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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
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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
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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.
Students will be able to:
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
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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.
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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
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:
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
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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
Students will be able to:
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
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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
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9
Students will betaught to:
3. Understand the
concept of algebraicexpressions.
Students will be able to:
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)
.
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10
15
(9 -13 A pr)
4 LINEAR
EQUATIONS.
Students will betaught to:
1. Understand anduse the concept of equality
Students will be able to:
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
.
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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
y Use concrete examples to
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
Students will betaught to:
1. Understand theconcept of ratio of
two quantities
Students will be able to:
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
y Use concrete examples to
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
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2. Understand theconcept of
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
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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
Students will be able to:
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
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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
Students will be taught
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
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15
26
(25 -29 Jun)
8 COORDINATES
Students will be taught
to:
1. Understand and usethe concept of coordinates.
Students will be able to:
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
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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
y Introduce the concept of
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
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17
28
(9-13 Julai)
9 LOCI IN TWO
DIMENSIONS
Students will betaught to:
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
Students will betaught to:
2. Understand theconcept of
the intersection of two loci
Students will be able to:
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
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18
29
(16-20 Julai)
10 CIRCLES.
Student will be taught
to:1. Regconise and
draw parts of a
circle
Student will be able to:
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
y Introduce the concept of
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
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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
y Explore the relationship
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
y Explore the relationship
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
y Explore the relationship
between the area of a sector and the angle at the centre of the circle using dynamicgeometry software.
Include combinedshapes
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32
(7-10 Ogos)
CUTI NUZULQUR AN (6 OGOS )
11 TRANSFORMATIONS
Student will be taught to:
1. Understand the concept of transformations
Student will be able to:
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.
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:
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
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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
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37
(10 ± 14 Sept)
12 SOLID
GEOMETRY II
Students will betaught to:
1. Understandgeometric
properties of prisms ,
pyramids,
cyclinders, conesand spheres
Students will be able to:
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
2. Understand theconcept of
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)
3. Understand theconcept of
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
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39(24-28 Sept)
13 STATISTICS
Students will be
taught to:
1. Understand the
concept of data
Students will be able to:
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
2. Understand theconcept of
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
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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)