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Pupil’s BookMaths 6A3rd EditionDr Fong Ho Kheong Gan Kee Soon Chelvi Ramakrishnan

PrefaceMy Pals Are Here! Maths (3rd Edition) is a comprehensive, task-based andlearner-centred programme designed to provide pupils with a solid foundation inmathematics and opportunities to become efficient problem solvers.My Pals Are Here! Maths (3rd Edition) continues to make learning mathematics funand rewarding through the use of engaging illustrations, photographs, hands-onactivities and interactives that help reinforce and consolidate learning for pupils ofdifferent abilities.appears.A calculator may be used whenChallenge yourself to solvenon-routine questions byapplying relevant heuristicsand thinking skills inPut On Your Thinking Cap!Chapter Wrap-UpAlgebra We can simplify.algebraic expressions x 2, 2y 4, 3z andw are examples of5.algebraic expressions We can find thevalue of an algebraicexpression if we knowthe value of the letterin the expression.Examples: x x x 3x 2x 5x 7x 4x 1 2x 32x 4NEW!Solving AlgebraicEquationsSimplifying AlgebraicExpressionsAlgebraicExpressions Solving an algebraicequation such as3x 6 9 means tofind the value of x suchthat the value of3x 6 is 9.9xxxThe value of 2x 6is 14 when x 4.1C20151053a 3-digit num3 ber6 on a piece of4papThe digit in theer.hundreds4 placeis 20% of the digitThe digit in thetens place is 80%in the tens placof the digite.What is the 3-diin the ones placgit number shee.wrote?of the block of clay.3 If Rajesh buysEach smaller piece wasa vacuum cleaner at a discount 9.50 more. Ifof 10% of the sellinhe buys it at adiscount of 15%money does he, he will have 13.2 g price, he needshave?Method 25 left. How much3 6 344of the block of clay.the following topics:You may want to revisit P5 Fractions and DivisionWord Problems P4 Whole Numbers:Numbers P5 Operations of WholeChapter 1 Algebra9/5/17 9:23 amMaths Sharing136Chapter 4 PercentagedWorkbook A:fractionPut On Youwhole numbers and atwor Thinof dividingkingExplore the relationRevishipew 2, pages 119– Cap! pages 117–118128a whole number.1Share 6 apples equally2What is 6 fifths 3?04.indd 1363What is 6 seventhsamong 3 children. HowBefore you learn .Aisyah says that there are 2 quartersConsolidate theconcepts you havelearnt in each chapter inChapter Wrap-Up!L1Ad 38(M)MPAHTB6A 02.ind12of the2into equal pieces. Each piece was 6Devi had 3 of a pizza. She cut itcut it into?How many equal pieces did Devi16Become active learnersand collaborate withyour classmates inHands-On Activity!Workbook A:Practice 1,pages 21–221EA RNNEW!9/5/17 1:56 PMin . Do you agree? Explain.Chapter 2 Fractions38child receive?1 , 2 and 3 ?a proper fractionDividing a proper fraction byd 30Use the list ofsuggested topics fromearlier levels to revisitrelated concepts withyour parents.many apples does eachMaster the conceptyou have learntthrough engaging andinteractive applets inApp-tivity!9/5/17 1:57 PMHow many sixths2are there in 3 ?16161243 6pizza.16Devi cut it into 4 equal pieces.ARLE NHands-On ActivityDivide a proper fraction by a properfraction.Work in pairs.NEW!by3?your answers inWhat do you notice fromDiscuss and explain.(M)MPAHTB6A 01.indNEW!2 836 97b1453 124c(M)MPaHTB6Ast form.r as a fraction in its simpleDivide. Express each answeaSolving Word Problemsof clayMonthMetho2d 1 Sophia wrote1DShare your thoughts withyour teachers, createyour own mathematicsquestions and becomeaware of your ownmathematical thinking inMaths Sharing!Four Monthsblock. What fraction of the3of clay into 6 equal piecesMiss Tan cut 4 of a0blockJanuary FebruaryMarchwas each smaller piece?AprilTR YTR Yx 3 31in Singapore Over25Each smaller piece wasx 1 is the answerto the equation3x 6 9.30Amount of Rain63x 9 63nking Cap!The bar graphshowin a particular year s the monthly amount of rainfrom. Between whicdecrease in theh two months was January to April in Singaporeamount of rain?there the greatestpercentage30Practise new conceptslearnt in parallelquestions with helpfrom your teacher inTRY! x 3 6, 3x 12and 4x 3 15 areexamples of algebraicequations.Example:When x 4,2x 6 2 4 68 614Put On Your Thi1Total Rainfall (cm)For the Pupil:.then quartersprovided by your teacher into halves,1Fold the rectangular strip of paper11.quarters there are in 2 . Then, find 2 4Use your model to find how many112141Your partner finds 2 4.232 . What do you notice?Compare your answers in 1 and4to find 2 8.Switch roles. Repeat 1 to 31App-tivity n 2 Dividing by a Proper4516/8/17 9:25 am05 (M)MPAHTB6A 02.indd45

For the Teacher:NEW!CirclesUse scenarios pupils canrelate to in the chapteropeners to capture theirinterest, provide anengaging introduction tothe topics and jump-startlearning.Lesson3Teach concepts in concisesteps using real-lifecontexts, manipulativesand meaningful visuals inLEARN.9/5/17 1:55 PMBernard is standing at point O onthe ground. He walks 1 m fromthat point in a straight line.His friends do the same, but indifferent directions. Together, theyform a circle.(a) What does the distance of1 m represent?(b) If two children directly oppositeeach other hold a string that passesthrough the startpoint, what does the string represent?Hands-On ActivityWork in groups.1Use the circle cut-outs providedby your teacher. Fold a circle intoquarters. Mark thecentre of the circle as O.2Mark three points, A, B and C onthe circle.Measure the length between eachofthese three points and the centreO.What do you notice?Measure the diameter of the circle.Compare it with the lengths inWhat do you notice about the diameter of the circle and its radius?4Switch roles. Repeat 1 to 3with other circle cut-outs.5What do you notice about the diameterTR Y1aAssessunderstandingwhen pupils applyconcepts learnt inReview.AOiSummative Review 1In the figure, O is the centre ofdiameters.ii1the circle. Name theWhich line is not a diameter? Explain.Simplify3a 5 2ofaa circle9.bTheradiusdiameter?22 .of the circle as the size of the circleis 6 cm. What is the length of itsENEW!FBB139130 08 (M)MPAHTB6A 05.inddD139C7/11/17 9:58 AM3How many sixths are there in 2 ?4Find the value of 2 8 .353 oranges cost p. Find the cost of 47 orangesDuring a sale, Nathan bought a wallet that cost 45 after a 10% discount. What was theusual price of the wallet?7in terms of p.84How can I check my answer?I can work backwards to checkChapter 3 Ratiomy answer.(M)MPAHTB6A 03.indd 849/5/17 1:56 PMChapter 1 ReviewGive an algebraic expression for the following.Find the value of each expression when n 8.aUnderstanding of relatedconcepts from earlierlevels is also assessedwith LOOK BACKquestions.The figure shows a circle in a square of side 10cm. Find the area of the shaded region.(Take π 3.14.)10 (M)MPAHTBP6A SR 1.indd 1767/11/17 9:59 AM5n24Find the missing numbers. Draw models to help you.5Pam has 3 friends. Pam and her friends share x equally.aab540 8 7caHow much will each person get? Express your answer in terms of x.bIf x 28, how much will each of them receive?aFind the perimeter of the square in terms of w.bFind the length of the square when its perimeter is 36 cm.Sam’s father is 3 times as old as Sam. Sam’s mother is 5 years younger than Sam’sfather. Sam’s mother is 31 years old. How old is Sam?OO K8COO K9BA12 219x 6 8x 1The length of a square is w cm.6BAb7y 3yn 73cSimplify.P4 Whole Numbers: Word ProblemsAll the chairs in the school hall can be arranged in stacks of 7 or stacks of 13.There are less than 100 chairs in the hall. How many chairs are there?P5 Operations of Whole NumbersSimplify 9 12 2 (15 10).CWorkbook A:Chapter 1 Review, pages 17–18Maths Journal, page 19Chapter 1 Algebra(M)MPAHTB6A 01.indd 29Summative Review 1b3n 93Summative Reviewprovides more practiceto do a cumulativeconsolidation ofconcepts learnt.NEW!10 cm176They earn 3500 altogether.Step 47523 units 21001 unit 2100 3 7005 units 700 5 350096What fraction of Cindy’ssalary is Belinda’s salary?What fraction of Belinda’ssalary is Cindy’s salary?How much is Belinda’s salary?CindyTotal number of units 3 2OLesson 1 Radius, Diameter andCircumferenceWhat do I need to find?I need to find the ratio of Belinda’s salaryto Cindy’s salary.Then, I need to find their totalsalaries.A strawberry cake recipe needs w eggs for every 200 g of flour.How many eggs are needed for 1000 g of flour?ABCD is a parallelogram. EAB is a straight line. BCD 130 . Find EAD.cThe diameter of a circle is 15 cm.What is the length of its radius?AEStep 3the problem? 2100CDWhat have I gathered fromHow do I solve it?I can draw a model.Belinda1increases?AStep 1Step 2NEW!C3Use suggested questionsto facilitate classroomdiscussions that promotemathematical reasoning.Belinda’s salary is 3 of Cindy’ssalary. Belinda earns 2100.2How much do they earnaltogether?5Describe circles, explore the relationships between different lengthsin a circle and relate the sizes ofcircles to their diameters.B1NEW!(M)MPAHTB6A 05.indd 137LEARNEA RL3π is the ratio of thecircumference of acircle to its diameter.K2Radius, Diameter and CircumferenceArea of a CircleComposite FiguresBefore you learn .The number of playing cardsMariana had was 8 of the numberof playing cards Ben had.5They had 26 playing cards altogether. Find the ratio of the numberof playing cards Ben had tothe total number of playingcards they had altogether. Useto show how many playingcards Ben had.N1Solving Word ProblemsSolving word problemsLdeaBig InsIntroduce concepts throughcontext-based tasks inBefore you learn. At the endof each task, a question is posedto develop pupils’ creative andcritical thinking skills.Yes! Can you identifyall the other shapesyou see?Look, Jane! The windowsof the cruise ship arecircles!LessoNEW!L5KCHAPTER299/5/17 10:46 am

CONTENTS1 AlgebraLessonLessonLessonLesson1234Using Letters to Represent NumbersEvaluating Algebraic ExpressionsSimplifying Algebraic ExpressionsSolving Word Problems671517212 Fractions323 Ratio68Lesson 1 Dividing a Fraction by a Whole NumberLesson 2 Dividing by a Proper FractionLesson 3 Solving Word ProblemsLesson 1 Ratio and FractionLesson 2 Comparing RatiosLesson 3 Solving Word Problems333949697784

4 Percentage1065 Circles1376 Angles in Geometric Figures164Lesson 1 Finding PercentagesLesson 2 Percentage ChangeLesson 3 Solving Word ProblemsLesson 1 Radius, Diameter and CircumferenceLesson 2 Area of a CircleLesson 3 Composite FiguresLesson 1 Finding Unknown Angles in Geometric FiguresSummative Review 1107110122138147152165176

CHAPTER1AlgebraThe first machine adds 3 to 12 to get 15.What do the other machines do?What happens if I replace 12 with 30?123151552020828deaBig InsLesso1234Using Letters to Represent NumbersEvaluating Algebraic ExpressionsSimplifying Algebraic ExpressionsSolving Word ProblemsIn algebra, a letter isused to represent anunknown number.

Lesson1Using Letters toRepresent NumbersUsing Letters to Represent NumbersBefore you learn .Ryan has some pencils. Ben has 5 more pencils than Ryan. Use the letter x to represent thenumber of pencils Ryan has. Write an expression in terms of x for the number of pencilsBen has.LNEA R1ARani has 3 sweets.aShe gets 1 more sweet. How many sweets does she have now?3 1 4Rani has 4 sweets now.bShe gets 4 more sweets. How many sweets does she have now?3 4 7Rani has 7 sweets now.cHer friend gives her some sweets. How many sweets does she have now?Her friend gave her an unknown number of sweets.We can use the letter x to represent the unknownnumber. The letter x can represent any number.?x3Rani has (x 3) sweets now.x 3 is an example of an algebraic expression in terms of x.Lesson 1Using Letters to Represent Numbers7

LNEA R1BaiAdd 0 to 6iiAdd 0 to xx 0 x6 0 6biSum of 11 and 3iiSum of n and 3n 311 3 14ci4 more than 86 0 0 6 6x 0 0 x xii4 more than yy 48 4 12Is x 5 the same as 5 x?TR Y1AMr Tan is the form teacher of Primary 6B. The pupils do not know his age.Let Mr Tan be x years old now. Find Mr Tan’s age in terms of x.DescriptionMr Tan’s age nowMr Tan’s Age (Years)xMr Tan’s age 3 years from nowMr Tan’s age 5 years from nowMr Tan’s age 10 years from nowTR Y1B8Give an algebraic expression for each of the following.aAdd 5 to xbSum of z and 8c3 more than pChapter 1Algebra

LNEA R2AAiden has 20 cookies.aTom has 5 cookies. How many more cookies does Aiden have than Tom?20 5 15Aiden has 15 more cookies than Tom.bTom has 12 cookies. How many more cookies does Aiden have than Tom?20 12 8Aiden has 8 more cookies than Tom.cTom has y cookies. How many more cookies does Aiden have than Tom?20AidenTomy?Aiden has (20 y ) more cookies than Tom.20 y is another example of an algebraic expression.Is 20 y the same as y 20?LNEA R2BaiSubtract 3 from 7iia 37 3 4bi1 less than 12Subtract 3 from aii1 less than xx 112 1 11Lesson 1Using Letters to Represent Numbers9

My Pals Are Here! Maths (3rd Edition) is a comprehensive, task-based and learner-centred programme designed to provide pupils with a solid foundation in mathematics and opportunities to become efficient problem solvers. My Pals Are Here! Maths (3rd Edition) continues to make learning mathematics fun