Yearly Lesson Oct

8/6/2019 Yearly Lesson Oct

1/41

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME TEACHING AND

LEARNING ACTIVITIES

STRATEGIES

1. Standard

Form

( weeks )

1.1 Understand

and use theconcept ifsignificant

figure.

I Round off positive

numbers to a givennumber of significantfigures when the

numbers are:

a. greater than 1b. less than 1

II Perform operations of

addition, substraction ,

multiplication and

division, involving a fewnumbers and state theanswer in specific

significant figures.

III Solve problems

involving significantfigures.

Discuss the significance if zero

in a number.

Discuss the use of significant

figures in everyday life andother areas.

Teaching Aids

-mahjong paper- pictures

CCTS

-working outmentally

-Decision making-Identifying

relationship

Moral Values

-Cooperation

- rational

-being systematic-conscientious

Vocabulary

-Significance-Significant

figure

-relevant

-round off-accuracy


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

1.2 Understand and

use the concept ofstandard form tosolve problems

I State positive numbers in

standard form when thenumbers are:a. greater than or

equal to 10

b. less than 1

II Convert numbers instandard form to

single numbers.

\

III Perform operations ofaddition, subtraction,multiplication and

division, involvingany two numbers and

state the answers in

standard form.

IV Solve problemsinvolving numbers in

standard form.

Use everyday life situations

such as in health, technology,industry,construction and business

involving numbers in standard

form.

Use the scientific calculator toexplore numbers in standard

form.

Teaching Aids

-flash card-scientificCalculator

CCTS-working out

mentally-identifying

relationship

Moral ValuesCooperation,rational, being

systematic

Vocabulary

-standard form-single number

-scientificnotation


3/41

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

2.QuadraticExpressions andEquations

( weeks )

2.1 understand theconcept of

quadratic

1 expression;

I Identify quadratic expressions;

II

III Form quadratic

expressions

by multiplying any two

linear

expressions;

IV Form quadratic expressions

based on specific situations;

Discuss the characteristics ofquadratic expressions of the

form 02 =++ cbxax , where a,

b and c are constants, a 0 andx is an unknown.

Vocabulary:quadraticexpression

constant

constant factorunknown

highest powerexpand

coefficient

term

factorisecommon factor

perfect squarecross method

inspection

common factorcomplete

factorisation

2.2 factorise

quadratic

expression;

I Factorise quadratic

expressions

of the form cbxax ++2 ,

where

b = 0 orc = 0;

II Factorise quadratic

expressions

of the form px2q, p andq

are perfect squares;

Discuss the various methods to

obtain the desired product.


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III Factorise quadratic

expressions of the form

cbxax ++2 , where a, b

and c not equal to zero;

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES


5/41

2 IV Factorise quadraticexpressions containing

coefficients with

common factors;


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

2.3 understand the

concept of quadraticequation;

I identify quadratic equations

with one unknown;

II write quadratic equations in

general form i.e.

02

=++ cbxax ;

III form quadratic equations based

on specific situations;

Discuss the characteristics of

quadratic equations.

Vocabulary :

QuadraticequationGeneral form

Substitute

RootTrial and error

methodSolution

Moral Values:

DiligenceRationalityJustice

CCTS

Identifying

relationshipClassifying

CatogerisingDrawing

diagramsIdentify patternsProblem solving

Teaching Aids

CD courseware

2.4 understand anduse

the concept of

roots of

quadratic

equations to

solve problems.

I Determine whether a givenvalue

is a root of a specific quadratic

equation;

II Determine the solutions for

quadratic equations by:

- trial and error method;

- factorisation;

III Solve problems involving

1 quadratic equations.

Discuss the number of roots ofa quadratic equation.

Use everyday life situations.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

3. Sets

( Week )

3.1 Understand theconcept of set

I Sort given objects intogroups.

II Define sets by :

a. Descriptions

b. Using set notation

III Identify whether a givenobject is an element of a set

and use the symbol or

IV Represent sets by using Venn

Diagrams

V List the elements and state thenumber of elements of a set

VI Determine whether a set is an

empty set

VII Determine whether two sets

are equal.

a) Discuss the definition ofset.

b) Explain how to define sets.

c) Explain the meaning ofor.

d) Discuss the difference

between the representation ofelements and the number of

elements in Venn diagrams.

e) Use examples to list

elements and state the numberof elements of a set.

f) Discuss with examples.

Teaching Aids:Flash cards

CCTS:

Classifying

TranslatingIdentifying

relationships

Moral Values:Paying attention

Vocabulary:- Set

- Element- Description

- Label

- Set Notation- Denote

- Venn diagram- Empty set

- Equal set


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

3.2 Understand and usethe concept of

subset, universal set

and the complementof a set.

I Determine whether a given setis a subset of a specific set and

use the symbol or.

II Represent subset using Venn

Diagram

III List the subsets for a specificSet

IV Illustrate the relationshipbetween set and universal set

using Venn diagrams

V Determine the complement of agiven set.

VI Determine the relationshipbetween set, subset, universal

set and the complement of aset.

a) Discuss with everyday lifesituations.

b) Explain with examples.

c) Verify the relationshipbetween set and universal

sets.

d) Explain the meaning of thecomplement set.

e) Simplify by using setnotations.

Teaching Aids:Laptop

Diagrams

CCTS:

TranslatingCategorizing

Moral Values:

Being hard-workingBeing honest

Vocabulary:

- Subset

- Universal set- Complement of a

set


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

3.3 Perform operations

on sets :-the intersection of sets.

-the union of sets.

I Determine the

intersection ofa) two sets

b) three setsand use the

symbol .

II Represent the intersection ofsets using Venn diagrams.

III State the relationship between

a) A B and A

b) A B and B

IV Determine the complement of

the intersection of sets.

V Solve problems involving theintersection of sets.

VI Determine theunion of

a) two setsb) three sets,

and use the

a) Discuss the definition of

intersection and use the

symbol .

b) Explain the relationshipbetween

i) A B and A

ii) A B and Bby using Venn diagram.

Teaching Aids:

LaptopDiagrams

Text book

CCTS:

Describing

Drawing diagramsProblem-solving

Moral ValuesPaying attention

Cooperation

Concentration

Vocabulary- Intersection

- Union- Operation


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

symbol .

VII Represent the union of thesets using Venn diagrams.

VIII State the relationship

between

a) A B and A

b) A B and B

IX Determine the complement of

the union of sets.

X Solve problems involving the

union sets.

XI Determine the outcome of

combined operations on sets.

XII Solve the problems involvingcombined operation on sets.

c) Discuss thedefinition of union

and use the symbol .d) Explain the relationship

between

i) A B and A

ii) A B and Bby using Venn diagram.


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

4. MathematicalReasoning

4.1 understand theconcept of statement

I Determine whether a given

sentence is a statement;

II Determine whether a given

statement is true or false;

Introduce this topic usingeveryday life situations.

Focus on mathematical

sentences

Statements consisting of:

words only, e.g. Five is

greater than two.;

numbers and words, e.g.

5 is greater than 2.;

numbers and symbols, e.g.

5 > 2.

CCTS:Making General

Statement

Moral Value:

Cooperation

Teaching Aids:Multimedia

III Construct true or false

statement

using given numbers and

mathematical symbols;

Discuss sentences consisting

of:

words only;

numbers and words;numbers and mathematical

symbols;The following are not

Vocabulary:

StatementTrue

FalseMathematical

sentence

Mathematical


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

statements:

Is the place value of digit9 in 1928 hundreds?;

4n5m + 2s; Add the two numbers.;

x + 2 = 8.

statement

Mathematicalsymbol

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

II determine whether astatement

that contains the quantifier

all is true or false;

Examples: All squares are four sidedfigures.

Every square is a four

sided figure.

Vocabulary:QuantifierAll

EveryAny

SomeSeveral

One of

Part ofNegate

ContraryObject

III Determine whether astatement can be generalised

to cover all cases by using thequantifier all;

Other quantifiers such asseveral, one of and part

of can be used based oncontext.

Teaching Aids:Multimedia


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LEARNING

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LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

IV Construct a true statement

using the quantifier all orsome, given an object and a

property.

Example:

Object: Trapezium.Property: Two sides are

parallel to each other.Statement: All trapeziums


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LEARNING LEARNING LEARNING OUTCOME TEACHING AND LEARNING STRATEGIES


15/41

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME TEACHING AND LEARNING

ACTIVITIES

STRATEGIES

have two parallel sides.Object: Even numbers.

Property: Divisible by 4.

Statement: Some even numbers

are divisible by 4

4.3 perform operationsinvolving the words

not or no, andand or on

statements;

I Change the truth value of a givenstatement by placing the word

not into the original statement;

II Identify two statements from a

compound statement that contains

III Form a compound statement bycombining two given statements

using the word and;

IV Identify two statement from a

compound statement that containsthe word or ;

V Form a compound statement by

Begin with everyday life situations.The negation no can be used

where appropriate.The symbol ~ (tilde) denotes

negation.

~p denotes negation ofp whichmeans notp or nop.

The truth table forp and ~p are asfollows:

p ~p

True

False

False

True

The truth values for p and q are

as follows:

The truth values for p orq are asfollows:

p q p orq

True True True

CCTS:Reasoning

Moral Value:

Confidence

VocabularyNegation

Not pNo p

Truth tableTruth value

And

Compoundstatement

Or

Teaching Aids:

Multimedia

p q p and q

True True True

True False False

False True False

False False False


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

5. The StraightLine

( Week)

5.1 understand theconcept of gradient of

a straight line;

I Determine the vertical andhorizontal distances between two

given points on a straight line.

II Determine the ratio of verticaldistance to horizontal distance.

Use technology such as theGeometer`s Sketchpad, graphing

calculators, graph boards,magnetic boards, topo maps as

teaching aids where appropriate.

Begin with concreteexamples/daily situations to

introduce the concept of gradient.

Discuss:

The relationship between

gradient and tan .

The steepness of thestraight line with different valueof gradient.

Carry out activities to find the ratio

Vocabulary:Straight line

SteepnessHorizontal distance

Vertical distanceGradient

Ratio

CCTS :Compare &contrast

MakingConnection &Association

Moral Value:

CooperationConscientious

Teaching Aids:

GSP,Gramatica,

Vertical

distance

Horizontal distance


17/41

of vertical distance to horizontaldistance for several pairs of points

on a straight line to conclude thatratio is constant.

Ruler, Set SquareGraphing

Calculators


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

5.2 understand theconcept of gradient of

a straight line inCartesian Coordinates

I Derive the formula for the gradientof a straight line;

m=y2-y1x2-x1

II Calculate the gradient of a straightline passing through two points;

III Determine the relationshipbetween the value of the:

a) steepness;b) direction of inclination, of a

straight line;

Discuss the value of gradient ifa. Pis chosen as (x1,y1) and

Q is (x2,y2)

b. Pis chosen as (x2,y2) andQ is (x1,y1)

Vocabulary:Acute angle

Obtuse angleInclined upwards to

the rightInclineddownwards to therightUndefined

CCTS :

Drawing diagramCompare &ContrastMaking Conclusion

Moral Value:CooperationConscientious

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES


19/41

5.3 understand theconcept of intercept

I Determine the x-intercept and they-intercept of a straight line;

II Derive the formula for the

gradient of a straight line in termsof the x-intercept and the y-

intercept;

III Perform calculations involvinggradient, x-intercept and y-intercept;

CCTS :Drawing diagram

Compare &Contrast

Making Conclusion

Moral Value:Cooperation

Conscientious

Vocabulary:x- intercepty-intercept

5.4 understand and useequation of a straightline;

I Draw the graph given an equationof the form y = mx + c;

II Determine whether a given pointlies on a specific straight line;

III Write the equation of the straight

line given the gradient and y-intercept;

Discuss the change in the form ofthe straight line if the value of mand c are changed

Carry out activities using thegraphing calculator, Geometer`sSketchpad or other teaching aids.

Verify that m is the gradient and c

is the y-intercept of a straight linewith equation y = mx + c.

Vocabulary:Linear equationGraphTable of valueCoefficientConstantSatisfyParallelPoint of

intersectionSimultaneousEquations


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

IV Determine the gradient and y-intercept of the straight linewhich equation is of the form:a) y = mx + c;

b) ax + by = c;

V Find the equation of the straightline whicha) 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 point;

VI Find the point of intersection of

two straight lines by:a)drawing the two straight lines

b)solving simultaneous equations

Discuss and conclude that the

point of intersection is the onlypoint that satisfies both equations.

Use the graphing calculator and

Geometer`s Sketchpad or otherteaching aids to find the point of

intersection.

CCTS :

Drawing DiagramProvingIdentify patternClassifying

Moral Value:


LEARNING

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LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES


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5.5 understand and usethe concept of parallel

lines

I Verify that two parallel lines havethe same gradient and vice versa.

II Determine from the given

equations whether two straightlines are parallel.

III Find the equation of the straight

line which passes through a givenpoint and is parallel to anotherstraight line.

IV Solve problems involvingequations of straight lines.

Explore properties of parallel linesusing the graphing calculator and

Geometer`s Sketchpad or otherteaching aids.

Vocabulary:Parallel lines

CCTS :

Compare &

ContrastDrawing Diagram

Problem SolvingIdentify Pattern

Moral Value:



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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING OUTCOME TEACHING AND LEARNING ACTIVITIES STRATEGIES

6. Statistics 6.1 understandthe conceptof class

interval

I Complete the classinterval for a set of datagiven one of the class

intervals,

II Determine

a) the upper limit andlower limit;

b) the upper boundry

and lower boundryof a class in a group

data;

III Calculate the size of aclass interval;

IV Determine the classinterval, given a set of

data and the number ofclasses;

V Determine the suitableclass interval for a given

set of data;

VI Construct a frequencytable for a given set of

data.

Use data obtained from activities and othersources such as researh studies to introduce theconcept of class interval.

Discuss criteria for suitable class intervals

CCTS:-planning-constructing-classifying- working outmentally

Moral Value:- cooperation- develop socialskills

Teaching Aids:-courseware

- white board


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


6. Statistics 6.2 understandand use the

concept ofmode and

mean of

groupeddata;

(i) determine the modalclass from the frequency

table of grouped data;

(ii) calculate the midpoint

of a class;

(iii) verify the formula forthe mean of group data;

(iv) calculate the meanfrom the frequency table of

grouped data;

(v) discuss the effect of thesize of class interval on a

accuracy of the mean for a

specific set of grouped data.

Use data obtained from activities and othersources such as researh studies to introduce the

concept of class interval.

Discuss criteria for suitable class intervals

CCTS- categorising

- identifying

Moral Value- cooperation

- develop socialskills

- rationality

Teaching Aids- caurseware


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


6.3 representand interpret

data inhistograms

with class

intervals ofthe same size

to solveproblems

I Draw a histogram basedon the frequency table of

a grouped data;

II Interpret information

from a given histogram;;

III Solve problem involvinghistograms;

Discuss the difference between histograms andbar chart

Use graphing calculator to explore the effect of

difference class interval on histogram

CCTS- categorising

- identifyingrelationship

Moral Value

- develop socialskills

- mental &physicalcleanliness- rationality

Teaching Aids- courseware- graph paper- graph charts- statistical data

6.4 represent

and interpretdata in

frequencypolygons tosolve

(i) draw a frequency

polygons based ona) a histogram;

b) a frequency table;

(ii) interpret information

from a given frequencypolygon;

(ii) solve problems

involving frequency

CCTS- constructing- drawingdiagram- interpreting- problem solving

Moral Value- develop socialskills- mental &

physical


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polygon. cleanliness- rationality

Teaching Aids

- courseware- graph paper

6.5 understand

the conceptof

cumulativefrequency;

(i) construct the cumulative

frequency

(ii) draw the ogive forungrouped data group data

CCTS

- constructing- drawing

diagram

Moral Value- develop social

skills- mental &

physicalcleanliness- rationality- patient- systematic

Teaching Aids- courseware- graph paper

- flexible rules


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


6.6 Understandand use the

concept ofmeasures of

dispersion to

solveproblem

(i) determine the range of aset of data

(ii) determine

a. the median

b. the first quartilec. the third quartile

d. the interquartilerange

from the ogive

(iii) interpret informationfrom an ogive

(iv) solve problems

involving datarepresentations and

measures of dispersion

Discuss the meaning of dispersion by comparinga few sets of data.

Graphing calculator can be used for this purpose.

Carry out a project/research and analyse as well

as interpret the data.Present the findings of the projects or research.

Emphasise the importance of honesty and

accuracy in managing ststistical research.

CCTS- interpreting

- describing- identifying

information

Moral Value- cooperation

Teaching Aids-courseware- graphingcalculator

- statistical data


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING

OUTCOME

TEACHING AND LEARNING ACTIVITIES STRATEGIES

7. Probability

( Week)

7.1 understandthe concept of

sample space;

I Determine

whether anoutcome is a

possibleoutcome

of an experiment;

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 setnotations.

Use concrete examples such as throwing a diceand tossing a coin.

Teaching Aids:

Dice

CardsCoins

Vocabulary:

Sample Space

OutcomesExperiment Possible

Outcome


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING

OUTCOME


7.2. understandthe 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 samplespace.

Discuss also impossible events for a sample space.

Discuss that the sample space itself is an event.

Moral Value:Coorperative learning

Vocabulary:

event

elementsubset

empty setimpossible event

7.3 understandand use the

concept ofprobability of

an event to

I Find the ratio of

the number of

times an event

occurs to the

Carry out activities to introduce the concept ofprobability. The graphing calculator can be used to

simulate such activities.

Enquiry learning

Probability


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solve problems. number of trials;

LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES

LEARNING

OUTCOME


II List all the

elements of a

sample space

which satisfy

certain conditions

using set notations;

III Calculate the

expected number

of times an event

will occur, given

the probability of

the event and

number of trials;

IV Solve problems

Involvingprobability;

V Predict the

occurrence of an

outcome and make

Discuss situation which results in:

probability of event = 1.

probability of event = 0.

Emphasise that the value of probability is between

0

Predict possible events which might occur in daily

situations.and 1.

Cooperative learning

Contextual learning


30/41

a decision based on

known information.

LEARNING

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LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

8. Circle III

( weeks)

8.1 Understandand use the concept

of tangents to acircle.

I Identify tangents to a circle;

II Make inference that thetangent to a circle is a straight

line perpendicular to the radius

that passes through the contactpoint;

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 propertiesrelated to two tangents to a

circle from a given point

outside the circle;

V Solve problems involvingtangents to a circle.

Develop concepts and abilitiesthrough activities using

technology such as theGeometers Sketchpad and

graphing calculator.

Vocabulary:Tangent to a

circleCircle

Perpendicular

RadiusCircumference

Semi circleCongruent

CCTS:

Making inference

Drawing diagram

Moral Values:Diligence

Cooperation

Courage

Teaching Aids:Compass

Geometry setGSP


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

8.2 Understand and use

the properties of anglebetween tangent and

chord to solve problems

I Identify the angle in the

alternate segment which issubtended by the chord through

the contact point of the tangent;

II Verify the relationshipbetween the angle formed by

the tangent and the chord withthe angle in the alternate

segment which is subtended by

the chord;

III Perform calculations involvingthe 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 usingGeometers Sketchpad or other

teaching aids.

Vocabulary:

ChordsAlternate segment

Major sector

Subtended

CCTS:Identifying

information

Justifyrelationships

Problem solving


Cooperation

Courage

Teaching Aids:GSP

GRAPHMATICA


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

8.3 understand and usethe properties of

common tangents tosolve problems

I Determine the number ofcommon 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 two circles which;

a) intersect at two points;

b) intersect only at one point;c) do not intersect;


common tangents to two

circles;

IV Solve problems involvingtangents and common

tangents.

Discuss the maximum numberof common tangents for the

three cases.

Include daily situations.

Vocabulary:

Common tangent

CCTS:

Identifyinginformation

Justifyrelationships

Problem solving

Moral Values:

DiligenceCooperation

Courage

Teaching Aids:

GSPGRAPHMATICA


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

9.Trigonometry II

( weeks)

9.1 Understand and

use the concept of the

values of sin , cos

and tan (0

360) to solveproblems

I Identify the quadrantsand

angles in the unit circle;

II Determine:

a. the value of y-coordinate;

b. the value of x-coordinate;

c. the ratio of y-coordinate to

x-coordinate;

of several points on the

circumference of the unit

circle;

III Verify that, for an angle in

quadrant I of the unit circle :

sin = y-coordinate ;

cos = x-coordinate;

coordinatecoordinate

tan

=

x

y ;

Explain the meaning of unit

circle.

determine the values of

Begin with definitions of sine,cosine and tangent of an acute

angle.y

y

OP

PQ===

1sin

xx

OP

OQ===

1cos

x

y

OQ

PQ==tan

Explain that the concept

Vocabulary:

Quadrant

Sine

Cosine

Tan

CCTS:

Identifying

informationJustify

relationshipsMaking

connection


CooperationRationality

Teaching Aids:GSP

GRAPHMATICAGeometry set

0

y

x

P (x,y)

y1

x Q


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IV Determine the values of

a. sine;

b. cosine;

c. tangent;

of an angle in quadrant I of

the unit circle;

V Determine the values of

a. sin ;

b. cos ;

c. tan ;

for 90 360;

VI Determine whether the

values of:

a. sine;

b. cosine;

c. tangent,

of an angle in a specific

quadrant is positive or negative;

sin = y-coordinate ;cos = x-coordinate;

coordinate

coordinatetan

=

x

y

can be extended to angles in

quadrant II, III and IV.

Use the above triangles tofind the values of sine, cosine

and tangent for 30, 45, 60.

Teaching can be expanded

through activities such asreflection.

Use the Geometers

Sketchpad to explore the

1

45

1

2

3

30

260


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VII Determine the values of

sine, cosine and tangent forspecial angles;

VIII Determine the values of

the angles in quadrant I

which correspond to the

values of the angles in

other quadrants;

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 respectivevalues of the corresponding

angle in quadrant I;

X Find the values of sine,

cosine and tangent of the

change in the values of sine,cosine and tangent relative to

the change in angles.


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angles between 90and

360;

XI Find the angles between 0

and 360 , given the value of

sine , cosine or tangent.

XII Solve problems involving

sine, cosine and tangent.

Relate to daily situations


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

9.2 Draw and use the

graphs of sine, cosine

and tangent

I Draw the graphs of sine,

cosine and tangent for angles

between 0and 360

II Compare the graphs of sine ,

cosine and tangent for angles

between 0and 360


graphs of sine, cosine and

tangent.

Use the graphing calculator

and GSP to explore the

feature of the graphs of

y = sin , y= cos , y = tan

Discuss the feature of thegraphs of

y = sin , y= cos , y = tan

Discuss the examples of these

graphs in other area

CCTS:

Problem Solving

Compare andcontrast

Drawing graphs

MORAL

VALUES:Cooperation

HonestyDiligence

Integrity

T.AIDS:

GSPGraph paper


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

10. Angles of

Elevationand

Depression

( week )

10.1 Understand and

use the concept ofangle 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

situationinvolving:

a. the angle of elevation;

b. the angle of depression, usingdiagrams;


the

angle of elevation and the

angle of depression.

Use daily situations to introduce

the concept.

Include two observations on the

same horizontal plane.

Involve activities outside theclassroom.

Vocabulary :

Angle ofelevation

Angle of

depressionHorizontal line

Moral Values:Rationality

Cooperation

CCTS:Working out

mentallyCompare and

contrastIdentifying

relationship

Decision makingProblem solving

Teaching Aids:Models

CD courseware


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LEARNING

AREA/WEEKS

LEARNING

OBJECTIVES


LEARNING ACTIVITIES

STRATEGIES

11. Lines andplanes in three

dimensions

( weeks)

11.1 understand anduse

the concept of

anglebetween lines and

planes to solveproblems.

I Identify planes

II Identify horizontal planes,vertical planes and inclined

planes;

III Sketch a three dimensionalshape 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;

Carry out activitiesusing daily situation

and 3-dimensional

models.

Differentiate between2-dimensional and 3-

dimensional shapes.

Involve planes found innatural surroundings.

Begin with 3-dimensional

models.

CCTS:Describing

Interpreting

Drawingdiagrams

Problem solving

Moral Values:

RespectCooperation

Vocabulary:

Horizontal planeVertical plane

3-dimensional

Normal to a planeOrthogonal

projectionSpace diagonal

Angle between

two planes

Approaches:

ConstructivismExploratory

Cooperative


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VII Draw and name the

orthogonal projection of aline

on a plane;

VIII Determine the angle between

3 a line and a plane;

4

IX Solve problems involving the

angle between a line and a

plane.

Include lines in 3-dimensionalshapes.

Use 3-dimensionalmodels to give clearer

pictures.

Learning

11.2. Understand anduse the concept of

angle between twoplanes to

solve problems.

I Identify the line of

intersection between two

planes;

II Draw a line on each

plane which is perpendicularto the line of intersection of

the two planes at a point

on the line ofintersection;

III Determine the angle between

two planes on a model and agiven diagram;

Use 3-dimensional models togive clearer pictures.


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IX Solve problems involvinglines and planes in 3-dimensional

shapes.

Yearly Lesson Oct

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