.

Include daily life

situation.

Quadratic

Expression

Constant

Constant factor

Unknown

Highest powerExpand

CoefficientTerm

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2.2 factorise

quadratic

expression

i) factorise quadratic expressions

of the form ax + bx + c, where b

= 0 or c = 0

ii) factorise quadratic expressions

of the form px-q, p and q are

perfect squares

iii) factorise quadratic expressionsof the form ax+bx +c, where a, b

and c are not equal to zero.

iv) factorise quadratic expressions

containing coefficient with

common factors

Discuss the various

methods to obtain

the desired product

Begin with the case

a = 1

Explore the use of

graphing calculatorto factorise

quadraticexpressions

ict

cooperative

learning

constructivism

i) identifying

patterns

ii) identifyingrelations

iii) using

algorithm and

relationship

- systematic

- rationale

- consistence

1 ia also a perfect

square

Factorization methodsthat can be used are

- Cross method;

- Inspection

Factories

Common factorPerfect square

Cross methodInspection

Common factor

Complete

factorization

WEEK 4

23/1 27/1/12CHINESE NEW YEAR

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VOCABULARY

WEEK 5

30/1 3/2/12

2.3 Understand

the concept of

quadratic

equations;

(i) identify the 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

Contextual

Learning

Constructivism

Enquiry

Discovery

(i) identifying

patterns

(ii) identifying

relations

(iii) recognizing

and

representing

Rationale Include everyday life

situations

Differentiate quadratic

equations and quadratic

expressions

quadratic equations

general form

2.4 Understand

and use the

concept of rootsof quadraticequations to solve

problems.

(i) determine whether a given

value is a root of a specific

quadratic equations;(ii) determine the solutions for

quadratic equations by :

a) trial and

improvement method

b) factorisations;

(iii) solve problems involvingquadratic equations

Discuss the number

of roots of a

quadratic

equations.

Use everyday life

situations.

Mastery

Learning

Thinking Skill

(i) finding all

possible

solutions

(ii) using

algorithm

and

relationship

(iii) problemsolving

(iv) drawing

diagram

Determination

Rationale

There are quadratic

equations that cannot be

solved by

factorizations.

Check the rationality ofthe solutions

substitute

roots

trial and improvement

method

solution

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VOCABULARY

3.0

SETS

WEEK 68/2 10/2/12

3.1 understand

the concept of

sets;

(i) sort given objects into

groups;

(ii) define sets by :

a) descriptions;

b) using sets notation

(iii) identify whether a given

object is an element of a set and

use the symbol or;

(iv) represent sets by using Venndiagrams;

(v) list the elements and state the

number of elements of a set;

(vi) determine whether a set is anempty set;

(vii) determine whether two sets

are equal;

Use everyday life

examples to

introduce theconcept of sets.

Discuss thedifference between

the representationof elements and the

number of the

elements in Venn

diagrams.

Discuss why {0}

and {} are notempty sets.

Contextual

learning

Mastery learning

Communication

method of

learning

ICT

Cooperative

learning

Identify relations

Comparing anddifferentiating

Drawing

diagram

Recognizing and

representing

Cooperation

Rational

Neatness

Systematic

The word set refers to

any collection or group

of objects.

The notation used for

sets is braces, { }.The same elements in a

set need not be

repeated.

Sets are usually denoted

by capital letters.The definition of sets

has to be clear andprecise so that the

elements can be

identified.

The symbol (epsilon) is read is an

element of or is amember of.

The symbol is readis not an element of

or is not a member of.

The notation n(A)

denotes the number of

elements in set A.

The symbol (phi) or{ } denotes an emptyset.

An empty set is alsocalled a null set.

Vocabulary:

set

element

description

labelset notation

denote

Venn diagram

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VOCABULARY

WEEK 7

13/2 17/2/12

3.2 understand

and use the

concept of subset,

universal set and

the complementof a set;

(i) determine whether a givenset 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 setusing Venn diagram;

(v) determine the complement of

a given set;

(vi) determine the relationship

between set, subset,universal set and the

complement of a set;

Begin with

everyday life

situations.

Discuss therelationship

between sets and

universal sets.

Constructive

Contextual

learning

Communication

method of

learning

Cooperativelearning

Comparing and

differentiating

Classifying

Drawing

diagram

Making

inferences

Estimating

Rational

Determination

Precise

An empty set is a subset

of any set.

Every set is a subset of

itself.

The symbol denotes auniversal set.

The symbol A denotesthe complement of set

A.

Include everyday life

situations.

Vocabulary:

subset

universal setcomplement of a set

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WEEK 8

20/2 24/2/12

3.3 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 ofsets using Venn diagram;

iii) state the relationship between

a) A B and A ;

b) A B and B;

(iv) determine the complement ofthe intersection of sets ;

(v) solve problems involving theintersection of sets :

(vi) determine the union of :

a) two sets;

b) three sets ;

and use the symbol U ;

(vii) represent the union of setsusing Venn diagram;

(viii) state the relationshipbetween

a) A U B and A ;

b) A U B 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 operation on sets ;

(xii) solve problems involvingcombined operations on sets.

Discuss cases when

:

A B =

A B

Contextual

learning

Mastery learning

Communication

method

ICT

Cooperativelearning

Mastery learning

Communication

method oflearning

ICT

Multiple

intelligence

Enquiry discovery

Identify relations

Comparing &

differentiating

Drawing

diagram

Recognizing &representing

Estimating

Identify relations

Comparing &

differentiating

Drawingdiagram

Recognizing &

representing

Makinginferences

Accurate

Cooperation


situations.

Vocabulary

Intersection

Common elements

Complement

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VOCABULARY

WEEK 9

27/2 3/3/12

WEEK 105/3 9/3/12

TEST 1

10/3 18/3/12 MID TERM 1 BREAK

4.0

MATHEMA-

TICAL

REASONING

WEEK 11

19/3 23/3/12

4.1 Understand

the concept of

statement

(i) determine whether a given

sentence is a statement

(ii) determine whether a givenstatement is true or false;

(iii) construct true or false

statement using given numbersand mathematical symbols.

Introduce this topic

using everyday life

situations.

Focus on

mathematical

sentences.

Discuss sentences

consisting of:

wordsonly;

numbers

and words; numbers

and

mathematical

symbols;

ICT, contextual

and

constructivism

ICT,Constructivism

Constructivism

Identifyingrelation,

classifying

Identifying

relation

Cooperation

Rationale,honesty

Rationale,

honesty

Statements consisting

of:

words only,e.g. Five is greaterthan two.;

numbers andwords, e.g. 5 is

greater than 2.;

number andsymbols, e.g. 5

> 2

The following are notstatements:

Is the place

value of digit 9 in1928 hundreds?;

4n 5m + 5s;

Add the twonumbers.;

x + 2 = 8

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WEEK 12

26/3 -30/3/12

4.2 Understand

the concept of

quantifiers all

and some

(i)construct statements using

the quantifier:

a) all

b)some

(ii)determine whether a

statement that contains the

quantifier all is true or

false.

(iii) determine whether astatement can be generalized

to cover all cases by using the

quantifier all

(iv) construct a true statementusing the quantifier all or

some, given an object and aproperty.

Start with everyday

life situations.

Constructivism. Identifying

patterns.

Identifying

relation.

Motivated. Quantifier such as

"Every" and " any"

can be introduced based

on context.

Examples: All squares are four

sided figures.

Every square is afour sided figures.

Any square is a foursided figure.

Other quantifiers such

as several, one ofand part of can be

used based on context.

Example:

Object: Trapezium.

Property: Two sidesare parallel to each

other.

Statement: Alltrapeziums have two

parallel sides.

Object: Even numbers.

Property: Divisible by

4.

Statement: Some evennumbers are divisible

by 4.Vocabulary:

Quantifier

All , Every

Any ,Some

Several

One ofPart of

Negate, Contraryobject

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WEEK 13

2/4 6/4/12

4.3 Perform

operations

involving the

words not or

no, and andor on

statements.

i. Change the truth value of 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 bycombining two given statements

using the word and,

iv. identify two statements from a

compound statement that contains

the word or,

v. form a compound statement by

combining two given statementsusing the word or,

vi. determine the truth value of a

compound statement which is the

combination of two statements

with the word and,

vii. determine the truth value of acompound statement which is the

combination of two statements

with the word or,

Begin with

everyday life

situations.

Cooperative

learning

Mastery learning

Inquiry

discovery

Logical

reasoning

Simulation

Classifying

freedom

kindness

sincerity

The negation no can

be used where

appropriate.

The symbol

(tilde) denotes negation. p denotes

negation of p with

means not p or no

p.

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WEEK 14

9/4 13/4/12

4.4 Understand

the concept of

implication

(i) identify the antecedent and

consequent of an implication ifp,

then q

(ii) write two implications from a

compound statement containingif and only if

(iii) construct mathematical

statements in the form of

implication:a) If p, then q

b) p if and only ifq;

(iv) determine the converse of a

given implication;

(v) determine whether the

converse of an implication is trueor false

Start with everyday

life situations

Constructivism

Mastery learning

Mastery learning

Cooperativelearning

Enquiry-discovery

Logical

reasoning

Logical

reasoning

Finding all

possible

solutions

Logicalreasoning

Finding all

possible

solutions

Finding all

possible solutionIdentifying

relations

systematic

Determination

sharing

Systematic

Determination

Rational

Implication if p, then

q can be written as p q, and p if andonly if q can be written

as p q, whichmeans p q andq p.ImplicationAntecedent

ConsequentThe converse of an

implication is not

necessarily true.

Example 1:

If x < 3, then x < 5

(true) .Conversely:

If x < 5, then x < 3(false).

converse

Example 2:

If PQR is triangle, then

the sum of the interior

angles of PQR is 180.(true)

Conversely:

If the sum of the

interior angles of PQR

is 180, then PQR is a

triangle.(true)

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WEEK 15

16/4 20/4/12

4.5 understanding

the concept of

argument;

(i) identify the premise and

conclusion of a given simple

argument;

(ii) make a conclusion based ontwo given premises for:

a) Argument Form I;

b) Argument Form II;

c) ArgumentForm III;

iii) complete an argument given a

premise and the conclusion

Start with everyday

life situations.

www.math.ohiou.e

du/ vardges/math306/slides

Constructivism

Mastery

Learning

Encourage

students toproduce

arguments based

on previous

knowledge.

Comparing and

Differentiating

Classifying

Self AccessLearning

Cooperation

Rational

Honesty

Logical

Reasoning

Limit to arguments with

true premises.

Argument

Premiseconclusion

Names for argument

form, i.e.

syllogism(Form I),

modus ponens(FormII) and modus tollens

(Form III), need not beintroduced.

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4.6 understand

and use the

concept of

deduction and

induction to solveproblems.

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 generalisation based onthe pattern of numerical sequence

by induction

iv)use deduction and induction in

problem solving.

Use specific

examples/activities

to introduce the

concept.

i.e :

a)reasoning by

deduction:

e.g. circle area : r2

r = 3,

A = (32) = 9

b)reasoning byinduction:

Always used by the

scientist to create

formulae

Mastery learning

Constructivism

Enquiry

discovery

Multipleintelligence

Identifying

Pattern

Classifying

Logical

reasoning

Makinggeneralization

Determination

Honesty

Rationale

Determinationsystematic

Limit to cases where

formulae can be

induced.

Specify that:Making conclusion by

deduction is definite,

Making conclusion by

induction is not

necessarily definite.

Reasoning

Deduction

Induction

Pattern

Special conclusion

General statementGeneral conclusion

Specific caseNumerical sequence

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5.0

STRAIGHT

LINE

WEEK 16

24/4 27/4/12

5.1 Understand

the concept

of gradient of

a straight

line.

(i) determine the

vertical and horizontal

distances between two given

points on a straight line.

(ii) determine the ratio

of vertical distances to

horizontal distance

Use technology

such as the

Geometers

Sketchpad,

graphingcalculators, graph

boards, magnetic

board, topo maps

as teaching aids

where appropriate.

Begin withconcrete examples/

daily situations to

introduce the

concept of

gradient.

Discuss;

Therelationship

between gradient

and tan .

Thesteepness of the

straight line with

different valuesof gradient.

Carry out activities

to find the ratio of

vertical distance to

horizontal distance

for several pairs of

point on a straightline to conclude

that the ratio is

constant.

Contextual

learning

ICT

Graphic

Calculator

Identify patterns

Identify concept

Identify relation

Rationale

Systematic

Cooperation

Accurate

Straight line

Steepness

Horizontal distance

Vertical distance

GradientRatio

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WEEK 17

30/4 4/5/12

5.2 Understand

the concept

of gradient of

straight line

in Cartesiancoordinates.

Students will be able to;

(i) derive the formula

for the gradient of a straight

line.(ii) calculate the

gradient of a straight line

passing through two points.

(iii) determine the

relationship between thevalue of the gradient and the;

a) steepnessb) direction of inclination

of a straight line.

Discuss the value

of gradient if;

(i)P is chosen as (x1,

y1) and Q is (x2,y2).

(ii)Q is chosen as (x1,

y1) and P is (x2,

y2).

Enquiry

discovery

ICT

Finding all

possible solution.

Arranging

sequentially

Collecting andhandling data

Representing and

interpreting data

Comparing &

differentiating

Neatness

Systematic

Rationale

Acute angle

Obtuse angle

Inclined upwards to the

right

Inclined downwards tothe right

Undefined.

The gradient of a

straight line passingthrough P(x1,y1) and

Q(x2, y2) is :

12

12

xx

yym

=

WEEK 18

7/5 11/5/12

5.3 Understand

the conceptof intercept


(i) Determine the x-

intercept and the y-intercept

of a straight line.

(ii) Derive the formula for

the gradient of a straight line

in terms of the x-interceptand y-intercept.

( ii i) Perform calculat ions

involving gradient, x-

intercept and y-intercept.

Constructivism

Self-accessLearning

Comparing &

differentiatingUsing algorithm

& relationship.

Drawing graph.

Rational

SystematicAccuracy

x-intercept

y-intercept

Emphasize that x-

intercept and y-

intercept are written in

the form of coordinates.

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WEEK 19

14/5 18/5/12

WEEK 20

21/5 25/5/12

MID YEAR EXAMINATION

28/5 -10/6/12MID YEAR BREAK

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WEEK 21

11/6 15/6/12

5.4 Understand

and use

equation of a

straight line


(i) Draw the graph given anequation of the form

y=mx+c(ii) Determine whether a

given point lies on a specific

straight line.

( ii i) Write the equation of

the straight line given the

gradient and y-intercept.( iv) Determine the gradient

and y-intercept of thestraight line which the

equation is in the form of;

a) y = mx + c

b) ax + by = c

(v) Find the equation of thestraight 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

given points.(vi) Find the point of

intersection of two straight

lines by;

a) Drawing the twostraight lines.

b) Solving simultaneousequations.

Discuss the

changes in the form

of the straight lines

with various values

ofm and c.


using the graphing

calculator, the

GeometersSketchpad or other

teaching aids.

Verify that m is

the gradient and c

is the y-intercept of

a straight line withequation

y = mx + c .

Discuss and

conclude that the

point of

intersection is the

only point thatsatisfies both

equations.

Use the graphing

calculator, theGeometers

Sketchpad or other

teaching aids tofind the point of

intersection.

Cooperative

Learning

Multiple

Intelligence

Enquirydiscovery

ICT

Identify pattern

Classifying

Drawing graph

Representing &

interpreting data.Making

generalization

Identify relation

Cooperation

Sharing

Neatness

Rational

Linear equation

Graph

Table of values

Coefficient

ConstantSatisfy

Parallel

Point of intersection

Simultaneous equations

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WEEK 22

18/6 22/6/12

5.5 Understand

and use the

concept of

parallel lines.


(i) verify that two parallel

lines have the same gradient

and vice versa(ii) determine from the

given equations whether two

straight lines are parallel.

(iii) find the equation of the

straight line which passesthrough a given point and is

parallel to another straightline.

(iv) solve problems

involving equations of

straight lines.

Explore properties

of parallel lines

using the graphing

calculator and

GeometersSketchpad or other

teaching aids

Mastery

Learning

ICT

Self-access

Learning

Comparing &

differentiating

Identify pattern

Identify Concept

Finding allpossible

Solutions

Making

generalization

Rational

Systematic

Sharing

Parallel lines

6.0

STATISTICSIII

WEEK 23

25/6 29/6/12

6.1.Understand

the concept ofclass interval;

(i) complete the class interval

for a set of data given one ofthe class intervals;

(ii) determine:

a)the upper limit and

lower limit;

b)the upper

boundary and lowerboundary of a class

in a grouped data;

(iii) calculate the size

of a class interval;

determine the class

interval, given a set of data

and the number of classes;(v) determine a suitable class

intervals for a given set of

data;

(vi) construct a frequency table

for a given set of data.

Use data obtained

from activities andother sources such

as research studies

to introduce the

concept of class

interval.

Discuss criteria for

suitable class

intervals.

contextual

cooperatives

learning

enquiry-

discovery

working out

mentally

making

inferences

classifying

collecting and

handling data

co operations

systematic

tolerance

Size of class interval =

[upper boundary lower boundary]

Statistics

Class interval data

Grouped data

Upper limitLower limit

Upper boundary

Lower boundary

Size of class interval

Frequency table

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WEEK 24

2/7 6/7/12

6.2 understand

and use the

concept of mode

and mean ofgrouped data;

(i) determine the modal class from

the frequency table of grouped

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 groupeddata;

(v) discuss the effect of the size of

class interval on the accuracy

of the mean for a specific set of

grouped data.

Discuss the

difference between

mode and mean.

constructivism

self-access

learning

representing and

interpreting data

arrangingsequentially

using algorithm

and relationship

working outmentally

making

inferences

hardworking

consistent

systematic

mode

modal class

mean

midpoint of a class

6.3 represent and

interpret data in

histograms with

class intervals of

the same size tosolve problem;

(i) draw a histogram based on the

frequency table of grouped

data;

(ii) interpret information from agiven histogram;

(iii) solve problems involving

histograms.

Discuss the

difference between

histogram and bar

chart.

Use graphing

calculator to

explore the effect

of different classinterval onhistogram.

enquiry-

discovering

drawing

diagrams

collecting and

handling data

representing and

interpreting data

estimating

neatness

diligence

systematic

hardworking

systematic

uniform class interval

histogram

vertical axis

horizontal axis

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WEEK 25

9/7 13/7/12

6.4 Represent and

interpret data in

frequency

polygons to solveproblems

i) draw the frequency

polygon based on:

a. a histogram

b. a frequencytable

ii) interpret information

from a given frequency

polygon

iii) solve problems involving

frequency polygon

Constructivism

Cooperative

Learning

Drawing

diagrams

Interpreting

diagrams

Cooperation When drawing a

frequency polygon add

a class with 0 frequency

before the first classand after the last class


situations

Vocabulary:

frequency polygon

6.5 Understand

the concept ofcumulative

frequency

Student will be able to:

i) construct thecumulative frequency table for:

a) ungrouped datab) grouped data

ii) draw the ogive for:

a) ungrouped data

b) grouped data

constructivism

contextual

learning

Identifying

patterns

Identifyingrelations

Logical

reasoning

Hardworking

Neatness

Systematic

Diligence

When drawing ogive:

- usethe upper

boundaries;- add a

class with zero

frequency before

the first class

Vocabulary:

cumulative frequency

ungro

uped data

ogive

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6.6 Understand

and use the

concept of

measures ofdispersion to

solve problems

(i) determine the range of a set

of data.

(ii) determine :

a) the medianb) the first quartile

c) the third quartile

d) the interquartile range

from the ogive.

(iii) interpret information from

an ogive

Discuss the

meaning of

dispersion by

comparing a fewsets of data.

Graphing

calculator can be

used for this

purpose.

ICT

Enquiry-

discovering

Representing &

interpreting data

Classifying,comparing &

differentiating

Punctuality

Consistent

For grouped data:

Range = [midpoint of

the last class midpoint

of the first class]

Vocabulary:

Range

Measures of

dispersion

Median

First quartile

Third quartile

Interquartile range

7.0

PROBABI-

LITY

WEEK 26

16/7 20/7/12

7.1 understand

the concept ofsample space

(i)determine whether an outcome

is a possible outcome of anexperiment

(ii) list all the possible outcomes

of an experiment

(a) from activities

(b) by reasoning

(iii) determine the sample space ofan experiment

(iv) write the sample space by

using set notations.

Use concrete

examples such asthrowing a die and

tossing a coin

Definition of

sample space

Enquiry

discovery

constructivism

cooperative

learning

Logical -

reasoning

Collecting andhandling data

systematic Sample space

Outcome

Experiment

Possible outcome

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7.2 understand

the concept of

events

(i) identify the elements of a

sample space which satisfy given

conditions

(ii) list all the elements of a

sample space which satisfy certain

conditions using set notations

(iii) determine whether an event is

possible for a sample space

Discuss that an

event is a subset of

the sample space.

Discuss also

impossible events

for a sample space.

Discuss that the

sample space itselfis an event.

Definition of event

Cooperative

learning

Identifying

Comparing

co operations An impossible event is

an empty set.

EventElement

Subset

Empty set

Impossible event

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WEEK 27

23/7 27/7/10

7.3 understand

and use the

concept of

probability of anevent to solve

problems

(i) find the ratio of the number of

times an event occurs to the

number of trial;

(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 event andnumber of trials;

(iv) solve problems involving

probability;

(v) predict the occurrence of an

outcomes and make a decision

based on known information.


to introduce the

concept of

probability.

The suggested

activities maybe

done in pairs or

individually:

(i) flipping ofcoins and

tabulating results.(ii) flipping of

book pages to

record the last

digit.

(iii) wheel of

fortune(colour,number,

alphabet)

Discuss situation

which results in:

~Probability of

event = 1~Probability of

event = 0

Emphasize that the

value of probability

is between 0 and 1.Predict possible

events which might

occur in dailysituations.

Cooperative

learning

Representing and

interpreting data

Logicalreasoning

Systematic

Rational

Diligence

Accuracy

Probability

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8.0

CIRCLE III

WEEK 28

30/7 3/8/12

8.1 Understand

and use the

concept of

tangents to acircle

Students will be able to :

(i) identify tangents to a circle;

(ii) make inference that the

tangent to a circle is astraight line perpendicular 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 n circle;b)outside the circle;

(iv) determine the properties

related to two tangents to a

circle from a given point

outside the circle;

(v) solve problems involvingtangents to a circle.

Develop concepts

and abilities

through activities

using technologysuch as the

Geometers

Sketchpad and

graphing

calculator.

Constructivism

Contextual

learning

Thinking skill

Learning how to

learn

Identifying

patterns

Identifyingrelations

Comparing and

differentiating

Makinginference

Drawing

diagrams

Systematic

Neatness

Tangent to a circle

Perpendicular

Radius

CircumferenceSemicircle

Congruent

A

Two tangents to a

circle.

Relate to PythagorasTheorem.

8.2 Understand

and use the

properties of

angle between

tangent and chord

to solve

problems.

i) identify the angle in the

alternate segment which 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 issubtended by the chord;

iii) perform calculations involving

the angle in alternate segment;iv) solve problems involving

tangent to a circle and angle in

alternate segment.

Explore the

property of angle in

alternate segment

using Geometers

Sketchpad or other

teaching aids.

Enquiry

Discovery

Cooperative

learning

Integrating ICT

into teaching andlearning

Classifying

Identifying

patterns

Identifying

relations

Comparing and

differentiate

Determination

Diligence

Chord

Alternate segment

Major sector

Subtended

B

C

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WEEK 29

6/8 10/8/12TEST 2

WEEK 30

13/8 17/8/12

8.3 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 properties related

to 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 involvingcommon tangents to two circles;

iv) solve problems involving

tangents and common tangents.

Discuss the

maximum number

of common

tangents for the

three cases.

Include daily

situations.

Self access

learning

Problem solving

Cooperative

learning

Integrating ICT

into teaching and

learning

Finding possible

solutions

Working out

mentally

Tolerance

Consistent

Systematic

Emphasis that the

length of common

tangent are equal.

Common tangents

Include problems

involving Pythagoras

Theorem.

18/8 26/8/12 MID TERM 2 BREAK

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9.0

TRIGONO-

METRY II

WEEK 31

27/8- 30/8/12

9.1 understand

and use the

concept of the

values of sine cos and

tangent

( 0 360)

to solve problems

(i) identify the quadrants and

angles in the unit circle.

(ii) Determine :

a) the value of y- coordinate

b) the value of x- coordinatec) the ratio of y- coordinateto x- coordinate; of

several points on the

circumference of the unit

circle.

(iii) verify that, for an angle inquadrant 1 of the unit circle:

a) sine = y- coordinateb) cos = x- coordinate;

c) tangent = y- coordinate

x- coordinate

(iv) determine the values of:a) sineb) cosine

c) tangent

of an angle in quadrant 1 in the

unit circle;

Mastery learning

ICT

Self access

learning

Communication

method of

learningSelf access

learningCommunication

method of

learning

Constructivism

Self accesslearning

Communicationmethod of

learning

Identify relations Neatness

RationaleSincerity

Rationale

Systematic

Diligence

Rationale

Systematic

Diligence

Determination

PoliteRationale

The unit circle is the

circle of radius 1 with

its centre at the origin

quadrant

Sine

Cosine

Tangent

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WEEK 32

3/9 7/9/12

(v) determine the values of

a) sine ,

b) cos ,

c) tan ,

for 36090 ;

(vi) determine whether the values

of;a) sine;

b) cosine;

c) tangent,

of an angle in a specific quadrant

is positive or negative;

(vii) determine the values of sine,

cosine and tangent for specialangles:

(viii) determine the values of the

angles in quadrant I which

correspond to the values of the

angles in other quadrants;

Explain the

concept

sine = y-

coordinate;cos = x-

coordinate

coordinatex

coordinatey

=tan

can be extended toangles in quadrant

II, III and IV.

Use the abovetriangles to find the

values of sine,

cosine and tangent

for .60,45,30

Teaching can be

expanded throughactivities such as

reflection.

Cooperativelearning

Self Access

learning

Cooperative

learning

Self Access

learning

Mastery learning

Enquiry

discovery

Enquiry

discovery

Self Accesslearning

Comparing

Differentiating

DeterminationPolite

Rationale

Systematic

Consistent

Rationale

Cooperation

Hard working

Diligence

Freedom

Rationale

Diligence

Consistent

27

451

1

2

2

60

30

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WEEK 33

10/9 14/9/12

9.2 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.(ix) state the relationships

between the values of :a) sine;

b) cosine; and

c) tangent;

of angles in quadrant II, III and IV

with their respective values of the

corresponding angle in quadrantI;

(x) find the values of sine, cosine

and tangent of the angles between

90o and 360o;

(xi) find the angles between 0o

and 360o, given the values of sine,cosine or tangent;

(xii) solve problems involving

sine, cosine and tangent.

Use the Graphing

calculator and

Geometers

Sketchpad toexplore the feature

of the graphs of

y = sine , y = cos

y = tan .

Discuss the feature

of the graphs of

y = sine , y = cos

y = tan .

Discuss theexamples of these

graphs in other

area.Use the

Geometers

Sketchpad to

explore the change

in the values of

sine, cosine andtangent relative to

the change inangles.

Relate to daily

situations.

Contextual

learning

Cooperative

learning

Inquiry

discovery

Self access

learning

Constructivisme

Mastery learningCooperative

learning

Cooperative

learning

Self access

learning

Cooperative

learning

Self accesslearning

Constructivisme

Drawing graphs

Comparing

Problems

solvingIdentifying

relations

Neatness

Systematic

Rationale

Hard working

Rationale

Sincerity

Hard working

Cooperation

RationaleDiligence

Cooperation

Honesty

Polite

Sincerity

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10.0

ANGLE OF

ELEVATION

AND

DEPRESSION

WEEK 34

18/9 - 21/9/12

10.1 Understand

and use the

concept of angle

of elevation andangle of

depression to

solve problems.

i) identify:

a) the horizontal l ine;

b) the angle of elevation;

c) the angle of depression,or a particular situation;

ii)represent a particular situation

involving:

a) the angle of elevation;

b) the angle of depression,using diagrams;

iii) solve problem involving the

angle of elevation and

depression.

Use daily situations

to introduce the

concept.

Constructivism

Enquiry

discovery

ICT

Drawing

diagrams

Identifying

relations.Recognizing

and

representing

Collecting and

handling data.

Rationale

Systematic

Neatness

Include two

observations on the

same horizontal plane.

Involve activities

outside the classroom.

Angle of elevationAngle of depression

Horizontal line

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11.0

LINES AND

PLANES

WEEK 35

24/9 - 28/9/12

11.1 understand

and use the

concept of angle

between lines andplanes to solve

problems.

(i) identify planes.

(ii) identify horizontal planes,

vertical planes and inclinedplanes,

(iii) sketch a three

dimensional shape and

identify the specific planes,

(iv) identify :

a) lines that lies on a

plane,

b) lines that intersect

with a plane

(v) identify normal to a given

plane,

(vi) determine the orthogonal

projection of a line on a

plane;

(vii)draw and name theorthogonal projection of a

line on plane;

(viii) determine the angle

between a line and a plane;

(ix) solve problems involving

the angle between a line and aplane.


using daily

situations and 3-

dimensionalmodels.

Differentiate

between 2-

dimensional and 3-

dimensionalshapes. Involve

planes found innatural

surroundings.

Begin with 3-

dimensional

models.

Use 3- dimensionalmodels to give

clearer pictures.

Contextual

Learning

Inquiry-Discovery

Cooperative

Learning

Working out

mentally

Drawingdiagrams

Identifying

relations

Rationale

Systematic

Accuracy

Diligence

Horizontal plane

Vertical plane

3-dimensional

Normal to a planeOrthogonal

Projection

Space diagonal

Include line in 3-dimensional shapes.

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WEEK 36

1/10 - 5/10/12

11.2 understand

and use the

concept of angle

between twoplanes to solve

problems.

(i) identify the line of

intersection between two

planes;

(ii) draw a line on each planewhich 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 amodel and a given diagram;

(iv) Solve problems involvinglines and planes in 3-

dimensional shapes.

Use 3-dimensional

models to give

clearer pictures.

Contextual

Learning

Enquiry-Discovery

Cooperative

Learning

Working out

mentally

Drawingdiagrams

Identifying

relations

Rational

Systematic

Accuracy

Diligence

Angle between two

planes.

WEEK 37

8/10- 12/10/12

WEEK 38

15/10

19/10/12

REVISION FOR FINAL EXAMINATION

WEEK 39,

40 - 41

22/10 9/11/12FINAL EXAMINATION

31

RPT_F4_2012

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