Yearly Plan Form 2 2012

8/3/2019 Yearly Plan Form 2 2012

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1

YEARLY LESSON PLAN 2011

WEEK LEARNING AREA /

LEARNING OBJECTIVES

LEARNING OUTCOMES SUGGESTED T & L

ACTIVITIES

POINTS TO

NOTE

REMARKS

1

(4 ± 6 Jan)

1 DIRECTED NUMBERS

Students will be taught to:

1. Perform computationsinvolving multiplication

anddivision of integers to solve

problems..

Students will be able to:

i. Multiply integers.

ii. Solve problems involving multiplication of integers.

iii. Divide integers

iv. Solve problems involving division of integers

y Use concrete materials such ascoloured chips andmultiplication tables to

demonstrate multiplication anddivision of integers..

y Complete multiplication table by regconising patterns.

y Solve problems related to real-life situations.

Begin multiplicationinvolving twointegers only.

Relate division of

integers tomultiplication

Division by zero is

undefined

2

(9 ± 13 Jan)

2. Perform computations

involving combined

operations of addition,subtraction ,multiplicationand division of integers tosolve problems.

i. Perform computations involving combined

operations of addition subtraction,

,multiplication and division of integers.

ii. Solve problems involving combinedoperations of addition, subtraction,multiplication and division of integer including the use of brackets.

.

y Eg.

(-2) ± 3 + ( -4)

4 x (-3) ÷ (-6)y Use calculators to compare and

verify answers.

y Solve problems related to real ±

life situations such as moneyand temperature

Emphasise the order

of operations

Cobinedoperationsalsoknown as mixedoperations.

3

(16- 20 Jan)

3. Extend the concept of integers to fractions tosolve problems

i. Compare and order fractions

ii. Perform addition, subtraction, multiplicationand division of fractions

y Compare fractions usinga) number line

b) scientific calculators

Begin with twofractions



2

4

(23 ± 29 Jan)

CUTI TAHUN BAR U CINA DAN CUTI BERGANTI

5

(30 Jan ± 3 Feb)

4. Extend the conceptof integers todecimals to solve problems.

i. Compare and order decimals.

ii. Perform addition, subtraction, multiplication anddivision on decimals.

y Compare decimals usinga) number lines

b) scientific calculators.

Begin with twodecimals

5. Performcomputations

involving directednumbers ( integers,fractions anddecimals)

i. Perform addition, subtraction, multiplicationand division involving two directed numbers

ii. Perform computations involving combination of two or more operations on directed numbersincluding the use of brackets.

iii. Pose and solve problems involving directednumbers

y Explore addition, subtraction,multiplication and divisionusing standard algorithm andestimation.

y Perform operations on

integers .Eg -2 + (-3) x 4

y Perform operations onfractions.

Eg )2

1

5

3()

4

1( v

y Perform operations ondecimals

Eg 2.5 ± 1.2 x (-0.3)

y Perform operations on

integers , fractions anddecimals

Eg )4()

5

225.1( v

y Solve problems related to

real-life situations

Emphasise on theorder of operations



3

6

(6 ± 10 Feb)

CUTI MAULIDUL R ASUL (6 FEB 2012)

CUTI THAIPUSAM (7 FEB 2012)

2 SQUARES,SQUARE

ROOTS, CUBES AND

CUBE ROOTS

Students will be taught to:

1. Understand and use theconcept of squares of

numbers.


i. State a number multiplied by itself as anumber to the power of two and vice-versa.

ii. Determine the squares of numbers withoutusing calculators.

iii. Estimate the squares of numbers

iv Determine the squares of numbers usingcalculators

y Regconise squares of

numbers as the areas of theassociated squares

12 22 32

y Use pencil-and ± paper

method, mental and speed

calculations to evaluatesquares of numbers whereappropriate.a. The sum of odd and

even numbers. b. The product of odd and

even numbers.c. The difference between

odd and even numbers.

y Use estimation to check whether answers are

reasonable eg27 is between 20 and 30272 is between 400 and 900

y Explore square numbersusing calculators

152 read as fifteento the power of two , fifteen

squared or thesquae of fifteen

Emphasise that a2 is a notation for a x a

Include integers,

fractions anddecimalsEg(-8)

2= (-8) x(-8)

)(5

32=

5

3x5

3

0.62 = 0.6 x 0.6

Emphasis that thesquare of anynumber is greater than or equal tozeroEmphasise thereasonableness of answers

Discuss thatreadings from

calculators maybeapproximations



4

7

( 13 ± 17 Feb)

:

v. List perfect squares

vi. Determine if a number is a perfect square

vii. Pose and solve problems involving squares of numbers

y Explore perfect squares. Perfect squares arewhole numbers

The perfectsquares are 1, 4, 9,16, 25, «..

Emphasise thatdecimals andfractions are not perfect squares

2. Understand and usethe concept of square roots of positive numbers

i. Determine the relationship between squares andsquare roots.

ii. Determine the square roots of perfect squareswithout using calculator.

iii.Determine the square roots of numbers withoutusing calculators

y Explore the concept of

square roots using areas of squares.

. is a symbol for

square root.

5 read as`square

root of five¶

aa !2

Finding the squareroot is the inverseof squaring

Numbers includefractions anddecimals

Limit to

a) fractions thatcan be reducedsuch that thenumerators anddenominators are perfect squares b) decimals thatcan be written in

the form of thesquare of another decimals.



5

8

(20 ± 24 Feb)iv. Multiply two square roots.

v. Estimate square roots of numbers

vi. Find the square roots of numbers usingcalculators

vii Pose and solve problems involving squares andsquare roots

y :Investigate multiplications

involving square roots of a) the same number

b) different numbers

y Use estimation to check

whether answers arereasonable

Eg. 7 is between 4 and 9

7 is between 2 and 3

y Use calculators to explore the

relationship between squaresand square roots

Emphasise that

ab

ba

aa

aa

!v

!

!v

2)(

Emphasise thereasonaleness of answers

9

(27 Feb - 3 Mac)

3. Understand and usethe concept of cube

of numbers

i. .State a number multiplied by itself twice as anumber to the power of three and vice-versa

ii. Determine cubes of numbers without usingcalculators

y Regconise cube of a number

as the volume of the

associated cube.

y Use pencil- and- paper method, speed and mental

calculations to evaluatecubes of numbers.

43 read as ` four the power of

three¶ or `four cubed¶ or `thecube of four¶

Include integers,fractions anddecimals.

Emphasise that a3

is a notation for a x a x a

13 23 33



6

:

iii..Estimate cubes of numbers

iv. Determine cubes of numbers using calculators

v. Pose and solve problems involving cubes of numbers

y .Explore estimation of cubes

of numbers eg0.48 is between 0.4 and 0.50.483 is between 0.064 and

0.125y Explore cubes of numbers

using calculators

i.

5

2

5

2

5

2

5

2 3)(

x x

!

ii. 0.23 =0.2 x 0.2 x 0.2

Discuss thatcubes of negativenumbers arenegative

Emphasise the

reasonableness of answers

10(5 ± 9 Mac)

MID-TERM EXAMINATION

11(12 ± 16 Mac)

MID- TERM HOLIDAYS

12

(19 ± 23 Mac)4. Understand and use the

concept of cube rootsof numbers

i. Determine the relationship between cubes andcube roots:

ii. Determine the cube roots of integers withoutusing calculators

y Use calculators to explore

the relationship betweencubes and cube roots.

3 is the

symbol for cuberoot of a number

38 read as :

`cube root of

eight¶

Limit to numberswhose cube rootsare integers, for example :

...,.27,8,1 sss



7

. iii. Determine the cube roots of numberswithout using calculators

iv. Estimate cube roots of numbers

v. Determine cube roots of numbers usingcalculators

vi. Pose and solve problems involving cubesand cube roots

vii. Perform computations involving addition,subtraction, multiplication, division and

mixed operations on squares, square roots,cubes and cube roots

y Explore estimation of cuberoots of numbers eg.

20 is between 8 and 27320 is between 2 and 3

y Explore the relationship

between cubes and cuberoots using calculators

Limit to :a) Fractions that

can be reduced

such that thenumerators

anddenominatorsare cubes of integers

b) Decimals thatcan be written

in the form of cube of another decimal

13

(26 ± 30 Mac)

3 ALGEBRAIC

EXPRESSIONS II

Students will be taught

to:1. Understand the

concept of algebraic terms intwo or moreunknowns


i . Identify unknowns in algebraic terms in twoor more unknowns

ii. Identify algebraic terms in two or moreunknowns as the product of the unknownswith a number.

y Students identify unknownsin given algebraic terms eg.3ab : a & b are unknowns

-3d2 : d is an unknown

y Use examples of everydaysituations to explainalgebraic terms in two or more unknowns

a2

= a x ay3 = y x y x y

In general is yn ntimes y multiplied by itself

2pqr means 2 x p

x q x r



8

14

(2 -6 A pr)

iii. Identify coefficients in given algebraaic termsin two or more unknowns

iv. Identify like and unlike algebraic terms in twoor more unknowns

v. State like terms for a given algebraic term.

.

a2 b means1 x a2 x b

= 1 x a x a x b

-rs3

means-1 x r x s3

= -1 x r x s x s x s

Coefficients inthe term 4pq

Coefficients of pqis 4.Coefficient of q is4pCoefficient of p is

4q

2. Performcomputationsinvolvingmultiplication anddivision of two or more terms.

i. Find the product of two algebraic terms.

ii. Find the quotient of two algebraic terms.

iii. Perform multiplication and division involvingalgebraic terms

y Explore multiplication and

division of algebraic termsusing concrete materials or

pictorial representations.Eg.Find the area of a wallcovered by 10 pieces of tileseach measuring x cm by y

cmy Eg

a) 4rs x 3r = 12 r 2s b) 2p

2÷ 6pq =

q

p

q p

p p

36

2!

vv

vv

y Perform multiplication and

division such as6pq2 x 3p ÷ 2qr



9

Students will betaught to:

3. Understand the

concept of algebraicexpressions.


i. Write alg.ebraic expressions for given situationsusing letter symbols

ii. Regconise algebraic expressions in two or moreunknowns.

iii. Determine the number of terms in givenalgebraic expressions in two or more unknowns

iv. Simplify algebraic expressions by collecting

like terms

v. Evaluate expressions by substituting numbersfor letters

y Use situations to demonstrate

the concept of algebraicexpression.

y Eg

a)A

dd 7 to a number : n + 7 b) A number multiplied by 2and then 5 added :(n x 2) + 5 or 2n + 5

y Investigate the difference between expressions such as

2n and n + 2; 3(c + 5) and3c + 5: n2 and 2n ; 2 n2 and(2n)2

2xy is anexpression with 1

term

5 + 3ab is anexpression with 2terms.

4. Performcomputationsinvolvingalgebraicexpressions..

i. Multiply and divide algebraic expressions by anumber.

ii. Perform :a) addition b) subtractioninvolving two algebraic expressions

iii. Simplify algebraic expressions

y Use situations to explain

computations involvingalgebraic expressionsa) 8 (3x ± 2 )

b) (4x ± 6) ÷2 or 2

64 x

y Investigate why 8(3x ± 2) =

24x ± 16

y Add and subtract algebraicexpressions by removing

bracket and collecting liketerms

y Simplify algebraic

expressions such asa) 3x ± (7x ± 5x) b) 5(x + 2y) ± 3(2x ± 2y)

c) ½ (a + 7b ±c) +

3

1(4 ± b

± 2c)

.



10

15

(9 -13 A pr)

4 LINEAR

EQUATIONS.


1. Understand anduse the concept of equality


i. State the relationship between two quantities byusing the symbols `=¶ or `¶

y Use concrete examples to

illustrate `=¶ and `¶

y Discuss cases such asa) If a = b then b = a

eg. 2 + 3 = 4 + 1 then4 + 1 = 2 + 3 b) If a=b and b=c, then a=ceg 4+5 = 2+7 and 2+7=3+6then 4+5 =3+6

`=¶ read as ` isequal to¶

`¶ read as `is notequal to µ

Relate to the balance methodfor equations

2. Understand anduse the concept of linear equations in

one unknown

i. Regconise linear algebraic terms

ii. Regconise linear algebraic expressions.

iii. Determine if a given equation isa) a linear equation b) a linear equation in one unknown

iv. Write linear equation in one unknown for given

statements and vice versa

y Discuss why given algebraic

terms and expressions arelinear

y Students complete sequencesof integers, find the missingterms, and identify thelargest and the smallest value

of integers from given sets of integers.

y Given sets of integers,

students order them onnumber lines.

y Select linear equations given

a list of equationsEgX+3=5: x-2y=7, xy=10,x=3=5, x-2y=7 are linear equationsx + 3 = 5 is a linear equationin one unknown

y Include examples fromeveryday situations

.



11

16

(16 ± 20 A pr))

3. Understand theconcept of

solutions of linear equations in oneunknown.

i. Determine if a numerical value is a solution of agiven linear equation in one unknown.

ii. Determine the solution of a linear equation inone unknown by trial and improvement method.

iii. Solve equations in the foem of a) x = a = b b) x ± a = bc) ax = b

d) b

a

x

!

where a, b, c are integers and x is an unknown

iv. Solve equations in the form of ax + b = c wherea, b, c are integers and x is an unknown

v. Solve linear equations in one unknown

vi. Pose and solve problems involving linear equations in one unknown


explain solutions of linear equation in one unknown.Eg

Relate x + 2 =5 to + 2=5

y .Solve and verify linear equations in one unknown byinspection and systematictrial using whole numberswith and without the use of calculators

y Involve examples from

everyday situations.

The solutions of equations are also

known as theroots of theequations

Trial andimprovementmethod should bedone

systematically.

Emphasise theappropriate use of equal sign

17

(23 ± 27 A pr)

5 RATIOS,RATESAND

PROPORTIONS


1. Understand theconcept of ratio of

two quantities


i. Compare two quantities in the form a:b or b

a.

ii. Determine whether given ratios are equivalentratios

iii. Simplify ratios to the lowest terms

iv State ratios related to a given ratio

.

y Use everyday examples tointroduce the concept of ratio


explore:a) equivalent ratios b) related ratios

Include quantitiesof different unitsThe ratio 3:5means 3 parts to 5 parts and read as`three to five¶

IncludeGiven x: y find

a) y : x b) x : x ± yc) x : x + y



12


proportion to solve problems.

i. State whether two pairs of quantities is a proportion.

ii. Deermine if a quantity is proportional to another quantity given two values of each quantity.

iii. Find the value of a quantity given the ratio of the two quantities and the value of another quantity.

iv. Find the value of a quantity given the ratio andthe sum of the two quantities.

v. Find the sum of two quantities given the ratio of the quantities and the difference between the

quantities.

vi. Pose and solve problems involving ratios and

proportions.

y Use everyday examples to

introduce the concept of proportion.

y Verify the method of crossmultiplication and use it tofind the missing terms of a proportion.

d

c

b

a!

read as `a to b as

c to d¶

Begin withunitary method

Emphasise that if

d

c

b

a! then

ad = bc (b 0,d 0)

18

(30A pr ± 4 Mei)

CUTI HAR I PEKERJA ( 1 MEI 2012 )

3. Understand and usethe concept of ratioof three quantities tosolve problems.

i. Compare three quantities in the form a:b:c.

ii. Determine whether given ratios are equivalentratios.

iii. Simplify ratio of three quantities to the lowestterms.

iv. State the ratio of any two quantities given ratioof three quantities.

v. Find the ratio of a:b:c given the ratio of a:b and b:c

vi. Find the value of the other quantities , given theratio of three quanities and the value of one of the quantiies.

y Use everyday examples ointroduce the concept of ratio

of three quantities.

y y Use concrete examples to

explore equivalent ratios.

Include quantitiesof different units

a:b = p:q b: c = m : nwhen a) q = m

b) q m

Begin withunitary method



13

.

vii. Find the value of each of the three quantitiesgiven :

a) the ratio and the sum of three quantites b) the ratio and the difference between two of

the three quantities

viii. Find the sum of three quantites given the ratioand difference between two or threequantities

ix. Pose and solve problems involving ratio of three quantities.

19

(7 ± 11 Mei)

6 PYTHAGORAS¶

THEOREM

Students will be taughtto:

1. Understand thr relationship betweenthe sides of a right-angled triangle


i. Identify he hypotenuse of right-angled triangles.

ii. Determine the relationship between the lengthsof the sides of a right ±angled triangle

iii. Find the length of the missing side of a right ±

angled triangle using the Pythagoras µ theorem.

iv. Find the length of sides of geometric shapesusing Pythagoras¶ theorem

v. Solve problems using the Pythagoras¶ theorem

y Students identify thehypotenuse of right-angledtriangles drawn in differentorientations

y Use dynamic geometry

software, grid papers or geo- boards to explore and

investigate the Pythagoras¶theorem

Emphasise that

a2 = b2 + c2 is

the Pythagoras¶theorem.Begin with the

Pythagorean

Triples eg.

(3, 4, 5)

( 5, 12, 13)

Include

combined

geometricshapes

20,21

(14-25 Mei)

MID-YEAR EXAMINATION

22,23

(28 Mei ± 10 Jun)

MID-YEAR HOLIDAYS

C

A B

b

c

a



14

24

(11 ± 15 Jun)2. Understand and usethe converse of the

Pythagoras¶ theorem

i. Determine whether a triangle is a right-angledtriangle.

ii. Solve problems involving the conversePythagoras¶ theorem

y Explore and investigate the

converse of the Pythagoras¶theorem through activities

Note that :

If a2 > b2 + c2 ,

then A is an

obtuse angle.

If a2

< b2

+

c2

,then A is an

acute angle

25

( 18-22 Jun)

7 GEOMETRICAL

CONSTRUCTION


to:

1. Perform

constructions usingstraight edge ( ruler and set square) andcompass

Students will be able to :

i. Construct a line segment of given length.

ii. Construct a triangle given the length of thesides.

iii. Construct :a) perpendicular bisector of a given line

segment b) perpendicular to a line passing through a

point on the line

c) perpendicular to a line passing through a point not on the line

iv Construct :

a) angle of 60r and 120r b) bisector of an angle

v. Construct triangles givena) one side and two angles

b) two sides and one angle

vi. Construct :a) parallel lines b) parallelogram given its sides and an angle

y Relate constructions to

properties of rhombus andisosceles triangle

y Relate the construction to the

properties of equilateraltriangle

Explore situation when twodifferent triangles can beconstructed.

Emphasis onaccuracy of

drawing .Includeequilateral ,isosceles andscalene triangles.Emphasise theconstructions in aLearning

Outcome (iii) areused to construct

an angle of 90r

Emphasise theuse of the bisector of anangle to construct

angles of 30r, 45r and 15r and etc

Measure anglesusing protractors



15

26

(25 -29 Jun)

8 COORDINATES


to:

1. Understand and usethe concept of coordinates.


i. Identify the x-axis, y-axis and the origin on aCartesian plane.

ii. Plot points and state the coordinates of the points given distances from the y-axis andx-axis

iii. Plot points and state the distances of the pointsfrom the y-axis and x-axis given coordinates of the points

iv. State the coordinates of points on Cartesian

plane

y Introduce the concept of

coordinates using everydayexamples.

EgState the location of :a) a seat in the classroom b) a point on square grids

y Introduce Cartesian

coordinates as a systematicway of marking the locationof a point..

Coordinates of

origin is (0,0)

For LearningOutcomes ii ± iiiinvolve the firstquadrant only

Involve all thefour quadrants.

2. Understand and usethe concept of scales for the coordinatesaxes.

i. Mark the values on both axes by extending thesequence of given values on the axes

ii. State the scales used in given coordinates axeswherea) scales for axes are the same b) scales for axes are different.

iii. Mark the values on both axes with reference tothe scales given.

iv. State the coordinates of a given point withreference to the scales given.

v. Plot points, given the coordinates, with referenceto the scales given.

iv. Pose and solve problems involving coordinates

y Use dynamic geometrysoftware to explore and

investigate the conceptscales.

y Explore the effects of shapes

of objects by using differentsales

y Explore positions of placeson topography maps.

y Pose and solve problems

involving coordinates of vertices of shapes such as :

y Name the shape formed by

A(1,5), B (2,5), C(4,3) andD(3,3)

Emphasise thatthe scales used onthe axes must beuniform.

Scales should bewritten in the

form:

a) 2 unitsrepresents 3units

b) 1 : 5



16

4. Understand anduse the concept of midpoint.

i. Identify the midpoint of a straight line joiningtwo points.

ii. Find the coordinates of the midpoint of a

straight line joining two points witha) common y- coordinates b) common x- coordinates

iii. Find the coordinates of the midpoint of the line

joining two points.

iv. Pose and solve problems involving midpoints


midpoints through activitiessuch as folding , constructing, drawing and counting.

y Use dynamic geometry

software to explore andinvestigate the concept of midpoints.

The formula of

midpoint for points (x1,y1) and(x2,y2) is

)2

21,

2

21(

y y x x

need not beintroduced

Involve shapes

27

(2- 6 Julai)

3. Understand and usethe concept of distance betweentwo points on aCartesian plane

i. Find the distance between two points with

a) common y-coordinates b) common x coordinates.

ii. Find the distance between two points usingPythagoras theorem

iii. Pose and solve problems involving distance between two points.

y Discuss different methods of finding distance between two points such as :

a) inspection

b) moving one point to theother.

c) computing the difference between the x-coordinatesor y-coordinates

y Students draw theappropriate right ±angled

triangle using the distance between the two points as thehypotenuse.

Emphasise thatthe line joiningthe points are parallel to the x-axis or parallel to

the y-axis

Include positiveand negativecoordinates

The formula for distance betweentwo points (x1,y1)and (x2,y2) is

)2

12(

)21( 2

y y

x x

need not beintroduced



17

28

(9-13 Julai)

9 LOCI IN TWO

DIMENSIONS


1. Understand the

concept of two-dimensional loci

Student will be able to:

i. Describe and sketch the locus of a moving

object.

ii. Determine the locus of points that are of :

a) constant distance from a fixed point b) equidistant from two fixed pointsc) constant distant from a straight line.d) equidistant from two intersecting lines

iii.Construct the locus of a set of all points that

satisfies the condition.a) the point is at a constant distance from a

fixed point b) the point is at equidistant from two fixed

pointsc) the point is at a constant distance from a

straight lined) the point is at equidistant from two

intersecting line

y Use everyday examples suchas familiar routes and simple

paths to introduce theconcept of loci

y Discuss the locus of a pointin a given diagram.e.g. Describe a locus of a

point equidistant fromA and C

Emphasise theaccuracy of drawings.

Relate to properties of isosceles triangle

Emphasise locusasa) path of a

moving point b) a point or set

of pointsthat satisfiesgiven conditions



the intersection of two loci


i. Determine the intersections of two loci bydrawing the loci and locating the points thatsatisfy the conditions of the two loci.

y Use everyday examples or

games to discuss theintersection of two loci.

.

y Mark the points that satisfy

the conditionss.

a. Equidistant from A andC.

b. 3 cm from A.

Limited to locidiscussed inLearningO bjective 9.1

A B

D C



18

29

(16-20 Julai)

10 CIRCLES.

Student will be taught

to:1. Regconise and

draw parts of a

circle


i. Identify circle as a set of points equidistant froma fixed point.

ii. Identify parts of a circle :a) center b) circumferencec) radius

d) diameter e) chordf) arcg) sector h) segment


circle as a locus.

y Use dynamic geometrysoftware to explore partsof acircle

iii. Draw:a) a circle given the radius and centre b) a circle given the diameter c) a diameter passing through a specific point

in a circle given the centred) a chord of a given length passing through a

point on the circumferencee) sector given the size of the angle at the centre

and radius of the circle

iv. Determine the :a) center b) radius

of a given circle by construction

2. Understand and

use the concept of circumference to

solve problems

i. Estimate the value of T

ii. Derive the formula of the circumference of a

circle.

iii. Find the circumference of a circle, given itsa) diameter b) radius

iv. Find thea) diameter b) radiusgiven the circumference of a circle

v. Solve problems involving circumference of circles

y Measure diameter andcircumference of circular

objects..y Explore the history of T

y Explore the value of T

using dynamic geometrysoftware

Developed

through activities

The ratio of thecircumference tothe diameter isknown as T and

read as `pi µ

EmphasiseT = 3.142 or

7

22



19

30

(23 ± 27 Julai)

3. Understand anduse the

concept of arc of a

circle tosolve problems

i. Derive the formula of the length of the arc.

ii. Find the length of arc given the angle at the

centre and the radius

iii. Find the angle at the centre given the length of

the arc and the radius of a circle

iv. Find the length of radius of a circle given thelength of the arc and the angle at the centre

v. Solve problems involving arcs of a circle


between the length of arc andangle at the centre of a circleusing dynamic geometrysoftware

Include combined shapes

The length of arcis proportional tothe angle at the

centre of a circle

31

(30 Jul -3 Ogos)

4. Understand anduse the concept of

area of a circle tosolve problems

i. Derive the formula of the area of a circle.

ii. Find the area of a circle given thea) radius b) diameter

iii. Finda) radius b) diameter given the area of a circle

iv. Find the area of a circle given the

circumference and vice-versa

v. Solve problems involving area of circles


between the radius and thearea of a circlea) using dynamic geometry

software b) through activities such as

cutting the circle intoequal sectors and the

rearranging them intorectangular form

Include findingthe area of the

annulus

5. Understand anduse the concept of area of sector of acircle to solve

problems

i. Derive the formula of the area of a sector .

ii. Find the area of a sector given the radius andangle at the centre

iii. Find the angle at the centre given the radiusand area of a sector

iv. Find the radius given the area of a sector andthe angle at the centre

v. Solve problems involving area of sectors andarea of circles


between the area of a sector and the angle at the centre of the circle using dynamicgeometry software.

Include combinedshapes



20

32

(7-10 Ogos)

CUTI NUZULQUR AN (6 OGOS )

11 TRANSFORMATIONS

Student will be taught to:

1. Understand the concept of transformations


i. Identify a transformation as a one±to-onecorrespondence between points in a plane

ii. Identify the object and its image in a giventransformation

y Explore concepts in

transformational geometryusing concrete materials,drawings , geo-boards and

dynamic geometry software

A one-to-one

correspondence between points of a plane is alsocalled a mappingIncludetransformationsin arts and natureThe object ismapped onto theimage

2. Understand and use theconcept of translations

i. Identify a translation

ii. Determine the image of an object under agiven

translation

iii. Describe a translationa) by stating the direction and distance of

themovement

b) in the form ¹ º ¸©

ª¨b

a

iv. Determine the properties of translation.

v. Determine the coordinates of :a) the image , given the coordinates of

theobject

b) the object given the coordinates of the

imageunder a translation.

vi. Solve problems involving translations

y Explore translations given in

the form ¹ º

¸©ª

¨

b

a

y Investigate the shapes andsizes, lengths and angles of the images and the objects

Grid papers may be used

¹ º

¸©ª

¨

b

aa is the

movement parallel to the x ± axis and b is themovement

parallel to y±axis

Emphasise thatunder atranslation, theshapes, sizes andorientations of theobject and itsimage are the

same.



21

:

3. Understand and use theconcept of reflections

i. Identify a reflection

ii. Determine the image of an object under areflection on a given line.

iii. Determine the properties of reflections.

iv. Determinea) the image of an object given the axis

of

reflection b) the axis of reflection given the object

andits image.

v. Determine the coordinates of a) the image , given the coordinates of

the

object. b) the object, given the coordinates of

theimage

under a reflection.

vi. Describe a reflection given the objectand

image.

vii. Solve problems involving reflections.

y Explore the image ofan

object under a reflection bydrawing , using tracing paper, or paper folding

y Investigate the shapes andsizes, lengths and angles of the images and objects

The line is knownas line of

reflection or axisof reflection

Emphasise thatunder a reflectiona) the shapes and

sizes of theobject and its

image are thesame and

b) the orientationof the image islaterally

inverted ascompared tothat of the

object

Emphasise thatall points on theaxis of reflectiondo not changetheir positions.Include x-axisand y-axis as axes

of reflection.

35

(27-30 Ogos)

4. Understand and use theconcept of rotations

i. Identify a rotation.

ii. Determine the image of an object under a

rotation given the centre, the angle anddirection

of rotation

iii. Determine the properties of rotations.

iv. Determine :a) image of an object, given the centre ,

angleand direction of rotation

b) the centre, angle and direction of rotation,

given the object and the image

y Explore the image of an

object under a rotation bydrawing and using tracing paper

Emphasise thatunder rotation,the shapes, sizes

and orientationsof an object and

the image are thesame.

Emphasise thatthe centre of rotation is the

only point thatdoes not changeits position



22

v. Determine the coordinates of

a) the image, given the coordinates of the

object

b) the object, given the coordinates of theimage

vi. Describe a rotation given the object andimage

vii. Solve problems involving rotations

Include 90r and

180r as angles of

rotation

36

(3-7 Sept)

5. Understand and use theconcept of isometry

i. Identify an isometry

ii. Determine whether a giventransformation is an

isometry

iii. Construct patterns using isometry

y Using tracing paper to

explore isometry

Isometry is atransformation

that preserves theshape and the sizeof the object

6. Understand and use theconcept of congruence

i. Identify if two figures are congruent.

ii. Identify congruency between two figuresas a

property of an isometry.

iii. Solve problems involving congruence.

y Explore congruency under translations, reflectios androtations

Emphasise thatcongruent figureshave the samesize and shaperegardless of their orientation

7. Understand and use the properties of quadrilateralsusing concept of transformations

i. Determine the properties of quadrilateralsusing

reflections and rotations

y Explore the properties of various quadrilaterals bycomparing the sides, anglesand diagonals

Quadrilateralsinclude squares,rectangles,rhombus, parallelogramsand kites



23

37

(10 ± 14 Sept)

12 SOLID

GEOMETRY II


1. Understandgeometric

properties of prisms ,

pyramids,

cyclinders, conesand spheres


i. State the geometric properties of prisms ,

pyramids, cyclinders, cones and spheres

y Explore and investigate properties of geometricsolids using concrete models

Include 90r and180r as angles of

rotation


nets

i. Draw nets for prisms , pyramids, cyclinders andcones

ii. State the types of solids given their nets.

iii. Constuct models of solids given their nets

y Explore the similarities anddifferences between nets of prisms, pyramids, cyclinders

and cones using concretemodels

Net is also knownas layout.

Prisms includecubes andcuboids

38(18-21 Sept)

CUTI HAR IMALAYSIA (17 SEPTEMBER 2012)


surface area

i. State the surface areas of prisms, pyramids,cyclinders and cones

ii. Find the surface area of prisms, pyramids,cyclinders and cones

iii. Find the surface area of spheres using thestandard formula

iv. Find dimensions:a) length of sides b) heightc) slant heightd) radiuse) diameter

of asolid given its surface area and other relevant information

v. Solve problems involving surface areas.

y Explore and derive the

formulae of the surface areasof prisms , pyramids,cyclinders andcones

Standardformula for surface area of

sphere isr

T42

where r is theradius



24

39(24-28 Sept)

13 STATISTICS

Students will be

taught to:

1. Understand the

concept of data


i. Classify data according to those that can be

collected by :a) counting b) measuring

ii. Collect and record data systematically

y Carry out activities tointroduce the concept of data

as a collection of information

or factsy Discuss methods of

collecting data such ascounting , observations,measuring usingquestionnaires and interviews


frequency

i. Determine the frequency of data

ii. Determine the data witha) the highrst frequency b) the lowest frequencyc) frequency of a specific value

iii. Organise data bu constructinga) tally charts b) frequency tables

iv. O btain information from frequency tables

y Use activities to introduce

the concept of frequency

Use tally charts torecord data

Use two columnsor two rows to present data

40

(1-5 Okt)3. Represent andinterpreting data

in :i. pictogramsii. barchartsiii. line graphsto solve problems

iv. Construct bar charts to represent data

v. O btain information from bar charts

vi. Solve problems involving bar charts

vii. Represent data using line graphs

viii. O btain information from line graphs

ix Solve problems involving line graphs

y Use everyday situations tointroduce pictograms, bar charts and line graphs.

Includebar charts

representing twosets of data.

Use vertical andhorizontal bars.Include vertical

and horizontal bar charts usingscales such as

a) 1: 1 b) n, where n is a

whole number

Emphasise on theuse of suitablescales for line

graphs



25

Discuss on thechoice of usingvarious method torepresent data

effectively

41

(8-12 Oktober)

R EVISION

42, 43(15 -22 Oktober)

FINAL EXAMINATION

CUTI HAR I R AYA AIDILADHA (25-26 OKTOBER)

Yearly Plan Form 2 2012

Documents

Transcript of Yearly Plan Form 2 2012