2019 National Curriculum Tests Key Stage 2 - GOV.UK
2019 national curriculum testsKey stage 2Mathematics testmark schemesPaper 1: arithmeticPaper 2: reasoningPaper 3: reasoning
2019 key stage 2 mathematics test mark schemesContents1. Introduction32. Structure of the test33. Content domain coverage34. Explanation of the mark schemes55. General marking guidance5.1 Applying the mark schemes5.2 General marking principles5566. Marking specific types of question: summary of additional guidance6.1 Answers involving money6.2 Answers involving time6.3 Answers involving measures141415167. Mark schemes for Paper 1: arithmetic178. Mark schemes for Paper 2: reasoning229. Mark schemes for Paper 3: reasoning30Page 2 of 40
2019 key stage 2 mathematics test mark schemes1. IntroductionThe Standards and Testing Agency (STA) is responsible for the development and delivery ofstatutory tests and assessments. STA is an executive agency of the Department for Education.The 2019 tests assess the national curriculum. This test has been developed to meet thespecification set out in the test framework1 for mathematics at key stage 2.A new test and new mark schemes will be produced each year.Key stage 2 tests are marked by external markers, who receive training to ensure the publishedmark schemes are applied consistently and fairly. The mark schemes are provided to showteachers how the tests are marked. The pupil examples are based on responses gathered fromthe test trialling process.Scaled score conversion tables are not included in this document. Conversion tables will beproduced as part of the standards maintenance process. Scaled score conversion tables2 forthe 2019 tests will be published in July 2019. The standards confirmation meeting will takeplace in June 2019.2. Structure of the testThe test comprises: Paper 1: arithmetic (40 marks) Paper 2: reasoning (35 marks) Paper 3: reasoning (35 marks).3. Content domain coverageThe 2019 test meets the specification in the test framework. Table 1 sets out the areas of thecontent domain that are assessed in papers 1, 2 and 3.The references are taken from the test framework. A question assessing 4C7, for example, setsout to ‘multiply two-digit and three-digit numbers by a one-digit number using a formal writtenlayout’ and is taken from the year 4 programme of /scaled-scores-at-key-stage-2Page 3 of 40
2019 key stage 2 mathematics test mark schemesTable 1: Content domain coverage of the 2019 key stage 2 mathematics testWhere two references are given, the primary reference is given first.Paper 1: arithmeticPaper 2: reasoningPaper 3: reasoningQu.Content domainreferenceQu.Content domainreferenceQu.Content G2a/4P3a6G2a/5G2a6R1Page 4 of 40
2019 key stage 2 mathematics test mark schemes4. Explanation of the mark schemesThe marking information for each question is set out in the form of tables (sections 7, 8 and 9).The purpose of the mark scheme is to define the acceptable answers for each question withinthe test. Answers other than those listed may be acceptable if they meet the marking criteria.The ‘Qu.’ column on the left-hand side of each table provides a quick reference to the questionnumber and part.The ‘Requirement’ column may include two types of information: a statement of the requirements for the award of each mark, with an indication of whethercredit can be given for an appropriate method examples of some different types of correct answer.The ‘Mark’ column indicates the total number of marks available for each question part.The ‘Additional guidance’ column indicates alternative acceptable answers and guidance,such as the range of acceptable answers, where necessary. This column may also providedetails of specific types of answer which are unacceptable. For most questions, however, therewill be unacceptable answers that are not listed.5. General marking guidance5.1 Applying the mark schemesTo ensure consistency of marking, the most frequent procedural queries are listed insection 5.2 along with the action the marker will take. This is followed by further guidance insection 6 relating to marking questions involving money, time and other measures. Unlessotherwise specified in the mark scheme, markers will apply these guidelines in all cases.A small number of general marking principles have been changed this year to clarify theguidance. This does not change the underlying principles or how they are applied.Recording marks awardedPupils’ test papers are scanned so that marking can be conducted on screen by trained markers.For each question, markers record the award of 3, 2, 1 or 0 marks as appropriate, according tothe mark scheme criteria. There is provision in the software to record questions not attempted.The software aggregates marks automatically.Page 5 of 40
2019 key stage 2 mathematics test mark schemes5.2 General marking principlesTable 2: General marking principles for all papers1. The answer does notmatch closely any ofthe examples given inthe mark scheme.Markers will use their judgement to decide whether theanswer corresponds with details in the ‘Requirement’column of the mark scheme. Reference will also be made tothe ‘Additional guidance’ column.2. The answer isprovided in a nonstandard way.Pupils may provide evidence in any form as long as itsmeaning can be understood. Diagrams, symbols or wordsare acceptable for explanations or for presenting an answer.3. The correct answeror working has beencrossed out or erasedand not replaced.The mark(s) will not be awarded for crossed-out or erasedanswers or working.4. More than one answeris given.If all answers given are correct (or a range of answers isgiven, all of which are correct), the mark(s) will be awardedunless the mark scheme states otherwise. If both correctand incorrect answers are given, the mark(s) will not beawarded unless the mark scheme states otherwise.5. No answer is given inthe expected place,but the correct answeris given elsewhere.Where a pupil has unambiguously indicated the correctanswer, the mark(s) will be awarded. In particular, wherea word or number is expected, a pupil may meet therequirement by annotating a graph or labelling a diagramelsewhere in the question.6. The answer is correct,but the wrong workingis shown.A correct final answer will be awarded the mark(s).7. The pupil has usedalternative notationfor a decimal point ina number.No alternative notation is accepted as representing adecimal point in a number, e.g. a comma.8. The pupil has useda symbol as athousands separator.If the pupil has used a comma as a thousands separator(positioned either correctly or incorrectly) and the digits arein the correct order, then the mark(s) will be awarded.Refer to section 6 for guidance on marking specific typesof question.If any other symbol, e.g. decimal point or apostrophe, isused, the mark(s) will not be awarded, although methodmarks may still be available.Page 6 of 40
2019 key stage 2 mathematics test mark schemes9. The answer in theanswer box is wrongdue to a transcriptionerror.A transcription error occurs when a pupil miscopies theiranswer from the end of their working into the answer box.Each part (integer, numerator, denominator) of a mixednumber is considered separately when applyingtranscription error rules.Where appropriate, detailed guidance will be given in themark scheme. For questions with no guidance, markswill only be awarded for a transcription error if the wronganswer is due to: transposed digits in a number (e.g. 243 is writtenas 324)OR one digit changed in a number of 4 or more digits(e.g. 2,345 is written as 2,845).The mark(s) will not be awarded for any other transcriptionerror including: a decimal point positioned incorrectly (e.g. 12.34 iswritten as 1.234 or 1234) a change by a power of 10 (e.g. 200 is written as 20or 2,000) a digit added or removed (e.g. 123,456 written as1233,456 or 12,456) a negative sign added or removed.10. The answer isnumerically oralgebraicallyequivalent to theanswer in themark scheme.Answers should be given as single values in their simplestform unless the mark scheme states otherwise, e.g. for 536 30, the answer 500 6 will not be awardedthe mark.will be awardedFor integer answers, e.g. 20, the answer 20180the mark; 4 will not be awarded the mark.For decimal answers that include recurring digit(s), theremust be an unambiguous. indication of the recurring digit(s).For example, for 16 , 0.16 or 0.16 will be awarded the mark and.for 17 , 0.142857 or 0.142857 will be awarded the mark.For fraction answers that can be expressed as a mixednumber, the fraction paired with the integer must be aproper fraction, e.g. 1 64 will not be awarded the markalthough method marks may still be available.Where alternative responses are acceptable, this will beindicated in the ‘Additional guidance’ column.Page 7 of 40
2019 key stage 2 mathematics test mark schemesTable 3: General marking principles for paper 1 only (arithmetic)11. The answer in theanswer box is wrongdue to a misread ofnumbers given inthe question.Misreads are not allowed in Paper 1; the mark(s) will notbe awarded.12. The pupil has notrecorded their workingbeneath the given longmultiplication orlong division.If a pupil carries out their working somewhere on the pageother than beneath the given question as expected, thenthe pupil must start by rewriting the original question inorder for it to be considered as a formal method.13. The answer tothe long divisionquestion expresses aremainder.If a pupil reaches an integer answer using a formal methodwith no more than one arithmetic error, for example 25,then the mark(s) will be awarded for 25 r0 or 25.0, but themark(s) will not be awarded for an answer of 250Please note that the operation sign does not need to begiven for long multiplication, provided the pupil’s workingshows the intention to multiply.For answers with a remainder, the remainder must beexpressed correctly.If a pupil shows a remainder that is the same size as thedivisor or larger, for example, a remainder of 28 or 29 whendividing by 28, the mark(s) will not be awarded because themethod is incomplete.If a pupil reaches a non-integer answer using a formalmethod with no more than one arithmetic error, for examplewhen dividing by 28, the pupil reaches the answer 6 r14,or 6.5, but thethen the mark(s) will be awarded for 6142814mark(s) will not be awarded for 6 r28 or 6.14 or 61414. The long divisionmethod involvessubtracting chunksof different sizes.If a pupil’s formal method involves subtracting chunks, it isnot necessary to show a separate addition of the chunks.If the answer is not the correct total for their chunks, thenthat is treated as one arithmetic error.A method is considered as chunking when the size of thechunks are shown alongside the algorithm.It should be noted that this method will only be accepted ifall chunks are of different sizes.Page 8 of 40
2019 key stage 2 mathematics test mark schemesTable 4: General marking principles for papers 2 and 3 only (reasoning)15. More than one methodis given.If a pupil gives more than one method, then the intendedmethod is taken as the one which leads to the answer in theanswer box or an identified answer elsewhere. If no answeris given, then all methods must be appropriate for themethod mark(s) to be awarded.16. There appears to bea misread of numbersor information givenin the question thataffects the pupil’sworking and/orexplanation.This occurs when a pupil misreads a number given in thequestion and consistently uses a different number that doesnot alter the original intention or difficulty of the question.For example, if 243 is misread and written as 248, bothnumbers may be regarded as comparable in difficulty.However, if 243 is misread and written as 245 or 240, themisread number may be regarded as making the questioneasier. The misread of a number may affect the award ofmarks. Any misread number must be seen, not implied.Where appropriate, detailed guidance will be given in themark scheme. If no guidance is given, markers will examineeach case to decide whether the mark(s) will be awarded.The mark(s) will not be awarded if: it is a ONE-mark questionthere is more than one misread number in a questionthe mathematics is simplifiedit is an ‘explain’ questionit is a misread of other information (not numbers)the misread number is the same as any other numberin the question.For TWO-mark questions that have a method mark,one mark will be awarded if an appropriate method iscorrectly followed through with the misread number togive the correct follow-through answer, provided themathematics has not been simplified.For THREE-mark questions, refer to the additional guidance.17. A misread or anarithmetic errorresults in an answerwith multiple decimalplaces.In some instances, a misread or an arithmetic error in amethod leads to an answer with one or more decimalplaces. In such cases, the method mark(s) will be awardedfor an answer that is correctly truncated or roundedprovided the method is appropriate and the additionalguidance does not specify otherwise. For example, 1.2345is truncated to 1.2Page 9 of 40
2019 key stage 2 mathematics test mark schemes18. The pupil has reversedvalues within acalculation involvingsubtraction ordivision.When values within the calculation are reversed, the mark(s)will only be awarded when the answer corresponds to thecorrect calculation. For example, if the correct calculation is12 4, the method mark(s) may be awarded for 4 12 3,but not for an answer other than 3Reversed values within a calculation are not acceptable in‘explain’ questions.19. The pupil omits anoperation sign withintheir working.If the correct sign of , , , or for an arithmetic operationis missing, then the mark(s) will only be awarded if theworking shown by the pupil is clear enough to indicate thatthe required operation has been performed. This applieseven if the results of the required operation are incorrect.Where carrying or decomposition figures are seen, this isevidence of intention. For example, where the following isseen in working, the layout of the response implies additionor subtraction:456123 if the answer is larger than the greater of the givenvalues, e.g. 679, then addition is implied if the answer is less than the first given value, e.g. 323,then subtraction is implied.Page 10 of 40
2019 key stage 2 mathematics test mark schemes20. The pupil has used ‘anappropriate method’.For some questions, the mark scheme allows the awardof the method mark(s) for ‘evidence of an appropriatemethod’, even if the answer is missing or incorrect. Refer tothe ‘Additional guidance’ column where appropriate.For the award of the method mark(s) for an appropriatemethod, there must be evidence of all the steps of theappropriate method (i.e. any method that would lead to thecorrect answer if there were no arithmetic errors and noadditional steps).This means that, for every step, either: the appropriate calculation to be carried out mustbe shownOR if the calculation has not been written down, thecorrect answer or correct follow-through answer mustbe shown.Where the calculation shown would lead to a correct finalanswer, even if the processed numbers do not appear to betaken from the question, a method mark may be awardedunless the mark scheme specifies otherwise.21. The pupil has used atrial and improvementmethod.‘Trial and improvement’ is regarded as an acceptablemethod, unless the mark scheme states otherwise.For a ‘trial and improvement’ method to be awarded themethod mark(s): there must be at least 3 trials, carried out correctly,which all reduce the range in which the answer isknown to lie there can be additional trials, which are correctly orincorrectly carried out, and which may not reduce therange in which the answer is known to lie a final answer is not needed, unless the mark schemestates otherwise.Page 11 of 40
2019 key stage 2 mathematics test mark schemes22. The answer in theanswer box is wrongbut the correct answeris reached in theworking.Extra working occurs when a pupil writes the correctanswer in their working, and then continues to process theinformation further.When the answer in the answer box is wrong and does notmatch the answer reached in the working, it is impossibleto know why the pupil has written a different answer andit is assumed that extra working has occurred. GMP 9 ontranscription errors still applies.If the extra working does not contradict the pupil'sappropriate method, the method mark(s) will be awarded.If the extra working contradicts the pupil's appropriatemethod, the method mark(s) will not be awarded.23. The pupil miscopies avalue from one part oftheir method into thenext part.There will be instances when a pupil reaches a value in theirworking, then restarts from a different value.The mark(s) will not be awarded if: it is a ONE-mark question there is more than one miscopy in the working the miscopy does not follow transcription error rules(see GMP 9).The method mark(s) will only be awarded if an appropriatemethod is correctly shown using the miscopied number(which must follow transcription error rules).24. The correct answeris embedded in theworking.An embedded answer occurs when a pupil shows thecorrect answer within their working but then selects thewrong answer from their working as their final answer orleaves the answer box blank. For example, if a pupil shows2.5 { 6 3 { 5 in the last line of their working and writes 5in the answer box, whereas the correct answer is 3, thenthis will affect the award of marks.Where appropriate, detailed guidance will be given in themark scheme. If no guidance is given, markers will examineeach case to decide whether the mark(s) will be awarded.For ONE-mark questions, the mark will not be awarded.For TWO-mark questions that have a method mark,one mark will be awarded, provided the pupil does not giveredundant extra working that contradicts work already doneor which adds to their appropriate method.For THREE-mark questions, refer to the additional guidance.Page 12 of 40
2019 key stage 2 mathematics test mark schemes25. The phrase ‘sight of’is used in the markscheme.For some questions, the mark scheme allows the mark(s)to be awarded for sight of a particular number or numberswithin a method. Such numbers are the correct answers topartial steps within a method.26. The answer correctlyfollows through fromearlier incorrect work.‘Follow-through’ marks for an answer will only be awardedwhen specifically stated in the mark scheme.27. The pupil has drawnlines which do notmeet at the correctpoint.Where the mark scheme states that ‘slight inaccuracies indrawing’ should be accepted, this means that the mark(s)will be awarded for responses marked within or on a circleof radius 2mm with its centre at the correct point.within the circle- acceptedon the circle- acceptedoutside the circle- not acceptedPage 13 of 40
2019 key stage 2 mathematics test mark schemes6. Marking specific types of question:summary of additional guidance6.1 Answers involving moneyAcceptWhere the signis given, e.g. 3.20, 7 Do not accept 3.20 7 7.00Any unambiguous indication ofthe correct amount, e.g.Incorrect placement of poundsor pence, e.g. 3.20p 320 3 20 pence 320p 3 20 3:20Incorrect placement of decimalpoint or incorr
Mathematics test mark schemes Paper 1: arithmetic Paper 2: reasoning Paper 3: reasoning 2019 national curriculum tests Key stage 2. Page 2 of 40 2019 key stage 2 mathematics test mark schemes Contents 1.Introd
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