Scheme of Work Mathematics Form 2

7/28/2019 Scheme of Work Mathematics Form 2

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Scheme Of Work Mathematics Form 2, 2011

Week/Date Topics Learning Outcomes Suggested Teaching and Learning

Activities

Remarks

1

(3/1-7/1)

1.1 Performcomputationsinvolvingmultiplication anddivision of integersto solve problems

1.2 Performcomputationsinvolving combinedoperations ofaddition,subtraction,

multiplication anddivision of integers to solveproblems

Students will be able to:i. Multiply integers.ii. Solve problems involvingmultiplication of integers.iii. Divide integers.iv. Solve problems involvingdivision of integers.

i. Perform computationsinvolving combinedoperations of addition,subtraction, multiplication anddivision of integers.ii. Solve problems involving

combined operations ofaddition, subtraction,multiplication and division ofintegersincluding the use of brackets

Use concrete materials such ascoloured chips and multiplicationtables to demonstratemultiplication and division ofintegers.Complete multiplication table byrecognising patterns.Solve problems related to real-lifesituations.e.g.( 2) 3 + ( 4)4 x ( 3) ( 6)Students use calculators tocompare and verify answers.

Solve problems related to real-life situationssuch as money and temperature.

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(10/1- 21/1)

1.3 Extend the conceptof integers tofractions to solveproblems.

1.4 Extend the conceptof integers todecimals to solveProblems

1.5 Performcomputationsinvolving directednumbers (integers,fractions and decimals)

i. Perform addition, subtraction,multiplication or divisioninvolving two directednumbers.ii. Perform computationsinvolving combination of twoor more operations ondirected numbers includingthe use of brackets.iii. Pose and solve problems involvingdirected numbers

Explore addition, subtraction,multiplication and division usingstandard algorithm andestimation.Perform operations on integers.e.g.

2 + ( 3) x 4Perform operations on fractions.Perform operations on decimals.e.g.2.5 1.2 x ( 0.3)

Perform operations on integers,fractions and decimals.Solve problems related to real-life situations.

4

(24/1-29/1)

2.1 Understand anduse the conceptof squares ofNumbers

i. State a number multiplied by itself as anumber to the power of two and vice-versa.ii. Determine the squares ofnumbers without usingcalculators.iii. Estimate the squares of

Recognise squares of numbersas the areas of the associated squares.Use pencil-and-paper method,mental and speed calculations toevaluate squares of numberswhere appropriate.


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2.2 Understand anduse the conceptof square roots ofpositive numbers.

numbers.iv. Determine the squares ofnumbers using calculators.v. List perfect squares.vi. Determine if a number is a perfect square.

vii. Pose and solve problemsinvolving squares of numbers.

i. State the square root of apositive number as thenumber multiplied by itselfequals to the given number.ii. Determine the square roots of perfectsquares without using calculator.iii. Determine the square roots of numberswithout using calculators.iv. Multiply two square roots.v. Estimate square roots ofnumbers.vi. Find the square roots of

numbers using calculators.vii. Pose and solve problemsinvolving squares and square roots.

Use estimation to check whetheranswers are reasonable.e.g.27 is between 20 and 30.272 is between 400 and 900.

Explore square numbers usingcalculators.Explore perfect squares.

Explore the concept of squareroots using areas of squares.Investigate multiplicationsinvolving square roots of:a) the same numberb) different numbers.Use estimation to check whetheranswers are reasonable.e.g.

7 is between 4 and 9

7 is between 2 and 3.Use calculators to explore therelationship between squares andsquare roots.

5

(31/1-4/2)Cuti Tahun Baru Cina

6

(7/2-11/2)

2.3 Understand anduse the concept ofcube of numbers.

2.4 Understand anduse the concept of cube rootsof numbers.

i. State a number multiplied by itself twice asa number to the power of three and viceversa.ii. Determine cubes of numbers without usingcalculators.iii. Estimate cubes of numbers.iv. Determine cubes of numbers using

calculators.v. Pose and solve problemsinvolving cubes of numbers.

i. State the cube root of anumber as the numbermultiplied by itself twiceequals to the given number.ii. Determine the cube roots of integers

Recognise cube of a number asthe volume of the associated cube.Use pencil-and-paper method,speed and mental calculations toevaluate cubes of numbersExplore estimation of cubes ofnumbers.

e.g.0.48 is between 0.4 and 0.50.483 is between 0.064 and 0.125Explore cubes of numbers using calculator.

Use calculators to explore therelationship between cubes andcube roots.Explore estimation of cube rootsof numbers.e.g.


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without usingcalculators.iii. Determine the cube roots of numberswithout usingcalculators.

iv. Estimate cube roots ofnumbers.v. Determine cube roots ofnumbers using calculators.vi. Pose and solve problemsinvolving cubes and cuberoots.vii. Perform computationsinvolving addition, subtraction,multiplication, division andmixed operations on squares, square roots,cubes and cube roots.

20 is between 8 and 27.3 20 is between 2 and 3.Limit to:a) Fractions that canbe reduced such that the numerators and

denominators arecubes of integers.b) Decimals that canbe written in the form of cube ofanother decimal.Explore the relationship between cubes andcube roots using calculators.

7

(14/2-18/2)

3.1 Understand the

concept ofalgebraic terms intwo or moreunknowns.

3.2 PerformcomputationsInvolving multiplication anddivision of two or

more terms.

i. Identify unknowns in algebraic terms in two

or more unknowns.ii. Identify algebraic terms in two or moreunknowns as the product of the unknownswith a number.iii. Identify coefficients in given algebraicterms in two or more unknowns.iv. Identify like and unlikealgebraic terms in two ormore unknowns.v. State like terms for a given algebraic term.

i. Find the product of twoalgebraic terms.ii. Find the quotient of twoalgebraic terms.

iii. Perform multiplication anddivision involving algebraic terms.

Students identify unknowns in

given algebraic terms.e.g.3ab : a & b are unknowns.

3d 2 : d is an unknown.Use examples of everydaysituations to explain algebraicterms in two or more unknowns.

Explore multiplication and divisionof algebraic terms using concretematerials or pictorialrepresentations.

e.g.Find the area of a w all covered by10 pieces of tiles each measuring

xcm byycm.Perform multiplication anddivision such as:6pq 2 x 3p 2qr

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(21/2-25/2)

3.3 Understand theconcept ofalgebraic

i. Write algebraic expressionsfor given situations usingletter symbols.

Use situations to demonstrate theconcept of algebraic expression.e.g.


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expressions.

3.4 Performcomputationsinvolvingalgebraicexpressions.

ii. Recognise algebraicexpressions in two or moreunknowns.iii. Determine the number ofterms in given algebraic

expressions in two or moreunknowns.iv. Simplify algebraicexpressions by collecting like terms.v. Evaluate expressions bysubstituting numbers for letters.

i. Multiply and divide algebraic expressionsby a number.ii. Perform:a) additionb) subtractioninvolving two algebraicexpressions.iii. Simplify algebraic expressions.

a) Add 7 to a number: n + 7.b) A number multiplied by 2 andthen 5 added: (n x 2) + 5 or2n + 5.Investigate the difference

between expressions such as2n and n + 2; 3(c + 5) and 3c + 5;n2 and 2n; 2n2 and (2n)2 .

Use situations to explaincomputations involving algebraicexpressions.

Investigate why 8(3x 2)= 24x 16.Add and subtract algebraicexpressions by removing bracketand collecting like terms.

Simplify algebraic expressions

9

(28/2-4/3)

4.1 Understand anduse the conceptof equality.

4.2 Understand anduse the conceptof linearequations in oneunknown.

i. State the relationshipbetween two quantities byusing the symbols = or .

i. Recognise linear algebraicterms.ii. Recognise linear algebraicexpressions.iii. Determine if a given equation is:

a) a linear equationb) a linear equation in oneunknown.iv. Write linear equations in one unknown forgiven statements

Use concrete examples toillustrate = and .

Discuss cases such as:a) Ifa = b then b = a.e.g. 2+3 = 4+1 then 4+1 = 2+3b) Ifa = b and b = c, then a =c.e.g. 4+5 = 2+7, then 2+7=3+6then 4+5 = 3+6Discuss why given algebraicterms and expressions are linear.

Given a list of terms, studentsidentify linear terms.e.g. 3x,xy,x23xis a linear term.

Select linear expressions given alist of algebraic expressions.e.g. 2x+ 3,x2y, xy + 2,x2 12x+ 3,x2yare linear expressions.Select linear equations given alist of equations.e.g.

x+ 3 = 5,x2y= 7,xy= 10x+ 3 = 5,x2y= 7 are linearequations.

x+ 3 = 5 is linear equation in


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one unknown.

Include examples from everydaysituations.

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(7/3-11/3)

4.3 Understand theconcept of

solutions of linearequations in oneunknown.

i. Determine if a numerical value is a solutionof a given linear equation in one unknown.

ii. Determine the solution of a linear equationin oneunknown by trial andimprovement method.iii. Solve equations in the form of:a)x+ a = bb)xa = bc) ax= bd) ax= bwhere a, b, c are integers andxis anunknown.iv. Solve equations in the form ofax+ b = c,where a, b, c are integers and x is anunknown.v. Solve linear equations in one unknown.

vi. Pose and solve problemsinvolving linear equations in one unknown.

Use concrete examples to explainsolutions of linear equation in one

unknown.e.g. Relatex+ 2 = 5 to + 2 = 5.Solve and verify linear equationsin one unknown by inspection andsystematic trial, using w holenumbers, with and without the use of calculators.Involve examples from everydaysituations.

(14/3-19/3) Cuti Pertengahan Semester 1

11

(21/3-25/3)Ujian Serentak 1

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(28/3- 1/4)

5.1 Understand theconcept of ratio oftwo quantities

5.2 Understand theconcept ofproportion tosolve problems.

i. Compare two quantities in the form a : bii. Determine whether givenratios are equivalent ratios.iii. Simplify ratios to the lowest terms.iv. State ratios related to a given ratio

i. State whether two pairs ofquantities is a proportion.ii. Determine if a quantity isproportional to anotherquantity given two values ofeach quantity.iii. Find the value of a quantity given the ratioof the two quantities and the value of anotherquantity.iv. Find the value of a quantity given the ratio

Use everyday examples tointroduce the concept of ratio.Use concrete examples toexplore:a) equivalent ratiosb) related ratios.

Use everyday examples tointroduce the concept ofproportion.Verify the method of crossmultiplication and use it to findthe missing terms of a proportion.


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13(4/4- 9/4)

5.3 Understand anduse the concept ofratio of threequantities to solveproblems.

and the sum of the two quantities.v. Find the sum of two quantities given theratio of the quantities and the differencebetween the quantities.vi. Pose and solve problems

involving ratios andproportions.vii. Find the value of each of the threequantities given:a) the ratio and the sum ofthree quantitiesb) the ratio and the difference between twoof the three quantities.viii. Find the sum of threequantities given the ratio andthe difference between two of the threequantities.ix. Pose and solve problemsinvolving ratio of threequantities.

i. Compare three quantities in the form a : b :c.ii. Determine whether givenratios are equivalent ratios.iii. Simplify ratio of threequantities to the lowest terms.iv. State the ratio of any twoquantities given ratio of threequantities.v. Find the ratio ofa : b : c given the ratio ofa : b and b : c. Include quantities ofdifferent units.a : b =p : q

b:c

=m

:nwhen a) q = m

b) q mBegin with unitary method.Simplify equivalentlowest terms value sumDifference vi. Find the value of the otherquantities, given the ratio of three quantitiesand the valueof one of the quantities.vii. Find the value of each of the threequantities given:

Use everyday examples tointroduce the concept of ratio ofthree quantities.

Use concrete examples toexplore equivalent ratios.


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14

(11/4-15/4)

6.1 Understand therelationshipbetween thesides of a right angledtriangle.

6.2. Understand anduse the converseof the Pythagorastheorem.

a) the ratio and the sum ofthree quantitiesb) the ratio and the difference between twoof the three quantities.viii. Find the sum of three

quantities given the ratio andthe difference between two of the threequantities.ix. Pose and solve problemsinvolving ratio of three quantities.

i. Identify the hypotenuse ofright-angled triangles.ii. Determine the relationshipbetween the lengths of thesides of a right-angledtriangle.iii. Find the length of the missing side of aright-angled triangle using the Pythagoras

theorem.iv. Find the length of sides ofgeometric shapes usingPythagoras theorem.v. Solve problems using thePythagoras theorem.

i. Determine whether a triangle is a right-angled triangle.ii. Solve problems involving the conversePythagoras theorem.

Students identify the hypotenuseof right-angled triangles draw n indifferent orientations.Use dynamic geometry software,grid papers or geo-boards toexplore and investigate thePythagoras theorem.

Explore and investigate theconverse of the Pythagorastheorem through activities.

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(18/4-22/4)

7.1 Performconstructionsusing straightedge (ruler andset square) andcompass.

i. Construct a line segment of given length.ii. Construct a triangle given the length of thesides.iii. Construct:a) perpendicular bisector ofa given line segmentb) perpendicular to a linepassing through a pointon the linec) perpendicular to a linepassing through a pointnot on the line.iv. Construct:

Relate constructions to propertiesof rhombus and isoscelestriangle.Relate the construction to theproperties of equilateral triangle.iv. Construct:a) angle of 60and 120b) bisector of an angle.Emphasise the use ofthe bisector of anangle to constructangles of 30 , 45 and15and etc.


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a) angle of 60and 120b) bisector of an angle.v. Construct triangles given:a) one side and two anglesb) two sides and one

angle.vi. Construct:a) parallel linesb) parallelogram given itssides and an angle.

Measure angles usingprotractors.Explore situation w hen twodifferent triangles can beconstructed.

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(25/4- 6/5)

8.1 Understand anduse the concept ofcoordinates

8.2 Understand anduse the conceptof scales for thecoordinate axes.

i. Identify thex-axis,y-axis andthe origin on a Cartesianplane.ii. Plot points and state thecoordinates of the pointsgiven distances from the

y-axis andx-axis.iii. Plot points and state thedistances of the points fromthey-axis andx-axis givencoordinates of the points.iv. State the coordinates ofpoints on Cartesian plane.

i. Mark the values on both axes by extendingthe sequence ofgiven values on the axes.ii. State the scales used in given coordinateaxes where:a) scales for axes are the

sameb) scales for axes aredifferent.iii. Mark the values on both axes, withreference to the scales given.iv. State the coordinates of agiven point with reference tothe scales given.v. Plot points, given thecoordinates, with reference to the scalesgiven.

i. Identify thex-axis,y-axis andthe origin on a Cartesianplane.ii. Plot points and state thecoordinates of the pointsgiven distances from the

y-axis andx-axis.iii. Plot points and state thedistances of the points fromthey-axis andx-axis givencoordinates of the points.iv. State the coordinates ofpoints on Cartesian plane.

Use dynamic geometry softwareto explore and investigate theconcept scales.Explore the effects of shapes ofobjects by using different scales.Explore positions of places on

topography maps.Pose and solve problemsinvolving coordinates of verticesof shapes such as:Name the shape formed by

A(1, 5), B(2, 5), C(4, 3) andD(3, 3).Three of the four vertices of asquare are ( 1, 1), (2, 5) and(6, 2). State the coordinates ofthe fourth vertex.


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(27/6-8/7)

concept of two dimensionalloci.

9.2 Understand theconcept of theintersection oftwo loci.

object.ii. Determine the locus of points that are of:a) constant distance from afixed pointb) equidistant from two

fixed pointsc) constant distance from astraight lined) equidistant from twointersecting lines.iii. Construct the locus of a set ofall points that satisfies thecondition:a) the point is at a constantdistance from a fixed pointb) the point is at equidistantfrom two fixed pointsc) the point is at a constantdistance from a straight lined) the point is at equidistant from two

intersecting lines.i. Determine the intersections oftwo loci by drawing the lociand locating the points thatsatisfy the conditions of thetwo loci.

familiar routes and simple pathsto introduce the concept of loci.Discuss the locus of a point in agiven diagram.e.g. Describe a locus of a point

equidistant fromA and C.

Use everyday examples orgames to discuss the intersectionof two loci.

Mark the points that satisfy theconditions:a) Equidistant fromA and C.b) 3 cm from A.

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( 11/7-15/7)

10.1 Recognise anddraw parts of acircle.

i. Identify circle as a set ofpoints equidistant from a fixed point.ii. Identify parts of a circle:a) centerb) circumference

c) radiusd) diametere) chordf) arcg) sectorh) segmentiii. Draw :a) a circle given the radiusand centreb) a circle given thediameter

Introduce the concept of circle asa locus.Use dynamic geometry softwareto explore parts of a circle.


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10.2 Understand and use theconceptof circumferenceto solve problems.

c) a diameter passingthrough a specific pointin a circle given the centre.d) a chord of a given lengthpassing through a point

on the circumferencee) sector given the size ofthe angle at the centreand radius of the circle.iv. Determine the:a) centerb) radiusof a given circle byconstruction.i. Estimate the value of .ii. Derive the formula of thecircumference of a circle.iii. Find the circumference of a circle, givenits:a) diameter

b) radius.iv. Find the:a) diameterb) radiusgiven the circumference of acircle.v. Solve problems involving circumference ofcircles.

Measure diameter andcircumference of circular objects.Explore the history of .Explore the value ofusingdynamic geometry software

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(18/7-29/7) 10.3 Understand and use theconceptof arc of a circleto solve problems.

10.4 Understand and use the

i. Derive the formula of thelength of an arc.ii. Find the length of arc given the angle atthe centre and the radius.iii. Find the angle at the centre given thelength of the arc and the radius of a circle.iv. Find the length of radius of a circle giventhe length of the arc and the angle at thecentre.v. Solve problems involving arcs of a circle

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

Explore the relationship betweenthe length of arc and angle at thecentre of a circle using dynamicgeometry software.

Explore the relationship between


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concept of area of a circle tosolve problems.

10.5 Understand and use theconceptof area of sectorof a circle to solve problems.

ii. Find the area of a circle given the:a) radiusb) diameter.iii. Find:a) radius

b) diametergiven the area of a circle.iv. Find the area of a circle given thecircumference and vice versa.v. Solve problems involving area of circles

i. Derive the formula of the area of a sector.ii. Find the area of a sectorgiven the radius and angle atthe centre.iii. Find the angle at the centre given theradius and area of a sector.iv. Find the radius given the area of a sectorand the angle at the centre.v. Solve problems involving area of sectors

and area of circles.

the radius and the area of a circle:a) using dynamic geometrysoftwareb) through activities such ascutting the circle into equal

sectors and rearranging theminto rectangular form.

Explore the relationship betweenthe area of a sector and the angleat the centre of the circle usingdynamic geometry software.

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11.1 Understand theconcept oftransformations.

11.2 Understand and use theconceptof translations.

.i. Identify a transformation as a one-to-onecorrespondencebetween points in a plane.ii. Identify the object and itsimage in a given transformation.

i. Identify a translation.ii. Determine the image of anobject under a giventranslation.iii. Describe a translation:a) by stating the directionand distance of themovement

b) in the formba

iv. Determine the properties of translation.v. Determine the coordinates of:a) the image, given thecoordinates of the objectb) the object, given thecoordinates of the imageunder a translation.

Explore concepts intransformational geometry usingconcrete materials, drawings,geo-boards and dynamicgeometry software.

Explore translations given in theformbaInvestigate the shapes andsizes, lengths and angles of theimages and the objects.


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vi. Solve problems involvingtranslations.

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11.3 Understand and use theconceptof reflections.

11.4 Understand and use theconceptof rotations.

i. Identify a reflection.ii. Determine the image of anobject under a reflection on a given line.iii. Determine the properties of reflections.iv. Determine:a) the image of an object,given the axis ofreflectionb) the axis of reflection, giventhe object and its image.using the method ofconstructionv. Determine the coordinates of:a) the image, given thecoordinates of the objectb) the object, given thecoordinates of the imageunder a reflection.vi. Describe a reflection given the object andimage.vii. Solve problems involving reflections.

i. Identify a rotation.ii. Determine the image of anobject under a rotation giventhe centre, the angle anddirection of rotation.iii. Determine the properties of rotations.iv. Determine:a) image of an object, giventhe centre, angle anddirection of rotationb) the centre, angle anddirection of rotation, giventhe object and the image.using the method ofconstructionv. Determine the coordinates ofa) the image, given thecoordinates of the object;b) the object, given thecoordinates of the image under a rotation.

Explore the image of an objectunder a reflection by drawing,

using tracing paper, or paperfolding.Investigate the shapes andsizes, lengths and angles of theimages and objects.

Explore the image of an objectunder a rotation by drawing and using tracingpaper.


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vi. Describe a rotation given the object andimage.vii. Solve problems involving rotations.

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11.5 Understand and use theconceptof isometry.

11.6 Understand and use theconceptof congruence.

11.7 Understand and use thepropertiesof quadrilateralsusing concept oftransformations.

i. Identify an isometry.ii. Determine whether a given transformationis an isometry.iii. Construct patterns using isometry.

i. Identify if two figures arecongruent.ii. Identify congruency betweentwo figures as a property ofan isometry.iii. Solve problems involvingcongruence.

i. Determine the properties of quadrilateralsusingreflections and rotations.

Use tracing papers to exploreisometry.

Explore congruency undertranslations, reflections androtations.

Explore the properties of variousquadrilaterals by comparing thesides, angles and diagonals.

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(22/8-26/8)Ujian Serentak 2

(29/8-3/9)Cuti Pertengahan Semester 2

32-33

(5/9-16/9)

12.1 Understandgeometricproperties ofprisms, pyramids,cylinders, conesand spheres.

12.2 Understand theconcept of nets.

12.3 Understand theconcept ofsurface area.

State the geometric properties of prisms,pyramids, cylinders, cones and spheres.

i. Draw nets for prisms,pyramids, cylinders and cones.ii. State the types of solids given their nets.iii. Construct models of solids given theirnets.

i. State the surface areas ofprisms, pyramids, cylindersand cones.

Explore and investigateproperties of geometric solidsusing concrete models.

Explore the similarities anddifferences between nets ofprisms, pyramids, cylinders andcones using concrete models.

Explore and derive the formulaeof the surface areas of prisms,pyramids, cylinders and cones.


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ii. Find the surface area ofprisms, pyramids, cylindersand cones.iii. Find the surface area ofspheres using the standard

formula.iv. Find dimensions:a) length of sidesb) heightc) slant heightd) radiuse) diameterof a solid given its surface area and otherrelevant information.v. Solve problems involving surface areas

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13.1 Understand theconcept of data

13.2 Understand theconcept offrequency.

13.3 Represent andinterpret data in:i. pictogramsii. bar chartsiii. line graphsto solveproblems.

i. Classify data according to those that canbe collected by:a) countingb) measuring.ii. Collect and record data

systematically.

i. Determine the frequency ofdata.ii. Determine the data with:a) the highest frequencyb) the lowest frequencyc) frequency of a specific value.iii. Organise data by constructing:a) tally chartsb) frequency tables.iv. Obtain information from frequency tables.

i. Construct pictograms torepresent data.ii. Obtain information frompictograms.iii. Solve problems involvingpictograms.iv. Construct bar charts torepresent data.v. Obtain information from bar charts.vi. Solve problems involving bar charts.vii. Represent data using line

Carry out activities to introducethe concept of data as acollection of information or facts.Discuss methods of collectingdata such as counting,

observations, measuring, usingquestionnaires and interview s.

Use activities to introduce theconcept of frequency.

Use everyday situations tointroduce pictograms, bar chartsand line graphs.


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graphs.viii. Obtain information from line graphs.ix. Solve problems involving line graphs

36(3/10-7/10) Ulangkaji

37-39

(10/10-28/10)Peperiksaan Akhir Tahun

40-42

(31/10-18/11)

..

(21/11-2/1) Cuti Akhir Tahun

Scheme of Work Mathematics Form 2

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Transcript of Scheme of Work Mathematics Form 2