[PDF] 2017 Key Stage 2 Year 6 - Mathematics Papers 1 2 3 Mark Schemes.pdf | Plain Text

Mathematics test mark schemes Paper 1: arithmetic Paper 2: reasoning Paper 3: reasoning 2017 national curriculum tests Key stage 2

Page 2 of 36 Contents 1. Introduction 3 2. Structure of the key stage 2 mathematics test 3 3. Content domain coverage 3 4. Explanation of the mark schemes 5 5. General marking guidance 5 5.1 Applying the mark schemes 5 5.2 General marking principles 6 6. Marking specific types of question: summary of additional guidance 13 6.1 Answers involving money 13 6.2 Answers involving time 14 6.3 Answers involving measures 15 7. Mark schemes for Paper 1: arithmetic 16 8. Mark schemes for Paper 2: reasoning 21 9. Mark schemes for Paper 3: reasoning 27 2017 key stage 2 mathematics test mark schemes

Page 3 of 36 1. Introduction The Standards and Testing Agency (STA) is responsible for the development and delivery of statutory tests and assessments. STA is an executive agency of the Department for Education. The 2017 test assesses the 2014 national curriculum. This test has been \ developed to meet the specification set out in the test framework for mathematics at key\ stage 2. The test frameworks are on the GOV.UK website at www.gov.uk/government/publications/key-stage-2- mathematics-test-framework. A new test and mark schemes will be produced each year. The key stage 2 tests will be marked by external markers. Scaled score conversion tables are not included in this document. Conversion tables will be produced as part of the standards maintenance process. Scaled score conversion tables for the 2017 tests will be published at www.gov.uk/guidance/scaled-scores-at-key-stage-2 in July 2017. The mark schemes are provided to show teachers and markers how the tests are marked. The pupil examples are based on answers gathered from the test trialling process. 2. Structure of the key stage 2 mathematics test The key stage 2 mathematics test materials comprise: • Paper 1: arithmetic (40 marks) • Paper 2: reasoning (35 marks) • Paper 3: reasoning (35 marks). 3. Content domain coverage The 2017 test meets the specification set out in the test framework. T\ able 1 sets out the areas of the content domain that are assessed in papers 1, 2 and 3. The references are taken from the test framework. A question assessing 4C7, for example, sets out to ‘multiply two-digit and three-digit numbers by a one-digit number using a formal written layout’ and is taken from the year 4 programme of study. 2017 key stage 2 mathematics test mark schemes

Page 4 of 36 Table 1: content domain coverage of the 2017 key stage 2 mathematics test\ Paper 1: arithmeticPaper 2: reasoningPaper 3: reasoning Qu. Content domain reference Qu. Content domain reference Qu. Content domain reference 1 4N2b 1a4S2 15C6b 2 4C2 1b4S2 23C8 3 4F4 25C6b 34C8 4 4C6b 34C6a 4a6N5/6S1 5 3C1 44C4/4S2 4b6N5/6S1 6 5F8 54N2b 53M9a/4F10b 7 4C2 65F8 65S1 8 3C7 74M4c 76P2 9 4C6a 85C4 86C5 10 4C7 94F2 95S1/4S2 11 4C2 105N4 104M5 12 4F4 11a6A2 116G5 13 3N2b 11b6A2 124C8 14 6C9 126G2b 136G2a/4G4 15 6F5a 135M9a 146R1/5M9a 16 5C6a 146R4 153G2 17 5C7b 155N3b 165C8b 18 6F9a 165G4b 176F11/6F3 19 5C6b 176P3 185C5c/5C5d 20 6C7b 186R2 194N6 21 4F8 196C8/5M9a 205M7b/5C7a 22 6C7a 206F11 21a6F4/6A3 23 5F4 215M9b/6R3 21b6F4/6A3 24 6C7a 226R3 226A1 25 5F8 236F4 236A4 26 6F4 246M8b/6R1 27 6F5b 28 6F5b 29 6R2 30 6F4 31 6R2 32 6F4 33 6F9b 34 6R2 35 5F5 36 6C7b 2017 key stage 2 mathematics test mark schemes

Page 5 of 36 4. Explanation of the mark schemes The marking information for each question is set out in the form of tabl\ es (sections 7, 8 and 9) . The purpose of the mark scheme is to define the acceptable answers for\ each question within the test. Answers other than those listed may be acceptable if they meet\ the marking criteria. The ‘Qu.’ column on the left-hand side of each table provides a quick reference to the question number and 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 an appropriate method • examples of some different types of correct answer. The ‘Mark’ column indicates the total number of marks available for each quest\ ion part. The ‘Additional guidance’ column indicates alternative acceptable answers and guidance, such as the range of acceptable answers, where necessary. This column may also provide details of specific types of answer which are unacceptable. For most questions, however, there will be unacceptable answers that are not listed. 5. General marking guidance 5.1 Applying the mark schemes To ensure consistency of marking, the most frequent procedural queries are listed in section 5.2 along with the action the marker will take. This is followed\ by further guidance on pages 13 to 15 relating to marking questions involving money, time and other measures. Unless otherwise specified in the mark scheme, markers will apply thes\ e guidelines in all cases. Recording marks awarded Marking will take place on screen with markers viewing scanned images of pupils’ responses. Marks will be entered into the marking system in accordance with the guidance for the on-screen marking software. For each question, markers will record the award 3, 2, 1 or 0 as appropriate, according to the mark scheme criteria. There will be provision in the software to record questions not attempted. The software will aggregate marks automatically. 2017 key stage 2 mathematics test mark schemes

Page 6 of 36 5.2 General marking principles Table 2: General marking principles for all papers 1. The pupil’s answer does not match closely any of the examples given in the mark scheme. Markers will use their judgement to decide whether the answer corresponds with details in the ‘Requirement’ column of the mark scheme. Reference will also be made to the ‘Additional guidance’ column. 2. The pupil has answered in a non-standard way.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 presenting an answer. 3. The corr ect answer or working has been crossed out or erased and not replaced. The mark(s) will not be awarded for crossed-out or erased answers or working. 4. Mor e than one answer is given. If all answers given are correct (or a range of answers is given, all of which are correct), the mark(s) will be awarded unless the mark scheme states otherwise. If both correct and incorrect answers are given, the mark(s) will not be awarded unless the mark scheme states otherwise. 5. No answer is given in the expected place, but the correct answer is given elsewhere.Where a pupil has unambiguously indicated the correct answer, the mark(s) will be awarded. In particular, where a word or number is expected, a pupil may meet the requirement by annotating a graph or labelling a diagram elsewhere in the question. 6. The pupil’ s answer is correct, but the wrong working is shown. A correct final answer will be awarded the mark(s). 7. The pupil has used alternative notation for a decimal point in a number.No alternative notation is accepted as representing a decimal point in a number, e.g. a comma. Refer to section 6 for guidance on marking specific types of question. 8. The pupil has used a symbol as a thousands separator. If the pupil has used a comma as a thousands separator (positioned either correctly or incorrectly) and the digits are in the correct order, then the mark(s) will be awarded. If any other symbol, e.g. decimal point or apostrophe, is used, the mark(s) will not be awarded. 2017 key stage 2 mathematics test mark schemes

Page 7 of 36 9. The answer in the answer box is wrong due to a transcription error.A transcription error occurs when a pupil miscopies their answer from the end of their working into the answer box. Where appropriate, detailed guidance will be given in the mark scheme. For questions with no guidance, marks will only be awarded for a transcription error if the wrong answer is due to: • transposed digits in a number (e.g. 243 is written as 324) OR • one digit changed in a number of 4 or more digits (e.g. 2,345 is written as 2,845). The mark(s) will not be awarded for any other transcription error including: • a decimal point positioned incorrectly (e.g. 12.34 is written as 1.234 or 1234) • a change by a power of 10 (e.g. 200 is written as 20 or 2,000) • a digit added or removed (e.g. 123,456 written as 1233,456 or 12,456) • a negative sign added or removed. 10. The pupil’ s answer is numerically or algebraically equivalent to the answer in the mark scheme. Answers should be given as single values in their simplest form unless the mark scheme states otherwise, e.g. for = 536 − 30, the answer 500 + 6 will not be awarded the mark. For integer answers, e.g. 20, the answer 20 1 will be awarded the mark; 80 4 will not be awarded the mark. For decimal answers that include recurring digit(s), there must be an unambiguous indication of the recurring digit(s). For example, for 1 6, 0.16 or 0.1 6 will be awarded the mark and for 1 7, 0.142857 or 0. 14285 7 will be awarded the mark. Where alternative responses are acceptable, this will be indicated in the ‘Additional guidance’ column. . . . 2017 key stage 2 mathematics test mark schemes

Page 8 of 36 Table 3: General marking principles for paper 1 only (arithmetic) 11. The answer in the answer box is wrong due to a misread of numbers given in the question.Misreads are not allowed in paper 1; the mark(s) will not be awarded. 12. The pupil has not recorded their working beneath the given long multiplication or long division. If a pupil carries out their working somewhere on the page other than beneath the given question as expected, then the pupil must start by rewriting the original question in order for it to be considered as a formal method. Please note that the operation sign does not need to be given for long multiplication, provided the pupil’s working shows the intention to multiply. 13. The pupil’ s answer to the long division question includes a remainder. If a pupil reaches an integer answer using a formal method with no more than one arithmetic error, for example 25, then the mark(s) will be awarded for 25 r0 or 25.0, but the mark(s) will not be awarded for 250 For answers with remainders, the remainder must be expressed correctly. If a pupil shows a remainder that is the same size as the divisor or larger, for example, a remainder of 28 or 29 when dividing by 28, the mark(s) will not be awarded because the method is incomplete. If a pupil reaches a non-integer answer using a formal method with no more than one arithmetic error, for example when dividing by 28, the pupil reaches the answer 6 r14, then the mark(s) will be awarded for 6 14 28 or 6.5, but the mark(s) will not be awarded for 6 r 14 28 or 6.14 or 614 14. The pupil’ s long division method involves subtracting chunks of different sizes. If a pupil’s formal method involves subtracting chunks, it is not necessary to show a separate addition of the chunks. If the answer is not the correct total for their chunks, then that is treated as one arithmetic error. It should be noted that this method will only be accepted if all chunks are of different sizes. 2017 key stage 2 mathematics test mark schemes

Page 9 of 36 Table 4: General marking principles for papers 2 and 3 only (reasoning) 15. Mor e than one method is given.If a pupil gives more than one method, then the intended method is taken as the one which leads to the answer in the answer box or an identified answer elsewhere. If no answer is given, then all methods must be appropriate for the method mark(s) to be awarded. 16. Ther e appears to be a misread of numbers or information given in the question that affects the pupil’s working and/or explanation.This occurs when a pupil misreads a number given in the question and consistently uses a different number that does not alter the original intention or difficulty of the question. For example, if 243 is misread as 248, both numbers may be regarded as comparable in difficulty. However, if 243 is misread as 245 or 240, the misread number may be regarded as making the question easier. The misread of a number may affect the award of marks. Where appropriate, detailed guidance will be given in the mark scheme. If no guidance is given, markers will examine each case to decide whether the mark(s) will be awarded. The mark(s) will not be awarded if: • it is a ONE-mark question • there is more than one misread number in a question • the mathematics is simplified • it is an explanation question • it is a misread of other information (not numbers) • the misread number is the same as any other number in the question. For TWO-mark questions that have a method mark, one mark will be awarded if an appropriate method is correctly followed through with the misread number to give the correct follow-through answer, provided the mathematics has not been simplified. For THREE-mark questions, refer to the additional guidance. 17. A misr ead or an arithmetic error results in an answer with multiple decimal places. In some instances, a misread or an arithmetic error in a method leads to an answer with multiple decimal places. In such cases, the method mark(s) will be awarded for an answer that is correctly truncated or rounded provided the method is appropriate. For example, 1.2345 is truncated to 1.234 2017 key stage 2 mathematics test mark schemes

Page 10 of 36 18. The pupil has r eversed values within a calculation involving subtraction or division. When values within the calculation are reversed, the mark(s) will only be awarded when the answer corresponds to the correct calculation. For example, if the correct calculation is 12 � 4, the method mark(s) may be awarded for 4 � 12 = 3, but not for an answer other than 3 Reversed values within a calculation are not acceptable in ‘explain’ questions. 19. The pupil omits an operation sign within their working. If the correct sign of +, − , �, or � for an arithmetic operation is missing, then the mark(s) will only be awarded if the working shown by the pupil is clear enough to indicate that the required operation has been performed. This applies even if the results of the required operation are incorrect. For example, where the following is seen in working: 456 123 • if the answer is larger than the greater of the given values, e.g. 679, then addition is implied • if the answer is less than the first given value, e.g. 323, then subtraction is implied. 20. The pupil has used ‘an appropriate method’. For some questions, the mark scheme allows the award of the method mark(s) for ‘evidence of an appropriate method’, even if the answer is missing or incorrect. Refer to the ‘Additional guidance’ column where appropriate. For the award of the method mark(s) for an appropriate method, there must be evidence of all the steps of the appropriate method (i.e. any method that would lead to the correct answer if there were no arithmetic errors and no additional steps). This means that, for every step, either: • the appropriate calculation to be carried out must be shown OR • if the calculation has not been written down, the correct answer or correct follow-through answer must be shown. 2017 key stage 2 mathematics test mark schemes

Page 11 of 36 21. The pupil has used a trial and improvement method.‘Trial and improvement’ is regarded as an acceptable method, unless the mark scheme states otherwise. For a ‘trial and improvement’ method to be awarded the method mark(s): • there must be at least 3 trials, carried out correctly, which each reduce the range in which the answer is known to lie • there can be additional trials, which are correctly or incorrectly carried out, and which may not reduce the range in which the answer is known to lie • a final answer is not needed, unless the mark scheme states otherwise. 22. The answer in the answer box is wrong due to the pupil continuing to give extra working.Extra working occurs when a pupil writes the correct answer in their working, and then continues to process the information further. If the extra working does not contradict the pupil's appropriate method, the method mark(s) will be awarded. If the extra working contradicts the pupil's appropriate method, the method mark(s) will not be awarded. 23. The pupil miscopies a value from one part of their method into the next part. There will be instances when a pupil reaches a value in their working, then restarts from a different value. The mark(s) will not be awarded if: • it is a ONE-mark question • there is more than one miscopy in the working • the mathematics is simplified as a consequence of the miscopy • the miscopy does not follow transcription error rules (see point 9). The method mark(s) will only be awarded if an appropriate method is correctly shown using the miscopied number (which must follow transcription error rules). 2017 key stage 2 mathematics test mark schemes

Page 12 of 36 24. The corr ect answer is embedded in the working. An embedded answer occurs when a pupil shows the correct answer within their working but then selects the wrong answer from their working as their final answer or leaves the answer box blank. For example, if a pupil shows 2.5 { 6 = 3 { 5 in the last line of their working and writes 5 in the answer box, whereas the correct answer is 3, then this will affect the award of marks. Where appropriate, detailed guidance will be given in the mark scheme. If no guidance is given, markers will examine each case to decide whether the mark(s) will be awarded. For ONE-mark questions, the mark will not be awarded. For TWO-mark questions that have a method mark, one mark will be awarded, provided the pupil does not give redundant extra working that contradicts work already done or which adds to their appropriate method. For THREE-mark questions, refer to the additional guidance. 25. The phrase ‘sight of ’ is used in the mark scheme. For some questions, the mark scheme allows the mark(s) to be awarded for sight of a particular number or numbers within a method. Such numbers are the correct answers to partial steps within a method. The mark(s) will be awarded if the given value is written anywhere associated with that question. 26. The pupil’ s answer correctly follows through from earlier incorrect work. ‘Follow-through’ marks for an answer will only be awarded when specifically stated in the mark scheme. 27. 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 2 mm with its centre at the correct point’. within the circle - accepted on the circle - accepted outside the circ le - not accepted 2017 key stage 2 mathematics test mark schemes

Page 13 of 36 6. Marking specific types of question: summary of additional guidance 6.1 Answers involving money Accept Do not accept Where the £ sign is given, e.g. �3.20, �7 �3.20 �7 �7.00 Any unambiguous indication of the correct amount, e.g. �3.20p �3 20 pence �3 20 �3-20 �3:20 �3;20 Incorrect placement of pounds or pence, e.g. �320 �320p Incorrect placement of decimal point or incorrect use or omission of 0 or use of comma as a decimal point, e.g. �3.2 �3 200 �32 0 �3-2-0 �3,20 Where the p sign is given, e.g. 40p p 40p Any unambiguous indication of the correct amount, e.g. �0.40p 0 40p �0-40p 0:40p �0;40p Incorrect or ambiguous use of pounds or pence or use of comma as a decimal point, e.g. 0.40p �40p �0,40p £ 2017 key stage 2 mathematics test mark schemes

Page 14 of 36 AcceptDo not accept Where a unit is not given, e.g. �3.20, 40p �3.20 40p 320p �0.40 Any unambiguous indication of the correct amount, e.g. �3.20p �0.40 pence �3 20 pence �0 40p �3 20 �0-40 �3-20 �0:40 �3:20 �0;40 �3;20 �.40 3.20 0.40 320 40 3 pounds 20 Incorrect or ambiguous use of pounds or pence or use of comma as a decimal point, e.g. �320 �40 �320p �40p �3.2 0.4 3.20p 0.40p �3,20 0,40 �0,40p 6.2 Answers involving time Accept Do not accept A time interval, e.g. 2 hours 30 minutes 2 hours 30 minutes Any unambiguous, correct indication, e.g. Incorrect or ambiguous time interval or use of comma as a decimal point, e.g. (0)2 h 30 (0)2 h 30 min (0)2 30 (0)2-30150 minutes 150 2.5 hours 2 1 2 hours2.30 2.3 2.3 hours 2.3 h 2 h 3230 2.30 min 2,5 hours 2,30 Digital electronic time, e.g. (0)2:30 (0)2;30 2017 key stage 2 mathematics test mark schemes

Page 15 of 36 AcceptDo not accept A specific time, e.g. 8:40 am, 17:20 (0)8:40 am (0)8:40 twenty to nine Any unambiguous, correct indication, e.g. (0)8.40 (0)8;40 0840 (0)8 40 (0)8-40 Unambiguous change to 12 or 24-hour clock, e.g. 17:20 as 5:20 pm or 17:20 pm Incorrect time, e.g. 8.4 am 8.40 pm Incorrect placement of separators, spaces, etc. or incorrect use or omission of 0 or use of a comma as a decimal point, e.g. 840 8:4:0 8.4 084 8,40 6.3 Answers involving measures Accept Do not accept Where units are given, e.g. 8.6 kg kg m l 8.6 kg Any unambiguous indication of the correct measurement, e.g. 8.60 kg 8.6000 kg 8 kg 600 g Incorrect or ambiguous use of units or use of comma as a decimal point, e.g. 8600 kg 8 kg 600 8,60 kg 8,6000 kg If a pupil gives an answer with a unit different to the unit in the answer box, then their answer must be equivalent to the correct answer provided, unless otherwise indicated in the mark scheme. If a pupil leaves the answer box empty but writes the answer elsewhere on the page without any units, then that answer is assumed to have the units given in the answer box an\ d the conditions listed above. 2017 key stage 2 mathematics test mark schemes

Page 16 of 36 7. Mark schemes for Paper 1: arithmetic Qu.Requirement MarkAdditional guidance 1 1,040 1m 2 2,525 1m 3 1 1 6 OR 7 6 1m Accept equivalent mixed numbers, fractions or an exact decimal equivalent, e.g. 1.16 (accept any unambiguous indication of the recurring digit). Do not accept rounded or truncated decimals. 4 505 1m 5 285 1m 6 5.714 1m 7 5,100 1m 8 264 1m 9 8 1m 10 668 1m 11 4,088 1m 12 6 25 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 24 100 or 0.24 13 1,159 1m 14 56 1m 15 2 5 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 12 30 or 0.4 16 1,200 1m 17 83 1m 18 0.004 1m 19 2,345,000 1m 2017 key stage 2 mathematics test mark schemes

Page 17 of 36 Qu.Requirement MarkAdditional guidance 20 Award TWO marks for the correct answer of 42 If the answer is incorrect, award ONE mark for a formal method of division with no more than ONE arithmetic error, i.e. • long division algorithm, e.g. 42 r2 17 714  680 (40 × 17) 36 (error) − 34 (2 � 17) 2 Up to 2m Working must be carried through to reach a final answer for the award of ONE mark. OR 43 (error) 17 714 − 680 (40 � 17) 34 − 34 (2 � 17) 0 • short division algorithm, e.g. 4 1 r7 17 71 24 (error in carrying digit) Short division methods must be supported by evidence of appropriate carrying figures to indicate the use of a division algorithm, and be a complete method. The carrying figure must be less than the divisor. 21 5.55 1m 2017 key stage 2 mathematics test mark schemes

Page 18 of 36 Qu.Requirement MarkAdditional guidance 22 Award TWO marks for the correct answer of 109,963 If the answer is incorrect, award ONE mark for a formal method of long multiplication with no more than ONE arithmetic error, e.g. • 4781 � 23 14343 95620 209963 (error) OR • 4781 � 23 14343 95630 (error) 109973 Up to 2m Working must be carried through to reach a final answer for the award of ONE mark. Do not award any marks if the error is in the place value, e.g. the omission of the zero when multiplying by tens: 4781 × 23 14343 9562 (place value error) 23905 23 3 8 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 0.375 24 Award TWO marks for the correct answer of 19,228 If the answer is incorrect, award ONE mark for a formal method of long multiplication with no more than ONE arithmetic error, e.g. • 418 � 46 2508 16720 18228 (error) OR • 418 � 46 2508 16620 (error) 19128 Up to 2m Working must be carried through to reach a final answer for the award of ONE mark. Do not award any marks if the error is in the place value, e.g. the omission of the zero when multiplying by tens: • 418 � 46 2508 1672 (place value error) 4180 25 23.129 1m 26 11 20 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 0.55 2017 key stage 2 mathematics test mark schemes

Page 19 of 36 Qu.Requirement MarkAdditional guidance 27 1 5 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 4 20 or 0.2 28 5 16 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 0.3125 29 207 1mDo not accept 207% 30 3 1 6 OR 19 6 1m Accept equivalent mixed numbers, fractions or an exact decimal equivalent, e.g. 3.16 (accept any unambiguous indication of the recurring digit). Do not accept rounded or truncated decimals. Do not accept 2 7 6 31 35 1mDo not accept 35% 32 5 24 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 10 48 or 0.2083 (accept any unambiguous indication of the recurring digit). Do not accept rounded or truncated decimals. 33 180 1m 34 150 1mDo not accept 150% 35 85 1 2 1m Accept equivalent fractions or an exact decimal equivalent e.g. 171 2 or 85.5 2017 key stage 2 mathematics test mark schemes

Page 20 of 36 Qu.Requirement MarkAdditional guidance 36 Award TWO marks for the correct answer of 38 If the answer is incorrect, award ONE mark for a formal method of division with no more than ONE arithmetic error, i.e. • long division algorithm, e.g. 38 r2 59 2242  1770 (30 × 59) 474 (error) − 472 (8 � 59) 2 OR 35 (error) 59 2242 − 1770 (30 � 59) 472 − 472 (8 � 59) 0 Up to 2m Working must be carried through to reach a final answer for the award of ONE mark. • short division algorithm, e.g. 3 7 r48 (error) 59 224472 Short division methods must be supported by evidence of appropriate carrying figures to indicate the use of a division algorithm, and be a complete method. The carrying figure must be less than the divisor. 2017 key stage 2 mathematics test mark schemes

Page 21 of 36 8. Mark schemes for Paper 2: reasoning Qu.Requirement MarkAdditional guidance 1a 200 1m 1b 50 1m 2 The correct number circled as shown: 9,700 907 9,007 970 9,070 1mAccept alternative unambiguous positive indications, e.g. number ticked. 3 Three boxes completed correctly as shown: 5463 7 8 6 9 × 4856 1m 4 Award TWO marks for the correct answer of 1,609 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 5,895 + 1,344 = 7,239 8,848 – 7,239 Up to 2m Answer need not be obtained for the award of ONE mark. 5 Award TWO marks for three boxes completed correctly as shown: Number 1,000 more 3,500 4,500 85 1,085 8,099 9,099 14,250 15,250 If the answer is incorrect, award ONE mark for two boxes completed correctly. Up to 2m 6 Numbers in order as shown: 0.328 0.961.253 1.91m 2017 key stage 2 mathematics test mark schemes

Page 22 of 36 Qu.Requirement MarkAdditional guidance 7 Award TWO marks for three boxes completed correctly as shown: 60 months = 5years 72 hours = 3days 84 days = 12weeks If the answer is incorrect, award ONE mark for two boxes completed correctly. Up to 2m 8 Award TWO marks for the correct answer of 1,048 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 1,793 + 8,728 = 10,521 10,521 – 9,473 OR • 9,473 – 8,728 = 745 1,793 – 745 Up to 2m Answer need not be obtained for the award of ONE mark. 9 Both shapes ticked as shown: ✓ ✓ 1mAccept alternative unambiguous positive indications, e.g. shapes circled. 2017 key stage 2 mathematics test mark schemes

Page 23 of 36 Qu.Requirement MarkAdditional guidance 10 Award TWO marks for three boxes completed correctly as shown: to the nearest 10 84,520 to the nearest 100 84,500 to the nearest 1,000 85,000 If the answer is incorrect, award ONE mark for two boxes completed correctly. Up to 2m 11a 140 1mThe answer is a time interval (see page 14 for guidance). 11b 2 1m 12 Award TWO marks for both pyramids ticked as shown: Cube Square-based pyramid Triangular prism Triangular-based pyramid ✓✓ If the answer is incorrect, award ONE mark for: • the two pyramids and not more than one incorrect shape ticked OR • only one correct shape ticked and no incorrect shape ticked. Up to 2m Accept alternative unambiguous positive indications, e.g. Y. 2017 key stage 2 mathematics test mark schemes

Page 24 of 36 Qu.Requirement MarkAdditional guidance 13 Award TWO marks for the correct answer of �1.39 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 12 � 99p = �11.88 �11.88 – �10.49 Up to 2m Accept for ONE mark an answer of �139 OR �139p as evidence of an appropriate method. Answer need not be obtained for the award of ONE mark. 14 18 1mAccept 18:12 OR 12:18 15 2006 1mDo not accept ‘two thousand and six’ in words. 16 540 1m 17 Quadrilateral completed as shown: y x 0 –1 –2 –3 –4 –5 –6 1 2 3 4 5 6 6 5 4 3 2 1 –1 –2 –3 –4 –5 –6 1m Accept slight inaccuracies in drawing (see page 12 for guidance). 18 75 1m 19 Award TWO marks for the correct answer of �1.68 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 20 – 14.96 = 5.04 5.04 � 3 Up to 2m Accept for ONE mark an answer of �168 OR �168p as evidence of an appropriate method. Answer need not be obtained for the award of ONE mark. 2017 key stage 2 mathematics test mark schemes

Page 25 of 36 Qu.Requirement MarkAdditional guidance 20 An explanation showing that 0.25 is less than 2 5 , e.g. • 2 5 is 0.4 > 0.25 • 0.25 is 5 20 < 8 20 • 0.25 is 25% and 2 5 is 40% and 25% is smaller than 40% • 0.25 is a quarter. Y ou need 8 quarters to make 2, but only 5 lots of 2 5 to make 2 • 2 5 = 0.4 • 1 4 is 1 4 smaller than a half, but 2 5 is only 1 10 smaller, so 1 4 is smaller than 2 5 1m Do not accept vague, incomplete or incorrect explanations, e.g. • Because 1 4 is bigger than 2 5 • Because 1 4 comes rst on a number line • Because 0.25 is 1 4 Accept 2.5 10 as an equivalent to 1 4 in an explanation when comparing to 4 10 21 Award TWO marks for the correct answer of 12.5 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 250 � 20 OR • 20 km is 1cm 100 km is 5 cm 50 km is 2.5 cm 5 cm + 5 cm + 2.5 cm Up to 2m Answer need not be obtained for the award of ONE mark. Do not accept incorrect proportions in any step without evidence of the calculation performed. 22 1:4 1mAccept other equivalent ratios, e.g. 2:8 or 0.5:2 Do not accept reversed ratios, e.g. 4:1 or 8:2 2017 key stage 2 mathematics test mark schemes

Page 26 of 36 Qu.Requirement MarkAdditional guidance 23 Award TWO marks for the correct answer of 7 12 Up to 2m Accept equivalent fractions or an exact decimal equivalent, e.g. 0.583 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 1 4 + 1 6 = 3 12 + 2 12 = 5 12 1 – 5 12 OR • 1 4 + 1 6 + 1 6 OR • 1 – 1 4 – 1 6 OR • 1 12 3 12 + 4 12 OR • 60 90 90 + 60 = 150 1 – 150 360 Accept for ONE mark an answer between 0.58 and 0.59 inclusive. Answer need not be obtained for the award of ONE mark. 2017 key stage 2 mathematics test mark schemes

Page 27 of 36 9. Mark schemes for Paper 3: reasoning Qu.Requirement MarkAdditional guidance 1 10 1m 2 5 1m 3 95 � 6 OR 96 � 5 1m 4a 7 1mDo not accept –7 or 7– 4b –2 1mDo not accept 2– 5 � 302.27 1m 6 The correct time circled as shown: Leaves London Arrives Paris 12:01 15:22 12:25 15:56 13:31 16:53 14:01 17:26 14:31 17:53 15:31 18:53 16:01 19:20 1m Accept alternative unambiguous positive indications, e.g. 14:01 ticked or underlined. Accept 17:26 circled in addition to 14:01, provided no other time is circled. Do not accept only the arrival time 17:26 circled. 7 Triangle with vertices at (2,1) AND (2,4) AND (5,1) drawn on the grid as shown: y x 6 5 4 3 2 1 0 _ 1 _ 2 _ 3 _ 4 _ 5 _ 6 _5 _ 6 _ 4 _ 3 _ 2 _ 1 1 2 3 4 5 6 0 1m Accept slight inaccuracies in drawing (see page 12 for guidance). 2017 key stage 2 mathematics test mark schemes

Page 28 of 36 Qu.Requirement MarkAdditional guidance 8 Award TWO marks for any three of the following numbers written in any order: • 2 • 6 • 10 • 30 If the answer is incorrect, award ONE mark for two numbers correct. Up to 2m 9 5 1mDo not accept 300 (minutes). 10 68 (ml) OR 0.068 (l) 1m Do not accept incorrect units, e.g. 68 l OR 0.068 ml. 1132 1m 12 An explanation that shows Adam has four times as many balloons as Chen, e.g. • 24 � 6 is 4 times as many as 12 � 3 • 144 is four times 36 • 144 � 4 = 36 • 144 � 36 = 4 • 36 � 4 = 144 • Adam buys twice as many bags of twice as many balloons, so it’s doubled twice • 24 is double 12 and 6 is double 3, so it's doubled twice • Chen buys half the amount of bags and each bag has half the number of balloons, so he has 1 4 of the amount. 1m Do not accept vague or incomplete explanations, e.g. • Adam buys more bags and there are more balloons in each bag • Adam buys twice as many bags of twice as many balloons • 24 is double 12 and 6 is double 3. 2017 key stage 2 mathematics test mark schemes

Page 29 of 36 Qu.Requirement MarkAdditional guidance 13 The correct shape circled as shown: 1m Accept alternative unambiguous positive indications, e.g. shape ticked. 14 Award TWO marks for the correct answer of �0.90 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • �1.35 � 2 = � 2 .70 � 2.70 � 3 Up to 2m Accept for ONE mark an answer of �90p OR �0.9 as evidence of an appropriate method. Answer need not be obtained for the award of ONE mark. 15 The correct letter circled as shown: A C EL Z 1m Accept alternative unambiguous positive indications, e.g. letter ticked. 16 Award TWO marks for the correct answer of 750 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 450 � 2 = 900 2,400 – 900 = 1,500 1,500 � 2 Up to 2m Answer need not be obtained for the award of ONE mark. 2017 key stage 2 mathematics test mark schemes

Page 30 of 36 Qu.Requirement MarkAdditional guidance 17 Award TWO marks for all four rows completed correctly as shown: 1 21 1. 2 1 411. 3 5 100 1 1. 4 3 511. 5 If the answer is incorrect, award ONE mark for three rows completed correctly. Up to 2m Accept alternative unambiguous positive indications of the correct numbers, e.g numbers ticked. 18 Both numbers correct as shown: 9 +13 =22 square number prime number 1m Numbers must be in the correct order. Do not accept: 32 +13 =22 square number prime number 19 Award TWO marks for 12 AND 13 If the answer is incorrect, award ONE mark for: • only one correct number and no incorrect number OR • 12 AND 13 AND not more than one incorrect number. Up to 2m Accept for ONE mark an answer of 48 AND 52 AND no more than one incorrect number. 2017 key stage 2 mathematics test mark schemes

Page 31 of 36 Qu.Requirement MarkAdditional guidance 20 Award THREE marks for the correct answer of 14 If the answer is incorrect, award TWO marks for: • sight of 414 as evidence of 23 � 18 completed correctly OR • evidence of an appropriate method with no more than one arithmetic error, e.g. 20 � 20 = 400 23 × 18 230 184 314 (error) 400 – 314 = 86 Award ONE mark for evidence of an appropriate method. Up to 3m Answer need not be obtained for the award of ONE mark. A misread of a number may affect the award of marks. No marks are awarded if there is more than one misread or if the mathematics is simplified. TWO marks will be awarded for an appropriate method using the misread number followed through correctly to a final answer. ONE mark will be awarded for evidence of an appropriate method using the misread number followed through correctly with no more than one arithmetic error. 2017 key stage 2 mathematics test mark schemes

Page 32 of 36 Qu.Requirement MarkAdditional guidance 21a written in the first box 1mAccept equivalent fractions or an exact decimal equivalent, e.g. 0.375 21b 2 7 8 OR written in the last box 1m Accept equivalent fractions or an exact decimal equivalent, e.g. 2.875 22 Award TWO marks for the correct answer of 7 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 18 + 9 + 2 widths = 34 + 1 width 27 + 2 widths = 34 + 1 width 27 + 1 width = 34 34 – 27 OR • 34 – (18 + 9) Up to 2m Answer need not be obtained for the award of ONE mark. Award ONE mark for a method which uses algebraic representation correctly, e.g. • 34 + w = 18 + w + 9 + w 34 + w = 27 + w + w 23 Both numbers correct as shown: b = 10 �a – 1 1m 24 Award TWO marks for the correct answer of 9 If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g. • 6 � 6 � 6 = 216 216 � 6 = 36 36 � 4 OR • 216 � 24 Up to 2m Answer need not be obtained for the award of ONE mark. 3 8 23 8 2017 key stage 2 mathematics test mark schemes

Page 33 of 36 2017 key stage 2 mathematics test mark schemes [BLANK PAGE] This page is intentionally blank.

Page 34 of 36 2017 key stage 2 mathematics test mark schemes[BLANK PAGE] This page is intentionally blank.

Page 35 of 36 2017 key stage 2 mathematics test mark schemes [BLANK PAGE] This page is intentionally blank.

2017 key stage 2 mathematics test mark schemes Paper 1: arithmetic, Paper 2: reasoning and Paper 3: reasoning Print PDF version product code: STA/17/7739/p ISBN: 978-1-78644-278-9 Electronic PDF version product code: STA/17/7739/e ISBN: 978-1-78644-298-7 For more copies Additional printed copies of this booklet are not available. It can be downloaded from www.gov.uk/government/publications. � Crown copyright and Crown information 2017 Re-use of Crown copyright and Crown information in test materials Subject to the exceptions listed below, the test materials on this website are Crown copyright or Crown information and you may re-use them (not including logos) free of charge in any format or medium in accordance with the terms of the Open Government Licence v3.0 which can be found on the National Archives website and accessed via the following link: www.nationalarchives.gov.uk/doc/open-government-licence. When you use this information under the Open Government Licence v3.0, you should include the following attribution: ‘Contains public sector information licensed under the Open Government Licence v3.0’ and where possible provide a link to the licence. Exceptions – third-party copyright content in test materials You must obtain permission from the relevant copyright owners, as listed in the ‘2017 key stage 2 tests copyright report’, for re-use of any third-party copyright content which we have identified in the test materia\ ls, as listed below. Alternatively you should remove the unlicensed third-party copyright content and/or replace it with appropriately licensed material. Third-party content These materials contain no third-party copyright content. If you have any queries regarding these test materials contact the national curriculum assessments he\ lpline on 0300 303 3013 or email assessments@education.gov.uk.