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2016 national curriculum tests Key stage 1 Mathematics test mark schemes Paper 1: arithmetic and Paper 2: reasoningPage 2 of 24 2016 key stage 1 mathematics test mark schemes Contents 1. Introduction 3 2. Structure of the key stage 1 mathematics test 3 3. Content domain coverage 4 4. Explanation of the mark schemes 5 5. General marking guidance 5 5.1 Applying the m\sark schemes 5 5.2 General marking\s principles 6 6. Internal moderation procedures 7 7. Mark schemes for Paper 1: arithmetic 8 8. Mark schemes for Paper 2: reasoning 9 9. Example responses 17 \b.1 Examples of responses from question 5 17 \b.2 Examples of responses from question 28 18
Page 3 of 24 2016 key stage 1 mathematics test mark schemes 1. Introduction The Standards and Testing Agency (STA) is responsible for the \sdevelopment and de\slivery of statutory tests and \sassessments. STA is an executive a\sgency of the Depart\sment for Education.\s The 2016 tests are the frst assessment\s of the 2014 natio\snal curriculum. Thi\ss test has been developed to meet \sthe specifcation set\s out in the test fr\samework for mathem\satics at key stage 1\s. The test frameworks\s are on the GOV.UK website at www.gov.uk/sta. A new test and mark\s scheme will be dev\seloped each year. The key stage 1 tes\sts will be marked i\snternally by teachers t\so inform teacher as\ssessment. Scaled score conversion tables \sare not included in t\shis document. Conve\srsion tables will b\se produced as part of t\she standard-setting process. Scaled score conversion tables \sfor the 2016 tests will be publi\sshed at www.gov.uk/sta in June 201\s6. The standard-setting process will take place in May 2016. This mark scheme is \sprovided for teachers\s to use when markin\sg pupils’ responses. The pupil \s examples are based on responses gathered from the test trialli\sng process. 2. Structure of the key stage 1 mathematics test The key stage 1 mat\shematics test materi\sals comprise: • Paper 1: arithmeti\sc (25 marks) • Paper 2: reasoning (35 marks)\s The mathematics test\s is comprised of two\s components which ar\se presented to pupils a\ss two separate test p\sapers. The frst comp\sonent is an arithme\stic paper (Paper 1)\s. The second component (Paper 2)\s presents a range of m\sathematical problems. The test is \sadministered on paper. Each paper includ\ses material drawn f\srom the statutory se\sction of the key st\sage 1 national curriculum\s (2014).
Page 4 of 24 2016 key stage 1 mathematics test mark schemes 3. Content domain coverage The 2016 test meets \sthe specifcation set\s out in the test fr\samework. Table 1 sets out the\s areas of the content doma\sin that are assessed in the te\sst papers 1 and 2. \s The references below are taken from the test framewo\srk. A question asses\ssing 2M1, for example, sets out t\so ‘compare and order lengths, mass, v\solume / capacity an\sd record the results using >,
Page 5 of 24 2016 key stage 1 mathematics test mark schemes 4. Explanation of the mark schemes The marking inform\sation for each ques\stion is set out in \sthe form of tables \s(sections 7 and 8). The ‘Qu.’ column on the le\sft-hand side of eac\sh table provides a quick reference to the questio\sn number and part. The ‘Mark’ column indicates t\she total number of\s marks available fo\sr each question par\st. The ‘Requirement’ column may includ\se two types of info\srmation:• a statement of the \srequirements for the awar\sd of each mark, wit\sh an indication of \swhether credit can be given f\sor a correct method • examples of some di\sfferent types of correct answer. The ‘Additional guidance’ column indicates a\slternative acceptable a\snswers, and provides details of specifc types of answers which are unacceptable. Other guidance, such as the range of acceptable answer\ss, is provided as necessary. 5. General marking guidance 5.1 Applying the mark schemes To help you mark con\ssistently, the most frequent procedural queries ar\se listed along with\s the action you should t\sake. Unless otherwi\sse specifed in the m\sark scheme, you shou\sld apply these guidelines in\s all cases. Example responses are also included for\s the working mark \squestion and one ot\sher question in Paper 2: reasoning. This shoul\sd act as your guide\s when you are marking these que\sstions.
Page 6 of 24 2016 key stage 1 mathematics test mark schemes 5.2 General marking principles Table 2: General marking principles Possible issues when marking 1. The pupil’s answer does not match closely any of the examples in the mark scheme. Teachers will use the\sir judgement in de\sciding whether the answer \scorresponds with detail\ss in the ‘Requirement’ column of th\se mark scheme. Refe\sr also to the ‘Additi\sonal guidance’ colu\smn and to the examples of responses (where appropriate). 2. The pupil has answered in a non-standard way. Pupils may provide evidence in a\sny form as long as \s its meaning can be \sunderstood. Diagram\ss, symbols or words are acceptable for in\sdicating an answer. 3. There appears to be a misread of numbers affecting the working. A misread occurs when a pu\spil misreads a number given in the questi\son and consistently \suses a different number that does no\st alter the origin\sal intention or diffculty of the quest\sion. For example, \sif ‘43’ is misread as ‘48’, both nu\smbers may be regarded as comparable in diffculty. However, if ‘43’ is misread as ‘40’ or ‘45’, the \smisread number may be \sregarded as making the question\s easier. The misread of a number will affect the award of marks. No marks are awarded if there is more than one misread in a question o\sr if the mathemati\scs is simplifed by the mi\ssread. For 1-mark questions: no mark\s is awarded for one or more misreads. For 2-mark questions that hav\se a method mark: 1 mark is awarded if the correct method is correctly implemented with t\she misread number, provided this does not simplify t\she mathematics. 4. No answer is given in the expected place, but the correct answer is given elsewhere. Where a word or number response is expected,\s a pupil may meet the requirement by annotating a graph or labelling a dia\sgram elsewhere in the question. 5. The pupil’s answer is correct but the wrong working is shown. Always award the mark for a f\snal response that is correct. 6. The answer in the answer box is wrong, but the correct answer is shown in the working. Give precedence to the response given in th\se answer box over any other\s workings. However, in a 2-mark question, one mark \smay still be awarded for evidence of a complete, corr\sect method.
Page 7 of 24 2016 key stage 1 mathematics test mark schemes Possible issues when marking 7. The pupil’s answer correctly follows through from earlier incorrect work. ‘Follow through’ marks for an \sanswer may only be \s awarded when specifcally\s stated in the mark\s scheme. 8. The correct answer has been crossed (or rubbed) out and not replaced. No marks will be aw\sarded for crossed-out answers or\s working. 9. More than one answer is given. If all answers give\sn are correct (or a range of \s answers are given, all of wh\sich are correct), a mark will be awarded unless the mark\s scheme states otherwise. If both \scorrect and incorrect responses are given, no mark w\sill be awarded unless the mark\s scheme states otherw\sise. 10. The pupil reverses a digit in their answer. A reversed digit is acc\septable if it is cl\searly recognisable as the d\sigit intended; for\s example, a reversed 2 must clear\sly show the characte\sristics of a 2 rather than a 5.\s As a further exampl\se, where the answer is ‘61’\s and the response ‘ ’ is given, then th\sis should be awarded the mark. You should take a de\scision based upon yo\sur knowledge of the ch\sild’s writing. 11. The pupil transposes digits in their answer. A pupil transposes d\sigits by reversing their order e.g. ‘83’ instead of ‘38’\s. An answer with tran\ssposed digits should\s not be awarded the mark; for \sexample, a response of ‘16’ or ‘ ’ when the answer i\ss ‘61’ should not be\s marked as correct. 6. Internal moderation procedures We recommend teachers in\svolved in marking \sthe key stage 1 tes\sts undertake modera\stion activity to ensure marking is consist\sent across their school. Gui\sdance is published o\sn the GOV.UK website at www.gov.uk/sta.
Page 8 of 24 2016 key stage 1 mathematics test mark schemes 7. Mark schemes for Paper 1: arithmetic Equivalent answers \sare not acceptable e.g. 10\s + 4 instead of 14 Qu. Requirement Mark Additional guidanceP 4 none Practice question 114 1m 2 5 1m 3 8 1m 4 5\b 1m 5 15 1m 6 \b0 1m 7 6 1m 8 30 1m 9 5 1m 10 70 1m 11 43 1m 12 40 1m 13 61 1m 14 4 1m 15 7 1m 16 80 1m 17 18 1m 18 8 1m 19 72 1m 20 4 1m 21 11 1m 22 3 1m 23 57 1m 24 10 1m 25 15 1m
Page 9 of 24 2016 key stage 1 mathematics test mark schemes 8. Mark schemes for Paper 2: reasoning Qu. RequirementMark Additional guidance Aural questions P 7 (dots) none Practice question 1 6 tens and 3 ones ci\srcled, e.g. 10 10 10 1010 10 10 10 1 1 1 1 1 1 1 1 1m Accept any other cle\sar way of indicatin\sg the correct answer. 2 23 (children) 1m 3 12 91 1mAccept correct numbers in eith\ser order. Accept both answers \sgiven in one of th\se boxes. (Refer to general \smarking principles \s4, 10 and 11 on pages 6 a\snd 7) 4 10 1m 5 21, 23, 25, 27, 2\b 1mAll fve numbers mus\st be correct for the award of the mark. Accept repeated correct numbers e.g. 21, 23, 23, 25, 27\s, 2\b Numbers may be writ\sten in any order. Do not award the mark if addi\stional incorrect numbers are written inside the answer box. (Use the examples o\sf responses given on page 17 to help yo\su determine if the\s mark can be awarded.)
Page 10 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance Written questions 6 Letters written in \sthe correct order as shown: B D C A least full most full 1mAll letters must be\s in the correct order for the award of the mark. Accept any other cle\sar way of indicatin\sg the correct answer e.g. mat\sching each glass to the correct box. Accept the letters g\siven in the reverse order, provided the labels h\save been swapped. 7 12 (shells) 1m 8 Coins matched to th\se correct boxes as shown: Less than More than 1mAll four coins must \sbe matched correctly for the award of the mark. Accept any other cle\sar way of indicatin\sg the correct answer. Do not award the mark if a coi\sn is matched to both \sboxes.
Page 11 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance 9 Card indicated as shown\s: 19 ninety 15 fifteen 51 fifty-one 49 forty-nine 1m Accept any other cle\sar way of indicatin\sg the correct answer. Do not award the mark if othe\sr cards are indicated unless it \sis clear the correct card is the child’s fnal choice. 10 Third box ticked as show\sn: 1m Accept any other cle\sar way of indicatin\sg the correct box. Do not award the mark if othe\sr boxes are indicated unless it \sis clear that the co\srrect box is the child’s fnal choice. 11 13 (balloons) 1m 12 Two sentences ticked \sas shown: A square has sides of equal \ulen\bth. A square has curved sides. a rkscml 2cr 6pAlr hg riff\slymiE A square has five sides. 1m Both correct sentences must be\s indicated for the award of the mark. Accept any other cle\sar way of indicatin\sg the correct sentences. Do not award the mark if othe\sr sentences are indicated unless i\st is clear that the\s correct sentences are the child’s fnal choice.
Page 12 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance 13a Two numbers written \sthat total 19, e.g. 10 + 9 = 19 1m Accept any two numbers that t\sotal 1\b 13b Three numbers written \sthat total 19, e.g. 10 + 4 + 5 = 19 1m Accept any three numbers that tot\sal 1\b, including repeated numbers, e.g. 1\b + 0 + 0 14 8 (toy cars) 1m 15 \b3 (p) 1mAccept the answer £0\s.\b3p Do not award the mark for 0.\b3\sp or £\b3p 16a 45 written in the \sfrst box as shown: 45 \ 1m (Refer to general \smarking principles \s4, 10 and 11 on pages 6 a\snd 7) 16b 58 written in the se\scond box as shown: 58 \ 1m Accept any number in the range 57–59 inclusive. (Refer to general \smarking principles \s4, 10 and 11 on pages 6 a\snd 7) 17 D 1mAccept any other cle\sar way of indicatin\sg the correct shape. 18 35 (pencils) 1m Do not accept the correct number of pencils indicated, u\snless the answer 35 \s is also seen. 19 6 (bags) 1m
Page 13 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance 20 7 (counters) 1m Do not accept seven counter\ss drawn unless the answer 7 \sis also seen. (Refer to general \smarking principle 4\s on page 6) 21 penta\bon trian\ble octa\bon hexa\bon 1m All shapes must be c\sorrectly matched for the award of the mark. Do not award the mark if a sha\spe is matched to more than one name. Ignore any additional sh\sapes drawn. 22 Three correct fruits ticked as\s shown: 20p 40p 50p 30p 1mAccept any other cle\sar way of indicatin\sg the correct fruits shown on \sthe page e.g. 50p + 20p + 30p = \s100p or £1 (Refer to general \smarking principle 4\s on page 6) 23 Correct answer circled as shown: quarter turn half turn three-quarter turn full turn 1m Accept any other cle\sar way of indicatin\sg the correct rotation. Do not award the mark if othe\sr rotations are indicated unless i\st is clear that the\s correct answer is the ch\sild’s fnal choice. 24 150 (g) 1m
Page 14 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance 25 20 + 8 30 + 28 50 + 8 70 + 18 80 + 8 10 + 18 90 + 8 50 + 48 1mAll three pairs must be cor\srectly matched for the award of the mark. Do not award the mark if a sum\s is matched to more than one sum. Ignore any extra lines d\srawn from 20 + 8 26 Both calculations ci\srcled as shown: 10 + 4 4 × 10 10 + 10 + 10 + 10 4 + 4 + 4 + 4 1m Both correct calculations must\s be indicated for the a\sward of the mark. Accept any other cle\sar way of indicatin\sg the correct calculations, in\scluding evaluating only the correct two calculations, i.e. w\sriting 40 alongside\s each of the two correct calculations. Do not award the mark if othe\sr calculations have be\sen evaluated, and \sthe correct two have not be\sen indicated. Do not award the mark if more than two calculations are circled unless it is cle\sar that the correct calculations are the child’s fnal choice.
Page 15 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance 27 Award TWO marks for all shap\ses correctly shaded e.g. Shade 1 2 Shade 3 4 Shade 1 3 2m or Accept any other cle\sar way of indicatin\sg the correct fractions; e.g. \smarking the appropriate number of \ssections. Award ONE mark for any two shapes correctly shaded. 1m 28 Award TWO marks for the corr\sect answer of 13 (crayons) 2m or If the answer is in\scorrect or missing, awar\sd ONE mark for evidence \sof a complete, correct method, e.g. • 40 – 17 – 10 = (in\scorrect or no answer) • 17 + 10 = 26 (error) 40 – 26 = 1m (Use the examples o\sf responses given on pages 18-21 to help \syou determine how \s many marks can be a\swarded.) 29 Both signs written \scorrectly as shown: 10 + 5
Page 16 of 24 2016 key stage 1 mathematics test mark schemes Qu. RequirementMark Additional guidance 31 Clock face ticked as\s shown: 12 6 11 3 9 1111 10 2 8 4 5 7 12 6 1 3 9 11 10 2 8 4 5 7 12 6 11 3 9 1111 10 2 8 4 5 7 12 6 11 3 9 1111 1010 2 8 4 5 7 1m Accept any other cle\sar way of indicatin\sg the correct clock face. Do not award the mark if othe\sr clock faces are indicated unless i\st is clear that the correct clock face is the\s child’s fnal answer.
Page 17 of 24 2016 key stage 1 mathematics test mark schemes 9. Example responses 9.1 Examples of responses from question 5 Children must show all of\s the numbers 21, 23, 25, 27 and 29 for the award of the mark. No \sother numbers must \s be given as part of\s the child’s fnal answer. Ling: 1 markAaron: 0 marks Ling and Aaron have both written\s the correct fve numbers in \sthe answer space. Ling has not offered any other numbers so one mark can be awarded. Aaron has written other \snumbers so his answe\sr is not correct and no mark can be awarded. Kalila: 1 mark Umed: 0 marks Kalila and Umed have both written\s correct numbers in the \sanswer space. Kalila has written the co\srrect fve numbers in a random\s order and has not offered any other numbe\srs so one mark can be awarded. Umed has only written four \sof the fve numbers,\s so his answer is no\st fully correct and no mark can be awarded. Liam: 1 markNarinder: 0 marks Liam and Narinder have both left th\se answer box blank,\s but offered their responses elsewhere on the page. Liam shows the correct fve numbers clea\srly. Although additio\snal numbers are seen, they are not between the 20 and 30 and \scan be ignored. One mark can be awarded. Although Narinder shows the correct fve numbers, she has als\so written other nu\smbers between the 2\s0 and 30 making he\sr fnal answer incor\srect, so no mark can be awarded. 1 0 1 0 0 1
Page 18 of 24 2016 key stage 1 mathematics test mark schemes 9.2 Examples of responses from question 28 Children must show a compl\sete, correct method for the \saward of the method ma\srk. The working ma\sy contain one or more arithmetic errors. Peter: 2 marksAlia: 0 marks Both Peter and Alia have used a number\s line to solve the \sproblem. Peter has been awarded two marks because he has shown\s the correct fnal answer of \s13 even though it \sis not within the a\snswer box. Alia has recorded an incorrect method. She has\s used a number line\s, but after subtrac\sting two tens she h\sas only subtracted 6 instead\s of 7, so no mark can be awarded. Esne: 1 mark Nicky: 0 marks Esne and Nicky have used pictoria\sl methods and both \shave shown the inco\srrect answer ‘12’. Esne has recorded a correct pictorial metho\sd, showing 40 talli\ses and crossing off 27, i.e. 40 − 17\s – 10, but has made\s an error in counting the remaining tallies. B\secause her method i\ss correct, Esne can be awarded one mark. Nicky has also recorded a pictorial met\shod. She has shown \s40 tallies, but has\s crossed off 28 so her method i\ss not correct and no mark can be awarded. 2 0 1 0
Page 19 of 24 2016 key stage 1 mathematics test mark schemes Examples of responses from question 28 continued Shay: 1 mark Charlie: 0 marks Shay and Charlie have both transpos\sed digits in the fn\sal answer so two ma\srks cannot be awarded. In Shay’s working, 17 can be\s considered a reversal of a digit \sbecause the 17 is cl\searly seen in the q\suestion. Consequently her me\sthod (40 − 17 − 10\s =) is complete and\s correct and can be awar\sded one mark. In his answer box, Charlie may be trying to \swrite 13, but tran\ssposed digits are not acceptable. S\since he has not shown any working, \sno mark can be awarded. Alex: 1 mark Erin: 0 marks Alex and Erin have both crossed out some of th\seir work. Alex has written the co\srrect answer but has c\srossed it out and has not \sreplaced it. However\s, he can be awarded one mark for a complete, co\srrect method. In comparison, Erin had a complete met\shod (albeit with a\sn arithmetic error and no fnal answ\ser) but she crossed out the second part\s (30 − 10) resulting in an inco\smplete method so no mark can be awarded. 1 0 1 0
Page 20 of 24 2016 key stage 1 mathematics test mark schemes Examples of responses from question 28 continued Arnav: 1 mark Oliwa: 0 marks Arnav and Oliwia both recorded a calculation b\sut did not complete\s it. Even though t\she frst part of Arnav’s method is not visi\sble, we can assume t\shat he has added 17\s and 10 as he shows \sthe total 27 being\s subtracted from 40 in the writt\sen part of his meth\sod. One mark can be awarded for a complete,\s correct method, despite the\s omission of a fnal\s answer. Oliwia has not shown the a\sddition of 17 and \s10, so it is not clear where her ‘22’ has come\s from. We are not able to assum\se that she has a cor\srect method so no mark can be awarded. Harry: 1 mark Lucia: 0 marks Harry and Lucia both added 10 and\s 17 and then attem\spted a subtraction.\s Harry has subtracted 27 f\srom 40 so one mark can be awarded for a complete,\s correct method. Lucia made an arithmeti\sc error when adding 10 and 17 to reach 26. This arithm\setic error need not affect the method mar\sk, but Lucia went on to subtrac\st 40 from 26 which is an in\scorrect method. Consequ\sently no mark can be awarded. (If Lucia had reached the answer of 14, we wo\suld assume that she \sintended to subtrac\st 26 from 40, and one mark would be awarded for a complete, cor\srect method.) 1 0 1 0
Page 21 of 24 2016 key stage 1 mathematics test mark schemes Examples of responses from question 28 continued Anna: 1 mark Leroy: 0 marks Anna and Leroy both recorded a calculation w\sith no fnal answer. Anna shows a complete, c\sorrect method of 40 − 27 so one mark can be awarded. Leroy also recorded a complete, cor\srect method of 40 − \s17 − 10, but has crossed it out so no mark can be awarded. Tom: 1 mark Fleur: 0 marks To m and Fleur have both misread numbers in the \squestion. To m has misread 17 as 1\b. As all\s the arithmetic is correct and the questio\sn has not been made\s easier, one mark can be awarded for the method\s. Fleur has misread 17 as 10 and su\sbtracted 10 twice. \sAs her misread makes the quest\sion easier, no mark can be awarded. 1 0 1 0
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2016 key stage 1 ma\sthematics test mark \sschemes Paper 1: arithmeti\sc and Paper 2: reasoning Print PDF version p\sroduct code: STA/16/7366/p ISBN: \s\b78-1-78315-\b13-0 Electronic PDF version pr\soduct code: STA/16/7366/e ISBN: \s\b78-1-78315-\b14-7 For more copies Additional printed\s copies of this book\slet are not available. I\st can be downloaded\s from www.gov.uk/government/publications.\s © Crown copyright and C\srown information 20\s16 Re-use of Crown copyright and Crown information in test materials Subject to the exce\sptions listed below\s, the test material\ss on this website ar\se Crown copyright or Cr\sown information and yo\su may re-use them (not inc\sluding logos) free of charge in any format o\sr medium in accordance with the term\ss of the Open Gover\snment Licence v3.0 \swhich can be found \son the National Ar\schives website and accessed \svia the following \slink: www.nationalarchives.gov.uk/doc/open-government-licence. When you use this i\snformation under t\she Open Government Licence v3.0,\s you should include\s the following attribution: ‘Cont\sains public sector i\snformation licensed\s under the Open Government Licence v3.0’\s and where possible provide a link to th\se licence. Exceptions – third-party copyright content in test materials You must obtain perm\sission from the relevant copyright o\swners, as listed in \sthe ‘2016 key stage\s 1 tests copyright report’, for re-use of any third-party copyright c\sontent which we hav\se identifed in the\s test materials, as listed below. Alternatively you should\s remove the unlicense\sd third-party copyright c\sontent and/or replace it with appropriately licensed \smaterial. Third-party content These materials cont\sain no third-party copyright c\sontent. If you have any qu\series regarding these test mat\serials contact the n\sational curriculum \sassessments helpline \son 0300 303 3013 or e\smail assessments@educ\sation.gov.uk.