Rancangan Tahunan Math Form 3

8/8/2019 Rancangan Tahunan Math Form 3

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LEARNING AREA: LINES AND ANGLES II

WEEK LEARNING

OBJECTIVE

LEARNING OUTCOME SUGGESTED T & L

ACTIVITIES

VOCABULARY REMARKS

Understand and use properties of anglesassociated withtransversal and parallellines.

- Identify transversals,corresponding angles,alternate angles and interior angles- Determine that for parallellines :

-corresponding angle areequal

-alternate angles are equal- sum of interior angles is180 o

-Fine the value of corresponding angles,alternate angles and interior angles associated with

parallel lines.- Determine if two givenlines are parallel based on

the properties of anglesassociated with transversals- Solve problems involving

properties of anglesassociated with transversals.

- Explore the properties of angles associated withtransversal.- Discuss when alternate andcorresponding angles are nitequal.- Discuss when all anglesassociated with transversal are

equal and the implication on itsconverse.


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LEARNING AREA: POLYGONS IIWEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand the conceptof regular polygons.

-Determine if a polygons is aregular polygon-Fine the axes of symmetryand the number of axes of symmetry of a polygon.- Sketch regular polygons- Draw regular polygons bydividing equally the angle atthe centre- Construct equilateraltriangles, squares and regular hexagons

- Use models of polygons andsurroundings to identifyregular polygons- Explore properties of

polygons using rulers,compasses, protractors, grid

papers, templates, geo-boardsand flash cards.- Include examples of non-regular polygons developedthrough activities such a sfolding papers in the shape of

polygons.Understand and use theknowledge of exterior and interior angles of

polygons

- Identify the interior anglesand exterior angles of a

polygon.- Find the size of an exterior angle when the interior angleof a polygon is given andvise versa.- Determine the sum of theinterior angles of polygons.- Determine the sum of theexterior angles of polygons- Find the size of an interior angle of a regular polygongiven the number of sides

- Explore angles of different polygons through activitiessuch as drawing, cutting, and

pasting and measuring angles- Investigate the number of triangles formed by dividing a

polygon into several triangles by joining one chosen vertexof the polygon to the other vertices.-


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- Find the size of an exterior angle of a regular polygongiven the number of sides.

- Find the number of sides of a regular polygon given thesize of the interior or exterior angle.- Solve problems involvingangles and sides of polygons.

LEARNING AREA: CIRCLES II

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand and use properties of circlesinvolving symmetry,chords and arcs.

-Identify a diameter of acircle as an axis of symmetry- Determine that:

-a radius that is perpendicular to a chorddivides the chord into

twoequal parts and vise verse-perpendicular bisectorsof two chords intersect atthe centre- two chords that areequal in length areequidistant from thecentre and vice versa.

-chords of the same

- Explore through activitiessuch as tracing, folding,drawing, and measuring usingcompasses, rulers, threads,

protractor and filter papers.


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length cut arcs of thesame length

- Solve problems involving

symmetry, chords and arcs of circles.

Understand and use properties of angles incircles.

-Identify angles subtended by an arc at the centre andthe circumference of a circle.- Determine that anglessubtended at thecircumference by the samearc are equal.- Determine that angles

subtended at thecircumference and at thecentre by arcs of the samelength are equal.- Determine the relationship

between angle at the centreand angle at thecircumference subtended byan arc.- Determine the size of an

angle subtended at thecircumference in asemicircle.-Solve problems involvingangles subtended at thecentre and angles at thecircumference of circle.

-Explore properties of anglesin a circle by drawing, cuttingand pasting.

Understanding and use -Identify cyclic - Explore properties of cyclic


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the concept of cyclicquadrilaterals

quadrilaterals.- Identify the interior opposite angles of cyclic

quadrilaterals.- Determine the relationship

between interior oppositeangles of cyclicquadrilaterals.- Identify exterior angles andthe corresponding interior opposite angle of cyclicquadrilaterals.-Determine the relationship

between exterior angles andthe corresponding interior opposite angle of cyclicquadrilaterals.- Solve problems involvingangles of cyclicquadrilaterals.-Solve problems involvingcircle.

quadrilaterals by drawing,cutting and pasting.

LEARNING AREA: STATISTIC II

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Represent and interpretdata in pie chart to solve

-Obtain and interpretinformation from the pie

-Use everyday example fromsources such as newspapers,


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problems. chart.- Construct pie charts torepresent data.

- Solve problems involving pie charts- Determine suitablerepresentation of data.

magazines, reports and theinternet

Understand and use theconcept of mode,median, and mean tosolve problem.

-Determine the mode of setsof data and the mode of datagiven in frequency table.- Determine the mode andthe respective frequencyfrom photographs, bar chart,

line graph, and pie chart.-Determine the median for sets of data.- Determine the median of data in frequency tables.- Calculate the mean of setsof data and the mean data infrequency tables.- Solve problems involvingmode, median and mean.

-Use sets of data fromeveryday situation to evaluateand to forecast- Discuss appropriatemeasurement in differentsituation

- Use calculators to calculatethe mean for large sets of data- Discuss appropriate use of mode, median and mean incertain situations.


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LEARNING AREA: INDICES

WEEK LEARNINGOBJECTIVE

LEARNING OUTCOME SUGGESTED T & LACTIVITIES

VOCABULARY REMARKS

Understand the conceptof indices.

-Express repeatedmultiplication as a n and viceversa- Find the value of a n

- Express numbers in indexnotation

-Explore indices usingcalculators and spreadsheets.

Perform computationsinvolving multiplicationof numbers in indexnotation.

-Verify am x a n = am+n

- Simply multiplication of numbers and algebraic termsand expressed in indexnotation with the different

bases.

-Explore laws of indices usingrepeated multiplication andcalculators.

Perform computationsinvolving division of numbers in indexnotation

- Verify am x a n = am-n

- Simply multiplication of numbers and algebraic termsand expressed in indexnotation with the same base

Perform computationsinvolving raisingnumbers and algebraicterms in index notation toa power.

-Derive (a m )n = amn

- Simplify numbers andalgebraic terms andexpressed in index notationraised to a power.- Simplify multiplication anddivision of numbers andalgebraic terms and


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expressed in index notationwith different bases raised toa power.

- Perform combinedoperations involvingmultiplication, division andraised to a power on numbersand algebraic terms.

Perform computationsinvolving negativeindices

- Verify a -n = 1/a n

- State a -n as 1/a n and viseversa- Perform combined

operations of multiplication,division and raising to a

power involving negativeindices on numbers andalgebraic terms.

- Explore using repeatedmultiplication and the law of indices

Perform computationsinvolving fractionalindices

- Verify a 1/n = a- State a as a and viseversa- Find the value of a 1/n

-State a m/n as

(a)

(b)

-Perform combinedoperations of multiplications,division and raising to a

power involving fractional


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indices on number andalgebraic terms.-Find the value of am/n

Perform computationsinvolving laws of indices

-Perform multiplicationdivision, raised to a power or combination of theseoperations on severalnumbers express in indexnotation.- Perform combinedoperations of multiplication,division and raised to a

power involving positive,negative and fractionalindices.

LEARNING AREA: ALGEBRAIC EXPRESSIONS II

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand and use theconcept of expanding

brackets.

- Expand single brackets- Expand two brackets.

-Relate to concrete example.

Understand and use theconcept of factorization

- State factors of an algebraicterms

- Explore using concretematerial


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of algebraic expression tosolve problem.

- State common factors andthe HCF for several algebraicterms.

- Factorise algebraicexpression using commonfactor and the difference of two squares.-Factorise and simplifyalgebraic fractions.

Perform addition andsubtraction on algebraicfractions

-Add or subtract twoalgebraic fractions with thesame denominator.- Add or subtract two

algebraic fractions with onedenominator as a multiple of the other denominator - Add or subtract twoalgebraic fractions withdenominators without anycommon factor and with acommon factor.

Perform multiplicationand division on algebraic

fractions

-Multiply two algebraicfraction involving

denominator with one termand two terms.-Divided two algebraicfractions involvingdenominator with one termand two terms.Perform multiplication anddivision of two algebraic


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fractions using factorizationinvolving common factorsand the different of two

squares.

LEARNING AREA: ALGEBRAIC FORMULAE

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand the conceptof variable and constant

- Determine if a quantity in agiven situation is a variable or aconstant.- Determine the variable in agiven situation and represent itwith a letter symbol- Determine the possible valuesof a variable in a given situation.

-Use example of everydaysituations to explainvariables and constants.


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Understand the conceptof formulae to solve

problems

- Write a formula based on agiven statement and situation- Identify the subject of a given

formula- Express a specified variable asthe subject of a formulainvolving:

-on of the basic operation:+,-,x,/

- power or roots- combination of the basicoperations and powers or roots

-Find the value of a variablewhen it is the subject of theformula and when it is not thesubject of the formula- Solve problems involvingformulae.

LEARNING AREA: SOLID GEOMETRY III

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand and use theconcept of volume of right prisms and rightcircular cylinders to solve

-Derive the formula for volumeof prism and cylinders.- Calculate the volume of a right

prism in cubic units given the

- Use concrete models toderive the formula- Relate the volume of

prisms to right circular


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problems height and the area of the baseand given the dimensions of the

base.

-Calculate the height of a prismgiven the volume and the area of the base.-Calculate the area of the base of a prism given the volume and theheight.- Calculate the volume of acylinder in cubic units given areaof the base and the height of thecylinder.

-Calculate the volume of acylinder in cubic unit givenradius of the base and the heightof the height.- Calculate the height of acylinder, given the volume andthe radius of the base.- Calculate the radius of the baseof a cylinder given the volumeand the height.

-Convert volume in one metricunit to another:(a) mm3 ,cm3 and m 3

(b) cm3 ,ml and l - Calculate volume of liquid in acontainer - Solve problems involvingvolume of prism and cylinders

cylinders.


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Understand and use theconcept of volume of right pyramids and right

circular cones to solve problems

- Derive the formula for thevolume of pyramids and cones- Calculate the volume of

pyramids in mm3

,cm3

and m3

,given the height and area of the

base.- Calculate the volume of

pyramids in mm3 ,cm3 and m 3,given the height and dimensionsof base.- Calculate the height of a

pyramid given the volume andthe dimension of the base.

- Calculate the area of the baseof a pyramid given the volumeand the height.- Calculate the volume of a conein mm3 ,cm3 and m 3 given theheight and radius of the base.- Calculate the height of a cone,given the volume and the radiusof the base.- Calculate the radius of the base

of a cone given the volume andthe height.- Solve problems involvingvolume of pyramids and cones.

- Use concrete models toderive the formula.- Relate volume of pyramids

to prism and cones tocylinders.

Understand and use theconcept of volume of sphere to solve problems

-Calculate the volumes of asphere given the radius of thesphere.- Calculate the radius of a sphere


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given the volume of the sphere.- Solve problems involvingvolume of sphere.

Apply the concept of volume to solve problemsinvolving compositesolids

- Calculate the volume of composite solids- Solve problems involvingvolume of composite solids.

- Use concrete models toform composite solids- use examples from real-lifesituations.

LEARNING AREA: SCALE DRAWINGS

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand the conceptof scale drawing

- Sketch shapes of the same sizeas the object using grid paper.- sketch shapes smaller than theobject using grid paper -sketch shapes larger than theobject using grid paper.-Draw geometric shapesaccording to scale 1: n where n=1,2,3,4,5, ,1/10-Draw composite shapesaccording to a given scale usinggrid paper and blank paper.- Redraw shapes on grids of different sizes.- solve problems involving scaledrawing.

-Explore scale drawing usingdynamic geometry software,grid paper, geo-board or graph papers.


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LEARNING AREA: TRANSFORMATIONS II



VOCABULARY REMARKS

Understand and use theconcept of similarity.

- Identify if given shapes aresimilar - Calculate the lengths of unknown sides of two similar shapes.

- Involve examples fromeveryday situation.

Understand and use theconcept of enlargement.

- identify an enlargement-Find the scale factor, given theobject and its image of anenlargement when scale factor >0 and scale factor


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- Calculate the area of image,area of object, scale factor of anenlargement.

-Solve problems involvingenlargement.

LEARNING AREA: LINEAR EQUATIONS II

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand and use theconcept of linear equations in two variables

- Determine if an equation is alinear equation in two variables.- Write linear equations in twovariable from given information.- Determine the value of avariable given the other variables.- Determine the possiblesolutions for a linear equation intwo variables.

-Derive linear equations intwo variables relating to real-life situations.- Explore using graphiccalculators, dynamicgeometry software andspreadsheets to solve linear equations and simultaneouslinear equation.

Understand and use theconcept of twosimultaneous linear equations in twovariables to solve

problems.

- Determine if two givenequations are simultaneouslinear equations.- Solve two simultaneous linear equations in two variables bysubstitution and elimination.- Solve problems involving twosimultaneous linear equation intwo variables.

-Use trial improvementmethod- Use examples from real-lifesituations.


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LEARNING AREA: LINEAR INEQUALITIES



VOCABULARY REMARKS

- Identify the relationship greater than and less than base on givensituations.- Write the relationship betweentwo given numbers using thesymbol > or , .

Understand and use theconcept of linear inequalities in oneunknown

-Determine if a givenrelationship is a linear inequality-Determine the possiblesolutions for a given linear inequality in one unknown:(a) x>h(b)xh(d) xh(b)xh(d)x


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- Construct linear inequalitiesusing symbols:(a) > or or m+k (b) x-k > m-k (c) kx > km(d) x/k > m/k from given information.

Perform computations tosolve inequalities in one

variable

- Solve a linear inequality byadding a number and subtracting

a number on both sides of theinequality- Solve a linear inequality bymultiplying a number anddividing a number on both sidesof the inequality.-Solve linear inequalities in onevariable using a combination of


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operations.Understand the concept of simultaneous linear

inequalities in onevariable.

- Represent the common valuesof two simultaneous linear

inequalities on a number line.- Determine the equivalentinequalities for two given linear inequalities.- Solve two simultaneous linear inequalities.

LEARNING AREA: GRAPHS OF FUNCTIONS

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand and use theconcept of function.

-State the relationship betweentwo variables based on the giveninformation.- Identify the dependent andindependent variables in a givenrelationship involving twovariables.- Calculate the value of thedependent variable, given thevalue of the independentvariable.

- Explore using functionmachines.

Draw and use graphs of functions

-Construct tables of values for given functions.-Draw graph of functions usinggiven scale.-Determine from graph the value


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of y, given value of x and viseversa-Solve problems involving

graphs of functions.

LEARNING AREA: RATIOS,RATES AND PROPORTIONS II

WEEK LEARNING

OBJECTIVE


ACTIVITIES

VOCABULARY REMARKS

Understand the concept of rate and performcomputations involvingrates.

- Determine the rates involved ingiven situations and identify thetwo quantities involved.- Calculate the rate given twodifferent quantities.- Calculate a certain quantitygiven the rate and the other quantity.-Convert rates from one unit of measurement to another.- Solve problems involving rates.

- Use real-life situations thatinvolve rates.

Understand and use theconcept of speed.

- Identify two quantities involvein speed.- Calculate and interpret speed.- Calculate the distance, giventhe speed and the time.-Calculate the time, given thespeed and distance.- Convert speed from one unit

-Use examples fromeveryday situations.


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measurement to another.- Differentiate between uniformspeed and non-uniform speed.

Understand and use theconcept of average speed - Calculate the average speed invarious situations- Calculate the distance, giventhe average speed and the time.- Calculate the time, given theaverage speed and the distance.- Solve problems involvingspeed and average speed.

- Use examples from dailysituations.-Discuss the difference

between average speed andmean speed.

Understand and use theconcept of acceleration.

- Identify the two quantitiesinvolved in acceleration.

- Calculate and interpretacceleration.

LEARNING AREA: TRIGONOMETRY

WEEK LEARNING

OBJECTIVE


ACTIVITIES

NOTES REMARKS

Understand and usetangent of an acute anglein a right-angled triangle.

- Identify the hypotenuse- Identify the opposite side andthe adjacent side with respect toone of the acute angles.-Determine the tangent of anangle- Calculate the tangent of anangle given the lengths of sidesof the triangle.- Calculate the lengths of sides

-Use right-angled triangleswith real measurements anddevelop through activities.- Discuss the ratio of theopposite side to the adjacentside when the angleapproaches 90 o.-Explore tangent of a givenangle when the size of thetriangle varies


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of a triangle given the value of tangent and the length of another side.

proportionally.-Explore tangent of a givenangle when the size of angle

varies.Understand and use sineof an acute angle in aright-angled triangle.

- Determine the sine of an angle-Calculate the sine of an anglegiven the lengths of sides of thetriangle.- Calculate the lengths of sidesof a triangle given the value of sine and the length of another side.

-Explore sine of a givenangle when:(a) the size of the trianglevaries proportionally(b) the size of the anglevaries.

Understand and usecosine of an acute anglein a right-angled triangle.

- Determine the cosine of anangle.-Calculate the cosine of an anglegiven the lengths of sides of thetriangle- Calculate the lengths of sidesof a triangle given the value of cosine and the length of another

side.

-Explore cosine of a givenangle when:(a) the size of the trianglevaries proportionally(b) the size of the anglevaries.

Use the values of tangent,sine and cosine to solve

problems.

- Calculate the value of other trigonometric ratios given thevalue of a trigonometric ratio.- Convert the measurement of angles from degrees and minutes- Convert the measurement of angles from degrees and minutes


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to degrees.-Find the value of tangent, sine,cosine of 30 o, 45 o, and 60 o

without using scientificcalculator.-Find the value of tangent, sine,and cosine using scientificcalculator.- Find the angles given the valueof tangent, sine and cosine usingscientific calculators.-Solve problems involvingtrigonometric ratios.

Rancangan Tahunan Math Form 3

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