MATEMATIKmbsskl.edu.my/panitia_math/files/2017/01/Form-1.pdfForm1Mathematics KSSM 3 1.2.3 Perform computations involving combined basic arithmetic operations of integers by followingtheorderofoperations

Form 1 Mathematics KSSM

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SEKOLAH MENENGAH (LAKI-LAKI) METHODISTJALAN HANG JEBAT,50150 KUALA LUMPUR.

KURIKULUM STANDARD SEKOLAH MENENGAH (KSSM)

RANCANGAN PELAJARAN TAHUNAN2017

MATEMATIKTINGKATAN 1


2

LEARNING AREA 1 : NUMBERS AND OPERATIONS

1. RATIONAL NUMBERS

W CONTENTSTANDARDS LEARNING STANDARDS NOTES VALUE THINKING

MAPW 1 – 2

5 Jan–

13 Jan

1.1 Integers 1.1.1 Recognise positive and negative numbersbased on real-life situations.

1.1.2 Recognise and describe integers.

1.1.3 Represent integers on number lines andmake connections between the valuesand positions of the integers with respectto other integers on the number line.

1.1.4 Compare and arrange integers in order

Relate to real-life situations such asleft and right, up and downmovement.

Hard-working

Curious

Hard-working

Tree Map

1.2 Basicarithmeticoperationsinvolvingintegers

1.2.1 Add and subtract integers using numberlines or other appropriate methods. Hence,make generalisation about addition andsubtraction of integers.

1.2.2 Multiply and divide integers using variousmethods. Hence make generalisation aboutmultiplication and division of integers.

Other methods such as concretematerials (coloured chips), virtualmanipulative materials and GSPsoftware.

Accurate

Systematical


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1.2.3 Perform computations involving combinedbasic arithmetic operations of integers byfollowing the order of operations.

1.2.4 Describe the laws of arithmetic operationswhich are Identity Law, CommunicativeLaw, Associative Law and Distributive Law.

1.2.5 Perform efficient computations using thelaws of basic arithmetic operations.

1.2.6 Solve problems involving integers.

Carry out exploratory activities.

Example of an efficient computationinvolving Distributive Law:2030 × 25 = (2000 + 30) × 25

= 50 000 + 750= 50 750

Efficient computations may differamong pupils.

Accurate

Logic

Criticalthinking

W 3 – 4

16 Jan–

24 Jan

1.3 Positiveandnegativefractions

1.3.1 Represent positive and negative fractionson number lines.

1.3.2 Compare and arrange positive and negativefractions in order.

1.3.3 Perform computations involving combinedbasic arithmetic operations of positive andnegative fractions by following the order ofoperations.

1.3.4 Solve problems involving positive andnegative fractions.

Rational

Accurate

Hard working

Criticalthinking

1.4 Positiveandnegativedecimals

1.4.1 Represent positive and negative decimalson number lines.

1.4.2 Compare and arrange positive and negativedecimals in order.

1.4.3 Perform computations involving combinedbasic arithmetic operations of positive andnegative decimals by following the order ofoperations.

Creative

Responsibiliyty


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1.4.4 Solve problems involving positive andnegative decimals.

W4

25 Jan–

26 Jan

1.5 Rationalnumbers

1.5.1 Recognise and describe rational numbers.

1.5.2 Perform computations involving combinedbasic arithmetic operations of rationalnumbers by following the order ofoperations.

1.5.3 Solve problems involving rational numbers.

Rational numbers are numbers thatcan be written in fractional form, thatis

, p and q are integers, q 0.

Logic

Systematical

Responsible

Tree Map

W5

29 Jan–

31 Jan

TAHUN BARU CHINA


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2. FACTORS ANDMULTIPLES

W 5 – 6

2 Feb –10 Feb

2.1 Factors,primefactors andHighestCommon

2.1.1 Determine and list the factors of wholenumbers, and hence make generalisationabout factors.

Cooperate Bubble Map


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Factor(HCF)

2.1.2 Determine and list the prime factors of awhole number, and hence express thenumber in the form of prime factorisation.

2.1.3 Explain and determine the common factorsof whole numbers.

2.1.4 Determine the HCF of two and three wholenumbers.

2.1.5 Solve problems involving HCF.

Also consider cases involving morethan three whole numbers.

Use various methods includingrepeated division and the use ofprime factorisation.

Double BubbleMap

2.2 Multiples,commonmultiplesandLowestCommonMultiple(LCM)

2.2.1 Explain and determine the commonmultiples of whole numbers.

2.2.2 Determine the LCM of two and three wholenumbers.

2.2.3 Solve problems involving LCM.

Also consider cases involving morethan three whole numbers.

Use various methods includingrepeated division and the use ofprime factorisation.

Helpfulness

Creative

Double BubbleMap


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3. SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS

W7

13 Feb–17 Feb

3.1 Squaresand squareroots

3.1.1 Explain the meaning of squares andperfect squares.

3.1.2 Determine whether a number is a perfectsquare.

3.1.3 State the relationship between squaresand square roots.

3.1.4 Determine the square of a number withand without using technological tools.

3.1.5 Determine the square roots of a numberwithout using technological tools.

3.1.6 Determine the square roots of apositive number using technologicaltools.

Explore the formation of squaresusing various methods including theuse of concrete materials.

Perfect squares are 1, 4, 9, ...

Relationship is stated based on theoutcome of exploration.

Square roots of a number are inpositive and negative values.

Limit to:

a) perfect squares

b) fractions when the numerators anddenominators are perfect squares

c) fractions that can be simplified suchthat the numerators and

denominatorsare perfect squares

d) decimals that can be written in theform of the squares of otherdecimals.

Sharing

Focus

Perfection

Camlness

Tolerance

Bridge Map

Circle Map

Bridge Map


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3.1.7 Estimate(i) the square of a number,(ii) the square roots of a number.

3.1.8 Make generalisation about multiplicationinvolving:(i) square roots of the same numbers,(ii) square roots of different numbers.

3.1.9 Pose and solve problems involvingsquares and square roots.

Discuss the ways to improvethe estimation until the bestestimation is obtained; whetherin the form of a range, a wholenumber or to a statedaccuracy.

Generalisations are madebased on the outcome ofexplorations.

Effort

Courage

Confidence

W8

20Feb –24 Feb

3.2 Cubesand cuberoots

3.2.1 Explain the meaning of cubes andperfect cubes.

3.2.2 Determine whether a number is a perfectcube.

3.2.3 State the relationship between cubesand cube roots.

3.2.4 Determine the cube of a number withand without using technological tools.

3.2.5 Determine the cube root of a numberwithout using technological tools.

Explore the formation of cubes usingvarious methods including the use ofconcrete materials.

Perfect cubes are 1, 8, 27, ...

Relationship is stated based on theoutcome of exploration.

Limit to:a) fractions when the numerators and

denominators are perfect cubes.b) fractions that can be simplified

such that the numerators anddenominators are perfect cubes.

c) decimals that can be written in theform of the cubes of otherdecimals.

Balance

Trust

Courage

Patient

Self

Circle Map

Bridge Map


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3.2.6 Determine the cube root of a numberusing technological tools.

3.2.7 Estimate(i) the cube of a number,(ii) the cube root of a number.

3.2.8 Solve problems involving cubes andcube roots.

3.2.9 Perform computations involving addition,subtraction, multiplication, division andthe combination of these operations onsquares, square roots, cubes and cuberoots.

Discuss the ways to improve theestimation until the best estimation isobtained; whether in the form of arange, a whole number or to a statedaccuracy.

awareness

Thrift


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LEARNING AREA 2 : RELATIONSHIP AND ALGEBRA

4. RATIOS, RATES AND PROPORTIONSW9

27Feb –3 Mac

4.1 Ratios 4.1.1 Represent the relation between threequantities in the form of a : b : c.

4.1.2 Identify and determine the equivalentratios in numerical, geometrical or dailysituation contexts.

4.1.3 Express ratios of two and threequantities in simplest form.

Examples of equivalent ratios ingeometrical context:

1 : 2 2 : 4

Including those involving fractions anddecimals.

Rational Bridge Map

4.2 Rates 4.2.1 Determine the relationshipbetweenratios and rates.


Involve various situations such asspeed, acceleration, pressure anddensity.

Involve conversion of units.

Rate is a special case of ratio thatinvolves two measurements of differentunits.

Volunteering

4.3 Proportions 4.3.1 Determine the relationshipbetween ratios and proportions.

4.3.2 Determine an unknown value in aproportion.

Carry out exploratory activities.Involve real-life situations.

Use various methods including crossmultiplication and unitary method.

Teamwork

W10

6Mac –10 Mac

4.4 Ratios, ratesandproportions.

4.4.1 Determine the ratio of threequantities, given two or more ratiosof two quantities.

4.4.2 Determine the ratio or the related valuegiven(i) the ratio of two quantities and the

value of one quantity.(ii) the ratio of three quantities and

Involve real-life situations Tidiness


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the value of one quantity.

4.4.3 Determine the value related to a rate.

4.4.4 Solve problems involving ratios, ratesand proportions, including makingestimations.

Thankfulness

W13

27Mac –31 Mac

4.5 Relationshipbetweenratios, ratesandproportionswithpercentages,fractions anddecimals

4.5.1 Determine the relationship betweenpercentages and ratios.

4.5.2 Determine the percentage of aquantity by applying the concept ofproportions.

4.5.3 Solve problems involving relationshipbetween ratios, rates and proportionswith percentages, fractions anddecimals.


Involve various situations.

Sincerity

Obedience

W 11

13 Mac-

17 Mac

UJIAN SELARAS 2017

W 12

20 Mac-

24 Mac

CUTI PERTENGAHAN PENGGAL 1


13


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5. ALGEBRAIC EXPRESSIONS

W 14

3 Apr–

7 Apr

5.1 Variablesandalgebraicexpressions

5.1.1 Use letters to represent quantities withunknown values. Hence, statewhether the value of the variablevaries or fixed, with justification.

5.1.2 Derive algebraic expressions basedon arithmetic expressions thatrepresent a situation.

5.1.3 Determine the values of algebraicexpressions given the values ofvariables and make connection withappropriate situations.

5.1.4 Identify the terms in an algebraicexpression. Hence, state thepossible coefficients for thealgebraic terms.

5.1.5 Identify like and unlike terms.

Letters as variables.

Involve real-life situations.

Will Power

Tree Map

Bubble Map

W15 -16

10 Apr–

21 Apr

5.2 Algebraicexpressionsinvolvingbasicarithmeticoperations

5.2.1 Add and subtract two ormore algebraicexpressions.

5.2.2 Make generalisation about repeatedmultiplication of algebraicexpressions.

5.2.3 Multiply and divide algebraicexpressions with one term.

Correlate repeated multiplication withthe power of two or more.

Patience


15


16

6. LINEAR EQUATIONS

W17

24 Apr–

28 Apr

6.1 Linearequations inone variable

6.1.1 Identify linear equations in onevariable and describe thecharacteristics of the equations.

6.1.2 Form linear equations in one variablebased on a statement or a situation,and vice-versa.

6.1.3 Solve linear equations in onevariable.

6.1.4 Solve problems involving linearequations in one variable.

Carry out exploratory activitiesinvolving algebraic expressions andalgebraic equations.

Use various methods such as trialand improvement, backtracking, andapplying the understanding ofequality concept.

Passion

Responsibility

Hardwork

Circle map

W 18

2 May–

5 May

6.2 Linearequations intwo variables

6.2.1 Identify linear equations in twovariables and describe the characteristicsof the equations.

6.2.2 Form linear equations in twovariables based on a statement or asituation, and vice-versa.

6.2.3 Determine and explain possiblesolutions of linear equations in two variables.

6.2.4 Represent graphically the linearequations in two variables.

State the general form of linearequations in two variables, which isax + by = c.

Including cases of (x, y) when(i) x is fixed and y varies,(ii) x varies and y is fixed.

Involve all quadrants of theCartesian system.

Understanding

Accountability

Honesty

Tree Map

Bubble Map


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W 19

8 May–

12 May

6.3 Simultaneouslinearequations intwo variables

6.3.1 Form simultaneous linear equationsbased on daily situations. Hence,represent graphically thesimultaneous linear equations in twovariables and explain the meaning ofsimultaneous linear equations.

6.3.2 Solve simultaneous linearequations in two variablesusing various methods.

6.3.3 Solve problems involvingsimultaneous linear equationsin two variables.

Use software to explore casesinvolving lines that are:(i) Intersecting (unique solution)(ii) Parallel (no solution)(iii) Overlapping (infinite solutions)

Involve graphical and algebraicmethods (substitution, elimination)

Use technological tools to exploreand check the answers.

Creativity

Reliability

W20–2115 May-25 May

PEPERIKSAAN PERTENGAHAN TAHUN 2017W22-2327 May-11 Jun CUTI PERTENGAHAN TAHUN


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7. LINEAR INEQUALITIES

W 24

12 Jun–

16 Jun

7.1 Inequalities 7.1.1 Compare the values of numbers,describe inequality and hence, formalgebraic inequality.

7.1.2 Make generalisation about inequalityrelated to(i) the converse and transitive

properties, additive andmultiplicative inverse,

(ii) basic arithmetic operations.

Use number lines to represent inequalityrelations, ‘>’, ‘<’, ‘≥’ and ‘≤’.

Involve negative numbers.

Carry out exploratory activities.Converse property if a < b, thenb > a.

Transitive property if a < b < c, thena < c.Additive inverse if a < b, then-a > -b.Multiplicative inverse if a < b, then

.

Basic arithmetic operations:when additions, subtractions,multiplications or divisions performedon both sides.

Respect

Perfection

Tree Map

Circle Map

W 25

19 Jun–

22 Jun

7.2 Linearinequalitiesin onevariable

7.2.1 Form linear inequalities based ondaily life situations, and vice-versa.

7.2.2 Solve problems involving linearinequalities in one variable.

7.2.3 Solve simultaneous linearinequalities in one variable.

Number lines can be used to solveproblems.

Selfrespect

W 2523 Jun–

28 JunCUTI HARI RAYA PUASA


19


20

LEARNING AREA 3 : MEASUREMENT AND GEOMETRY

8. LINES AND ANGLES

W 27

28 Jun–

7 Jul

8.1 Lines andangles

8.1.1 Determine and explain thecongruency of line segments andangles.

8.1.2 Estimate and measure the size ofline segments and angles, andexplain how the estimation isobtained.

8.1.3 Recognise, compare and explain theproperties of angles on a straight line,reflex angles, and one whole turnangles.

8.1.4 Describe the properties ofcomplementary angles, supplementaryangles and conjugate angles.

8.1.5 Solve problems involvingcomplementary angles, supplementaryangles and conjugate angles.

8.1.6 Construct(i) line segments,(ii) perpendicular bisectors of line

segments,(iii) perpendicular line to a straight

line,(iv) parallel linesand explain the rationale ofconstruction steps.

8.1.7 Construct angles and angle bisectors,and explain the rationale ofconstruction steps.


Usea) compasses and straight edge tool

only,b) any geometrical tools,c) geometry softwarefor constructions.

Use the angle of 60 as the firstexample for construction usingcompasses and straightedge toolonly.

Focus

Sharing

Tidiness

Tidiness

Tree Map

Tree Map

Circle Map


21

W 28

10 Jul–

14 Jul

W 29

17 Jul–

21 Jul

8.2 Anglesrelated tointersectinglines

8.2.1 Identify, explain and draw verticallyopposite angles and adjacent anglesat intersecting lines, includingperpendicular lines.

8.2.2 Determine the values of angles relatedto intersecting lines, given the values ofother angles.

8.2.3 Solve problems involvingangles related to intersectinglines.

Creativity

8.3 Anglesrelated toparallel linesandtransversals

8.3.1 Recognise, explain and drawparallel lines and transversals.

8.3.2 Recognise, explain and drawcorresponding angles, alternateangles and interior angles.

8.3.3 Determine whether two straight linesare parallel based on the propertiesof angles related to transversals.

8.3.4 Determine the values of anglesrelated to parallel lines andtransversals, given the values ofother angles.

8.3.5 Recognise and represent angles ofelevation and angles of depression inreal-life situations.

8.3.6 Solve problems involving anglesrelated to parallel lines andtransversals.

Include angles of elevation andangles of depression.

Helpfulness

Intentions

Curious


22


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9. BASIC POLYGONS

W 30

24 Jul–

28 Jul

9.1 Polygons 9.1.1 State the relationship betweenthe number of sides, verticesand diagonals of polygons.

9.1.2 Draw polygons, label vertices ofpolygons and name the polygonsbased on the labeled vertices.

Carry out exploratory activities. Confidence Bridge Map

9.2 Propertiesof trianglesand theinteriorandexteriorangles oftriangles

9.2.1 Recognise and list geometricproperties of various types oftriangles. Hence classify trianglesbased on geometric properties.

9.2.2 Make and verify conjectures about(i) the sum of interior angles,(ii) the sum of interior angle and

adjacent exterior angle,(iii) the relation between exterior

angle and the sum of theopposite interior anglesof a triangle.

9.2.3 Solve problems involving triangles.

Geometric properties include thenumber of axes of symmetry.

Involve various methods ofexploration such as the use ofdynamic software.

Use various methods including theuse of dynamic software.

Perfection

Honesty

Honesty

Bubble MapBrace Map

W 31

31 Jul–

4 Aug

9.3 Propertiesofquadrilaterals and theinterior andexteriorangles ofquadrilaterals

9.3.1 Describe the geometric properties ofvarious types of quadrilaterals. Henceclassify quadrilaterals based on thegeometric properties.

9.3.2 Make and verify the conjectures about(i) the sum of interior angles of a

quadrilateral,(ii) the sum of interior angle and

Geometric properties include thenumber of axes of symmetry.

Involve various exploratory methodssuch as the use of dynamic software.

Use various methods including theuse of dynamic software.

Courage

Will Power

Bubble MapBrace Map


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adjacent exterior angle of aquadrilateral, and

(iii) the relationship between theopposite angles in aparallelogram.

9.3.3 Solve problems involvingquadrilaterals.

9.3.4 Solve problems involving thecombinations of triangles andquadrilaterals.

Responsibility


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10. PERIMETER AND AREA

W 32

7 Aug–

11 Aug

10.1 Perimeter 10.1.1 Determine the perimeter of variousshapes when the side lengths are givenor need to be measured.

10.1.2 Estimate the perimeter of variousshapes, and then evaluate theaccuracy of estimation bycomparing with the measuredvalue.

10.1.3 Solve problems involving perimeter.

Various shapes including thoseinvolving straight lines and curves

Obedience Tree MapBridge Map

10.2 Area oftriangles,parallelograms, kitesandtrapeziums

10.2.1 Estimate the area of various shapesusing various methods.

10.2.2 Derive the formulae of the area oftriangles, parallelograms, kites andtrapeziums based on the area ofrectangles.

10.2.3 Solve problems involving areasof triangles, parallelograms,kites, trapeziums and thecombinations of these shapes.

Including the use of 1 unit × 1 unitgrid paper.

Carry out exploratory activitiesinvolving concrete materials or theuse of dynamic software

Patience

Hardworking

W 33

14 Aug–

18 Aug

10.3 Relationshipbetweenperimeterand area

10.3.1 Make and verify the conjectureabout the relationship betweenperimeter and area.

10.3.2 Solve problems involving perimeterand area of triangles, rectangles,squares, parallelograms, kites,trapeziums and the combinations ofthese shapes.

Cooperation


26


27

LEARNING AREA 4 : DISCRETE MATHEMATICS

11. INTRODUCTION TO SET

W 34

21 Aug–

25 Aug

11.1 Set 11.1.1 Explain the meaning of set.

11.1.2 Describe sets using:(i) description,(ii) listing, and(iii) set builder notation.

11.1.3 Identify whether an object is anelement of a set and represent therelation using symbol.

11.1.4 Determine the number of elements of aset and represent the number ofelements using symbol.

11.1.5 Compare and explain whether two ormore sets are equal and hence, makegeneralisation about the equality ofsets.

Carry out sorting and classifyingactivities including those involvingreal-life situations.

Including empty set and itssymbols, { } and .

Involve the use of set notation.

Example of set builder notation:

A = {x: x ≤ 10, x is even number}

Introduce the symbols and .

Introduce the symbol n(A).

Courtesy

Focus

Circle Map

11.2 Venndiagrams,universalsets,complement of a setandsubsets

11.2.1 Identify and describeuniversal sets andcomplement of a set.

11.2.2 Represent(i) the relation of a set and universal

set, and(ii) complement of a setthrough Venn diagrams.

Introduce the symbols for universalset (), complement of a set (A’) andsubset ().

Rationality Brace Map


28

W 36

4 Sept–

6 Sept

11.2.3 Identify and describe the possiblesubsets of a set.

11.2.4 Represent subsets using Venndiagrams.

11.2.5 Represent the relations betweensets, subsets, universal sets andcomplement of a set using Venndiagrams.

Concentration Brace Map

W 35

28 Aug–

1 Sept

CUTI PERTENGAHAN PENGGAL 2


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LEARNING AREA 5 : STATISTICS AND PROBABILITY

12. DATA HANDLING

W 36-38

7 Sept–

20 Sept

12.1 Datacollection,organizationandrepresentationprocess, andinterpretationof datarepresentation

12.1.1 Generate statistical questions andcollect relevant data.

12.1.2 Classify data as categorical ornumerical and constructfrequency tables.

12.1.3 Construct data representation forungrouped data and justify theappropriateness of a datarepresentation.

Use statistical inquiry approach forthis topic.

Statistical Inquiry

1. Posing / formulating real lifeproblems

2. Planning and collecting data3. Organising data4. Displaying / representing data5. Analysing data6. Interpretation and conclusion7. Communicating results

Statistical questions : questions thatcan be answered by collecting dataand where there will be variability inthat data.

Involve real life situations.

Collect data using various methodssuch as interview, survey, experimentand observation.

Numerical data : discrete orcontinuous

Data representation including varioustypes of bar charts, pie chart, linegraph, dot plot and stem-and-leafplot.

Use various methods to constructdata representations including theuse of software.

Systematical

Volunteering

Tree Map

Brace Map


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12.1.4 Convert a data representation toother suitable data representationswith justification.

12.1.5 Interpret various datarepresentations including makinginferences or predictions.

12.1.6 Discuss the importance ofrepresenting data ethically inorder to avoid confusion.

Involve histograms and frequencypolygons.

Focus Tree Map


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LEARNING AREA : MEASUREMENT AND GEOMETRY

13. THE PYTHAGORAS THEOREM

W 38-39/40

21 Sept–

4 Oct

13.1 ThePythagorasTheorem

13.1.1 Identify and define the hypotenuseof a right-angled triangle.

13.1.2 Determine the relationship betweenthe sides of right-angled triangle.Hence, explain the PythagorasTheorem by referring to therelationship.

13.1.3 Determine the length of the unknownside of(i) a right-angled triangle.(ii) combined geometric shapes.

13.1.4 Solve problems involving thePythagoras Theorem.

Carry out exploratory activities byinvolving various methods includingthe use of dynamic software.

Determine the length of sides byapplying the Pythagoras Theorem.

Effort

Courage

Bridge Map

13.2 Theconverse ofPythagorasTheorem

13.2.1 Determine whether a triangle is aright-angled triangle and givejustification based on the converseof the Pythagoras Theorem.

13.2.2 Solve problems involving theconverse of the PythagorasTheorem.

Understanding Tree Map


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Documents

MATEMATIKmbsskl.edu.my/panitia_math/files/2017/01/Form-1.pdfForm1Mathematics KSSM 3 1.2.3 Perform computations involving combined basic arithmetic operations of integers by followingtheorderofoperations