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2003 2 KEY STAGE LEVELS Ma KEY STAGE KEY STAGE KEY STAGE KEY STAGE 2003 Mathematics tests Mark schemes Test A, Test B and Mental mathematics test 3– 5First published in 2003 © Qualifications and Curriculum Authority 2003 Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without prior written permission of the publisher, unless within the terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced for the purpose of research, private study, criticism or review, or by educational institutions solely for educational purposes, without permission, provided full acknowledgement is given. Produced in Great Britain by the Qualifications and Curriculum Authority under the authority and superintendence of the Controller of Her Majesty’s Stationery Office and Queen’s Printer of Acts of Parliament. The Qualifications and Curriculum Authority is an exempt charity under Schedule 2 of the Charities Act 1993. Qualifications and Curriculum Authority 83 Piccadilly London W1J 8QA www.qca.org.uk/
1 Marking the mathematics tests As in 2002, external markers, employed by the external marking agencies under contract to QCA, will mark the test papers. The markers will follow the mark schemes in this booklet, which is supplied to teachers for information. This booklet contains the mark schemes for the levels 3–5 tests A, B and mental mathematics. Level threshold tables will be available on the QCA website on 23 June 2003 (www.qca.org.uk/). General guidance The structure of the mark schemes The marking information for each question is set out in the form of tables, which start on page 6 of this booklet. The ‘question’column on the lefthand side of each table provides a quick reference to the question number and the question part. The ‘mark’ column indicates the total number of marks available for each question part. On some occasions, the symbol or may be shown in the mark column. The ‘U’ indicates that there is a ‘Using and Applying Mathematics’ element in the question. The number, 1 or 2, shows the number of marks attributed to using and applying mathematics in this question. The ‘requirement’ column may include two types of information: ■ a statement of the requirements for the award of each mark, with an indication of whether credit can be given for correct working; ■ examples of some different types of correct response. The ‘additional guidance’ column indicates alternative acceptable responses, and provides details of specific types of response which are unacceptable. Other guidance, such as the range of acceptable answers, is provided as necessary. Additionally, for the mental mathematics test, general guidance on marking is given on page 18, together with a ‘quick reference’ mark scheme. Applying the mark schemes In order to ensure consistency of marking, the most frequent procedural queries are listed on pages 2 and 3 with the action the marker will take. This is followed by further guidance on pages 4 and 5 relating to the marking of questions that involve money, time and other measures. Unless otherwise specified in the mark scheme, markers will apply the following guidelines in all cases. U1 U2
2 Where appropriate, detailed guidance will be given in the mark scheme, which markers will follow. If no guidance is given, markers will examine each case to decide whether: the incorrect answer is due to a transcription error; the child has continued to give redundant extra working which does notcontradict work already done; the child has continued to give redundant extra working which doescontradict work already done.If so, the mark willbe awarded. If so, the mark willbe awarded. If so, the mark will notbe awarded. What if … The child’s response is numerically or algebraically equivalent to the answer in the mark scheme. The child’s response does not match closely any of the examples given. The child has responded in a nonstandard way. There appears to be a misreading affecting the working. No answer is given in the expected place, but the correct answer is given elsewhere. The response in the answer box is wrong, but the correct answer is shown in the working. Marking procedure Markers will award the mark unless the mark scheme states otherwise. Markers will use their judgement in deciding whether the response corresponds with the statement of the requirements given in the ‘requirement’ column. Reference will also be made to the additional guidance and, if there is still uncertainty, markers will contact the supervising marker. Calculations, formulae and written responses do not have to be set out in any particular format. Children may provide evidence in any form as long as its meaning can be understood. Diagrams, symbols or words are acceptable for explanations or for indicating a response. Any correct method of setting out working, however idiosyncratic, will be accepted. This is when the child misreads the information given in the question and uses different information without altering the original intention or difficulty level of the question. For each misread that occurs, one mark only will be deducted. In onemark questions – 0 marks are awarded. In twomark questions that have a method mark – 1 mark will be awarded if the correct method is correctly implemented with the misread number(s). Where a child has shown understanding of the question, the mark(s) will be given. In particular, where a word or number response is expected, a child may meet the requirement by annotating a graph or labelling a diagram elsewhere in the question.
3 What if … The child’s answer is correct but the wrong working is shown. The correct response has been crossed out and not replaced. More than one answer is given. The answer is correct but, in a later part of the question, the child has contradicted this response. Marking procedure A correct response will always be marked as correct. Any legible crossedout work that has not been replaced will be marked according to the mark scheme. If the work is replaced, then crossedout work will not be considered. If all answers are correct (or a range of answers is given, all of which are correct), the mark will be awarded unless prohibited by the mark scheme. If both correct and incorrect responses are given, no mark will be awarded. A mark given for one part will not be disallowed for working or answers given in a different part, unless the mark scheme specifically states otherwise. Recording marks awarded on the test paper In the shaded margin there is a mark box for each question part. For the written tests, the number of marks gained on each double page will be written in the total box at the bottom of the righthand page. For all of the tests, the total number of marks gained on each paper will be recorded on the front of the test paper, and on the mark sheet. All questions in the tests, even those not attempted by the child, will be marked with a ‘1’ or ‘0’ entered in the mark box. A twomark question which is correct has ‘1’ entered in both mark boxes. A twomark question which is incorrect, but which has sufficient evidence of working or method as required by the mark scheme will have ‘1’ entered in the first mark box and ‘0’ in the second. Otherwise ‘0’ will be entered in both mark boxes. Test A carries a total of 40 marks. Test B also carries a total of 40 marks. The mental mathematics test carries a total of 20 marks. The 2003 key stage 2 mathematics tests and mark schemes were developed by the Mathematics Test Development Team at QCA.
4 Accept ✓ Do not accept 8 Where the £ sign is given For example: £ 3.20 £ 7 ✓£3.20, £7, £7.00 ✓Any unambiguous indication of the correct amount eg £3.20p, £3 20 pence £3 20, £3,20, £320, £3:20 8 Incorrect or ambiguous use of pounds or pence eg £320, £320p 8 Incorrect placement of decimal point, or incorrect use or omission of 0 eg £3.2 £3 200, £32 0, £320 Marking specific types of question Responses involving money £ Accept ✓ Do not accept 8 Where the p sign is given For example: 40p ✓40p ✓Any unambiguous indication of the correct amount eg £0.40p 8 Incorrect or ambiguous use of pounds or pence eg 0.40p £40p p Accept ✓ Do not accept 8 Where no sign is given For example: £3.20, 40p ✓£3.20, 40p, £0.40 ✓320p ✓Any unambiguous indication of the correct amount eg £3.20p, £3 20 pence £3 20, £3,20, £320, £3:20 3.20, 320, 3 pounds 20 £0.40p, £.40p 40, 0.40, £.40 8 Incorrect or ambiguous use of pounds or pence eg £320, £320p £3.2 3.20p £40, £40p 0.4
5 Accept ✓ Do not accept 8 A time interval For example: 2 hours 30 minutes ✓2 hours 30 minutes ✓Any unambiguous indication eg 2 1/2hours, 2.5 hours 2h 30, 2h 30 min ✓Digital electronic time ie 2:30 8 Incorrect or ambiguous time interval eg 2.30, 230, 2,30 2.3, 2.3 hours, 2.3h, 2h 3 2.30 min Accept ✓ Do not accept 8 A specific time For example: 8:40am, 17:20 ✓8:40am, 8:40, twenty to nine ✓Any unambiguous, correct indication eg 08.40, 8.40, 0840 8 40, 840, 8,40 ✓Unambiguous change to 12 or 24 hour clock eg 17:20 as 5:20pm or 17:20pm 8 Incorrect time eg 8.4am, 8.40pm 8 Incorrect placement of separators, spaces, etc or incorrect use or omission of 0 eg 840, 8:4:0 8.4, 084, 84 Responses involving time Accept ✓ Do not accept 8 Where units are given (eg kg, m, l) For example: 8.6kg ✓8.6kg ✓Any unambiguous indication of the correct measurement eg 8.60kg, 8.6000kg 8kg 600g 8 Incorrect or ambiguous use of units eg 8600kg kg Responses involving measures Note If a child leaves the answer box empty but writes the answer elsewhere on the page, then that answer must be consistent with the units given in the answer box and the conditions listed above. If a child changes the unit given in the answer box, then their answer must be equivalent to the correct answer using the unit they have chosen, unless otherwise indicated in the mark scheme.
6 Test A questions 1–4 Question Requirement Mark Additional guidance 1a 1b65 24001m 1m 2Arrow drawn to 350, as shown:1mArrow should be closer to 350 than to 325 or 375 for award of the mark. Accept arrows not originating from the centre of the dial. 3Diagram completed as shown:1mAccept slight inaccuracies in drawing provided the intention is clear. 4Two numbers circled as shown:1m Do notaward the mark if additional incorrect numbers are circled. Accept alternative unambiguous indications, eg ticks, numbers crossed or underlined.
7 Test A questions 5–10 Question Requirement Mark Additional guidance 51111m 6a 6b£112 £161m 1mDo notaccept 36 or Tuesday or £1.12 7Diagram marked as shown:1mBoth squares must be correctly marked. Accept alternative indications, eg squares ticked, crossed or circled. 8Table completed as shown:1mBoth numbers must be correct for the award of the mark. 9a 9b41m 1m 10a 10bAn explanation which recognises that the numbers in circles are multiples of 5, eg ■ ‘Because all the circles are multiples of 5’; ■ ‘Because 35 is in the five times table’.1m 1mBoth numbers must be correct for the award of the mark. Answers may be written in either order. Do not accept vague or arbitrary explanations, eg ■ ‘Because you keep on adding 5’; ■ ‘Because the circles are 5 more each time’. U1
8 Test A questions 11–15 Question Requirement Mark Additional guidance 11a 11b42 111m 1m 12Award TWOmarks for the correct answer of 250 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 150t5e750 1000m750ewrong answerUp to 2m Calculation must be performed for the award of ONEmark. 1318 4561m 14a 14bTeri 51m 1mAccept recognisable misspellings. Do notaccept 16.8 15Award TWOmarks for all three shape names written in the correct order as shown: ■ rectangle ■ kite ■ square If the answer is incorrect, award ONE mark for two shape names written in the correct order.Up to 2mAccept recognisable misspellings. For the first shape, accept oblong or parallelogram. For the third shape, accept rhombus or parallelogram but do notaccept diamond.
9 Test A questions 16–18 Question Requirement Mark Additional guidance 16Award TWOmarks for all three numbers correct as shown: a multiple of 9OR a square number a factor of 96 If the answer is incorrect, award ONE mark for two numbers correct.Up to 2m 18 1m U1 17Award TWOmarks for the correct answer of If the answer is incorrect, award ONE mark for either 10.8in the first box or a number in the second box, which is 6.5 greater than the answer given in the first box.Up to 2m ANDNumbers must be in the correct order.
10 Test A questions 19–21 Question Requirement Mark Additional guidance 19Award TWOmarks for the correct answer of 50 If the answer is incorrect, award ONE mark for evidence of appropriate working using common units, eg 1500d30 = wrong answerUp to 2m Calculation must be performed for the award of ONEmark. Do not accept 1.5 d30 as evidence of appropriate working. 20Award TWOmarks for two different answers as shown: AND If the answer is incorrect, award ONE mark for any one of the above answers.Up to 2mThe two answers may be given in either order. Do notaccept ’5 and 2’ AND‘2 and 5’ for two marks. 21a 21bAnswer in the range 30% to 36% inclusive. An explanation which recognises that both teams won half their games, but both teams played a different number of games, eg ■ ‘Half of 30 is not the same as half of 24’; ■ ‘Because of 30 e15 but of 24 e12’; ■ ‘Because 15 is more than 12’. 1m 1mNo mark is awarded for circling ‘No’ alone. Do notaccept vague or arbitrary explanation, eg ■ ‘The netball team played more games’; ■ ‘Both teams won half their games’; ■ ’30 is more than 24’. If ‘Yes’ is circled but a correct unambiguous explanation is given, then award the mark. U1
11 Test A questions 22–26 Question Requirement Mark Additional guidance 22201m 23(10, 9)1mCoordinates must be in the correct order. Accept unambiguous answers written on the diagram. 24641m 25 OR1mAccept the four numbers listed in any order. U1 26Award TWOmarks for the correct answer of 20 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg ■ 30t£5e£150 £150m£110e£40 £40d£2e20 ■ £110d30e£3 each, with £20 left over £20d£2e10 30 – 10 e20 OR ■ a trial and improvement method, eg 30t£3e£90 10t£3p20t£5e£130 15t£3p15t£5e£120Up to 2m Calculation must be performed for the award of ONEmark. A ‘trial and improvement’ method must show evidence of improvement, but a final answer need not be reached for the award of ONEmark. U2
12 Test B questions 1–5 Question Requirement Mark Additional guidance 1a 1b 1c3 75 841m 1m 1m 2All five digits arranged to give a sum of 60, eg1mAccept digits in any order provided the sum of 60 is achieved. Do notaccept a digit used more than once, or digits outside the list given. U1 3a 3b45 15:131m 1m 4a 4b90 131m 1m 5The correct shape ticked, as follows:1mAccept alternative indications, eg shapes ringed, as long as the intention is clear.
13 Test B questions 6–11 Question Requirement Mark Additional guidance 6a 6b17 181m 1m 7Award TWOmarks for the correct answer of If the answer is incorrect, award ONE mark for either 22in the first box or a number in the second box, which is 10 more than half the answer given in the first box.Up to 2mNumbers must be in the correct order. 8Diagram completed with ONEof the four extra squares shown.1mAccept slight inaccuracies in drawing provided the intention is clear. Accept alternative indications, eg squares ticked or circled. Accept more than one square drawn ifallare correct. 9Award TWOmarks for the correct answer of 73p OR£0.73 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 195p38p(70t2)e373 373 – 300 Up to 2m Accept for ONEmark £73p OR0.73p OR£73 as evidence of appropriate method. Answer need not be obtained for the award of ONEmark. 10Diagram completed correctly as shown:1mAccept slight inaccuracies in drawing provided the intention is clear. A 11501mAccept –50 U1 AND
14 Test B questions 12–15 Question Requirement Mark Additional guidance 12Award TWOmarks for both fractions correct as shown: If the answer is incorrect, award ONE mark for one fraction correct.Up to 2mAccept fractions written in either order. OR 13Calculation completed correctly as shown: OR OR1m 14Award TWOmarks for one correct number written in each white section of the table, eg If the answer is incorrect, award ONE mark for three sections completed correctly.Up to 2mAccept more than one number in each section as long as allare correct. 100 2000 19 10 01 15Lengths written in correct order as shown:1mAccept use of equivalent units, eg 2.5cm Accept answers with missing or incorrect units.
15 Test B questions 16–18 Question Requirement Mark Additional guidance 16Award TWOmarks for the sequence completed as shown: If the answer is incorrect, award ONE mark for two numbers correct.Up to 2mAccept answers as fractions, eg ,1 Accept for ONEmark ■ the number in the third box is 96 AND ■ the number in the first box is half of the number in the second box. eg Do notaward any marks if all numbers are whole numbers. 1751m 18Award TWOmarks for the correct answer of 54 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 153m(3t15)e108 108d2Up to 2m Answer need not be obtained for the award of ONEmark. U1
16 Test B questions 19–21 Question Requirement Mark Additional guidance 19367.5OR3671m 20Award TWOmarks for all three answers correct, as shown: If the answer is incorrect, award ONE mark for evidence of appropriate method, eg ■ 2np3npne1500 1500d6 OR ■ a trial and improvement method, eg 1000p1500p500e3000 200p300p100e600 400p600p200e1200Up to 2m Accept for ONEmark any permutation of the correct answers, eg k = 750, m = 250, n = 500 Answer need not be obtained for the award of ONEmark. A ‘trial and improvement’ method must show evidence of improvement. 21a 21b£1.50 Award TWOmarks for the correct answer of 250 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 360d90e4 1000d41m Up to 2m Answer need not be obtained for the award of ONEmark. U1
17 Test B questions 22–24 Question Requirement Mark Additional guidance 22Award TWOmarks for boxes ticked and crossed as shown: If the answer is incorrect, award ONE mark for any three out of four boxes correctly completed.Up to 2mAccept alternative unambiguous indications such as YorN. ForTWOmarks, accept blank boxes as crosses. ForONEmark,do notaccept blank boxes as crosses. 23Equivalent of one third of each hexagon shaded, or a total of 1 hexagons shaded, eg 1mAccept part shapes shaded as long as the intention is clear. Accept inaccuracies in shading provided the intention is clear. 24Award TWOmarks for the correct answer of 112 500 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 45% of 250 000Up to 2m Answer need not be obtained for the award of ONEmark.
18 Mark scheme for the mental mathematics test Applying the mark scheme Please note that children will not be penalised if they record any information given in the question or show their working. Markers will ignore any annotation, even if in the answer space, and mark only the answer. Markers will accept an unambiguous answer written in the stimulus box, or elsewhere on the page. Full mark scheme information is given on page 20. In addition, a ‘quick reference’ mark scheme is provided on page 19. This is presented in a similar format to the children’s answer sheet. General guidance The general guidance for marking the written tests also applies to marking the mental mathematics test. In addition, the following principles apply. 1. Unless stated otherwise in the mark scheme, accept answers written in words, or a combination of words and figures. 2. Where units are specified, they are given on the answer sheet. Children are not penalised for writing in the units again. 3. Where answers are required to be ringed, do not accept if more than one answer is ringed, unless it is clear which is the child’s intended answer. Accept also any other way of indicating the correct answer, eg underlining.
19 Practice question 2 30 3 42 4 50 % 8 25 9 0.8 15 375 16 92 14 0.1 0.2 0.3 0.4 0.5 Time: 5 seconds Time: 15 seconds 1 1020 18 165 11 30 m 13 58 19 11 5 12 000 g Time: 10 seconds 7 6 £ 1.10 10 1 1 4 Accept 1.25 or or equivalent fractions 54 Words not acceptable 12 20 20 120 degrees 17 £ 1.90 Pizzas Small £ 6.50 Medium £ 7.5 0 Large £ 8.40 Mental mathematics 2003 quick reference mark scheme
20 Mental mathematics questions 1–20 Question Requirement Mark Additional guidance 110201mWordsnotacceptable. 2301m 3421m 450%1m Do notaccept 0.5 OR 6£1.101m 512 000g1m 8251m 90.81m 101OR1.25OR1mAccept equivalent fractions. 71mAccept any other way of indicating the answer, eg ticked or crossed. Do notaccept if more than one answer is indicated unless the child’s intention is clear. 14 1mAccept any other way of indicating the answer, eg underlining. Do notaccept if more than one answer is indicated unless the child’s intention is clear. 1130m1m 12201m 13581m 153751m 16921m 17£1.901m 181651m 19111m 20120 degrees1m
For more information, contact: QCA key stage 2 team, 83 Piccadilly, London W1J 8QA For more copies, contact: QCA Publications, PO Box 99, Sudbury, Suffolk CO10 2SN (telephone 01787 884444; fax 01787 312950) Order ref:QCA/03/1009 (mark schemes pack) 254912 GNVQ GCE A LEVEL NVQ OTHER VOCATIONAL QUALIFICATIONS NATIONAL CURRICULUM 5–16 EARLY YEARS GCSE