We have almost every SATs paper within our archives including KS1 *Money Problems* and many other KS1, KS2 and KS3 SATs papers and worksheets. SATs papers are fantastic practise tools, especially for literacy, problem solving and maths. Alternative sources for study include the Bitesize resources and Revisewise for more SATs practice, SATs revision and SATs preparation!

Ma KEY STAGE 2 Mathematics tests Mark schemes LEVELS 2003 3– 5 2003 Test A, Test B and Mental mathematics test KEY STAGE KEY STAGE KEY STAGE Sourced from SATs-Papers.co.uk KEY STAGE http://www.SATs-Papers.co.uk First 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/ Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 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 left-hand 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 U1 or U2 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. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 1 What if … Marking procedure The child’s response is numerically or algebraically equivalent to the answer in the mark scheme. Markers will award the mark unless the mark scheme states otherwise. The child’s response does not match closely any of the examples given. 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. The child has responded in a non-standard way. 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. There appears to be a misreading affecting the working. 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 one-mark questions – 0 marks are awarded. In two-mark questions that have a method mark – 1 mark will be awarded if the correct method is correctly implemented with the misread number(s). No answer is given in the expected place, but the correct answer is given elsewhere. 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. The response in the answer box is wrong, but the correct answer is shown in the working. 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 not contradict work already done; If so, the mark will be awarded. the child has continued to give redundant extra working which does contradict work already done. 2 If so, the mark will be awarded. If so, the mark will not be awarded. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk What if … Marking procedure The child’s answer is correct but the wrong working is shown. A correct response will always be marked as correct. The correct response has been crossed out and not replaced. Any legible crossed-out work that has not been replaced will be marked according to the mark scheme. If the work is replaced, then crossed-out work will not be considered. More than one answer is given. 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. The answer is correct but, in a later part of the question, the child has contradicted this response. 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 right-hand 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 two-mark question which is correct has ‘1’ entered in both mark boxes. A two-mark 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. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 3 Marking specific types of question Responses involving money Where the £ sign is given For example: £ 3.20 £ £7 Accept ✓ Do not accept ✓ £3.20, £7, £7.00 ✓ Any unambiguous indication of the correct amount eg £3.20p, £3 20 pence £3 20, £3,20, £3-20, £3:20 Incorrect or ambiguous use of pounds or pence eg £320, £320p Incorrect placement of decimal point, or incorrect use or omission of 0 eg £3.2 £3 200, £32 0, £3-2-0 Where the p sign is given For example: p 40p Accept ✓ Do not accept ✓ 40p ✓ Any unambiguous indication of the correct amount eg £0.40p Incorrect or ambiguous use of pounds or pence eg 0.40p £40p Where no sign is given For example: £3.20, 40p Accept ✓ ✓ £3.20, 40p, £0.40 ✓ 320p ✓ Any unambiguous indication of the correct amount eg £3.20p, £3 20 pence £3 20, £3,20, £3-20, £3:20 3.20, 320, 3 pounds 20 £0.40p, £.40p 40, 0.40, £.40 4 Sourced from SATs-Papers.co.uk Do not accept Incorrect or ambiguous use of pounds or pence eg £320, £320p £3.2 3.20p £40, £40p 0.4 http://www.SATs-Papers.co.uk Responses involving time A time interval For example: 2 hours 30 minutes Accept ✓ Do not accept ✓ 2 hours 30 minutes ✓ Any unambiguous indication eg 21/2 hours, 2.5 hours 2h 30, 2h 30 min Incorrect or ambiguous time interval eg 2.30, 2-30, 2,30 2.3, 2.3 hours, 2.3h, 2h 3 2.30 min ✓ Digital electronic time ie 2:30 A specific time For example: 8:40am, 17:20 Accept ✓ Do not accept ✓ 8:40am, 8:40, twenty to nine ✓ Any unambiguous, correct indication eg 08.40, 8.40, 0840 8 40, 8-40, 8,40 ✓ Unambiguous change to 12 or 24 hour clock eg 17:20 as 5:20pm or 17:20pm Incorrect time eg 8.4am, 8.40pm Incorrect placement of separators, spaces, etc or incorrect use or omission of 0 eg 840, 8:4:0 8.4, 084, 84 Responses involving measures Where units are given (eg kg, m, l) For example: kg 8.6kg Accept ✓ ✓ 8.6kg ✓ Any unambiguous indication of the correct measurement eg 8.60kg, 8.6000kg 8kg 600g Do not accept Incorrect or ambiguous use of units eg 8600kg 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. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 5 Test A questions 1–4 Question Requirement Mark 1a 65 1m 1b 2400 1m Arrow drawn to 350, as shown: 1m Additional guidance 2 Arrow 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. 3 Diagram completed as shown: 1m Accept slight inaccuracies in drawing provided the intention is clear. 4 Two numbers circled as shown: 1m Do not award the mark if additional incorrect numbers are circled. Accept alternative unambiguous indications, eg ticks, numbers crossed or underlined. 6 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Test A questions 5–10 Question Requirement Mark 5 111 1m 6a £112 1m 6b £16 1m Diagram marked as shown: 1m Additional guidance 7 Do not accept 36 or Tuesday or £1.12 Both squares must be correctly marked. Accept alternative indications, eg squares ticked, crossed or circled. 8 Table completed as shown: 9a 9b 1m Both numbers must be correct for the award of the mark. 1m 4 1m 1m 10a Both numbers must be correct for the award of the mark. Answers may be written in either order. 10b An explanation which recognises that the numbers in circles are multiples of 5, eg ■ ‘Because all the circles are multiples of 5’; ■ 1m U1 Do not accept vague or arbitrary explanations, eg ■ ‘Because you keep on adding 5’; ■ ‘Because the circles are 5 more each time’. ‘Because 35 is in the five times table’. Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 7 Test A questions 11–15 Question Requirement Mark 11a 42 1m 11b 11 Additional guidance 1m 12 Award TWO marks for the correct answer of 250 Up to 2m If the answer is incorrect, award ONE mark for evidence of appropriate working, eg Calculation must be performed for the award of ONE mark. 150 t 5 e 750 1000 m 750 e wrong answer 13 18 456 1m 14a Teri 1m Accept recognisable misspellings. Do not accept 16.8 14b 15 5 1m Award TWO marks for all three shape names written in the correct order as shown: ■ rectangle ■ square If the answer is incorrect, award ONE mark for two shape names written in the correct order. 8 Accept recognisable misspellings. For the first shape, accept oblong or parallelogram. kite ■ Up to 2m Sourced from SATs-Papers.co.uk For the third shape, accept rhombus or parallelogram but do not accept diamond. http://www.SATs-Papers.co.uk Test A questions 16–18 Question 16 Requirement Mark Award TWO marks for all three numbers correct as shown: a multiple of 9 Additional guidance Up to 2m OR a square number a factor of 96 If the answer is incorrect, award ONE mark for two numbers correct. 17 Award TWO marks for the correct answer of Up to 2m Numbers must be in the correct order. AND If the answer is incorrect, award ONE mark for either 10.8 in the first box or a number in the second box, which is 6.5 greater than the answer given in the first box. 18 1m U1 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 9 Test A questions 19–21 Question 19 Requirement Mark Award TWO marks for the correct answer of 50 Additional guidance Up to 2m If the answer is incorrect, award ONE mark for evidence of appropriate working using common units, eg 1500 d 30 = wrong answer 20 Calculation must be performed for the award of ONE mark. Do not accept 1.5 d 30 as evidence of appropriate working. Award TWO marks for two different answers as shown: Up to 2m The two answers may be given in either order. Do not accept ’5 and 2’ AND ‘2 and 5’ for two marks. AND If the answer is incorrect, award ONE mark for any one of the above answers. 21a Answer in the range 30% to 36% inclusive. 1m 21b An explanation which recognises that both teams won half their games, but both teams played a different number of games, eg 1m U1 No mark is awarded for circling ‘No’ alone. Do not accept vague or arbitrary explanation, eg ■ ■ ‘Half of 30 is not the same as half of 24’; ■ ‘Because e 12’; ‘The netball team played more games’; ■ ‘Both teams won half their games’; ■ ■ ’30 is more than 24’. of 30 e 15 but of 24 ‘Because 15 is more than 12’. If ‘Yes’ is circled but a correct unambiguous explanation is given, then award the mark. 10 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Test A questions 22–26 Question Requirement Mark 22 20 1m 23 (10, 9) 1m Additional guidance Coordinates must be in the correct order. Accept unambiguous answers written on the diagram. 24 64 1m 25 1m U1 Accept the four numbers listed in any order. OR 26 Award TWO marks for the correct answer of 20 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg ■ U2 Calculation must be performed for the award of ONE mark. 30 t £5 e £150 £150 m £110 e £40 £40 d £2 e 20 ■ Up to 2m £110 d 30 e £3 each, with £20 left over £20 d £2 e 10 30 – 10 e 20 OR ■ a trial and improvement method, eg 30 t £3 e £90 10 t £3 p 20 t £5 e £130 15 t £3 p 15 t £5 e £120 Sourced from SATs-Papers.co.uk A ‘trial and improvement’ method must show evidence of improvement, but a final answer need not be reached for the award of ONE mark. http://www.SATs-Papers.co.uk 11 Test B questions 1–5 Question Requirement Mark 1a 3 1m 1b 75 1m 1c 84 1m 2 All five digits arranged to give a sum of 60, eg 1m Additional guidance Accept digits in any order provided the sum of 60 is achieved. U1 Do not accept a digit used more than once, or digits outside the list given. 3a 45 1m 3b 15:13 1m 4a 90 1m 4b 13 1m The correct shape ticked, as follows: 1m 5 12 Sourced from SATs-Papers.co.uk Accept alternative indications, eg shapes ringed, as long as the intention is clear. http://www.SATs-Papers.co.uk Test B questions 6–11 Question Requirement Mark 6a 17 1m 6b 18 Additional guidance 1m 7 Award TWO marks for the correct answer of Up to 2m Numbers must be in the correct order. 1m Accept slight inaccuracies in drawing provided the intention is clear. AND If the answer is incorrect, award ONE mark for either 22 in the first box or a number in the second box, which is 10 more than half the answer given in the first box. 8 Diagram completed with ONE of the four extra squares shown. Accept alternative indications, eg squares ticked or circled. Accept more than one square drawn if all are correct. 9 Award TWO marks for the correct answer of 73p OR £0.73 Up to 2m If the answer is incorrect, award ONE mark for evidence of appropriate method, eg Accept for ONE mark £73p OR 0.73p OR £73 as evidence of appropriate method. 195 p 38 p (70 t 2) e 373 Answer need not be obtained for the award of ONE mark. 373 – 300 10 Diagram completed correctly as shown: 1m U1 Accept slight inaccuracies in drawing provided the intention is clear. A 11 50 Sourced from SATs-Papers.co.uk 1m Accept –50 http://www.SATs-Papers.co.uk 13 Test B questions 12–15 Question 12 Requirement Mark Award TWO marks for both fractions correct as shown: Up to 2m Additional guidance Accept fractions written in either order. OR If the answer is incorrect, award ONE mark for one fraction correct. 13 Calculation completed correctly as shown: 1m OR OR 14 Award TWO marks for one correct number written in each white section of the table, eg 100 Accept more than one number in each section as long as all are correct. 2000 19 Up to 2m 1001 If the answer is incorrect, award ONE mark for three sections completed correctly. 15 Lengths written in correct order as shown: 1m Accept use of equivalent units, eg 2.5cm Accept answers with missing or incorrect units. 14 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Test B questions 16–18 Question 16 Requirement Award TWO marks for the sequence completed as shown: Mark Up to 2m If the answer is incorrect, award ONE mark for two numbers correct. Additional guidance Accept answers as fractions, eg ,1 Accept for ONE mark ■ 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 not award any marks if all numbers are whole numbers. 17 5 18 Award TWO marks for the correct answer of 54 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 1m Up to 2m U1 Answer need not be obtained for the award of ONE mark. 153 m (3 t 15) e 108 108 d 2 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 15 Test B questions 19–21 Question Requirement 19 367.5 OR 367 20 Award TWO marks for all three answers correct, as shown: Mark Additional guidance 1m Up to 2m U1 Accept for ONE mark any permutation of the correct answers, eg If the answer is incorrect, award ONE mark for evidence of appropriate method, eg ■ k = 750, m = 250, n = 500 2n p 3n p n e 1500 1500 d 6 Answer need not be obtained for the award of ONE mark. OR ■ a trial and improvement method, eg A ‘trial and improvement’ method must show evidence of improvement. 1000 p 1500 p 500 e 3000 200 p 300 p 100 e 600 400 p 600 p 200 e 1200 21a £1.50 21b Award TWO marks for the correct answer of 250 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 1m Up to 2m Answer need not be obtained for the award of ONE mark. 360 d 90 e 4 1000 d 4 16 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Test B questions 22–24 Question 22 Requirement Award TWO marks for boxes ticked and crossed as shown: Mark Up to 2m Additional guidance Accept alternative unambiguous indications such as Y or N. For TWO marks, accept blank boxes as crosses. If the answer is incorrect, award ONE mark for any three out of four boxes correctly completed. 23 Equivalent of one third of each hexagon shaded, or a total of 1 hexagons shaded, eg For ONE mark, do not accept blank boxes as crosses. 1m Accept part shapes shaded as long as the intention is clear. Accept inaccuracies in shading provided the intention is clear. 24 Award TWO marks for the correct answer of 112 500 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg Up to 2m Answer need not be obtained for the award of ONE mark. 45% of 250 000 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk 17 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. 18 Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk Mental mathematics 2003 quick reference mark scheme Practice question 12 20 13 58 Time: 5 seconds Words not acceptable 1 1020 2 30 14 3 42 15 4 50 % 5 12 000 g 0.1 0.2 0.3 0.4 0.5 375 Time: 15 seconds 16 92 17 Pizzas Small £6.50 Medium £7.50 Large £8.40 Time: 10 seconds 6 £ 1.10 £ 7 18 8 165 19 1.90 11 25 20 9 0.8 10 14 11 30 1 Accept 1.25 or 5 or 4 equivalent fractions m Sourced from SATs-Papers.co.uk 120 degrees http://www.SATs-Papers.co.uk 19 Mental mathematics questions 1–20 Question Requirement Mark 1 1020 1m 2 30 1m 3 42 1m 4 50% 1m 5 12 000g 1m 6 £1.10 Additional guidance 1m 7 1m Words not acceptable. Do not accept 0.5 OR Accept any other way of indicating the answer, eg ticked or crossed. Do not accept if more than one answer is indicated unless the child’s intention is clear. 8 25 1m 9 0.8 1m 10 1 OR 1.25 OR 1m 11 30m 1m 12 20 1m 13 58 1m 14 1m Accept equivalent fractions. Accept any other way of indicating the answer, eg underlining. Do not accept if more than one answer is indicated unless the child’s intention is clear. 15 1m 16 92 1m 17 £1.90 1m 18 165 1m 19 11 1m 20 20 375 120 degrees 1m Sourced from SATs-Papers.co.uk http://www.SATs-Papers.co.uk EARLY YEARS NATIONAL CURRICULUM 5–16 GCSE GNVQ GCE A LEVEL NVQ OTHER VOCATIONAL QUALIFICATIONS 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) Sourced from SATs-Papers.co.uk 254912 http://www.SATs-Papers.co.uk