Edexcel GCSE Mathematics A Linear Foundation

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.viiiA01 MSAF TG GCSE 0877 FM.indd 817/05/2010 13:26

Written by examiners. the Assessment Pack contains: editable end-of-chapter tests for you to use oradapt for student assessment. All answers areprovided. a bank of AO2 and AO3 questions for extrapractice of these assessment objectives examination practice papers, to help yourstudents become familiar with the types ofquestions they will be asked in the exam. Formative and summative electronic tests are availablethrough our online ResultsPlus Booster C and ResultsPlus Progress tests. References to the specification are given in studentfriendly language in the Student books and in full in theTeacher’s Guide. The Teacher Guide CD contains electronic copies ofthe scheme of work and the specification both of whichcontain references to the relevant sections of theStudent book, Practice books and Teacher Guide. A blank self-assessment sheet is available on theTeacher Guide CD to enable students to reflect on atopic. Cross referencing on the self-assessment sheetpoints students back to the book if they need to revise.A topic from Edexcel’s GCSE Mathematics courseAs well as the concise Starters, Main teaching and learning points and Plenary, the lesson notes also contain:Specificationreferences for the2010 specificationand for Functionalskills.Photocopiable remediationexercise worksheetsprovide extra questionsand help support students.Objectives that link directlyto the specification and areincluded in each section inthe Student Book.Chapter 1 NumberSection 1.2 Understanding prime factors, LCM and HCFSpecificationGCSE 2010Nc Use the concepts and vocabulary offactor (divisor), multiple, common factor,Highest Common Factor (HCF), LeastCommon Multiple (LCM), prime numberand prime factor decomposition.Questions are targeted at the grades indicated1.2 Understanding prime factors, LCMand HCF1Concepts and skills Find the prime factor decomposition of positive integers.Functional skillsFS PerformanceLevel 1 Use appropriate checkingprocedures at each stagePrior key knowledge, skills and concepts 2Find the highest common factor (HCF) and the least common multiple (LCM) of two orthree numbers.FS Process skillsExamine patterns and relationshipsWrite down all the factors of each of the following numbers.a 12 .b 30 .c 36 .d 40 .Complete the following factor trees.aKey mathematicalvocabulary pulledout; this is alsoavailable on theActiveTeachwith written andspoken definitionsin English and amultilingual spokenglossary.ActiveTeach resourcesMultiples and factors quizLadder methodBBB Video: SupercrossStudents should be able to find factors, multiples and prime numbers.3D54 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). Tell 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. 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. Discuss why this method would not be appropriate for large numbers (e.g. 240 and 280).9.24Main teaching and learning333Write 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 .6Explain how writing large numbers as the product of prime factors can be used to findthe LCM and HCF.a 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 .c 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 .Remind 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.)7(ii) 6 and 10 .(iv) 16 and 20 .Multiples are thenumbers in the timestable of the given number.a Use your answers to question 3 to write 42, 70 and 84 as products of their prime factors. Suggest that students use the Venn diagram method to find the HCF and LCM of threelarge numbers (e.g. 240, 300 and 420). Students 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.b Find the HCF and LCM of 42 and 70.c Find the HCF and LCM of 70 and 84.Plenary 8Find the HCF and LCM of the following pairs of numbers.Ask for the HCF of pairs of small numbers e.g. 2 and 6 (2), 4 and 10 (2), 6 and 12 (6).a 60 and 84 .b 70 and 105 .Ask for the LCM of pairs of small numbers e.g. 2 and 6 (6), 4 and 10 (20), 6 and 12 (12).c 72 and 96 .d 84 and 96 .highest common factor (HCF)lowest common multiple (LCM)M01 MSAH TG GCSE 0822 BLAD.indd 4C(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 .Explain that there are different methods that can be used to do this depending on thesize of the numbers involved.Enrichmentprime factor21Use this factor tree to write 54 as a product of its prime factors.6Common misconceptions48410Students should already know their multiplication tables up to 10 10. c7021Check 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)ResourcesLinkswww.heinemann.co.uk/hotlinksb42L1 Add, subtract, multiply and divide whole numbers using a range of mental methods.StarterPrior knowledge,skills andconceptshighlightedwhere applicable.GWrite down thefactors in pairs.Hints help studentstackle the work ontheir own.512/02/2010 15:05M01 MSAH TG GCSE 0822 BLAD.indd 512/02/2010 15:05Sections detailing common misconceptions,and possible enrichment activities to challengestudents and check their understanding arealso included where appropriate.Teaching and LearningSaving you time and guiding you through the newspecification, the Teacher’s guide contains concise,easy-to-read Lesson plans and extra Guided PracticeWorksheets which are available as editable Word filesand pdfs on the CD-ROM. At a glance specification references and detail. Starter ideas to check that students have the requiredprior knowledge. Main teaching and learning points to help you teachthe topic itself. Plenary questions to test understanding andapplication of the mathematics.ixA01 MSAF TG GCSE 0877 FM.indd 917/05/2010 13:26

Introduction (Continued)Chapter 1 Number Common misconceptions, and possible enrichmentactivities are also included where appropriate. Editable scheme of work available on the CD-ROM. Guided practice worksheets with remediationquestions. As these are support worksheets, some ofthe questions may fall below grade levels. Integrates fully with ActiveTeach if installed.Digital productsActiveTeachICT is seamlessly incorporated into mathematics lessonsby using the unique, networkable, VLE compatibleActiveTeach.ActiveTeach is a front-of-class teaching tool allowingyou to display the Student Books on your whiteboardor through your VLE, while giving access to a wealth ofactivities, video clips, quizzes and other activities. BBC Active clips bring maths to life. Accompanying each clip are teacher mediated questions, and aworksheet for students to complete.ResultsPlus interactive problem-solving activitiesprovide whole class practice of the new AO2 and AO3style questions with our unique three-part tool.ResultsPlus knowledge checkers test AO1 recall with amultiple choice test at the end of each chapter.High-quality interactive content integrates seamlesslywith the Student Book.Multi-lingual glossary gives audio translations forcommon maths terms in five languages.My lessons area allows you to personalise content byadding your own links, interacting directly with the textand saving your annotations, enabling you to reapplyyour thinking the next time you deliver the lesson.ResultsPlus Booster CEasy to adopt, set up and administer, ResultsPlusBooster C is an online service that takes borderline D/Cstudents through highly targeted practice to boost theirperformance and help them get that all-important C grade. Dynamically generated guided practice questions,labelled by grade, give students a variety of practice tomeet their needs exactly. Edexcel exam-style questions onscreen, give thebenefits of instant examiner feedback, and familiaritywith the new GCSE question types and requirements. Online delivery ensures total currency of questions forthe new specification. Links to other course components, give students andteachers a clear, consistent learning experience. Advanced reporting tools give unmatched insight intostudent performance, enabling teachers to pinpointexactly where individuals are going wrong. Works alongside ResultsPlus Progress to allow youto address the weak areas that ResultsPlus Progressdiagnoses.ResultsPlus Progress testsOur online diagnostic assessment service helps youimprove your students’ performance before it’s too late.Great for embedding Assessment for Learning into yourcourse, 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 areperfect for both linear and modular courses. Each topic test can be taken individually or linked withothers to create more comprehensive unit, termly ormock-style assessments.SupportPlus websitewww.edexcelmaths.com/supportplusOur dedicated website with information about thespecifications, training events, support and samplematerials. An Edexcel Maths users-only area givesdetailed support including Interactive Schemes of Work Teaching Resources – Lesson Plans and PracticeWorksheets Exam Question Editor Updates from Subject Leader Graham Cumming ICT Blog Community Area Answers to questions in printed materials not includedwith the bookIcons used in the Student books 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. Non-calculator indicates questions wherestudents must not use a calculator to find the answer. Itdoes NOT indicate that the subject area covered by thequestion will only appear in the non-calculator paper ofthe exam.A02A03xA01 MSAF TG GCSE 0877 FM.indd 1017/05/2010 13:26

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_MSAF