[PDF] 2012 Key Stage 2 Year 6 - Mathematics Test Level 6 Mark Schemes.pdf | Plain Text

0 1 2 Ma KEY STAGE 2 LEVEL 6 Mathematics tests Mark schemes Paper 1 and Paper 2 National Curriculum assessments

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2012 KS2 Level 6 mathematics tests mark schemes 3 Marking the Level 6 mathematics tests The Standards and Testing Agency (STA) is responsible for the development and delivery of statutory tests and assessments in 2012. The STA is an executive agency of the Department for Education (DfE). The test papers will be marked by external markers employed by the external marking agency under contract to the STA. This booklet contains the mark schemes for the level 6 mathematics Paper 1 and Paper 2. Level threshold table will be available at www.education.gov.uk/ks2 from 10 July 2012. 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 10 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 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 specific types of response which are unacceptable. Other guidance, such as the range of acceptable answers, is provided as necessary. Applying the mark schemes In order to ensure consistency of marking, the most frequent procedural queries are listed on pages 4 and 5 along with the action the marker will take. This is followed by further guidance on pages 6 and 7 relating to the marking of questions that involve money, time and other measures. Specific guidance on marking responses involving coordinates, probability and algebra is given on pages 8 and 9. Unless otherwise specified in the mark scheme, markers will apply the following guidelines in all cases.

2012 KS2 Level 6 mathematics tests mark schemes What if… Marking procedure The pupil’s response is numerically equivalent to the answer in the mark scheme. Markers will award the mark unless the mark scheme states otherwise. 4

2012 KS2 Level 6 mathematics tests mark schemes What if… Marking procedure 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 specifically 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 accepted on the circle accepted outside the circle not accepted Recording marks awarded Marking will take place on-screen with markers viewing scanned images of pupil scripts. Marks should be input on screen in accordance with the guidance given on the use of the on-screen marking software. For multiple marked questions markers will record the award of 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 (NR: no response). The software will aggregate mark totals automatically. Further details on recording of marks and the use of the online system will be given at marker training. 5

2012 KS2 Level 6 mathematics tests mark schemes 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 Incorrect 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 £0.40p Incorrect 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 20 Incorrect or ambiguous use of pounds or pence, eg £320 £40 £320p £40p £3.2 0.4 3.20p 0.40p 6

2012 KS2 Level 6 mathematics tests mark schemes Do not accept2 hours 30 minutesAny unambiguous, correct indication, eg212.5 hours2h 302h 30 min2 30150 minutes150Digital electronic time, ie2:30Incorrect or ambiguous time interval, eg2.302-302,302302.32.3 hours2.3h2h 32.30 minA timeintervalfor 2 hours 30minutesA specific8:40amIncorrect time, egtime8:40for example:twenty to nine8:40am, 17:20Any unambiguous, correct indication, eg08.408.4am8.408.40pm0840Incorrect placement of separators, spaces, etc or8 40incorrect use or omission of 0, eg8-408408,408:4:0Unambiguous change to 12 or 24 hour clock, eg8.417:20 as 5:20pm or 17:20pm084Do not acceptWhere unitsare given(eg kg, m, l)for 8.6kg8.6kgAny unambiguous indication of the correctmeasurement, eg8.60kg8.6000kg8kg 600gIncorrect or ambiguous use of units, eg8600kgkg Responses involving time Accept Responses involving measures Accept 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. 7

2012 KS2 Level 6 mathematics tests mark schemes Do not acceptFor example:(5, 7)Unconventional notation, eg(05, 07)(five, seven)x y(5, 7)(x = 5, y = 7)Incorrect or ambiguous notation, eg(7, 5)y x(7, 5)(5x, 7y)(5x, y)7(x – 5, y – 7)Condone! Do not accept A probabilityshould beexpressed asa decimal,fraction orpercentage only.For 70.7 70%10Equivalent decimals, fractions and percentages,eg0.70070100355070.0%A probability correctly expressed in one acceptableform, which is then incorrectly converted but is still lessthan 1 and greater than 0, eg 70 18=100 25The first four categories of error below should beignored if accompanied by an acceptable response,but should not be accepted on their own.However, to avoid penalising the first three types oferror below more than once within each question,do not award the mark for the first occurrence ofeach type of error unaccompanied by an acceptableresponse. Where a question part carries more than onemark, only the final mark should be withheld.! A probability that is incorrectly expressed,eg7 in 107 over 107 out of 107 from 10! A fraction with other than integers in the numeratorand/or denominator.A probability expressed as a percentage without apercentage sign.A probability expressed as a ratio, eg7:10, 7:3, 7 to 10A probability greater than 1or less than 0 Responses involving coordinates Accept Responses involving probability Accept 8

2012 KS2 Level 6 mathematics tests mark schemes Condone! Do not accept Unambiguous use of a different case or variable, egN used for x used for nWords used to precede or follow equations orexpressions, egt = n + 2 tiles or tiles = t = n + 2for t = n + 2Unambiguous letters used to indicate expressions, egt = n + 2 for n + 2! Unconventional notation, eg:n × 2 or 2 × n, or n2or n + n for 2nn × n for n2n 1n ÷ 2 for 2 or 2 n2 + 1n for 2 + n2 + 0n for 2Within a question that demands simplification, donot accept as part of a final answer involving Accept within a method when awarding partial credit,or within an explanation or general working.Embedded values given when solving equations, egin solving 3x + 2 = 32,3 × 10 + 2 = 32 for x = 10To avoid penalising the two types of error below morethan once within each question, do not award themark for the first occurrence of each type within eachquestion. Where a question carries more than onemark, only the final mark should be withheld.! Words or units used within equations orexpressions, egn tiles + 2n cm + 2Do not accept on their own. Ignore if accompanying anacceptable response.Ambiguous letters used to indicate expressions, egn = n + 2 for n + 2For example:2 + nn + 22nn2n2 Responses involving algebra Accept 9

2012 KS2 Level 6 mathematics tests mark schemes 2 2 5 2 2 4 2 3 3 2 OR • 2 2 2 2 3 3 3 3 OR • 2 2 2 2 3 7 8 9 OR • 2 2 2 2 3 3 3 Paper 1 - Calculator not allowed Question Requirement Mark Additional guidance 1 1m –1 4 9 14 19 2 Fulfills all four of the conditions: • No 1s • Four 2s • More 3s than 4s • The same number of 4s and 5s 2m Do not allow, for 2m or 1m, anything other than eight numbers given, eg one section left blank or Gives a combination of numbers that fulfils three 1m of the four conditions above 3 25 % 1m Equivalent fractions or decimals 10

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 4 5 cm 2m U1 or Answer of 2.5 1m OR Shows understanding of a correct method even if there are computational errors, eg • 90 ÷ 3 = 36 (error) 12 ÷ 2 = 6 36 ÷ 6 = 6 5 Gives a correct explanation with a number x such 1m that 50 ≤ x < 55, or -5 < x < 5, as an example, eg: U1 • 53 to the nearest hundred is 100, and to the nearest ten is 50 and 2 × 50 = 100 • If it’s 50 or more but less than 55 it will round to 100 (nearest hundred) and 50 (nearest ten) and 100 is double 50 • 0 is 0 to the nearest 100 and 0 to the nearest 10 and twice 0 is 0 ✓ Minimally acceptable explanation, eg: • 51 rounds to 50 and 100 • 54 50 and 54 100 • 50 rounds to 100 • 0 rounds to 0 Incomplete or incorrect explanation, eg: • They used 51 • 50 x 2 = 100 • They could use between 50 and 55, which round to 100 6 103 2m or Shows a complete correct method with not more 1m than one computational error, eg: • 152 + 197 = 339 (error) 339 – 246 = 93 • 349 – 246 = 97 (error) • 152 + 197 = 349 349 – 246 11

2012 KS2 Level 6 mathematics tests mark schemes 1 1 4 > Question Requirement Mark Additional guidance 7a Indicates Yes and gives a correct explanation, eg: 1m ✓ Minimally acceptable explanation, eg: U1 • 3 3 = 9 , 9 < 9 9 • 27 27 3 of 9 is 3 not 4 • 4 is over a third of 9 3 of 9 is 3 9 is closer to a half than a third • 0.33, 0.44 9 should be • 0.33... < 0.44... 3 , not 3 • It is one ninth bigger • If you divide 4 by a 1 you get 4 • 12 9 3 3 3 = 12 , 12 < 9 3 of 27 = 9 and 9 of 27 = 12 ! Inaccuracies in diagrams Throughout the question, condone provided the pupil’s intention to divide into thirds, ninths and/or eighteenths is clearly shown, and the correct sections are shaded ! Indicates No, or no decision made, but explanation clearly correct Condone provided the explanation is more than minimal Incomplete or incorrect explanation, eg: • If you draw a pie chart for 4 1 shaded 9, more than 3 is • Put them into 27ths and 4 1 3 × 3 = 9 12

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 7b Indicates No and gives a correct explanation, eg: • The fractions are equal; if you multiply the numerator and denominator by the same number the fractions are equivalent 1m ✓ Minimally acceptable explanation, eg: U1 • Equal • Equivalent • Same 9 = 18 • 9 is half of 9 9 x 2 = 9 not 18 • 18 is half of 18 18 ÷ 2 = 18 which is 9 not 9 • To double the fraction, you don’t double the numerator and the denominator, you just double the numerator • To halve the fraction, you don’t halve the denominator, only the numerator • You only double the top number • You only halve the top number ! Indicates Yes, or no decision made, but explanation clearly correct Condone provided the explanation is more than minimal Incomplete explanation, eg • If you double the top and the bottom number of 4 , you get 8 9 18 13

2012 KS2 Level 6 mathematics tests mark schemes 1 Question Requirement Mark Additional guidance 8a Gives both correct values, ie 1m 700 (or 701) and 1000 (or 999) (in either order) 8b Indicates Elementary and gives a correct explanation that places the speed clearly within the correct section on the graph, eg: • 30 words in one minute is 300 words in ten minutes • 30wpm = 900 words in 30 minutes • Darren is between 25 and 35 words per minute so she is the same as Darren 1m ✓ Minimally acceptable explanation, eg: U1 • 300 every 10 • Point equivalent to 30 words per minute (eg 300 words in 10 minutes) clearly indicated on the graph • 25-35, same as Darren • 20 × 30 = 600 ! Small number of minutes used, where regions are closer together Accept points equivalent to 30 words per minute where the number of minutes is 2.5 or greater eg, accept • 30 words in one minute is 75 words in 2 minutes eg, do not accept • I looked at 1 minute on the graph and found where 30 words is on the graph Incomplete explanation eg: • I read up from 10 minutes • Between 25 and 30 words per minute • Same as Darren 9a Gives a value for y such that 10y + 2 is a 1m prime number, eg: • 0 2 • 1.7 9b Gives a value for y such that 10y + 2 is a 1m square number, eg: • −0.1 • 0.2 • 0.7 • 1.4 14

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 10a Gives three integers other than 2, 2, 6 (in any order) whose product is 24, eg: • 1, 1, 24 • 1, 24, 1 • 1, 2, 12 • 1, 3, 8 • 1, 4, 6 • 2, 3, 4 1m ! Non-integer(s) used As this shows understanding of volume, condone provided the three values given have a product of 24 eg, accept • 1.5, 2, 8 10b 7 1m 11 Divides the pie chart into two correct sectors and shades/labels correctly, eg • 1m ✓ Unambiguous indication of shading/labelling eg • Other ! Given key ignored Condone incorrect shading provided their labelling is unambiguous eg, accept • 11 year-old girls ! Additional sectors shown Ignore provided the sector(s) for 11 year-old girls are clearly indicated eg, accept • Boys Not 11 year-old girls 15

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 12a 5 : 1 1m Ratio not simplified, eg • 15 : 3 12b 2006 2m U1 or Identifies that Tom will be 18 and Ben will 1m be 6, eg: • 3 : 1 = 18 : 6 • 13 : 1 14 : 2 = 7 : 1 15 : 3 = 5 : 1 16 : 4 = 4 : 1 17 : 5 18 : 6 16

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 13 Shows a correct quadrilateral, eg • 2m ! Shading omitted Accept provided the quadrilateral drawn is U1 unambiguous ! Lines not ruled or accurate Accept slight inaccuracies in drawing provided the pupil's intention is clear OR • or Shows a quadrilateral with an area of 24cm2 but 1m not a perimeter of 26cm, eg • OR • 17

2012 KS2 Level 6 mathematics tests mark schemes 14Completes both fractions correctly, ieCompletes one of the fractions correctlyORShows both correct values, even if they are notfractions in their simplest forms, eg• 2 610 and 3.85 seen2mor1m Question 18

2012 KS2 Level 6 mathematics tests mark schemes 2 - Calculator allowed RequirementMarkAdditional guidance1a10 years old1m1b3 cm1m✓ Answers in the range of 2.9 – 3.1 inclusive! Change of unit, eg0.03mCondone, provided cm is replaced by m22.089 in first box1m✓ Equivalent fractions2.095 in second box1m3aGives a correct probability, eg:• 1• 3• 0.5• 50%• Half1m! A probability that is incorrectly expressedCondoneeg:• 3 in 6• 3 over 6• 3 out of 6• 3 from 6A probability expressed as a percentagewithout a percentage signA fraction with other than integers in thenumerator and/or denominatorA probability expressed as a ratioeg:• 3:6• 3:3• 1 to 2! Do not accept 'equal' or 'even chance'without an acceptable answereg, accept• equal, so half• evens, because it is 3 in 6eg, do not accept• equal• even chance3b41mU1 2 6 19

2012 KS2 Level 6 mathematics tests mark schemes 4B1m✓ Unambiguous indication513Shows the value 9.5 or equivalentORShows a complete correct method with not morethan one computational error, eg:• 123.5190 × 20• 190 123.520 = 9 (error) , 9 ≈ 142mor1m✓ £13! 13gFor 1m, accept as evidence of correct method610241m✓ 322! 32 × 32Condone32 Question 20

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 7 Gives all three possible values for k, in any order, 1m eg 15, 16, 17 Gives both possible values for w, in either order, 1m eg 6, 7 As evidence of a correct method: Gives a completely correct response to at least one question part OR Makes not more than three errors or omissions throughout the question, eg: • For the 1st part: 15, 16, 17, 18 [one error] For the 2nd part: 7 [one omission] • For the 1st part: 14, 15, 16 [one error, one omission] For the 2nd part: 6, 7, 8 [one error] • For the 1st part: 15 [two omissions] For the 2nd part: 7 [one omission] OR Includes non-integers within an otherwise correct response for at least one question part, eg: • For the 1st part: 15, 15.5, 16, 16.5, 17 • For the 1st part: 14.5 < k

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 9 b = 50 1m a = 20 1m U1 As evidence of a correct method, in either part, shows or implies that the angles in one of the triangles are a, b and b eg, in the first question part • 80, 50, 50 seen • (180 – 80) ÷ 2 • (360 – 160) ÷ 2 ÷ 2 eg, in the second question part • 180 – 2 × 80 • (360 – 160 × 2) ÷ 2 eg, correct answers transposed 1m ! Incomplete or no working shown Provided at least one correct angle is credited, award this mark ! In the second question part 80, 80, 20 is insufficient without any indication of the position of the equal angles 10 Equation circled as shown: 1m ✓ Unambiguous indication b = 2a a = 2b + 3c a = 5c a = 6c a + b = 5 22

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 11 Draws a correct view of the prism in any orientation, using the isometric grid, eg: • • Draws a correct view, using the isometric grid, but the only error is either to omit one external line or to show some incorrectly indicated hidden lines, eg 2m ✓ Some or all internal lines drawn, eg • ! Lines not ruled or accurate Accept provided the pupil's intention is clear ! Extended edges or Condone 1m ! Prism enlarged For 2m or 1m, accept provided a consistent scale factor has been used for all lengths • OR Draws a view of a prism with an L-shaped cross section, using the isometric grid with all external lines and no incorrectly indicated hidden lines shown, but with incorrect dimensions OR Shows an understanding that the net forms a prism with an L-shaped cross-section, showing all external lines and no incorrectly indicated hidden lines, but does not use the isometric grid, eg • ! For 2m, some or all hidden lines shown Do not accept unless hidden lines are dotted or otherwise shown as hidden eg, do not accept • For 2m, any external line omitted ! For 1m, L-shaped cross-section The cross-section must have a line of symmetry eg, for 1m do not accept • OR Draws a correct view of the cross-section, using the isometric grid, eg • ! For 1m, additional lines shown with correct cross-section Ignore 23

2012 KS2 Level 6 mathematics tests mark schemes Question Requirement Mark Additional guidance 12 Completes the table for Zhang correctly with 2m frequencies of 7 (for 9 points) and 4 (for 10 points), ie U1 7 4 or Shows one of the values 109, 110, 102 or 103 OR Shows a correct method for Zhang that scores one more than the total for Park. 1m ! For 1m, a total that uses less than 12 arrows for Zhang Condone ! For 1m, accept a follow through for their incorrect total for Park 13 4 3m U1 or Shows or implies at least two of these three steps correctly: 1. A correct method for evaluating the area of the circle in which the squaring is interpreted correctly 2. A correct method for finding 60% of a quantity 3. Division by 450 eg: • Shows the value 3.7(...) or 3.8 [1, 2 and 3 but rounding omitted] • Shows the value 1696.(...) or 1697 [1 and 2] • π × 900 × 6 ÷ 10 [1 and 2] • 3.142 × 302 × 60 ÷ 100 ÷ 450 [2 and 3] • 3.142 × 302 = 188.52 (error) 188.52 × 0.6 ÷ 450 = 0.25(...) [2 and 3] • 2827.(...) ÷ 450 [1 and 3] 2m Ambiguous implication for method eg, 6.284 to imply 1 and 3 or Shows or implies one of the three steps above 1m correctly, eg: • Shows the value 2827.(...) or 2828 [1] • 3.142 × 900 [1] • π × 30 × 30 [1] • 60% of 188.52 (error) = 113.(...) [2] • 3.142 × 30 = 94.26 (error) 94.26 ÷ 450 = 0.2(...) [3] 24

2012 KS2 Level 6 mathematics tests mark schemes 25

2012 KS2 Level 6 mathematics tests mark schemes 26

2012 KS2 Level 6 mathematics tests mark schemes 27

For more copies STA Orderline, PO Box 29, Norwich NR3 1GN Tel: 0300 303 3015 Fax: 01603 696 487 Website: http://orderline.education.gov.uk STA/12/5686 (Mark schemes pack) 1070.01