[PDF] 2004 Key Stage 2 Year 6 - Mathematics Test A B Mental Levels 3-5 Mark Schemes.pdf | Plain Text

Mathematics tests Mark schemes Test A, test B and mental mathematics test 20 04 Ma KEY STAGE 2 LEVELS 3– 5 20 04

First published in 2004 © Qualifications and Curriculum Authority 2004 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 2003, 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 21 June 2004 (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 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 the 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 16, 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. U2 U1

2 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; the child has continued to give redundant extra working which does contradict work already done. If so, the mark willbe awarded. If so, the mark willbe awarded. If so, the mark will notbe awarded.

3 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 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 2004 key stage 2 mathematics tests and mark schemes were developed by the Mathematics Test Development Team at QCA. 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.

4 Marking specific types of question – summary of additional guidance Responses involving money Accept Do not accept 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 £3-20 £3:20 £3. 20 Where the p sign is given, for example: 40p 40p Any unambiguous indication of the correct amount, eg £0.40p Where no sign is given, for example: £3.20, 40p £3.20 40p 320p £0.40p Any unambiguous indication of the correct amount, eg £3.20p £0.40p £3 20 pence £. 40p £3 20 40 £3,20 0.40 £3-20 £.40 £3:20 3.20 320 3 pounds 20 p £ 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 p £ Incorrect or ambiguous use of pounds or pence, eg 0.40p £40p Incorrect or ambiguous use of pounds or pence, eg £320 £40 £320p £40p £3.2 0.4 3.20p

5 Responses involving measures Accept Do not accept 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 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 8-40 8,40 Unambiguous change to 12 or 24 hour clock, eg 17:20 as 5:20pm or 17:20pm An incorrect or ambiguous time interval, eg 2.30 2-30 2,30 2.3 2.3 hours 2.3h 2h 3 2.30 min Accept Do not accept 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 kg kg Note If a child leaves the answer box empty but writes the answer elsewhere on the page, then thatanswer 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. 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 Incorrect or ambiguous use of units, eg 8600kg Responses involving time

6 Test A questions 1–6 1m 5 Up to 2m Question Requirement Mark Additional guidance 1a 1b 1c 115 30 69 1m 1m 1m 2 OR 28 1 4 Accept equivalent fractions. 3a 3b £2.45OR245p juice and apple OR milk and melon 1m 1m Accept recognisable misspellings. Accept items written in either order. Accept numerical substitutes for the required pairing, ie 65p and 15p OR 55p and 25p 4 Answer in the range 8.4 to 8.6cm inclusive. 1m Accept 8 cm 12 Award TWOmarks for all three calculations completed correctly as shown: 5 { 12 ÷ 9+ If the answer is incorrect, award ONE mark for two calculations completed correctly, eg 5 { 12 ÷ 9+ 3 5 4 5 3 4 Answers to the calculations are not required for the award of the mark. Accept for ONEmark 4, 3, * OR 4, *, 5 OR 4, *, 3 OR *, 3, 5 where * is any number or blank. 6a 6b 15 25 1m 1m

7 Question Requirement Mark Additional guidance 7 Award TWOmarks for the correct answers of A ANDE. If the answer is incorrect, award ONE mark for: „ only one answer correct OR „ two answers correct and one incorrect. Up to 2m Answers may be given in either order. Accept unambiguous indications on the diagram. 8 10.8 1m 9a 9b 5 Answer in the range 6 degrees to 7.5 degrees inclusive. 1m 1m Do notaccept a list of months. 10a 10b £2.86 Award TWOmarks for the correct answer of £2.02 OR202p If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 4.69 + 3.29 = 7.98 10 – 7.98 = wrong answer 1m Up to 2m Accept for ONEmark £202p OR £202OR2.02p as evidence of appropriate working. Calculation must be performed for the award of ONEmark. 11 9:20 1m The answer is a specific time (see page 5 for guidance). 12 Award TWOmarks for a correct number written in each of the four boxes. If the answer is incorrect, award ONE mark for three boxes completed correctly. Up to 2m Accept more than one number in each box, provided all are correct. even not even a square number 0OR4OR16 OR36OR64 1OR9OR25 OR49OR81 not a square number evenAND not square AND less than 100 oddAND not square AND less than 100 Test A questions 7–12

8 Test A questions 13–18 Question Requirement Mark Additional guidance 13 One net ticked as shown: 9 1m Accept alternative unambiguous indications of the correct shape, provided the intention is clear, eg net circled. 14 Award TWOmarks for all four boxes completed correctly as shown: If the answer is incorrect, award ONE mark for three boxes completed correctly. Up to 2m U1 15 90 1m 16 360 1m 17 221.2 1m 18 Award TWOmarks for the correct answer of 21 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 5 + 2 = 7 15 ÷ 5 {7 OR 5 new 2 old 10 new 4 old 15 new 6 old Up to 2m AwardONEmark for an answer of 6 ORfor 6 shown with no evidence of an incorrect method. Answer need not be given for the award of ONEmark.

9 Test A questions 19–22 Question Requirement Mark Additional guidance 19 An explanation which recognises that the sum of adding three odd numbers is always odd, eg „ ’Because odd + odd + odd = odd’; „ ’Because three odd numbers can’t add up to an even number’; „ ’Because an odd number of odd numbers makes an odd number’. 1m U1 Do not accept numerical exemplification without further explanation, eg „ ‘Because 21 + 23 + 7 = 51’; „ ‘Because 21 + 23 + 6 = 50’. Do notaccept vague or arbitrary explanations, eg „ ‘Because 50 is even’; „ ‘Because you can only do it with two odd numbers’. 20 (5, 2) 1m Coordinates must be in the correct order. Accept unambiguous answers written on the diagram. 21 5 1m 22 Award TWOmarks for the correct answer of 15 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg „ 60 ÷ 4 = wrong answer OR „ a ‘trial and improvement’ method, eg 30{5 – 60 = 90 10{5 – 60 = –10 20{5 – 60 = 40 OR „ 5x – 60 = x x = wrong answer Up to 2m U1 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.

10 Test A questions 23–25 Question Requirement Mark Additional guidance 23a 23b 3 hours 35 minutes 15:15 1m 1m The answer is a time interval (see page 5 for guidance). The answer is a specific time (see page 5 for guidance). Accept quarter past three. 24 £180 1m Do notaccept 180%. 25 Award TWOmarks for the correct answer of 64 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 48 ÷ 3 = 16 16{4 = wrong answer Up to 2m U1 Calculation must be performed for the award of ONEmark.

11 Test B questions 1–3 Question Requirement Mark Additional guidance 1 One number circled as shown: 770 69 651 72 750 1m Do notaward the mark if additional incorrect numbers are circled. Accept alternative unambiguous indications, eg ticks, numbers crossed out or underlined. 2 Diagram completed correctly as shown: 1m Accept slight inaccuracies in drawing, provided the intention is clear. 3 Diagram completed correctly as shown: 1m Lines need not touch the clocks, provided the intention is clear. Do notaccept times which have been matched to more than one clock.

12 Test B questions 4–9 Question Requirement Mark Additional guidance 4a 4b 2 Blue 1m 1m Accept 100m ANDrelay. Accept B or recognisable misspellings. 5a 5b 8 80 1m 1m 6 An explanation which recognises that a multiple of 5 can end in 0 as well as 5, eg „ ‘Because 10 is a multiple of 5’; „ ‘Because it can end in 0’; „ ‘Because some numbers end in 0’. 1m U1 No mark is awarded for circling ‘No’ alone. Do notaccept vague or arbitrary answers, eg „ ‘Because not all multiples of 5 end in 5’. If ‘Yes’ is circled but a correct, unambiguous explanation is given, then award the mark. 7 Calculation completed correctly as shown: { 2= 8 0 1 4 5 1m U1 8 AANDF 1m Answers may be given in either order. Accept alternative indications, eg shapes ticked or circled, provided the intention is clear. 9a 9b £14.60 Award TWOmarks for the correct answer of £4.45 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 1.95 + 1.25 + 1.25 1m Up to 2m Do notaccept £14.6 Accept for ONEmark £445 OR £445p as evidence of an appropriate method. Accept for ONEmark £8.10 OR £19.05ORthe correct total of £4.45 and the answer given for 9a as evidence of an appropriate method. Answer need not be obtained for the award of ONEmark.

13 Test B questions 10–13 Question Requirement Mark Additional guidance 10a 10b 2002 2000 1m 1m 11 Award TWOmarks for the correct answer of 384 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 7 + 5 + 4 = 16 16{24 OR 7{24 5{24 + 4 {24 Up to 2m Answer need not be obtained for the award of ONEmark. 12a 12b Triangle drawn in any orientation as shown: Triangle drawn in any orientation as shown: 1m 1m Accept slight inaccuracies in drawing, provided the intention is clear. 13a 13b £200 Award TWOmarks for the correct answer of 37p OR£0.37 OR for finding the correct difference between £199.63 and the answer given for 13a. If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 74.68 + 65.90 + 59.05 = 199.63 200 – 199.63 OR for evidence of an appropriate method to find the correct difference between £199.63 and the answer given for 13a. 1m Up to 2m Answer to 13a must be a multiple of £10 for the award of TWOfollow- through marks. Answer need not be obtained for the award of ONEmark. Accept for ONEmark £37p OR0.37p OR£37 as evidence of appropriate method.

14 Test B questions 14–20 Question Requirement Mark Additional guidance 14 { 4 2 3 1m U1 15a 15b 4.4 1.2 OR for finding the correct difference between 5.6 and the answer given for 15a 1m 1m 16a 16b Answer in the range 46m to 47m inclusive. 55 1m 1m 17a 17b 1 in the first box 2 in the second box 34 1 2 1m 1m Accept equivalent fractions or decimals, eg 1.5 Accept equivalent fractions or decimals, eg 2.75 18 Answer in the range 93 degrees to 97 degrees inclusive. 1m 19a 19b 813.75 58.17 1m 1m Do notaccept –58.17 20 A = B = OR A = B = OR A = B = OR A = B = OR A = B = 15 0 12 2 9 4 3 8 0 10 1m U1 Answers must be whole numbers. Accept negative numbers, eg A = 12 and B = –3 Do notaccept A = 6 and B = 6

15 Test B questions 21–24 Question Requirement Mark Additional guidance 21 22 1m 22 Award TWOmarks for the correct answer of 12 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 7.2 ÷ 3 {5 Up to 2m U1 Answer need not be obtained for the award of ONEmark. Accept for ONEmark 1.2 OR120 as evidence of appropriate method. 23 Award TWOmarks for the correct answer of 2051 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg (4099 + 3) ÷ 2 OR continuation of sequence, eg 259, 515, 1027, wrong number Up to 2m Answer need not be obtained for the award of ONEmark. 24 Award TWOmarks for the correct answer of 2.4 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 6{8 = 48 (48g fibre in one loaf) 48 ÷ 20 OR 800 ÷ 20 = 40 (one slice weighs 40g) 6% of 40 Up to 2m Answer need not be obtained for the award of ONEmark.

16 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. Ignore any annotation, even if in the answer space, and mark only the answer. Accept an unambiguous answer written in the stimulus box, or elsewhere on the page. Full mark scheme information is given on page 18. In addition, a ‘quick reference’ mark scheme is provided on page 17. 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.

17 Practice question 2 38 6 99 11 14 5.2 15 0.075 19 220 cm 2 20 60 degrees Time: 10 seconds Bus times 07:15 07:35 07:55 08:15 7 20 minutes Time: 15 seconds 4 6 Time: 5 seconds 1 48 hours 12 4500 m 13 –14 ° C 17 55 8 5 10 3 4 2 3 1 100 1 20 3 210 5 44 9 £1.65 10 40 18 100 140 260 300 340 16 890 Mental mathematics 2004 quick reference mark scheme Accept 0.25 or equivalent fractions 1 4 Donotaccept 14 – Accept 165p

18 Mental mathematics questions 1–20 Question Requirement Mark Additional guidance 1 48 hours 1m 2 38 1m 3 210 1m 4 6 1m 5 44 1m 6 99 1m 7 20 minutes 1m 8 510 34 2 3 1 10 0 1 20 1m Accept 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. 9 £1.65 1m 10 40 1m 11 14 1m Accept equivalent fractions. Accept 0.25 12 4500m 1m 13 –14°C 1m Do notaccept 14– 14 5.2 1m 15 0.075 1m 16 890 1m 17 55 1m 18 340 300 260 140 10 0 1m Accept 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. 19 220 cm 2 1m 20 60 degrees 1m







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/04/1252 (mark schemes pack) 259401 EARLY YEARS NATIONAL CURRICULUM 5–16 GCSE GNVQ GCE A LEVEL NVQ OTHER VOCATIONAL QUALIFICATIONS