Assessing Maths Literacy in grade 11 - AMESA

ASSESSING MATHS LITERACY IN GRADE 11Jackie ScheiberRADMASTE Centre, Wits Universityjackie.scheiber@wits.ac.zaMathematical Literacy was introduced in Grade 10 in 2006. In 2007 teachers willhave to assess Grade 11 Maths Literacy learners for the first time.During this workshop participants will• Answer a typical Grade 11 Maths Literacy question• Study the requirements for the Grade 11 Maths Literacy examination as listed inthe Subject Assessment Guidelines MATHEMATICAL LITERACY (January2007).• Study the Description of the Levels in the Mathematical Literacy AssessmentTaxonomy• Analyse the Maths Literacy question in terms of the requirements and thetaxonomy• Study the Assessment Frameworks for Papers 1 and 2 and complete a similarframework for the given question.56

A TYPICAL GRADE 11 MATHS LITERACY QUESTIONQUESTION 1Mrs Phumzile owns a taxi business. The table below shows a list of MrsPhumzile's income and expenditure for her business, for the month of February2007.INCOME EXPENDITUREPetrol R 1 065,70Washing of taxi R 60,00Servicing of taxi ( oil change, spark plugs etR 546,09cetera)Fares paid by taxi commuters R7 842,00Insurance for the taxi (in case of an accident) R 305, 45Taxi-driver salary R 3 500,00Taxi association fee R 200,001.1 Determine, for February 2007:1.1.1 The total income1.1.2 The total expenditure1.2 Did Mrs Phumzile’s taxi business make a profit or a loss for the monthof February?1.3 Calculate the profit or loss for this month(1)(2)(1)(2)1.4 Hence determine the profit margin for the monthIncome − ExpensesUse the formula: Profit Margin =Expenses× 100% (3)1.5 Mandla works as a taxi driver for Mrs Phumzile. His basic salary isR35,00 per hour. On Monday 18 February he worked from 06:00 to15:30 and had 1 hour off for lunch.1.5.1 How many hours did he work on that day?1.5.2 How much money did he earn on that day?Mrs Phumzile asks Mandla to transport passengers to a wedding 170km away. Mandla drives the taxi at an average speed of 90 km/h. Howmany hours will the journey take? (Use the formula: Distance = Speedx Time to calculate your answer.) Write your answer correct to twodecimal places.(2)(2)(4)[17]57

The requirements for the grade 11 mathematics literacy examination as listed in thesubject assessment guidelines mathematical literacy (January 2007).According to the Subject Assessment Guidelines, the following the time allocationsand number of papers is recommended for the final examinations for Grades 10, 11and 12:GRADE 10 – one 3-hour paper of 150 marksGRADE 11 – two 2 ½ hour papers of 100 marks eachGRADE 12 – two 3-hour papers of 150 marksAccording to the Subject Assessment Guidelines, an examination should• Give equal weighting to the four Learning Outcomes and should attempt toexamine all of the Assessment Standards determined for the grade• Consist of questions which all focus on a context• Consist of questions which integrate Assessment Standards from more than oneLearning Outcome• Be differentiated according to the Mathematics Literacy taxonomy with thefollowing proportion of marks allocated to each of the levels:o 30% of the marks at the knowing levelo 30% of the marks at the applying routine procedures in a variety of contexts levelo 20% of the marks at the applying multi-step procedures in a variety of contextslevelo 20% of the marks at the reasoning and reflecting level.TABLE 1 – REQUIREMENTS FOR GRADE 11LEVEL 1 LEVEL 2 LEVEL 3 LEVEL 4(30%) (30%) (20%) (20%)Knowing Applying routine Applying multistepprocedures reflectingReasoning andprocedures infamiliar contexts in a variety ofcontextsLO125%LO225%LO325%PAPER 1(2 ½ hours - 100 marks)Paper 1 is intended to be abasic knowing and routineapplication paperConsists of between 5 and8 shorter questionsPaper 2(2 ½ hours – 100 marks)Paper 2 is intended to be an applicationsand reasoning and reflecting paperConsists of between 4 and 6 longerquestions.These questions will require more58

LO425%Questions focus on acontext60% on Level 1 and 40%on Level 2interpretation and application of theinformation providedQuestions focus on a context20% on Level 2, 40% on Level 3 and40% on Level 4TABLE 2 – DESCRIPTION OF THE LEVELS IN THE MATHEMATICALLITERACY ASSESSMENT TAXONOMYLEVEL 1 (30%) LEVEL 2 (30%) LEVEL 3 (20%) LEVEL 4 (20%)Knowing• Calculate usingthe basicoperations,including:-Algorithms for +,–, x and ÷-Appropriaterounding ofnumbers- Estimation- Calculating apercentage of agiven amount- measurement• Know and useappropriatevocabulary such asequation, formula,bar graph, piechart, Cartesianplane, table ofvalues, mean,median and mode• Know and useformulae such asthe area of aApplying RoutineProcedures InFamiliar Contextsc) Performswell-knownprocedures infamiliar contexts.All the informationrequired to solvethe problem isimmediatelyavailable to thestudentd) Solvesequations bymeans of trial anderror or algebraicprocessese) Draw datagraphs forprovided dataf) Drawalgebraic graphsfor given equationsg) Measuredimensions (e.g.length, weight andtime) usingappropriateApplying multi-stepprocedures in avariety of contextsh) Solveproblems usingwell-knownprocedures. Thisrequiredprocedure is,however, notimmediatelyobvious from theway the problemis posed. Learnerswill have todecide on themost appropriateprocedure to solvethe solution to thequestion and mayhave to performone or morepreliminarycalculationsbeforedetermining asolutioni) Select themost appropriateReasoning andreflectingk) Pose and answerquestions aboutwhat mathematicsthey require tosolve a problemand then to selectand use thatmathematicalcontent.k) Interpret thesolution theydetermine to aproblem in thecontext of theproblem andwhere necessaryto adjust themathematicalsolution to makesense in thecontextl) Critique solutionsto problems andstatements aboutsituations madeby others59

ectangle, atriangle and acircle where eachof the requireddimensions isreadily availableRead informationdirectly from atable (e.g. the timea particular busdeparts from theterminal)measuringinstrumentssensitive to levelsof accuracydata from optionsin a table ofvalues to solve aproblemj) Decide onthe best way torepresent data tocreate a particularimpressionm) Generalizepatterns observedin situations,make predictionsbased on thesepatterns and/orother evidenceand determineconditions thatwill lead todesired outcomes60

34the schoolbuildingGlobalwarmingCrimeStatistics2.1.2 3 3 32.1.3 2 2 22.2.1 3 3 32.2.2 4 2 2 42.3.1 1 1 12.3.2 5 5 52.3.3a 1 1 12.3.3b 2 2 23,1 2 2 23,2 2 2 4 43.3.1 4 1 5 53.3.2a 2 2 23.3.2b 2 2 23.3.3a 2 2 23.3.3b 2 2 23.3.4 2 2 24,1 2 2 24,2 3 3 34.3.1 2 2 24.3.2 4 4 427 21 30 22 22 39 39 100 100211163