[PDF] 2006 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 Ma KEY STAGE 2 LEVELS 3–5 2006 2006

First published in 2006 © Qualifi cations and Curriculum Authority 2006 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 Qualifi cations and Curriculum Authority under the authority and superintendence of the Controller of Her Majesty’s Stationery Offi ce and Queen’s Printer of Acts of Parliament. The Qualifi cations and Curriculum Authority is an exempt charity under Schedule 2 of the Charities Act 1993. Qualifi cations and Curriculum Authority 83 Piccadilly London W1J 8QA www.qca.org.uk

1 Marking the mathematics tests As in 2005, 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 19 June 2006 (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 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, 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 specifi c 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 specifi ed in the mark scheme, markers will apply the following guidelines in all cases.

2 What if ... Marking procedure The pupil’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 pupil’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 pupil has responded in a non-standard way.Calculations, formulae and written responses do not have to be set out in any particular format. Pupils 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 pupil misreads the information given in the question and uses different information without altering the original intention or diffi culty 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. No answer is given in the expected place, but the correct answer is given elsewhere.Where a pupil has shown understanding of the question, the mark(s) will be given. In particular, where a word or number response is expected, a pupil 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 pupil has continued to give redundant extra working which does not contradict work already done the pupil 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.

3 What if ... Marking procedure The pupil’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 pupil 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 specifi cally states otherwise. The pupil has drawn lines which do not meet at the correct point.Markers will interpret the phrase ‘slight inaccuracies in drawing’ to mean ‘within or on a circle of radius 2mm with centre at the correct point’. within the circle acceptedon the circle acceptedoutside the circle not accepted Recording marks awarded on the test paper All questions, even those not attempted by the pupil, will be marked with a ‘1’ or ‘0’ entered in each marking space. A two-mark question which is correct will have ‘1’ entered in both marking spaces. A two-mark question which is incorrect, but which has suffi cient evidence of working or method as required by the mark scheme, will have ‘1’ entered in the fi rst marking space and ‘0’ in the second. Otherwise ‘0’ will be entered in both marking spaces. For the written tests, the total number of marks gained on each double page will be written in the space 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. 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 2006 key stage 2 mathematics tests and mark schemes were developed by the Mathematics Test Development Team at Edexcel.

4 Marking specifi c types of question – summary of additional guidance Responses involving money Question 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 £3:20Incorrect placement 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: 40p p 40p Any unambiguous indication of the correct amount, eg £0.40pIncorrect or ambiguous use of pounds or pence, eg 0.40p £40p Where no sign is given for example: £3.20, 40p £3.20 40p 320p £0.40 Any unambiguous indication of the correct amount, eg £3.20p £0.40p £3 20 pence £.40p £3 20 £.40 £3,20 40 £3-20 0.40 £3:20 3.20 320 3 pounds 20Incorrect or ambiguous use of pounds or pence, eg £320 £40 £320p £40p £3.2 0.4 3.20p

5 Responses involving time Question Accept Do not accept A time interval for example: 2 hours 30 minutes2 hours 30 minutes Any unambiguous, correct indication, eg 2 1 2 hours 2.5 hours 2h 30 2h 30min 150 minutes 150 Digital electronic time, ie 2:30Incorrect or ambiguous time interval, eg 2.30 2-30 2,30 2.3 2.3 hours 2.3h 2h 3 2.30 min A specifi c time for example: 8:40am, 17:208:40am 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 17:20pmIncorrect 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 Question Accept Do not accept Where units are given (eg kg, m, l) for example: 8.6kg kg 8.6kg Any unambiguous indication of the correct measurement, eg 8.60kg 8.6000kg 8kg 600gIncorrect or ambiguous use of units, eg 8600kg Note If a pupil 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 pupil 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 1–3 Question Requirement Mark Additional guidance 1Numbers written in correct order as shown: 109 190 901 910 1091 1m 2One line of symmetry correctly positioned on each diagram as shown: 1mAccept slight inaccuracies in drawing provided the intention is clear. The length of the line is unimportant provided the intention is clear. 3a 3bGraph completed as shown: 0 2 4 6 Number of birds 8 Blackbird Sparrow Robin Blue tit Other 1 4 1m 1mAccept bar for ‘blue tit’ in the range 2.5 to 3.5 exclusive. Accept bar for ‘other’ within 2mm of correct length. Accept equivalent fractions, eg 5 20 Do not accept 5

7 Test A questions 4–8 Question Requirement Mark Additional guidance 4a 4b4 1501m 1m 5Diagram completed as shown: 30 70 20 1m 6a 6b1 hour 20 minutes 3:251m 1mThe answer is a time interval (see page 5 for guidance). The answer is a specifi c time (see page 5 for guidance). 7a 7bBoxes ticked as shown: Boxes ticked as shown: 1m U1 1m U1 Accept alternative unambiguous indications such as Y or N. Accept alternative unambiguous indications such as Y or N. 8a 8b451 1101m 1m

8 Test A questions 9–13 Question Requirement Mark Additional guidance 9Award TWO marks for the correct answer of 5 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 5 × 25 = 125 12 × 10 = 120 125 – 120 = wrong answerUp to 2m Calculation must be performed for the award of ONE mark. 1017171m 11All numbers matched correctly as shown: 3 4 2 10 1 4 2 5 0.25 0.4 0.75 0.2 1m Do not award the mark if additional incorrect lines are drawn. Lines need not touch the numbers provided the intention is clear. 12a 12b4 MondayAND Thursday1m 1mDo not accept a list of days of the week. Accept unambiguous abbreviations or recognisable misspellings. Accept days written in either order. 13Award TWO marks for numbers written in the correct regions as shown: factors of 30 658 7 factors of 40 If the answer is incorrect, award ONE mark for any three numbers written in the correct regions.Up to 2mDo not accept numbers written in more than one region. Accept alternative indications such as lines drawn from the numbers to the appropriate regions of the diagram.

9 Test A questions 14–15 Question Requirement Mark Additional guidance 14a 14b 2000 1800 1945 computer 1810 tin can 1876 telephone Answer for tin can joined to the time line in the range 1805 to 1815 exclusive. Answer for computer joined to the time line in the range 1940 to 1950 exclusive.1m 1mLines need not touch the time line provided the intended accuracy is clear. 15a 15bTwo numbers circled as shown: 71 72 73 74 75 An explanation which recognises that 1003 is not a multiple of 3, eg: ‘Because 1003 is not divisible by 3’ ‘Because 1003 is not a multiple of 3’ ‘Because 1003 is not in the 3 times table’ ‘Because I divided 1003 by 3 and there was a remainder’ ‘Because 1003 ÷ 3 has a decimal answer’ ‘Because 1 + 0 + 0 + 3 = 4, and 4 is not a multiple of 3’ ‘Because 1003 has a digital sum of 4’ ‘Because 1002 is the nearest in the 3 times table’ ‘Because 1000 is not divisible by 3’ ‘Because 999 is divisible by 3’.1m 1m U1 Do not award the mark if additional incorrect numbers are circled. Accept alternative unambiguous indications, eg ticks, crosses. No mark is awarded for circling ‘No’ alone. Do not accept vague or arbitrary explanations, eg: ‘Because 1003 ends in 3’ ‘Because 1003 is in the third column’ ‘Because if you keep going in 3s you will go past it’. If ‘Yes’ is circled but a correct unambiguous explanation is given, then award the mark.

10 Test A questions 16–20 Question Requirement Mark Additional guidance 16Award TWO marks for three shapes drawn correctly on the diagram as shown: If the answer is incorrect, award ONE mark for: the ‘L’ shape and any one of the two circles drawn correctly OR both circles drawn correctly AND the ‘L’ shape drawn in the correct square but orientated incorrectly.Up to 2mAccept slight inaccuracies in drawing provided the intention is clear. Circles need not be shaded. 17a 17b6 An explanation which recognises that a total of 10 children read between 4 and 6 books, eg: ‘10 children altogether read between 4 and 6 books, and 7 + 1 makes 8, so that leaves 2 children’ ‘Because 7 add 1 is 8, and you need 2 more’ ‘Because 10 children read 4 to 6 books’ ‘8 and 2 more make 10 children altogether’ ‘1 + 7 = 8, 8 + 2 = 10’.1m 1m U1 Do not accept vague or arbitrary explanations, eg: ‘Because 7 and 1 make 8’ ‘Because there are 2 children left’. 18196.451m 19Award TWO marks for the correct answer of 50 If the answer is incorrect, award ONE mark for evidence of appropriate working, eg 15 ÷ 3 = 5 5 × 10 = wrong answerUp to 2m U1 Calculation must be performed for the award of ONE mark. 20a 20bAnswer in the range 1 10 to 3 20 inclusive. Answer in the range 40 to 50 inclusive.1m 1mRange includes 1 7,1 8,1 9 and 1 10 Accept decimals (0.1 to 0.15 inclusive) or percentages (10% – 15% inclusive).

11 Test A question 21 Markers will use a transparent overlay of this page to mark pupils’ answers to this question. 72° 7cm 10 cm Question Requirement Mark Additional guidance 21Award TWO marks for a triangle drawn with an angle in the range 70° to 74° inclusiveAND length of sloping line in the range 6.9 cm to 7.1 cm inclusive (ie upper vertex of triangle within inner box on diagram). If the answer is incorrect, award ONE mark for: a completed triangle drawn with an angle in the range 70° to 74° inclusive. OR a completed triangle drawn with an angle in the range 69° to 75° inclusive AND length of sloping line in the range 6.8 cm to 7.2 cm inclusive.Up to 2mAccept drawings where any side has been extended past a vertex. Accept drawings which do not use the given 10 cm base line, provided they have used a line with a length in the range 9.9 cm to 10.1 cm inclusive. Accept for ONE mark drawings not using the given 10 cm base line which have a base line outside the range 9.9 cm to 10.1 cm, provided they have an angle in the range 70° to 74° inclusiveAND a sloping line in the range 6.9 cm to 7.1 cm inclusive. Accept for ONE mark drawings of incomplete triangles, provided they have an angle in the range 70° to 74° inclusiveAND a sloping line in the range 6.9 cm to 7.1 cm inclusive.

12 Test A questions 22–23 Question Requirement Mark Additional guidance 22Award TWO marks for the correct answer of 53 If the answer is incorrect, award ONE mark for evidence of appropriate working which contains no more than ONE arithmetical error, eg: long division algorithm wrong answer 16 848 800 48 –48 0 short division algorithm wrong answer 16 8 4 8 4 repeated addition / subtraction methods, eg 848 –400 25 × 16 448 –400 25 × 16 48 –48 3 × 16 0 wrong answer repeated halving, eg 848 ÷ 2 = 424 424 ÷ 2 = 212 212 ÷ 2 = 106 106 ÷ 2 = wrong answer Up to 2m In all cases accept follow through of ONE error in working. Calculation must be performed for the award of ONE mark. Do not award any marks if the fi nal answer is missing. Variations on algorithms are acceptable, provided they represent a viable and complete method. Short division methods must be supported by evidence of appropriate carrying fi gures to indicate use of a division algorithm. No mark is awarded for repeated addition / subtraction the wrong number of times. No mark is awarded for repeated halving the wrong number of times. 23Award TWO marks for all three numbers, as shown: 94, 95, 96 If the answer is incorrect, award ONE mark for: two numbers correct and none incorrect OR three numbers correct and one incorrect OR 93, 94, 95, 96, 97Up to 2m U1 Accept numbers written in any order. All three numbers and no incorrect numbers must be given for the award of TWO marks.

13 Test B questions 1–6 Question Requirement Mark Additional guidance 1a 1b4 5991m 1m 2Award TWO marks for the four lines drawn as shown: greater than 100 less than 100 equal to 100 11 × 11 4 × 5 × 6 56 + 27 + 17 835 – 745 4000 ÷ 50 If the answer is incorrect, award ONE mark for three correct lines drawn AND not more than one incorrect line drawn.Up to 2mDo not award any marks if two or more incorrect lines are drawn. Lines need not touch the boxes provided the intention is clear. 3a 3b5 21m 1m 4 9 1 + 9 1 + 1 9 = 201 OR 9 9 + 9 1 + 1 1 = 2011m U1 Accept the three two-digit numbers written in any order. 51251m 6a 6b£10.51 Award TWO marks for the correct answer of £2.26 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 34.99 + 12.75 = 47.74 50 – 47.74 OR 50 – 12.75 – 34.991m Up to 2m Accept for ONE mark £226 OR £226p as evidence of appropriate method. Answer need not be obtained for the award of ONE mark.

14 Test B questions 7–12 Question Requirement Mark Additional guidance 7a 7b First column of table completed correctly. Second column of table completed correctly.1m 1mAccept alternative unambiguous indications such as Y and N. 8a 8b£14.40 201m 1mDo not accept £14.4 Do not accept £20 9(5, 2)1mCoordinates must be written in the correct order. Accept unambiguous answers written on the diagram. 10Numbers circled as shown: 30 40 50 60 70 1mAccept alternative unambiguous indications, eg numbers ticked, crossed or underlined. 11Answer in the range 65 to 75 inclusive.1m 12 1 5 9 13 1m

15 Test B questions 13–15 Question Requirement Mark Additional guidance 13a 13bAny odd numbered multiple of 10, ie 10 OR 30 OR 50 OR 70 OR 90 OR any number ending with any of the pairs of digits above. An explanation which recognises that all multiples of 20 are also multiples of 10, eg: ‘Because all the numbers in the 20 times table are also in the 10 times table’ ‘Because all multiples of 20 are multiples of 10’ ‘Because 20 is in the 10 times table’ ‘All multiples of 20 go in box A because 10 goes into them’ ‘20 is a multiple of both 20 and 10, and so is 40, 60, etc’ ‘Because if it’s not a multiple of 10, it can’t be a multiple of 20’ ‘Because if it is a multiple of 20, it has to be a multiple of 10’ ‘Because 10 is a factor of 20’.1m 1m U1 Do not accept vague or arbitrary explanations, eg: ‘Because 40 is a multiple of 10’ ‘Because they would be in box A instead’ ‘Because all the multiples of 10 are multiples of 20’ ‘Because 10 is a multiple of 20’. 14£11.251m 15Any rectangle with an area of 8 squares, eg OR 1mAccept slight inaccuracies in drawing provided the intention is clear.

16 Test B questions 16–19 Question Requirement Mark Additional guidance 16Award TWO marks for four faces correctly shaded as shown: If the answer is incorrect, award ONE mark for: only the correct four faces marked AND at least two shaded correctly OR four faces shaded correctly AND one shaded incorrectly OR three faces shaded correctly AND none shaded incorrectly.Up to 2m U1 The width of each shaded rectangle is irrelevant provided the intention is clear. 17Award TWO marks for the correct answer of 60 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 800 – 500 = 300 300 ÷ 5Up to 2m U1 Answer need not be obtained for the award of ONE mark. 18a 18bAnswer in the range 3:10pm to 3:20pm inclusive. Answer in the range 13 degrees to 14 degrees inclusive.1m 1mThe answer is a specifi c time (see page 5 for guidance). 19Award TWO marks for the correct answer of 30 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 45 ÷ 3 = 15 15 × 2Up to 2m Answer need not be obtained for the award of ONE mark.

17 Test B questions 20–25 Question Requirement Mark Additional guidance 20Award TWO marks for all three numbers in order as shown: 129 AND 7492 AND 51 If the answer is incorrect, award ONE mark for two out of three numbers correct.Up to 2mDo not accept 129.0 OR 7492.0 OR 51.0OR any other equivalent answers with zeroes after the decimal point. 2140%1m Do not accept equivalent fractions or decimals. 22a 22b400 1200 g OR 1.2 kg OR for fi nding the correct difference between 1.6 kg and the answer given for 22a.1m 1mAnswer must be in grams. Accept 1200 OR 1.2 OR 1kg 200 g 23Two numbers circled as shown: 29 39 49 59 691m Do not award the mark if additional incorrect numbers are circled. Accept alternative unambiguous indications, eg numbers ticked, crossed or underlined. 24Diagram completed as shown: B A 1mAccept slight inaccuracies in drawing (see page 3 for guidance). 25Award TWO marks for the correct answer of 14 If the answer is incorrect, award ONE mark for evidence of appropriate method, eg 17.5 × 4 = 70 70 ÷ 5Up to 2m U1 Accept for ONE mark 140 OR 1.4 as evidence of appropriate method. Answer need not be obtained for the award of ONE mark.

18 Mark scheme for the mental mathematics test Applying the mark scheme Please note that pupils 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 pupil’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 fi gures. 2. Where units are specifi ed, they are given on the answer sheet. Pupils 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 pupil’s intended answer. Accept also any other way of indicating the correct answer, eg underlining.

Practice question 3 6 Time: 5 seconds 1 200 2 45 p 5 9900 4 3.4 17 0.70.0770.707 0.77 7.007 Time: 15 seconds 16 60 18 32 19 £ 11.70 20 15 girls 15 0.009 10 5 11 10 1 2 Accept 10.5 or equivalent fractions 12 –3 °C Donot accept 3 – 13 48 cm 2 141 10 Accept 0.1 or 10% or equivalent fractions 7 450 Time: 10 seconds 6 710 8 35p Mental mathematics 2006 quick reference mark scheme 19 9 150 mm Donot accept 15 cm

Mental mathematics questions 1–20 Question Requirement Mark Additional guidance 12001m 245p1m 361m 43.41m 599001m 67101m 74501m 835p1m 9150 mm1m Do not accept 15 cm 1051m 11 10 1 2 1mAccept 10.5 OR equivalent fractions. 12–3° C1m Do not accept 3– 1348 cm 2 1m 14 1mAccept 0.1 OR 10% OR equivalent fractions. 150.0091m 16601m 17 0.7 0.077 0.707 0.77 7.0071mAccept any other way of indicating the answer, eg underlining. Do not accept if more than one answer is indicated unless the pupil’s intention is clear. 18321m 19£11.701m 2015 girls1m 20 1 10



EARLY YEARS NATIONAL CURRICULUM 5 –16 GCSE GNVQ GCE A LEVEL NVQ OTHER VOCATIONAL QUALIFICATIONS For more information, contact: QCA, 83 Piccadilly, London W1J 8QA For more copies, contact: QCA Orderline, PO Box 29, Norwich NR3 1GN Tel: 08700 60 60 15 Fax: 08700 60 60 17 Email: orderline@qca.org.uk Order ref:QCA/06/1900 (mark schemes pack)270003