[PDF] 2002 Key Stage 2 Year 6 - Mathematics Test A B Mental Levels 3-5 Mark Schemes.pdf | Plain Text

2 R RR R PANTONE 300 CVUBlack Plate ASSET REF 2 Asset Graphics: 127059/05 Client: COI Job No. 01-8613/5 Job Title: Maths KS2 MS COVER 01-8613/5 First Proof: 8.2.02 Ma 2002 2 KEY STAGE 3– 6 LEVELS Mathematics tests Mark schemes 2 Test A, levels 3–5 Test B, levels 3–5 Mental arithmetic test, levels 3–5 Extension test C, level 6

First published in 2002 © Qualifications and Curriculum Authority 2002 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 2001, 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 arithmetic and the level 6 extension test C. Level threshold tables will be available on the QCA website on Wednesday 26 June (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 4 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. 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 arithmetic test, general guidance on marking is given on page 20, 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. Unless otherwise specified in the mark scheme, markers will apply the following guidelines in all cases.

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 not contradict work already done; the child has continued to give redundant extra working which does contradict work already done.If so, the mark will be awarded. If so, the mark will be awarded. If so, the mark will not be 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 non-standard 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 still uncertain, 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 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). 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 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. 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 grey 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 written tests, even those not attempted by the child, will be marked with a ‘2’, ‘1’ or ‘0’ entered in the mark box. A two-mark question which is correct has ‘2’ entered in the mark box. 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 mark box. Otherwise, ‘0’ will be entered in the mark box. For questions in the mental arithmetic tests, marks of either ‘1’ or ‘0’ are possible. Test A carries a total of 40 marks. Test B also carries a total of 40 marks. The mental arithmetic test carries a total of 20 marks. There is a total of 30 marks available in Test C. The 2002 key stage 2 mathematics tests and mark schemes were developed by the Mathematics Test Development Team at QCA.

4 Test A questions 1–3 Question Requirement Mark Additional guidance 1 Award TWO marks for the 2 lines drawn as shown: If the answer is incorrect, award ONE mark for at least one correct line drawn AND not more than one incorrect line drawn. Up to 2mDo not award any marks if two or more incorrect lines are drawn. 2a 2b1m 1m 3 Diagram completed as shown: 1m Accept slight inaccuracies in drawing provided the intention is clear. Accept answers without shading. 570 4 20050350

5 Test A questions 4–5 Question Requirement Mark Additional guidance 4a 4b 80p OR £0.80 £2.25 OR 225p 1m 1m Accept £0.80p OR 0.80 OR 80 OR £.80 OR £.80p OR £0 80 OR .80 OR 0 80 Do not accept £80p OR £80 OR £0.8 OR 0.80p Accept £2.25p OR 2.25 OR 225 OR £2 25 Do not accept £225p OR £225 5 Award TWO marks for the 3 shapes matched correctly as shown: If the answer is incorrect, award ONE mark for any two shapes correctly matched. Up to 2m Lines need not touch shapes or area boxes exactly provided the intention is clear. Do not accept shapes on the left which have been matched to more than one area on the right.

6 Test A questions 6–9 Question Requirement Mark Additional guidance 6a 6b £2.45 CC 1m 1m Accept £2.45p OR £2 45 Do not accept £245 OR £245p Accept ‘C’. Do not accept £1.55 7 All three numbers circled as shown: 1m Do not award the mark if additional incorrect numbers are circled. Accept unambiguous alternatives, eg ticks, numbers crossed or underlined. 8 Two cards ticked as shown: 1m Accept alternative unambiguous indications such as circling or a line joining a correct pair of cards. 91m

7 Test A questions 10–11 Question Requirement Mark Additional guidance 10a 10b Answer in the range 44p to 46p inclusive. 20p 1m 1m Accept £0.20p OR £0 20 Do not accept 0.20p OR £20p 11a 11b Award TWO marks for the correct answer of £21.80 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 3.50 ×4 = 14.00 1.95 ×4 = 7.80 14.00 + 7.80 = wrong answer An explanation which recognises that each square slab costs more than half a rectangular slab or equivalent, eg  ‘Half of £3.50 is £1.75, which is less than £1.95’;  ‘Two square slabs cost more than one rectangular slab’;  ‘Because 12 squares cost £23.40’;  ‘Because it would cost £1.60 more’. Up to 2m 1m Accept £21.80p OR £21 80 Accept for ONE mark £2180p OR £2180 OR £21.8 as evidence of appropriate working. Calculation must be performed for the award of ONE mark. Do not accept vague or arbitrary explanations, eg  ‘Because he would need more slabs’;  ‘Because square slabs are cheaper than rectangular slabs’;  ‘Because it costs more’;  ‘He is right because the square slabs are £1.95 each and the rectangular slabs are £3.50 each’.

8 Test A questions 12–15 Question Requirement Mark Additional guidance 12 Digits written in boxes as shown: 1m 13a 13b 83mm OR 8cm 3mm 29mm OR 2cm 9mm 1m 1mDo not accept 8.3mm Do not accept 2.9mm 14 8340 1m 15 Award TWO marks for the table completed as shown: If the answer is incorrect, award ONE mark for two of the three numbers completed correctly. Up to 2m For 0.25, accept .25 OR 1 4

9 Test A questions 16–18 Question Requirement Mark Additional guidance 16 0.21 1m Accept .21 17 (40, 27) 1m Coordinates must be written in the correct order. Accept unambiguous answers written on the diagram. 18a 18b Award TWO marks for correct answer as shown: If the answer is incorrect, award ONE mark for evidence of appropriate working, eg Listing of cost of apples: 75 90 150 180 225 270 An explanation that shows how it is possible to buy more apples but spend less money, eg  ‘Nika buys 2 bags of red apples, giving 20 apples for £1.80, and Hassan buys 3 bags of green apples, giving 18 apples for £2.25’. Up to 2m 1mBoth numbers must be correct for the award of the marks. Calculation must be performed for the award of ONE mark. Do not accept vague or arbitrary explanations, eg  ‘She got bigger bags than he did’;  ‘She bought a lot of small ones’. Ignore slight errors in arithmetic that do not contradict the explanation.

10 Test A questions 19–21 Question Requirement Mark Additional guidance 19 5 and 6 written in the boxes in either order as shown: 1m 20 –60 in first box. –140 in second box OR a number 80 less than the answer given in the first box provided both numbers are less than 0 Up to 2m Accept ‘minus 60’ Do not accept ‘60–’ Accept ‘minus 140’ Do not accept ‘140–’ If the answers given are ‘60–’ and ‘140–’ respectively, award ONE mark only. 21 Award TWO marks for boxes ticked and crossed as shown: If the answer is incorrect, award ONE mark for three out of four boxes correctly completed. Up to 2m Accept alternative unambiguous indications such as Yand N. Accept blank boxes as crosses.

11 Test A question 22 Question Requirement Mark Additional guidance 22 Award TWO marks for the correct answer of 42 If the answer is incorrect award ONE mark for evidence of appropriate working containing no more than one arithmetic error, eg  long division algorithm  short division algorithm  repeated addition / subtraction methods  factor / multiple methods, eg Up to 2m Calculation must be performed for the award of ONE mark. Short division methods must be supported by evidence of appropriate carrying figures to indicate use of a division algorithm. No mark is awarded for repeated addition / subtraction the wrong number of times.

12 Test A questions 23–24 Question Requirement Mark Additional guidance 23a 23b1m 1m If the answers for 23a and 23b are transposed, but otherwise correct, award ONE mark only, in the 23b box. 24 An appropriate explanation which recognises that: = and = OR = which is less than OR that is less than because 3 × is greater than 1 2 5 2 5 1 3 2 5 2 6 1 3 6 15 2 5 5 15 1 3 1m No mark is awarded for writing alone. Do not accept vague or arbitrary explanations, eg  ‘Because is bigger than ’;  ‘Because comes first on a number line’. 1 3 1 3 2 5 2 5 14 5

13 Test B questions 1–3 Question Requirement Mark Additional guidance 2a 2b1m 1m 3a 3b 7 15 1m 1m Accept ‘9 and 6’ or similar. 1a 1b 1c Diagram completed correctly as shown: 29 ×18 joined to the number line in the range 500 to 600 exclusive. 720 ÷45 joined to the number line in the range 0 to 100 exclusive. 759 – 484 joined to the number line in the range 200 to 300 exclusive. 1m 1m 1m Lines need not touch boxes or number line provided the intention is clear. Do not accept two or more lines emanating from the same left-hand box.

14 Test B questions 4–5 Question Requirement Mark Additional guidance 4 Triangles without a right angle drawn in any orientation on the grid, eg 1m Do not penalise lines drawn without a ruler, provided the intention is clear. Accept only triangles which have vertices at dots. 5 Award TWO marks for one line of symmetry drawn correctly on each diagram as shown: If the answer is incorrect, award ONE mark for lines of symmetry drawn correctly on any two diagrams. Up to 2m Accept slight inaccuracies in drawing provided intention is clear. Accept diagrams with more than one line drawn, provided all the lines are correct. The length of the line is unimportant provided the intention is clear.

15 Test B questions 6–11 Question Requirement Mark Additional guidance 6a 6b 74p OR £0.74 Award TWO marks for the correct answer of £4.38 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 2.96 ×3 = 8.88 8.88 – 4.50 1m Up to 2m Accept 74 OR 0.74 OR £0.74p OR 0 74 OR £.74 OR £.74p OR £0 74 OR .74 Do not accept £74p OR £74 OR 0.74p Accept for TWO marks £4.38p OR £4 38 Accept for ONE mark £438 OR £438p as evidence of an appropriate method. Answer need not be obtained for the award of the mark. 7 Arrow drawn between the marks for 425ml and 450ml exclusive. 1m 8a 8b 9 7 1m 1m Accept –7 9a 9b 4 12 1m 1m 10 1m 11a 11b £249.75 Award TWO marks for the correct answer of 82 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 1230 ÷15 OR 12.30 ÷0.15 1m Up to 2m Accept £249.75p OR £249 75 Do not accept £24975p OR £24975 Accept for ONE mark £82 OR 82p as evidence of an appropriate method. Do not accept 12.30 ÷15 as evidence of an appropriate method. Answer need not be obtained for the award of the mark. 32.45 253.117. 8

16 Test B questions 12–13 Question Requirement Mark Additional guidance 12 Award TWO marks for three letters in the correct regions of the sorting diagram, as shown: Award ONE mark for two letters in the correct regions of the sorting diagram. Up to 2mDo not accept letters that are written in more than one region. Accept alternative indications such as lines drawn from the shapes to the appropriate regions of the sorting diagram. 13a 13b Award TWO marks for the correct answer of 2 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg of 24 = 18 green = 24 – 18 – 4 1 5 3 4 Up to 2m 1m Answer need not be obtained for the award of the mark. Accept equivalent fractions. Do not accept ‘1 in 5’ OR ‘1 : 5’.

17 Test B questions 14–19 Question Requirement Mark Additional guidance 14a 14b £64.30 £4.50 1m 1m Accept £64.30p OR £64 30 Do not accept £6430 OR £6430p OR £64.3 Accept £4.50p OR £4 50 Do not accept £450 OR £450p OR £4.5 If the final ‘0’ is missing from both answers, ie answers given are £64.3 and £4.5 respectively, award ONE mark only in 14b. 15 12:02 1m Accept 1202 OR 12.02 OR 00:02 OR 0002 OR 00.02 Accept ‘two minutes past twelve’ or equivalent. Ignore am or pm. 16 520.608 1m 17a 17b Any value in the range 8.6 to 8.8 inclusive. Any value in the range 3.2 to 3.4 inclusive. 1m 1m 18 1m Accept unambiguous alternatives, eg the number crossed or underlined. 19 Diagram marked as shown: 1m Both triangles must be correctly marked. Accept slight inaccuracies in drawing, provided the intention is clear. Triangles need not be shaded.

18 Test B questions 20–22 Question Requirement Mark Additional guidance 20 Any pair of numbers which total 50, eg 30 and 20 1m Accept fractions and decimals. Accept zero in either box. Do not accept boxes left blank. 21 Award TWO marks for the correct answer of 45cm. If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 60 ÷4 ×3 Up to 2m Answer need not be obtained for the award of the mark. 22 Award TWO marks for the correct answer of 82 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg (4 ×10) + (7 ×6) OR (10 ×10) – (3 ×6) Up to 2m Answer need not be obtained for the award of the mark.

19 Mark scheme for the mental arithmetic 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 pages 21 and 22. In addition a ‘quick reference’ mark scheme is provided on page 20. This is presented in a similar format to the children’s answer sheet. General guidance The general guidance for the marking of the written tests also applies to the marking of the mental test. In addition, please apply the principles below. 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. Do not penalise children 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.

20 Time: 5 seconds Time: 10 seconds Time: 15 seconds Mental arithmetic 2002 quick reference mark scheme 6 £ 1.70 8 95 13 8.6 14 63 15 198 16 165 17 42 18 19 150 2 6058 3 56 5 5000 9 17.1 12 8 cm 10 7 Accept 22:15 or quarter past ten 10:15 20 Accept £3 or £3-00 or £3.00p £ 3.00 4 8 11 Practice question 1 10633 Accept £1-70 or £1.70p 1 41 401 4004 10 0 4 10 60 75 90 100 150 Words not acceptable

21 Mental arithmetic questions 1–15 Question Requirement Mark Additional guidance 1 106 1m 2 6058 1m Words not acceptable 3 56 1m 4 8 1m 5 5000 1m 7 10:15 1m Accept 22:15 OR quarter past ten. 8 95 1m 9 17.1 1m 10 1m Accept any other way of indicating the answer, eg crosses or ringed. Do not accept if more than one answer is indicated unless the child’s intention is clear. 11 1m 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. 12 8 1m 13 8.6 1m 14 63 1m 15 198 1m 6 £1.70 1m Accept any clear indication of the distinction between pounds and pence. Allow variants of £1.70 such as £1-70 OR £1 70 OR £1.70p Do not accept £170 OR £170p 1 41 401 4004 10 0 4 10

22 Mental arithmetic questions 16–20 Question Requirement Mark Additional guidance 16 165 1m 17 42 1m 18 1m 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. 19 150 1m 20 £3.00 1m Accept any clear indication of the distinction between pounds and pence. Allow any variants of £3.00 such as £3 OR £3-00 OR £3 00 OR £3.00p Do not accept £300 OR £300p OR £3p 60 75 90 100 150

23 Test C questions 1–3 Question Requirement Mark Additional guidance 1 Award TWO marks for the correct answer of If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg = = C = 15 – 5 – 6 15 6 15 2 5 5 15 1 3 4 15 Up to 2m Answer need not be obtained for the award of the mark. 2 Award TWO marks for the correct answer of 67 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 7 gaps = 77 1 gap = 11 Up to 2m Answer need not be obtained for the award of the mark. 3 Award TWO marks for the correct answers of 0.4 and 0.9 in either order. If only one answer is correct, in either box, award ONE mark. Up to 2m

24 Test C question 4 Question Requirement Mark Additional guidance 4 Award TWO marks for diagram completed as shown: If the diagram is incorrect, award ONE mark for: shape correctly rotated, and either not enlarged, or enlarged by the wrong scale factor; OR shape correctly enlarged from point B but not rotated; OR shape correctly enlarged and rotated but translated to another part of the grid. Up to 2m Accept slight inaccuracies in drawing provided the intention is clear. Do not penalise lines drawn without a ruler provided the intention is clear.

25 Test C questions 5–7 Question Requirement Mark Additional guidance 5a 5b Award TWO marks for the correct answer of 35 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 104 = 3 n – 1 105 = 3 n n = 105 ÷3 2 n+ 1 Up to 2m 1m Answer need not be obtained for the award of the mark. Accept equivalent expressions, eg n + n + 1 Accept the answer written in words, eg ‘twice the shape number add one’. 6a 6b Answer in the range 12:30pm to 1:00pm exclusive. Award TWO marks for the correct answer of 26 % OR 26.6 .% If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 40 ÷150 ×100 2 3 1m Up to 2m Accept answers with or without ‘pm’. Accept 26.6% OR 26.7% OR 26.6...% OR 27% Accept for ONE mark 26% Answer need not be obtained for the award of the mark. 7 Award TWO marks for table ticked as shown: If the answer is incorrect, award ONE mark for two out of three added ticks correctly placed. Up to 2m Accept alternative unambiguous indications eg, Yor N, or crosses in the table. Do not accept any row that has ticks in more than one box.

26 Test C question 8 Question Requirement Mark Additional guidance 8 Two more lines drawn which intersect at a fourth vertex located anywhere on the dotted line shown on the diagrams below, eg 1m Accept slight inaccuracies in drawing provided the intention is clear.

27 Test C questions 9–13 Question Requirement Mark Additional guidance 9 Award TWO marks for the correct answer of 2.25 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg algebraic manipulation to reach 18 = 8 t Up to 2m Answer need not be obtained for the award of the mark. 10 1m Accept alternative ways of indicating the correct answer, eg ticking the correct numbers. 11 Award TWO marks for the correct answer of 60% If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg ×80 75 100 Up to 2m Answer need not be obtained for the award of the mark. 12 Award TWO marks for the correct answer of 220 If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg 275 ÷5 ×4 Up to 2m Answer need not be obtained for the award of the mark. 13 Award TWO marks for the correct answer as shown: If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg A + B = 80 B + C = 70 A + 2B + C = 150 100 + B = 150 Up to 2m All three numbers must be correct for the award of the mark. Accept for ONE mark the correct three numbers but written in the incorrect boxes.

28 Test C questions 14–15 Question Requirement Mark Additional guidance 14a 14b OR =(Answer to 14a – 35º) 1m 1m If answers to and are transposed but otherwise correct, award ONE mark only in the 14b box. 15a 15b1m 1m Top box on left joined to 2w – 2 Lower box on left joined to –2 Do not accept two or more lines emanating from the same left-hand box.



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/02/858 (mark schemes pack) 01-8613/5 R RR R PANTONE 300 CVUBlack Plate ASSET REF 1 Asset Graphics: 127059/05 Client: COI Job No. 01-8613/5 Job Title: Maths KS2 MS COVER 01-8613/5 First Proof: 8.2.02 EARLY YEARS GCSE GNVQ GCE A LEVEL NVQ OTHER VOCATIONAL QUALIFICATIONS NATIONAL CURRICULUM 5–16