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# Mathematic form1

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### Mathematic form1

1. 1. MINISTRY OF EDUCATION MALAYSIAIntegrated Curriculum for Secondary SchoolsCurriculum SpecificationsMATHEMATICSForm 1Curriculum Development CentreMinistry of Education Malaysia2002
2. 2. CONTENTSPageWHOLE NUMBERS 1NUMBER PATTERNS AND SEQUENCES 4FRACTIONS 10DECIMALS 15PERCENTAGES 18INTEGERS 19ALGEBRAIC EXPRESSIONS 21BASIC MEASUREMENTS 23LINES AND ANGLES 26POLYGONS 28PERIMETER AND AREA 30SOLID GEOMETRY 32
3. 3. 11. Learning Area: Whole NumbersLearning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents will be taught to: Students will be able to:1. Understand theconcept of wholenumbers.Count; read and write wholenumbers in words or numerals.Students read and write wholenumbers while counting from agiven initial value to a final value ina certain specified interval.e.g. i. Count on in tens from 20 to100.ii. Count back in hundredsfrom 1200 to 200.Estimate values, including that ofreal-life situations by rounding.i. Count, read and write whole numbers.ii. Identify place value and value of eachdigit in whole numbers.iii. Round whole numbers.Emphasise therelationshipbetweenrounding andestimation.WholenumberPlace valueDigitIntervalRoundEstimateNearestLargerLargestSmallerSmallestNearest ten,hundred,thousand…hundredthousand.
5. 5. 3Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary4. Perform computationsinvolving combinedoperations ofaddition,subtraction,multiplication anddivision of wholenumbers to solveproblemsStudents explore combinedoperations of whole numbers byusing standard algorithm (rules ofcalculations), estimation, pencil-and-paper or calculator.Solve problems related to real-lifesituations.Students use calculators tocompare and verify answers.i. Perform computations involving anycombination of addition, subtraction,multiplication and division of wholenumbers, including the use ofbrackets.ii. Solve problems involving combinedoperations of addition, subtraction,multiplication and division of wholenumbers, including the use ofbrackets.Emphasise onthe order ofoperations andthe use ofbrackets.MultiplyMultiplicationDivideDivisionEstimateComputeSolveBracketOrder ofoperationsCombinedoperationCombination
6. 6. 42. Learning Area: Number Patterns and SequencesLearning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents will be taught to: Students will be able to:1. Recognise and extendnumber patterns andsequences formed bycounting on andcounting back inintervals of any size.Relate number sequence topatterns in real-life situations.e.g. Odd numbers are used asaddresses of houses on one side ofthe road and even numbers on theother.Use calculators to skip count(generate number sequences),explore number patterns, and solveproblems.i. Describe the pattern of a givennumber sequence.ii. Extend number sequences.iii. Complete missing terms in givennumber sequences.iv. Construct number sequences basedon given patterns.Do not includenegativenumbers.2. Recognise odd andeven numbers andmake generalstatements aboutthem.Explore general statements aboutodd and even numbers such as:a. The sum of odd and evennumbers.b. The product of odd and evennumbers.c. The difference between oddand even numbers.i. Identify and describe odd and evennumbers.ii. Make general statements about oddand even numbers.NumbersequencePatternTermSumProductDifferenceCount onCount backOddEvenSubtractMultiplyConstruct
7. 7. 5Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary3. Understand thecharacteristics ofprime numbers.Use calculators or computerprogrammes to explore primenumbers.Use sieve of Eratosthenes togenerate prime numbers less than100.i. Identify the characteristics ofprime numbers.ii. Determine whether a givennumber is a prime number.iii. Determine all the prime numbersless than 100.Emphasise thatNumber 1 is not aprime number.4. Understand thecharacteristics anduse the knowledge offactors of wholenumbers.Determine factors of wholenumbers by exploring andinvestigating.i. List factors of whole numbers.ii. Determine whether a number is afactor of another whole number.Emphasise that 1and the numberitself are factorsof any number.Prime numberFactorPrime Factor5. Understand thecharacteristics anduse the knowledge ofprime factors ofwhole numbers.Students explore and investigateto determine prime factors ofwhole numbers.State any given whole number asa product of its prime factors.i. Identify prime factors from a list offactors.ii. Find prime factor(s) of wholenumbers.iii. Determine whether a number is aprime factor of another wholenumber.
8. 8. 6Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary6. Understand and usethe knowledge ofmultiples of wholenumbers.Students use the divisibility test of2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and theircombinations.e.g.30 can be divided by 6.Therefore itcan be divided by 2 and 3 andvice-versa.i. List the multiples of wholenumbers.ii. Determine whether a number isthe multiple of another number.Emphasise thatthe list ofmultiples of anumber is also anumbersequence.Use smallnumbers todevelop theconcept.MultipleDivisibleDivisibility testCommonmultipleLowestCommonMultiple (LCM)Sequence
9. 9. 7Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary7. Understand thecharacteristics anduse the knowledge ofcommon multiplesand LowestCommon Multiple(LCM) of wholenumbers.Students find common multiplesand LCM by listing down themultiples of each given number.e.g.Multiples of 4 : 4, 8, 12, ……Multiples of 6 : 6, 12, ……Common Multiples of 4 and 6:12, 24, 36, 48, ……which are the multiples of 12.Use the method of “primefactorisation” to find commonmultiples and LCM.e.g.4 = 2 x 26 = 2 x 3Therefore the LCM of 4 and 6 is2 x 2 x 3 = 12.i. Find the common multiples of twoor three whole numbers.ii. Determine whether a number isthe common multiple of two orthree given numbers.iii. Determine the LCM of two or threegiven numbers.Emphasise that alist of commonmultiples is also anumbersequence.Use smallnumbers todevelop theconcept
10. 10. 8Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyUse algorithm to find the LCM.8. Understand and usethe knowledge ofcommon factors andHighest CommonFactors (HCF) ofwhole numbers.Students list down all the factors ofeach given number and identify thesame factors for each number.Students explore, identify anddetermine common factors ofwhole number.i. Find common factors of two or threewhole numbers.ii. Determine whether a number is acommon factor of two or three givenwhole numbers.iii. Determine the HCF of two or threegiven numbers.CommonFactorHighestCommonFactor (HCF)4, 62, 31, 32231, 1LCM = 2 x 2 x 3= 12
11. 11. 9Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents find the HCF by listingdown all the factors of each givennumber.Explore, identify and determine theHCF of whole numbers.Use the method of primefactorisations to find the commonprime factors and hence HCF.e.g.12 = 2 x 2 x 318 = 2 x 3 x 3Common Prime Factors: 2 and 3The HCF: 2 x 3 = 6Use algorithm to find HCF.
12. 12. 103. Learning Area: FractionsLearning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents will be taught to: Students will be able to:1. Understand and usethe knowledge offractions as part of awhole.Use concrete materials anddrawings to demonstrate theconcept of fractions such as:a. Folding a ribbon to find one-third of its length.b. The number of girls ascompared to the whole class.c. Folding papers.i. Read fractions.ii. Describe fractions as parts of awhole.iii. Represent fractions withdiagrams.iv. Write fractions for givendiagrams.54read as:Four over five2215read as: Fifteenover twenty twoUse the termsnumerator anddenominator.2. Understand and usethe knowledge ofequivalent fractions.Use concrete materials anddrawings to demonstrate theconcept of equivalent fractions.Use paper folding to explain andexplore:Why63is the same as21.Compare the values of twofractions by converting them tofractions with the samedenominator or the samenumerator.i. Find equivalent fractions for agiven fraction.ii. Determine whether two givenfractions are equivalent.iii. Compare the values of two givenfractions.iv. Arrange fractions in order.v. Simplify fractions to the lowestterms.Use number lines,concrete materials orthe concept ofequivalent fractionsto compare fractions.FractionDenominatorNumeratorEquivalentfractionsLowest termsArrangeOrder
13. 13. 11Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary3. Understand theconcept of mixednumbers and theirrepresentations.Use concrete materials, drawingsand number lines to representmixed numbers.Identify the use of mixed numbersin everyday situations.i. Recognise mixed numbers.ii. Represent mixed numbers withdiagrams.iii. Write mixed numbers based ongiven diagrams.iv. Compare and order mixednumbers on number lines.Mixed numberProperfractionImproperfractionNumber lineDenominator4. Understand theconcept of properfractions andimproper fractions.Use concrete materials anddrawings to demonstrate therelationship between mixednumbers and improper fractions.Use calculators to explore therelationship between mixednumbers and improper fractions.i. Recognise proper and improperfractions from given fractions.ii. Change mixed numbers intoimproper fractions.iii. Change improper fractions intomixed numbers.
14. 14. 12Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary5. Understand theconcept of additionand subtraction offractions to solveproblems.Use concrete materials, drawingsand symbols to demonstrate theprocess of addition and subtractionof fractions.Add and subtract fractions bywriting the fractions in theirequivalent forms with commondenominators including the use ofLCM.Perform addition and subtraction ofmixed numbers by:i) Adding and subtracting wholenumbers and fractionsseparately.ii) Writing mixed numbers in theform of improper fractions.Pose and solve problems related toeveryday situations.i. Perform addition involving:a. Fractions with commondenominators.b. Fractions with differentdenominators.c. Whole numbers andfractions.d. Fractions and mixednumbers.e. Mixed numbers.ii. Perform subtraction involving:a. Fractions with commondenominators.b. Fractions with differentdenominators.c. Whole numbers andfractions.d. Fractions and mixednumbers.e. Mixed numbers.iii. Solve problems involvingcombined operations of additionand subtraction of fractions.Addition andsubtraction involvingnot more than threenumbers.MixedNumberAddSubtractFractionSimplefractionLowest termEquivalentfractions
15. 15. 13Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary6. Understand theconcept ofmultiplication anddivision of fractionsto solve problems.Use concrete materials, drawingsand symbols to explore andinvestigate the process ofmultiplication and division offractions.Examples of multiplication:a. A whole number times afraction.3 x433 x43=49= 241b. A whole number times a mixednumber.4 x 1214 x 121= 4 x23=212= 6i. Multiply:a. A whole number by afraction or mixed number.b. A fraction by a wholenumber.c. A fraction by a fraction(include mixed numbers).ii. Solve problems involvingmultiplication of fractions.iii. Divide:a. A fraction by a wholenumber.b. A fraction by a fraction.c. A whole number by afraction.d. A mixed number by a mixednumber.iv. Solve problems involvingdivision of fractions.Emphasisemultiplication offractions asrepeated addition ofthe fractionsDivision involving notmore than threenumbers includingwhole numbers,fractions and mixednumbers.MultiplyDivideMixedNumberRepeatedadditionNumerator
16. 16. 14Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabularyc. A fraction times a fraction.654365x43=2415=857. Perform computationsinvolving combinedoperations ofaddition, subtraction,multiplication anddivision of fractionsto solve problems.Pose problems related to real-lifesituations.Use concrete materials anddiagrams to demonstratecomputations.i. Perform computations involvingcombined operations ofaddition, subtraction,multiplication and division offractions, including the use ofbrackets.ii. Solve problems involvingcombined operations ofaddition, subtraction,multiplication and division offractions, including the use ofbrackets.Limit the operationsto three numbersincluding wholenumbers and mixednumbers.Emphasise the orderof operations,including the use ofbrackets.MultiplicationAdditionSubtractionDivisionCombinedoperationMixed numberWholenumberBracket
17. 17. 154. Learning Area: DecimalsLearning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents will be taught to: Students will be able to:1. Understand therelationship betweendecimals andfractions.Use concrete materials, drawings,calculators and symbols to explainthe relationship between decimalsand fractions.i. Represent fractions101and1001asdecimals and vice-versa.ii. Represent fractions withdenominators 10,100 and 1000 asdecimals.iii. Read and write decimals tothousandths.iv. Change fractions to decimals andvice-versa.0.3 read as: zeropoint three0.05 read as:zero point zerofive3.29 read as:three point twonine.FractionDecimalDenominatorTenthsHundredthsThousandthsNumber linePlace valueValue of adigitRoundingDecimal point2. Understand the conceptof place value andvalue of each digit indecimals.Use number lines to compare andorder decimals.i. State the place value and value ofeach digit in decimals.ii. Compare the values of two givendecimals.iii. Arrange decimals in order.iv. Round decimals to the nearest wholenumber or up to three decimal places.Emphasise therelationshipbetweenrounding andestimation.
18. 18. 16Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary3. Understand the conceptof addition andsubtraction ofdecimals to solveproblems.Use concrete materials, drawingsand symbols.Solve problems related to everydaysituations.Use calculators or computers toverify answers.Use estimation strategies todetermine whether the solution isreasonable.i. Add decimals.ii. Solve problems involving addition ofdecimals.iii. Subtract decimals.iv. Solve problems involving subtractionof decimals.Include wholenumbers.Addition andsubtractionshould begin withtwo decimals.Limit to threedecimal places.AddSubtractDecimalMultiplyDivideMentallydivideMentallymultiplyReasonableEstimation4. Understand the conceptof multiplication anddivision of decimals tosolve problems.Relate to everyday situations.Use appropriate calculationmethods such as pencil-and -paper, calculators and computers.Mentally multiply decimals by 10,100 and 1000.Mentally multiply decimals by 0.1,0.01 and 0.001.Mentally divide decimals by 10,100 and 1000.Mentally divide decimals by 0.1,0.01 and 0.001.i. Multiply two or more decimals.ii. Solve problems involvingmultiplications of decimalsiii. Divide:a. A decimal by a whole number.b. A decimal by a decimal.c. A decimal by a fraction.iv. Solve problems involving division ofdecimals.For multiplicationand division,include wholenumbers.Begin with onedigit wholenumber
19. 19. 17Learning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note Vocabulary5. Perform computationsinvolving combinedoperation of addition,subtraction,multiplication anddivision of decimals tosolve problems.Pose problems related to everydaysituations.i. Perform computations involvingcombined operations of addition,subtraction, multiplication and divisionof decimals, including the use ofbrackets.ii. Solve problems involving combinedoperations of addition, subtraction,multiplication and division of decimals,including the use of brackets.Emphasise theorder ofoperationsincluding the useof brackets.Include wholenumbers andfractionsAdditionSubtractionMultiplicationDivisionDecimalBracketCombinedoperation
20. 20. 185. Learning area: PercentagesLearning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents will be taught to: Students will be able to:1. Understand theconcept ofpercentages and therelationship betweenpercentages andfractions or decimals.2. Performcomputations andsolve problemsinvolving percentages.Use concrete materials anddrawings to demonstratepercentages.e.g. Use ten by ten grids to discuss theequivalent percentages offractions and decimals. Forexample the fraction21has adecimal equivalent of 0.5, and 0.5has a percentage equivalent of50%. (21= 0.5 or 50%)Pose and solve problems involvingprofit and loss, simple interest,dividend, commission anddiscount.i. Express percentages as the numberof parts in every 100.ii. Change fractions and decimals topercentages and vice-versa.i. Find the percentage of a quantity.ii. Find the percentage one number is ofanother.iii. Find a number given the percentage.iv. Find the percentage of increase ordecrease.v. Solve problems involvingpercentages.Use the symbol% to representpercent.Includepercentageslarger than 100.30% of 240 = 723 of 12 = 25%8 is 20% of whatnumber? (40)Original amount: 15Increased to: 18Find percentage ofincrease.Original amount: 40Decreased to: 10Find percentage ofdecrease.PercentFractionDecimalIncreaseDecreaseDiscountProfitLossSimpleinterestDividendCommission
21. 21. 196. Learning Area: IntegersLearning Objectives Suggested Teaching and LearningActivitiesLearning Outcomes Points to Note VocabularyStudents will be taught to: Students will be able to:1. Understand and usethe knowledge ofintegers.Introduce integers in context (e.g.temperatures, sea levels and floorsof building).Students complete sequences ofintegers, find the missing terms,and identify the largest and thesmallest value of integers fromgiven sets of integers.Given sets of integers, studentsorder them on number lines.i. Read and write integers.ii. Represent integers on number lines.iii. Compare the values of two integers.iv. Arrange integers in order.v. Write positive or negative numbers torepresent word descriptions.– 32 read as:negative thirty-two.– 5 is less than – 2–15 is greater than–25Words description:e.g.i. 30 metresbelow sealevel: – 30ii. Weight gain of2 kg: 2The number 0 isneither positivenor negative.IntegerNegativenumberPositivenumberNumber lineTemperatureSea levelFloors of abuildingLess thanGreater thanWordsdescriptionMissingtermsLargestSmallest