lesson plan smklk f3

RPT 2013 MATEMATIK TING 3

LEARNING AREA/WEEKS

LEARNING OBJECTIVES LEARNING OUTCOMEStudents will be able to:

TEACHING AND LEARNING ACTIVITIES

STRATEGIES

1. LINES AND ANGLES IIWeek 1

Understand and use properties of angles associated with transversal and parallel lines.

i. Identify:a) transversalsb) corresponding anglesc) alternate anglesd) interior angles.

Explore the properties of angles associated with transversal using dynamic geometry software, geometry sets, acetate overlaysor tracing paper.

Vocabularyparallel linestransversalalternate angleinterior angleassociated

ii. Determine that for parallel lines:a) corresponding angles are equalb) alternate angles are equalc) sum of interior angles is 180°.

Discuss when alternate and corresponding angles are not equal.The interior angles on the same side of thetransversal are supplementary.

correspondingangleintersectinglinessupplementary

iii. Find the values of:a) corresponding anglesb) alternate anglesc) interior angles associated with

parallel lines.

Discuss when all angles associated with transversals are equal and the implication on its converse.

angleacetate overlay

iv. Determine if two given lines are parallel based on the properties of angles associated with transversals.

v. Solve problems involving properties of angles associated with transversals.

Limit to transversal intersecting parallel lines.

2. POLYGONS IIWeek 2

Understand the concepts of regular polygons.

i. Determine if a given polygon is a regular polygon.

Limit to polygons with a maximum of 10sides.Use models of polygons and surroundings to identify regular polygons.

Vocabularypolygonregularpolygonconvex

ii. Find:a) the axes of symmetryb) the number of axes of symmetry

of a polygon.

Explore properties of polygons using rulers, compasses, protractors, grid papers, templates, geo-boards, flash cards and dynamic geometry software.

polygonaxes ofsymmetrystraightedgesangle

iii. Sketch regular polygons. Include examples of non-regular polygons developed through activities such as folding papers in the shape of polygons.

equilateraltrianglesquareregular

iv. Draw regular polygons by dividing equally the angle at the centre.

Relate to applications in architecture. hexagon

v. Construct equilateral triangles, squares and regular hexagons.

Construct using straightedges and compasses.Emphasise on the accuracy of drawings.

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STRATEGIES

Understand and use the knowledge of exterior and interior angles of polygons.

i. Identify the interior angles and exterior angles of a polygon.

Explore angles of different polygons through activities such as drawing, cutting and pasting, measuring angles and usingdynamic geometry software.

Vocabularyinterior angleexterior anglecomplementaryangle

ii. Find the size of an exterior angle when the interior angle of a polygon is given and vice versa.

Investigate the number of triangles formed by dividing a polygon into several triangles by joining one chosen vertex of the polygon to the other vertices.

Sum

iii. Determine the sum of the interior angles of polygons.

iv. Determine the sum of the exterior angles of polygons.

v. Find:a) the size of an interior angle of a

regularb) polygon given the number of

sides.c) the size of an exterior angle of a

regular polygon given the number of sides.

d) the number of sides of a regular polygon given the size of the interior or

e) exterior angle.

vi. Solve problems involving angles and sides of polygons.

Include examples from everyday situations.

3. CIRCLES IIWeek 3 & 4

Understand and use properties of circles involving symmetry, chords and arcs.

i. Identify a diameter of a circle as an axis of symmetry.

Vocabularydiameteraxis of

ii. Determine that:a) a radius that is perpendicular to

a chord divides the chord into two equal parts and vice versa.

b) perpendicular bisectors of two chords intersect at the centre.

c) two chords that are equal in length are equidistant from the centre and vice versa.

d) chords of the same length cut arcs of the same length.

Explore through activities such as tracing, folding, drawing and measuring using compasses, rulers, threads, protractor, filterpapers and dynamic geometry software.

Chordperpendicularbisectorintersectequidistantarcsymmetrycentreradiusperpendicularsymmetry

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STRATEGIES

iii. Solve problems involving symmetry, chords and arcs of circles.

Understand and use properties of angles in circles.

i. Identify angles subtended by an arc at the centre and at the circumference of a circle.

Explore properties of angles in a circle by drawing, cutting and pasting, and using dynamic geometry software.

Vocabularyanglesubtendedsemicircle

ii. Determine that angles subtended at the circumference by the same arc are equal.

Include reflex angles subtended at the centre.

circumferencearcchord

iii. Determine that angles subtended:a) at the circumferenceb) at the centre by arcs of the same

length are equal.

Angle subtended by an arc is the same asangle subtended by the corresponding chord.

reflex anglecentre

iv. Determine the relationship between angle at the centre and angle at the circumference subtended by an arc.

v. Determine the size of an angle subtended at the circumference in a semicircle.

vi. Solve problems involving angles subtended at the centre and angles at the circumference of circles.

Understand and use the concepts of cyclic quadrilaterals.

i. Identify cyclic quadrilaterals. Explore properties of cyclic quadrilaterals by drawing, cutting and pasting and using dynamic geometry software.

Vocabularycyclicquadrilateral

ii. Identify interior opposite angles of cyclic quadrilaterals.

oppositeangleexterior angle

iii. Determine the relationship between interior opposite angles of cyclic quadrilaterals.

Interior

iv. Identify exterior angles and the corresponding interior opposite angles of cyclic quadrilaterals.

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STRATEGIES

v. Determine the relationship between exterior angles and the corresponding interior opposite angles of cyclic quadrilaterals.

vi. Solve problems involving angles of cyclic quadrilaterals.

vii. Solve problems involving circles.

4. STATISTICS IIWeek 5 – 6

Represent and interpret data in pie charts to solve problems.

i. Obtain and interpret information from pie charts.

Relate the quantities of the data to the sizeof angles of the sectors.Use everyday examples from sources such as newspapers, magazines, reports and theInternet.

Vocabularysectorpie chartanglesuitablerepresentation

ii. Construct pie charts to represent data.

A complete pie chart should include:i. The titleii. Appropriate labels for the groups of

data.Use calculators and computer software in constructing pie charts.

constructsize of sectorquantitydatasize of anglelabeltitle

iii. Solve problems involving pie charts. Pie charts are mainly suitable for categorical data. Include pictograms, bar charts, line graphs and pie charts.

pictogramsbar chartpie chart

iv. Determine suitable representation of data.

Discuss that representation of data depends on the type of data.

Understand and use the concepts of mode, median and mean to solve problems.

i. Determine the mode of:a) sets of data.b) data given in frequency tables.

Use sets of data from everyday situations to evaluate and to forecast.

Vocabularydatamodediscrete

ii. Determine the mode and the respective frequency from pictographs, bar charts, line graphs and pie charts.

Discuss appropriate measurement in different situations.

frequencymedianarrangeodd

iii. Determine the median for sets of data.

Involve data with more than one mode.Limit to cases with discrete data only.

evenmiddlefrequency

iv. Determine the median of data in frequency tables.

Emphasise that mode refers to the category or score and not to the frequency.Include change in the number and value of data.

tablemean

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STRATEGIES

v. Calculate the mean of:a) sets of datab) data in frequency tables

Use calculators to calculate the mean for large sets of data.

vi. Solve problems involving mode, median and mean.

Discuss appropriate use of mode, median and mean in certain situations.

5. INDICESWeek 8 – 9

Understand the concepts of indices.

i. Express repeated multiplication as an and vice versa.

Begin with squares and cubes.‘a ’ is a real number.Include algebraic terms.Emphasise base and index.a x a x …a = aⁿn factors a is the base, n is the index.

Vocabularyindicesbaseindexpower ofindex notationindex form

ii. Find the value of aⁿ. Explore indices using calculators and spreadsheets.

expressvaluereal numbers

iii. Express numbers in index notation. Involve fractions and decimals.Limit n to positive integers.

repeatedmultiplicationfactor

Perform computations Involving multiplication of numbers in index notation.

i. Verify Explore laws of indices using repeated multiplication and calculators.

Vocabularymultiplicationsimplifybase

ii. Simplify multiplication of:a) numbersb) algebraic terms expressed in

index notation with the same base.

Limit algebraic terms to one unknown. algebraic termverifyindex notationindiceslaw of indices

iii. Simplify multiplication of:a) numbersb) algebraic terms expressed in

index notation with different bases.

unknown

Perform computation involving division of numbers in index notation.

i. Verify Emphasise aº = 1.

ii. Simplify division of:a) numbersb) algebraic terms expressed in

index notation with the same base.

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STRATEGIES

Perform computations involving raising numbers andalgebraic terms in index notation to a power.

i. Derive m and n are positive

integers.

Vocabularyraised to a powerbase

ii. Simplify:a) numbersb) algebraic terms

expressed in index notation raised to a power.

Limit algebraic terms to one unknown.

iii. Simplify multiplication and division of:

a) numbersb) algebraic terms

expressed in index notation with different bases raised to a power.

Emphasise:

iv. Perform combined operations involving multiplication, division, and raised to a power on:

a) numbersb) algebraic terms.

Perform computations involving negative indices. i. Verify .

Explore using repeated multiplications and the law of indices.

Vocabularyverify

ii. State as and vice versa.n is a positive integer.Begin with n = 1.

iii. Perform combined operations of multiplication, division and raising to a power involving negative indices on:


Perform computations involving fractional indices. i. Verify .

a and n are positive integers.Begin with n = 2.

ii. State as and vice versa.

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STRATEGIES

iii. Find the value of

iv. State as :

a) or .

b) or .

v. Perform combined operations of multiplication, division and raising to a power involving fractional indices on:


vi. Find the value of .Limit to positive integral roots.

Perform computation involving laws of indices.

i. Perform multiplication, division, raised to a power or combination of these operations on several numbers expressed in index notation.

ii. Perform combined operations of multiplication, division and raised to a power involving positive, negative and fractional indices.

TOPICAL’S TEST 16. ALGEBRAIC

EXPRESSIONS IIIWeek 10 - 11

Understand and use the concept of expanding brackets.

i. Expand single brackets. Relate to concrete examples.Begin with linear algebraic terms.Limit to linear expressions.Emphasise:(a ± b)(a ± b) = (a ± b)²

Vocabularylinear algebraictermslike termsunlike termsexpansion

ii. Expand two brackets. Explore using computer software.Include:(a + b)(a + b)(a – b)(a – b)(a + b)(a – b)(a – b)(a + b)

expandsingle bracketstwo bracketsmultiply

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LEARNING AREA/WEEKS



STRATEGIES

Understand and use the concept of factorisation of algebraic expressions to solve problems.

i. State factors of an algebraic term. Explore using concrete materials and computer software.Emphasise the relationship between expansion and factorisation.

Vocabularyfactorisationsquarecommon factorterm

ii. State common factors and the HCF for several algebraic terms.

The difference of two squares means:

Limit to four algebraic terms.ab – ac = a(b – c)

limit answer to

ab + ac + bd + cd = (b + c)(a + d)

highest common factor (HCF)difference of two squares

iii. Factorise algebraic expressions:a) using common factorb) the difference of two squares.

iv. Factorise and simplify algebraic fractions.

Begin with one-term expressions for thenumerator and denominator.Limit to factorisation involving commonfactors and difference of two squares.Explore using computer software.

Vocabularynumeratordenominatoralgebraicfractionfactorisation

Perform addition and subtraction on algebraic fractions.

i. Add or subtract two algebraic fractions with the same denominator.

Explore using computer software.Relate to real-life situations.

Vocabularycommon factorlowest commonmultiple (LCM)

ii. Add or subtract two algebraic fractions with one denominator as a multiple of the other denominator.

The concept of LCM may be used.Limit denominators to one algebraic term.

multipledenominator

iii. Add or subtract two algebraic fractions with denominators:

a) without any common factorb) with a common factor.

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LEARNING AREA/WEEKS



STRATEGIES

Perform multiplication and division on algebraic fractions.

i. Multiply two algebraic fractions involving denominator with:

a) one termb) two terms.

Explore using computer software.Begin multiplication and division withoutsimplification followed by multiplication and division with simplification.

Vocabularysimplification

ii. Divide two algebraic fractions involving denominator with:

a) one termb) two terms

iii. Perform multiplication and division of two algebraic fractions using factorisation involving common factors and the different of two squares.

7. ALGEBRAIC FORMULAEWeek 12

Understand the concepts of variables and constants.

i. Determine if a quantity in a given situation is a variable or a constant.

Use examples of everyday situations to explain variables and constants.

Vocabularyquantityvariableconstant

ii. Determine the variable in a given situation and represent it with a letter symbol.

possible valueformulavalueletter symbol

iii. Determine the possible values of a variable in a given situation.

Variables include integers, fractions and decimals.

formulae

Understand the concepts of formulae to solve problems.

i. Write a formula based on a given:a) statementb) situation.

Symbols representing a quantity in a formula must be clearly stated.

Vocabularysubject of aformulastatement

ii. Identify the subject of a given formula.

powerroots

iii. Express a specified variable as the subject of a formula involving:

a) one of the basic operations: +, −, x, ÷

b) powers or rootsc) combination of the basic

operations and powers or roots.

formulae

iv. Find the value of a variable when it is:

a) the subject of the formulab) not the subject of the formula.

Involve scientific formulae.

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LEARNING AREA/WEEKS



STRATEGIES

v. Solve problems involving formulae. 8. SOLID GEOMETRY

IIIWeek 13 - 14

Understand and use the concepts of volumes of right prisms and right circular cylinders to solve problems.

i. Derive the formula for volume of:a) prismsb) cylinders.

Prisms and cylinders refer to right prismsand right circular cylinders respectively.Use concrete models to derive the formulae.

Vocabularyderiveprismcylinderright circular

ii. Calculate the volume of a right prism in cubic units given the height and:

a) the area of the baseb) dimensions of the base.

Limit the bases to shapes of triangles and quadrilaterals.

cylindercircularbaseradius

iii. Calculate the height of a prism given the volume and the area of the base.

Relate the volume of right prisms to right circular cylinders.

areacubic unitssquare

iv. Calculate the area of the base of a prism given the volume and the height.

rectangletriangledimension

v. Calculate the volume of a cylinder in cubic units given:

a) area of the base and the height.b) radius of the base and the height

of the cylinder.

heightcubic metrecubiccentimetrecubicmillimetre

vi. Calculate the height of a cylinder, given the volume and the radius of the base.

millilitrelitreconvert

vii. Calculate the radius of the base of a cylinder given the volume and the height.

metric unitliquidcontainer

viii. Convert volume in one metric unit to another:

a) mm³, cm³ and m³b) cm³, ml and l .

volume

ix. Calculate volume of liquid in a container.

Limit the shape of containers to rightcircular cylinders and right prisms.

x. Solve problems involving volumes of prisms and cylinders.

Understand and use the concept i. Derive the formula for the volume Include bases of different types of polygons. Vocabulary

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LEARNING AREA/WEEKS



STRATEGIES

of volumes of right pyramidsand right circular cones to solve problems.

of:a) pyramidsb) cones.

pyramidconevolumebase

ii. Calculate the volume of pyramids in mm³, cm³ and m³, given the height and:

a) area of the baseb) dimensions of base.

Use concrete models to derive the formula. heightdimension

iii. Calculate the height of a pyramid given the volume and the dimension of the base.

Relate volumes of pyramids to prisms and volumes of cones to cylinders.

iv. Calculate the area of the base of a pyramid given the volume and the height.

v. Calculate the volume of a cone in mm³, cm³ and m³, given the height and radius of the base.

vi. Calculate the height of a cone, given the volume and the radius of the base.

vii. Calculate the radius of the base of a cone given the volume and the height.

viii. Solve problems involving volumes of pyramids and cones.

Understand and use the conceptof volumes of sphere to solve problems.

i. Calculate the volume of a sphere given the radius of the sphere.

Include hemisphere Vocabularyspherehemispheresolid

ii. Calculate the radius of a sphere given the volume of the sphere.

compositesolidcombination

iii. Solve problems involving volumes of spheres.

volumeradius

Apply the concept of volumes i. Calculate the volume of a composite Composite solids are combinations of

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STRATEGIES

to solve problems involving composite solids.

solid. geometric solids.Use concrete models to form composite solids.

ii. Solve problems involving volumes of composite solids.

Use examples from real-life situations.

9. SCALE DRAWINGS IIIWeek 15

Understand the concepts of scale drawings.

i. Sketch shapes:a) of the same size as the objectb) smaller than the objectc) larger than the object

using grid papers.

Limit objects to two dimensional geometric shapes.

Vocabularysketchdrawobjectsgrid papergeo-boards

ii. Draw geometric shapesaccording to scale 1 : n, where n = 1, 2, 3, 4, 5 ,

.

Explore scale drawings using dynamic geometry software, grid papers, geo-boards or graph papers.

softwarescalegeometrical shapescompositen shapessize

iii. Draw composite shapes, according to a given scale using:

a) grid papersb) blank papers.

Emphasise on the accuracy of the drawings.Include grids of different sizes.

smallerlargeraccurateredraw

iv. Redraw shapes on grids of different sizes.

Emphasise that grids should be drawn on the original shapes.

v. Solve problems involving scale drawings.

Relate to maps, graphics and architectural drawings.

10. TRANSFORMATIONS IIWeek 16 - 17

Understand and use the concepts of similarity.

i. Identify if given shapes are similar. Emphasise that for a triangle, if the corresponding angles are equal, then the corresponding sides are proportional.

Vocabularyshapesimilarside

ii. Calculate the lengths of unknown sides of two similar shapes.

Involve examples from everyday situations. angleproportioncentre of enlargement

Understand and use the concepts of enlargement.

i. Identify an enlargement. Explore the concepts of enlargement using grid papers, concrete materials, drawings, geo-boards and dynamic geometry software.

transformationenlargementscale factorobjectimageinvariantreduction

ii. Find the scale factor, given the Emphasise the case of reduction. size

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STRATEGIES

object and its image of an enlargement when:

a) scale factor > 0b) scale factor < 0.

Emphasise the case when scale factor = ± 1Relate enlargement to similarity of shapes.

orientation

iii. Determine the centre of enlargement, given the object and its image.

Emphasise that the centre of enlargement is an invariant point.

similaritypropertiesarea

iv. Determine the image of an object given the centre of enlargement and the scale factor.

Emphasise the method of construction.

v. Determine the properties of enlargement.

vi. Calculate the:a) scale factorb) the lengths of sides of the imagec) the lengths of sides of the object

of an enlargement.

vii. Determine the relationship between the area of the image and its object.

Use grid papers and dynamic geometry software to explore the relationship between the area of the image and its object.

viii. Calculate the:a) area of imageb) area of objectc) scale factor

of an enlargement.

Include negative scale factors.

ix. Solve problems involving enlargement.

11. LINEAR EQUATIONS IIWeek 18

Understand and use the concepts of linear equations in two variables.

i. Determine if an equation is a linear equation in two variables.

Derive linear equations in two variables relating to real-life situations.

Vocabularyequationvariablelinear equation valuepossiblesolution

ii. Write linear equations in two Explore using graphic calculators, dynamic linear equation

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STRATEGIES

variables from given information. geometry software and spreadsheets to solve linear equations and simultaneous linear equations.

variablesolutionsubstitutionelimination

iii. Determine the value of a variable given the other variables.

simultaneouslinearequation

iv. Determine the possible solutions for a linear equation in two variables.

Understand and use the concepts of two simultaneouslinear equations in two variables to solve problems.

v. Determine if two given equations are simultaneous linear equations.

Include letter symbols other than x and y to represent variables.

vi. Solve two simultaneous linear equations in two variables by

a) substitutionb) elimination

Use trial and improvement method.

vii. Solve problems involving two simultaneous linear equations in two variables.

Use examples from real-life situations.

12. LINEAR INEQUALITIESWeek 19

Understand and use the concepts of inequalities.

i. Identify the relationship:a) greater thanb) less than

based on given situations.

Use everyday situations to illustrate the symbols and the use of “ > ” , “ < ” , “ “

and “ “.Emphasise that a > b is equivalent to b < a.

Vocabularyinequalitygreaterlessgreater than

ii. Write the relationship between two given numbers using the symbol “>” or “<”.

“ > “ read as “greater than”.“ < “ read as “less than”.

less thanequal toinclude

iii. Identify the relationship:a) greater than or equal tob) less than or equal to

based on given situations.

“ “ read as “greater than or equal to”.

“ “ read as “ less than or equal to”.

equivalentsolutionrelationshiplinearunknown

Understand and use the concepts of linear inequalities in one unknown.

i. Determine if a given relationship is a linear inequality.

number line

ii. Determine the possible solutions for h is a constant, x is an integer.

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STRATEGIES

a given linear inequality in one unknown:

a) x > h;b) x < h;c) x h;

d) x h. iii. Represent a linear inequality:

a) x > h;b) x < h;c) x h;

d) x h.on a number line and vice versa.

iv. Construct linear inequalities using symbols:

a) “ > “ or “ < “b) “ “ or “ “

from given information.

Involve examples from everyday situations.

Perform computations involving addition, subtraction, multiplication and division on linear inequalities.

i. State a new inequality for a given inequality when a number is:

a) added tob) subtracted from

both sides of the inequalities.

Emphasise that the condition of inequality is unchanged.

Vocabularyaddadditionsubtractsubtractionmultiply

ii. State a new inequality for a given inequality when both sides of the inequality are:

a) multiplied by a numberb) divided by a number.

Emphasise that when we multiply or divide both sides of an inequality by the same negative number, the inequality is reversed.

divisionmultiplicationdividerelationequivalentadding

iii. Construct inequalitiesa) x + k > m + kb) x – k > m – kc) kx > km

d) d)

from given information.

Information given from real-life situations.Include also <, and .

subtractingsimplestcollectisolatesolveaddsubtractmultiply

Perform computations to solve inequalities in one variable.

i. Solve a linear inequality by:a) adding a numberb) subtracting a number

Emphasise that for a solution, the variable is written on the left side of the inequalities.

divide

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STRATEGIES

on both sides of the inequality.ii. Solve a linear inequality by

a) multiplying a numberb) dividing a number

on both sides of the inequality.

Explore using dynamic geometry software and graphic calculators.

iii. Solve linear inequalities in one variable using a combination of operations.

Understand the concepts of simultaneous linear inequalities in one variable.

i. Represent the common values of two simultaneous linear inequalities on a number line.

Emphasise the meaning of inequalities such as:i.

ii.

iii.

iv.

Vocabularydeterminecommon valuesimultaneouscombininglinearinequalitynumber line

ii. Solve two simultaneous linear inequalities.

Emphasise that forms such as:i.

ii.

iii.are not accepted.

equivalent

13. GRAPHS OF FUNCTIONSWeek 20

Understand and se the concepts of functions.

i. State the relationship between two variables based on given information.

Involve functions such as:i. y = 2x + 3ii. p = 3q²+ 4q – 5iii. A = B³

iv. W =

Vocabularyfunctionrelationshipvariabledependentvariable

ii. Identify the dependent and independent variables in a given relationship involving two variables.

Explore using “function machines”. independentvariableordered pairscoordinate

iii. Calculate the value of the dependent variable, given the value of the independent variable.

planetable of valuesorigingraph

Draw and use graphs of functions.

i. Construct tables of values for given functions.

Limit to linear, quadratic and cubic functions.

x-coordinatey-coordinatex-axis

ii. Draw graphs of functions using given scale.

Include cases when scales are not given. y-axisscale

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STRATEGIES

iii. Determine from a graph the value of y, given the value of x and vice versa.

iv. Solve problems involving graphs of functions.

MID YEAR EXAMINATION 14. RATIO, RATE AND

PROPORTION IIWeek 21

Understand the concepts of rates and perform computations involving rate.

i. Determine the rate involved in given situations and identify the two quantities involved.

Emphasise the units in the calculation. Vocabularyratequantityunit of

ii. Calculate the rate given two different quantities.

Use real-life situations that involve rate. measurementspeeddistance

iii. Calculate a certain quantity given the rate and the other quantity.

timeuniformnon-uniform

iv. Convert rates from one unit of measurement to another.

differentiateaverage speeddistance

v. Solve problems involving rate. timeacceleration

Understand and use the concept of speed.

i. Identify the two quantities involved in speed.

Moral values related to traffic rules shouldbe incorporated.

retardation

ii. Calculate and interpret speed. Use examples from everyday situations.

iii. Calculate:a) the distance, given the speed and

the timeb) the time, given the speed and the

distance.iv. Convert speed from one unit of

measurement to another.Include the use of graphs.

v. Differentiate between uniform speed and non-uniform speed.

Understand and use the concepts of average speed.

i. Calculate the average speed in various situations.

Use examples from daily situations.

ii. Calculate:a) the distance, given the average

Discuss the difference between average speed and mean speed.

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STRATEGIES

speed and the time.b) the time, given the average speed

and the distance.iii. Solve problems involving speed and

average speed.

Understand and use the concepts of acceleration.

i. Identify the two quantities involved in acceleration.

Include cases of retardation.

ii. Calculate and interpret acceleration. Retardation is also known deceleration.

15. TRIGONOMETRYWeek 22

Understand and use tangent of an acute angle in a right-angledtriangle.

i. Identify the:a) hypotenuseb) the opposite side and the

adjacent side with respect to one of the acute angles.

Use only right-angled triangle.Use right-angled triangles with real measurements and develop through activities.

Vocabularyright-angledtriangleanglehypotenuseopposite side

ii. Determine the tangent of an angle. Tangent θ can be written as tan θ.Discuss the ratio of the opposite side to the adjacent side when the angle approaches 90º.

adjacent sideratiotangentvaluelength

iii. Calculate the tangent of an angle given the lengths of sides of the triangle.

Emphasise that tangent is a ratio.Limit to opposite and adjacent sides.Include cases that require the use of Pythagoras’ Theorem.

size

iv. Calculate the lengths of sides of a triangle given the value of tangent and the length of another side.

Explore tangent of a given angle when:i. The size of the triangle varies

proportionally.ii. The size of angle varies.

Understand and use sine of an acute angle in a right-angled triangle.

i. Determine the sine of an angle. Sine θ can be written as sin θ. Vocabularyratioright-angled

ii. Calculate the sine of an angle given the lengths of sides of the triangle.

Explore sine of a given angle when:i. The size of the triangle varies

proportionally.ii. The size of the angle varies.

lengthvaluehypotenuseopposite sidesize

iii. Calculate the lengths of sides of a triangle given the value of sine and the length of another side.

Include cases that require the use of Pythagoras’ Theorem.

constantincreaseproportiondegree

Understand and use cosine of i. Determine the cosine of an angle. Cosine θ can be written as cos θ. minute

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STRATEGIES

an acute angle in a right-angled triangle.

tangent

ii. Calculate the cosine of an angle given the lengths of sides of the triangle.

Explore cosine of a given angle when:i. The size of the triangle varie

proportionally.ii. The size of the angle varies.

anglecosinesinetriangle

iii. Calculate the lengths of sides of a triangle given the value of cosine and the length of another side.

Include cases that require the use of Pythagoras’ Theorem.

Use the values of tangent, sine and cosine to solve problems.

i. Calculate the values of other trigonometric ratios given the value of a trigonometric ratio.

ii. Convert the measurement of angles from:

a) degrees to degrees and minutes.b) degrees and minutes to degrees.

iii. Find the value of:a) tangentb) sinec) cosine

of 30º, 45º and 60º without using scientific calculator

Include angles expressed in:i. degreesii. degrees and minutes

iv. Find the value of:a) tangentb) sinec) cosine

using scientific calculator.

v. Find the angles given the values of:a) tangentb) sinec) cosine

using scientific calculators.

vi. Solve problems involving trigonometric ratios.

REVISION Week 23 – 26

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STRATEGIES

PMR’S TRIAL EXAMINATIONWeek 27

REVISION’S WEEKWeek 30 – 36

PMR’S EXAMINATIONWeek 37 - 38

PMR’S PROGRAMWeek 39 – 42

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lesson plan smklk f3

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