Transcript
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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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
WEEK LEARNINGOBJECTIVE
LEARNING OUTCOME SUGGESTED T & LACTIVITIES
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
LEARNING OUTCOME SUGGESTED T & L
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
WEEK LEARNINGOBJECTIVE
LEARNING OUTCOME SUGGESTED T & LACTIVITIES
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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
LEARNING OUTCOME SUGGESTED T & L
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.
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