Edexcel GCSE Mathematics B Modular Foundation

12 Pythagoras’ Theorem12.112.212.312.4Finding the length of the hypotenuse of a right-angled triangle (GM g)Finding the length of one of the shorter sides of a right-angled triangle (GM g)Checking to see if a triangle is right-angled or not (GM g)Finding the length of a line segment (GM g, A k)00000000Functional SkillsA01 MSBF TG GCSE 0952 FM.indd 8Healthy livingLearning to drive2012 OlympicsUniversityMoney managementKitchen designCoverage and range spread00000000000000Answers00Unit 1Unit 2Unit 300000003/06/2010 13:49

IntroductionEdexcel’s GCSE MathematicsmaterialsThis GCSE Mathematics course has been developedby Edexcel to support you in teaching our new GCSEMathematics specifications. All the materials have beenfully referenced to the specifications. The course offersthe following components for each of the Foundation andHigher Tiers:Support for teaching the newAssessment ObjectivesAssessment What it isObjectiveWhat thismeansApprox %of marksin theexamAO1Recalland useknowledgeof theprescribedcontent.Questionstesting yourknowledge ofeach topic.45-55AO2Selectand applymathematicalmethods ina range ofcontexts.Questionsasking youto decidewhat methodyou need touse to get tothe correctanswer.25-35AO3Interpretand analyseproblemsand generatestrategies tosolve them.15-25Problemsolving:Deciding howand explainingwhy Student Book with graded questions, lots of support for the new Assessment Objectives and our uniqueExaminer insight from Results Plus.ActiveTeach CD-ROM to support you in your useof ICT for whole-class teaching, and in your lessonplanning and management.Teacher’s Guide, providing lesson objectives, topicgrades, ideas for activities including the use of ICT inActiveTeach and resource sheets to support studentscompleting exercises in the Student Book. Wordand Pdf files of all material available on the CD-ROMwhich is included and which will integrate with theActiveTeach.Practice Books: with one-to-one matching of Studentbook exercises. Pdfs of the material for upload to theschool VLE or network are available separately and willintegrate with ActiveTeach.Targeted Practice Books: providing support for G toF students; extension material for A to A* students andBooster C material for those all important borderlineD/C students. Pdfs of the material for upload to theschool VLE or network are available separately and willintegrate with ActiveTeach.Assessment Pack containing End of chaptertests; extra AO2 and AO3 practice questions; anda set of Exam Practice Papers with mark schemes.Word and Pdf files of all material are available on theaccompanying CD-ROM which will integrate withActiveTeach.ResultsPlus Booster C, designed to boost thegrades of your D/C borderline students. It providesweb-delivered homeworks and tests for individualformative assessment with detailed teacher and pupilfeedback.ResultsPlus Progress tests provide web-deliveredindividual summative assessment matched to the newspecification.SupportPlus website contains information aboutthe specifications, training events, support and samplematerials. An Edexcel Maths-users-only area givesfurther detailed support for teaching the specification.The new assessment objectives means that questionstyles within the exam are changing, with more problemsolving, open-style questions being set. These newquestion types are clearly marked in the Student booksand also have dedicated spreads for further practice. Yetmore questions are available in the Practice Books andin the Assessment Pack. Further interactive support isoffered in the ActiveTeach with interactive examples andin the Assessment packThe examination and the courseWritten by examiners who thoroughly understand thenew specification, all the material you need to preparestudents for the examination is available from this courseand has been carefully developed and reviewed. All questions show targeted grades. ResultsPlus examiner tips help students to gain thoseextra few marks in the examination. Past exam questions and exam style questions canbe found in the Chapter Review at the end of eachchapter. These have been chosen or specificallywritten to ensure they are a true reflection of the styleof questions that might appear in the examination.ixA01 MSBF TG GCSE 0952 FM.indd 903/06/2010 13:49

Introduction (Continued) Referencesto the specifiare given ininsightstudentAdvanced reportingtoolscationgive nfull in thestudent performance, enabling teachers to pinpointTeacher’sGuide.exactly whereindividuals are going wrong. TheTeacherGuideCD rogressto allowyouoftheschemetheof workthethatspecification bothof whichto ences to the relevant sections of thediagnoses.Student book, Practice books and Teacher Guide. ResultsPlusA blank self-assessmentProgress sheettestsis available on theTeacherGuideCDtoenablestudentsto helpsreflectyouon aOur online diagnostic ssessmentimprove your students’ performance before it’s too sheetlate.pointsbackto the bookforif Learningthey needintoto revise.Greatfor studentsembeddingAssessmentyourcourse, it gives you access to exactly the information youneed, to help tackle areas of weakness for each student. Ten topic-based tests, all with 25 questions that areA topic from Edexcel’s GCSE Mathematicscourseperfectfor both linear and modular lowingAs well as the concise Starters, Main teaching and learning pointsandPlenary,thebelessonalso contain: Eachtopictest cantakennotesindividuallyor linked withyou to display the Student Books on your whiteboardothers to create more comprehensive unit, termly oror throughyourVLE, while giving accessto a wealth nObjectives that link directly mock-stylefor theactivities,referencesvideo clips,quizzes and othertoactivities.exercise worksheetsthe specification and are Writtenexaminers. the Assessmentcontains:Commonbymisconceptions,and possible Packenrichmentactivitiesare alsoincluded where editableend-of-chaptertestsappropriate.for you to use or Editableschemeof workavailable onAlltheCD-ROM.adaptfor studentassessment.answersare estions.Asoftheseare supportworksheets,some of a bankAO2 andAO3 questionsfor extrathe questionsmayfallbelowgradelevels.practice of these assessment objectives Integratesfully withActiveTeachif installed. examinationpracticepapers,to help yourstudents become familiar with the types ofquestionsthey will be asked in the exam.Digitalproducts Formative and summative electronic tests are availableActiveTeachthrough our online ResultsPlus Booster C and ResultsICTPlusis seamlesslyincorporated into mathematics lessonsProgress tests.by using the unique, networkable, VLE compatibleActiveTeach.2010 specificationprovide extra questionsin each section inSupportPluswebsite BBC Activebring maths to life. includedAccompanyingand for clipsFunctionaland help support students.the Student Book.skills.are teacher mediated questions, and aeach clipworksheet for students to complete.1.2 Understanding prime factors, LCM ResultsPlus interactive problem-solvingactivitiesand HCFprovide whole class practiceofthenewAO2 and AO3 style questions with our uniquethree-part tool. ResultsPlus knowledge checkerstest AO1 recall with a multiple choice test at the endof each chapter. High-quality interactive contentintegrates seamlesslyPrior knowledge, with the Student Book.skills andMulti-lingual glossary gives audio translations for conceptscommon maths terms in five languages.highlighted Mylessons area allows you to personalise content bywhereapplicable.adding your own links, interactingdirectly with the text and saving your annotations, enabling you to reapply your thinking the next time youdeliver the lesson.Key mathematical Chapter 1 NumberSpecificationGCSE 2010Nc Use the concepts and vocabulary offactor (divisor), multiple, common factor,Highest Common Factor (HCF), LeastCommon Multiple (LCM), prime numberand prime factor decomposition.Concepts and skillsFind the prime factor decomposition of positive integers.Find the highest common factor (HCF) and the least common multiple (LCM) of two orthree numbers.FS Process skillsExamine patterns and relationshipsFunctional skillsFS PerformanceLevel 1 Use appropriate checkingprocedures at each stagePrior key knowledge, skills and conceptsL1 Add, subtract, multiply and divide whole numbers using a range of mental methods.Students should already know their multiplication tables up to 10 10.Students should be able to find factors, multiples and prime otlinksActiveTeach resourcesMultiples and factors quizLadder methodBBB Video: SupercrossCheck that students understand the terms prime number, factor and multiple.List the factors of 12. (1, 2, 3, 4, 6, 12) List the multiples of 6 between 10 and 40. (12, 18,24, 30, 36) List the first ten prime numbers. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)Introduce the word ‘common’ into some questions.Find two common factors of 12 and 18. (1, 2, 3, 6) Find two common multiples of 3 and 4.(12, 24, 36 etc)Main teaching and learningTell students that they are going to find out how to write any positive whole number asa product of its prime factors. Check that students understand the meaning of the wordproduct.Explain that this can be done by using a factor tree (or repeated division). Draw a factortree to show how 120 can be broken down into its prime factors (see Example 4).Discuss the fact that you can start with any two numbers that multiply to give 120. Drawa second factor tree for 120 starting with a different factor pair to show that the sameresult is reached.Tell students that they are going to find the HCF and LCM of two numbers.Explain that there are different methods that can be used to do this depending on thesize of the numbers involved.Discuss the best method for finding the HCF and LCM for two small numbers (e.g. 4 and6). Show students how these can be found by making a list of the factors and first fewmultiples of 4 and 6.www.edexcelmaths.com/supportplusOur dedicated website with information aboutHintsthehelp studentsspecifications, training events, support andsampletackle the work onGown.materials. An Edexcel Maths users-only areatheirgivesdetailed support including Interactive Schemes of Work Teaching Resources – Lesson Plans andPracticeDWorksheets Exam Question Editor Updates from Subject Leader Graham Cumming ICT BlogC Community Area Answers to questions in printed materials not includedwith the bookSection 1.2 Understanding prime factors, LCM and HCFQuestions are targeted at the grades indicated12vocabulary pulled out; this is alsoResultsPlusBoosterCavailable on the Easy to adopt, set up and administer,ResultsPlus ActiveTeachBoosterC is an online service that takes borderline D/Cwithwritten and spokendefinitionsstudentsthrough highly targetedpractice to boost their in Englishandaperformance and help them get that all-important C grade.multilingual spoken Dynamically generated guided practice questions,glossary.Common misconceptionsRemind students to include the multiplication signs when writing a number as a productof its prime factors. (These are often incorrectly replaced by addition signs or commas.)EnrichmentSuggest that students use the Venn diagram method to find the HCF and LCM of threelarge numbers (e.g. 240, 300 and 420).3labelled by grade,give students a variety of practice toSections detailing common misconceptions,meet their needsandexactly.possible enrichment activities to challenge Edexcel exam-stylequestionsgive thearestudentsand checkonscreen,their understandingalso examinerincluded whereappropriate.benefits of instantfeedback,and familiaritywith the new GCSE question types and requirements. Online deliveryensurestotal currency of questions forTeachingandLearningthenewspecification.Saving you time and guiding you through the new specifiLinkscation,to othercomponents,give studentsthecourseTeacher’sguide containsconcise,andteachers a Lessonclear, consistentexperience.easy-to-readplans andlearningextra GuidedPracticeWorksheets which are available as editable Word filesand pdfs on the CD-ROM.841021.9.4333Write each of the following numbers as the product of its prime factors.b 40 .a 24 .c 50 .Remember to drawfactor trees first.d 72 .e 100 .How can factor trees be drawn before working through to find out how many factors there are?5a Write out all the factors of(i) 4 .(iv) 16 .(ii) 6 .(v) 20 .(iii) 10 .b Use part a to help you write down the highest common factor (HCF) of(i) 4 and 10 .(ii) 6 and 16 .(iii) 4 and 20 .(iv) 16 and 20 .(v) 10 and 16 .6a Write out the first ten multiples of(i) 4 .(ii) 6 .b Write out the first six multiples of(i) 10 .(ii) 16 .Factors are numbersthat go exactly intothe given number.(iii) 20 .Icons used in the Student booksc Use your answers to parts a and b to help you write down the lowestcommon multiple (LCM) of (i) 4 and 6 .(iii) 4 and 16 .(v) 6 and 20 .(ii) 6 and 10 .(iv) 16 and 20 .Multiples are thenumbers in the timestable of the given number.Assessment objective questions are classifiedas AO2 and/or 3. These questions follow the more openstructure demanded by QCDA for the new specificationand are not available in earlier GCSE publishingschemes.Functional skills indicates questions that coverfunctional elements of GCSE maths.* Quality of Written Communication (QWC)identifies questions that follow the style of QWCquestions in the exam.indicatesquestionswhereAt a Non-calculatorglance specificationreferencesand detail.studentsmusttonotuse athatcalculatorfind thethe requiredanswer. ItStarter ectareacoveredby theprior rpaperMain teaching and learning points to help you teach ofthethe exam.topic itself.7a Useyour answers to question 3 to write 42, 70 and 84 as products of their prime factors.A02A03.b Find the HCF and LCM of 42 and 70.c Find the HCF and LCM of 70 and 84.8lowest common multiple (LCM)12/02/2010 15:05c70Use this factor tree to write 54 as a product of its prime factors.2Ask for the LCM of pairs of small numbers e.g. 2 and 6 (6), 4 and 10 (20), 6 and 12 (12).highest common factor (HCF)Write down thefactors in pairs.54Ask for the HCF of pairs of small numbers e.g. 2 and 6 (2), 4 and 10 (2), 6 and 12 (6).prime factorb426Plenary4d 40 .Complete the following factor trees.21Students might like to know that the HCF of two numbers must be a factor of thedifference between them. So the HCF of 210 and 250 must be a factor of 40. They maylike to explore this and consider why this is the case.M01 MSAH TG GCSE 0822 BLAD.indd 4b 30 .c 36 .aDiscuss why this method would not be appropriate for large numbers (e.g. 240 and 280).Explain how writing large numbers as the product of prime factors can be used to findthe LCM and HCF.Write down all the factors of each of the following numbers.a 12 .Find the HCF and LCM of the following pairs of numbers.a 60 and 84 .b 70 and 105 .c 72 and 96 .d 84 and 96 .5 M01 MSAH TG GCSE 0822 BLAD.indd 5 12/02/2010 15:05 Plenary questions to test understanding andapplication of the mathematics.xA01 MSBF TG G

examination or assessment. Any resource lists produced by Edexcel shall include this and other appropriate resources. Copies of official specifications for all Edexcel qualifications may be found on the Edexcel website: www.edexcel.com A01_MSBF