Cambridge IGCSE Mathematics 0580 For Examination
Scheme of workCambridge IGCSE Mathematics0580For examination from 2015
Scheme of work – Cambridge IGCSE Mathematics (0580) from 2015ContentsOverview . 3Unit 1: Number . 6Unit 2: Algebra and graphs . 17Unit 3: Geometry . 29Unit 4: Mensuration . 34Unit 5: Co-ordinate geometry. 38Unit 6: Trigonometry . 41Unit 7: Matrices and transformations . 45Unit 8: Probability . 49Unit 9: Statistics . 52v1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20152
Scheme of work – Cambridge IGCSE Mathematics (0580) from 2015OverviewThis scheme of work provides ideas about how to construct and deliver a course. The syllabus has been broken down into teaching units with suggested teachingactivities and learning resources to use in the classroom. This scheme of work, like any other, is meant to be a guideline, offering advice, tips and ideas. It can never becomplete but hopefully provides teachers with a basis to plan their lessons. It covers the minimum required for the Cambridge IGCSE course but also addsenhancement and development ideas on topics. It does not take into account that different schools take different amounts of time to cover the Cambridge IGCSEcourse.Recommended prior knowledgeIt is recommended that candidates have followed the Secondary 1 Mathematics Curriculum Framework which can be foundat: rsec/cambridgesecondary1/resources or followed courses which cover the material contained in the UK NationalCurriculum for Mathematics at Key Stage 3 s3.3TUU3T3TUU3TOutlineWhole class (W), group work (G), pair (P) and individual activities (I) are indicated, where appropriate, within this scheme of work. Suggestions for homework (H) andformative assessment (F) are also included. The activities in the scheme of work are only suggestions and there are many other useful activities to be found in thematerials referred to in the learning resource list.Opportunities for differentiation are indicated as basic and challenging. There is the potential for differentiation by resource, length, grouping, expected level ofoutcome, and degree of support by the teacher, throughout the scheme of work. Timings for activities and feedback are left to the judgment of the teacher, according tothe level of the learners and size of the class. Length of time allocated to a task is another possible area for differentiation.The units within the scheme of work are:Unit 1: NumberUnit 2: Algebra and graphsUnit 3: GeometryUnit 4: MensurationUnit 5: Co-ordinate geometryUnit 6: TrigonometryUnit 7: Matrices and transformationsUnit 8: ProbabilityUnit 9: Statisticsv1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20153
Syllabus contentThe syllabus references use C for Core and E for Extended curriculum. In this scheme of work they are listed together using black text to identify where both the Coreand Extended curriculum cover the same content and blue text for where the content is only covered by the Extended curriculum.Teacher supportTeacher Support (http://teachers.cie.org.uk) is a secure online resource bank and community forum for Cambridge teachers, where you can download specimen andpast question papers, mark schemes and other resources. We also offer online and face-to-face training; details of forthcoming training opportunities are posted online.3TUU3TThis scheme of work is available as PDF and an editable version in Microsoft Word format; both are available on Teacher Support at http://teachers.cie.org.uk. If youare unable to use Microsoft Word you can download Open Office free of charge from www.openoffice.org.3TU3TUU3TU3TResource listThe resource list for this syllabus, including textbooks endorsed by Cambridge, can be found at www.cie.org.uk and Teacher Support http://teachers.cie.org.uk.UUUUEndorsed textbooks have been written to be closely aligned to the syllabus they support, and have been through a detailed quality assurance process. As such, alltextbooks endorsed by Cambridge for this syllabus are the ideal resource to be used alongside this scheme of work as they cover each learning objective.TextbooksThe most commonly used textbooks referenced in this scheme of work include:Barton, DEssential Mathematics for IGCSE Extended Teacher Resource Kit (Oxford University Press, 2012)Haighton, J et alCore Mathematics for Cambridge IGCSE (Nelson Thornes, 2012)Haighton, J et alExtended Mathematics for Cambridge IGCSE (Nelson Thornes, 2012)Morrison, K and Hamshaw, N Cambridge IGCSE Mathematics Core and Extended Coursebook (with CD-ROM) (Cambridge University Press, 2012)Nye, CIGCSE Core Mathematics (Heinemann, 2009)Nye, CIGCSE Extended Mathematics (Heinemann, 2009)Pearce, CCambridge IGCSE Maths Student Book (Collins Educational, 2011)Pemberton, SEssential Mathematics for Cambridge IGCSE Extended (with CD-ROM) (Oxford University Press, 2012)Pimental, R and Wall, TCambridge IGCSE Mathematics Second Edition updated with CD (Hodder Education, 2011)Rayner, DCore Mathematics for Cambridge IGCSE (with CD-ROM) (Oxford University Press, 2011)Rayner, DExtended Mathematics for Cambridge IGCSE (with CD-ROM) (Oxford University Press, 2011)Simpson, ACore Mathematics for Cambridge IGCSE (Cambridge University Press, 2010)Simpson, AExtended Mathematics for Cambridge IGCSE (Cambridge University Press, 2011)WebsitesThis scheme of work includes website links providing direct access to internet resources. Cambridge International Examinations is not responsible for the accuracy orcontent of information contained in these sites. The inclusion of a link to an external website should not be understood to be an endorsement of that website or thesite's owners (or their products/services).The particular website pages in the learning resource column of this scheme of work were selected when the scheme of work was produced. Other aspects of the siteswere not checked and only the particular resources are recommended.v1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20154
Websites in this scheme of work, and some other useful websites, timdevereux.co.uk/maths/maths UU3T3TUU3T3TUU3T3TUU3Tv1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20155
Scheme of work – Cambridge IGCSE Mathematics (0580) from 2015Unit 1: NumberRecommended prior knowledgeLearners should be able to add, subtract, multiply and divide confidently with integers and identify the correct operation from a word problem. They should be familiarwith directed numbers and have an understanding of a number line involving positive and negative values. They should understand how to round to the nearest wholenumber, 10, 100 and 1000 and have some familiarity with decimal places. Learners should be familiar with multiplying and dividing whole numbers and decimals by 10to the power of any positive or negative integer and recognise the equivalence of simple decimals, fractions and percentages, e.g. 0.25, ¼ and 25%. Learners need tounderstand 12 and 24 hour clock and be able to convert between these. They should also be confident in working with simple fractions and decimals, for examplewriting a fraction in its simplest form by cancelling common factors; adding and subtracting fractions with the same denominator; adding and subtracting decimals withthe same number of decimal places. They should be aware of the order of operations, including brackets and recognise the effects of multiplying and dividing bynumbers bigger than 1 or smaller than 1.ContextThis first unit revises and develops mathematical concepts in number that underpin the course. The work is fundamental to the study of all the other units and parts of itwill need to be revisited when teaching subsequent units. This unit is appropriate for all learners, with the exception of all of sections 1.2 and 1.17 and the indicatedparts of sections 1.5, 1.7, 1.10, 1.11, 1.12, and 1.16 which are only for extended learners. It is anticipated that learners studying the extended syllabus will work throughat a faster pace.OutlineIt is intended for the topics in this unit to be studied sequentially, although this is not essential as certain topics, for example Time (1.14), can be studied earlier as it is asimpler and probably quite familiar concept. Also you may want to study unit 1.16 after 1.12, as they are related, or you may choose to leave a gap between them sothat percentages can be revised when topic 1.16 is studied. This unit covers all aspects of number from the syllabus, namely fractions, decimals, percentages, ratios,indices, directed numbers, bounds, time, money and finance. Some teachers prefer to not teach number all in one block, it is possible to leave some sections until laterin the course, for example upper and lower bounds (1.10) and exponential growth and decay (1.17) could be taught later on in the course, similarly with other topics.Teaching timeIt is recommended that this unit should take approximately 30–35% (Core learners) 15–20% (Extended learners) of the overall IGCSE course.v1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20156
RefSyllabus contentSuggested teaching activities1.1Identify and use natural numbers,integers (positive, negative andzero), prime numbers, squarenumbers, common factors andcommon multiples, rational andA useful starting point would be to revise positive and negative numbers using anumber line and explain the difference between natural numbers and integers. (W)(Basic)irrational numbers (e.g. π,numbers.2 ), realIncludes expressing numbers as aproduct of prime factors.Finding the Lowest CommonMultiple (LCM) and HighestCommon Factor (HCF) of twonumbers.Learning t/numbers3TULearners would find it useful to have a definition of the terms (e.g. factor, multiple,square number) which can be found on the maths revision website. (W) (I) (Basic)U3TA fun activity would be to allocate a number to each learner in the class and ask themto stand up if they are, for example, “a multiple of 4”, “a factor of 18” etc. Use this toshow interesting facts such as prime numbers will have 2 people standing up(emphasises 1 is not prime); square numbers will have an odd number of peoplestanding up. See which are common factors/common multiples for pairs of numbers.This could be extended to HCF and LCM. (W) s.html3TUhttp://vimeo.com/101831240 thefactor tree approach3TUU3TCD-ROMPemberton. Unit 1 slides 9 and 10A follow-on activity would be for learners to identify a number from a description of itsproperties. For example, say to the class “which number less than 50 has 3 and 5 asfactors and is a multiple of 9?” Learners could then make up their own descriptions andtest one another. (G) (Basic)Another interesting task is to look a Fermat’s discovery that some prime numbers arethe sum of two squares, e.g. 29 25 4 52 22. Learners could see what primesthey can form in this way, and any they can’t form in this way. Learners can look for arule which tests whether or not a prime can be made like this. (I) (Challenging)PPPPMove on to looking at how to write any integer as a product of primes. One method thatcan be used is the factor tree approach which can be found online or in Pemberton’sEssential maths CD. After demonstrating, or showing the presentation, ask learners topractise using the method to write other numbers as products of primes. Then asklearners to look at finding the product of primes of other numbers, for example 60, 450,42, 315, but this time they can be encouraged to look for alternative methods, forexample by researching on the internet. Another useful method is the repeated divisionmethod. (I) (H)Learners would find it useful to have a definition of the terms rational, irrational and realnumbers which can be found on the Maths is Fun website. On the website there arequestions on rational and irrational numbers for learners to try. These start simple andsoon become more challenging. (I) (F)v1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20157
RefSyllabus contentSuggested teaching activitiesLearning resourcesExtended curriculum onlyIt is useful to start with revising simple Venn diagrams, for example with people whowear glasses in one circle and people with brown hair in another circle asking learnersto identify the type of people in the overlapping region. (W) (Basic)TextbooksBarton p.61-64Morrison p.172-179This can be extended to looking at general Venn diagrams concentrating more on theshading of the regions representing the sets A B, A B, A' B, A B', A' B, A B', A' B' and A' B' helping learners to understand the notation. An excellent activelearning resource is the Venn diagrams card sort in Barton’s Teacher Resource Kitpages 61-64. Ask learners to work in groups to complete this activity. (G)(Challenging)Past paperPaper 41, June 2012, Q8Use language, notation and Venndiagrams to describe sets andrepresent relationships betweensets.Definition of setse.g. A {x: x is a natural number}B {(x,y): y mx c}C {x: a Y x Y b}D {a, b, c, }NotationNumber of elements in set A n(A)“ is an element of ” “ is not an element of ” Complement of set A A’The empty set Universal setA is a subset of B A BA is a proper subset of B A BA is not a subset of B A BA is not a proper subset of B A BUnion of A and B A BIntersection of A and B A B1.3Calculate squares, square roots,cubes and cube roots of numbers.Learners would find it useful to know that (A B)' is the same as A' B' and that (A B)' is the same as A' B' and to understand the language associated with sets andVenn diagrams. Morrison and Hamshaw’s book pages 172-179, for example, usesVenn diagrams to solve problems involving sets.Learners need to be able to distinguish between a subset and a proper subset. Thework on Venn diagrams can be extended to look at unions and intersections when thereare three sets. (W) (Challenging)Ask learners to try the past paper question. (H) (F)Using simple examples illustrate squares, square roots, cubes and cube roots ofintegers. (W) (Basic)Past paperPaper 32, June 2012, Q3Extend the task by asking more able learners to square and cube fractions anddecimals without a calculator, it may be worth doing topic 1.8 first to help with this. (W)(Challenging)An interesting activity is to look at finding the square root of an integer by repeatedsubtraction of consecutive odd numbers until you reach zero. For example, for 25subtract in turn 1, 3, 5, 7, and then 9 to get to 0. Five odd numbers have beensubtracted so the square root of 25 is 5. Ask learners to investigate this method forother, larger, square numbers. (I) (H)v1.0 4Y11Cambridge IGCSE Mathematics (0580) – from 20158
RefSyllabus contentSuggested teaching activitiesLearning resourcesAnother interesting challenge is to look at the palindromic square number 121.(Palindromic means when the digits are reversed it is the same number). Ask learnersto find all the palindromic square numbers less than 1000. (I) (H)Ask learners to try the past paper question. (H) (F)1.4Use directed numbers in practicalsituations.An effective start for this topic is to draw a number line from -20 to 20, then point tovarious numbers (both positive and negative) asking learners, for example, “what is 5more than this number?”, “What is 6 less than this number?” (W)You can keep it simple by using only integers (Basic) or extend the task by usingdecimals or fractions. 3TAn interesting extension to this is to then look at directed numbers in the context ofpractical situations. For example, temperature changes, flood levels, bank credits anddebits. Learners can see weather statistics for over 29000 cities online atweatherbase.com, which can be used for them to investigate a variety of temperaturechanges involving positive and negative temperatures. (G) (Basic)1.5Use the language and notation ofsimple vulgar and decimal fractionsand percentages in appropriatecontexts.Recognise equivalence and convertbetween these forms.Learners would find it useful to have a definition of the terms (e.g. numerator,denominator, equivalent fractions, simplify, vulgar fraction, improper fraction, mixednumber, decimal fraction, and percentage). A fun activity would be to ask learners toproduce a crossword with the terms defined. Ask them to add any other terms that theycan think of to do with fractions, decimals and
Scheme of work – Cambridge IGCSE Mathematics (0580) from 2015 v1.0 4Y11 Cambridge IGCSE Mathematics (0580) – from 2015 6 Unit 1: Number Recommended prior knowledge Learners should be able to add, subtract, multipl
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