M1.          (a)     A number in the range 3.5 to 5, inclusive.
1

(b)     Correct addition of 59.5 and 80.3 to make 139.8
          OR
          Estimation such as 60 + 81 <145.
No mark is awarded for drawing a conclusion. The mark is awarded for correct calculation even if conclusion is wrong.
1
[2]

 

M2.          (a)     £79.35
Accept any clear indication of the distinction between pounds
and pence.
Accept £79.35p OR £79 35
Accept 79.35 OR 7935p written outside the answer box..
Do not accept incorrect answers, eg::
£7935 OR £7935p
Do not accept 7935 OR 79.35p written outside the answer box.
1

(b)     16
No mark is awarded for an answer which is not a whole
number, eg:: 15.38
1
[2]

 

M3.          Award TWO marks for the correct answer of 288
          If the answer is incorrect, award ONE mark for an appropriate calculation such as
          12 × 24 = incorrect answer.
up to 2
[2]

 

M4.          £56
Accept also £56 00 (with clear space between 6 and 0) or £56.00p.
[1]

 

M5.          75 (spoonfuls)
[1]

 

M6.          Award TWO marks for the correct answer of 138.
          If the answer is incorrect, award ONE mark for evidence of an appropriate
method, such as (92 + 184) ÷ 2
OR
92 × 
Calculation need not be performed for the award of the mark.
Up to 2
[2]

 

M7.          9 (boxes)
[1]

 

M8.          (a)     56 (boys)
1

(b)     Chooses an appropriate sequence of computation which indicates that the difference between 48 and 104 needs to be calculated
or gives a similar verbal explanation
Award the mark even if the answer is incorrect if there is evidence of an appropriate calculation. Any horizontal or vertical method of setting out (or mixture of both is acceptable).
Suitable methods might include:
(i)      
(ii)      104 – 40 = 64
64 – 8=56
(iii)     
1
[2]

 

M9.          Explanation which recognises that the largest two-digit number (99) added
to itself only gives a three-digit number (198), eg
•    ‘Because if you do 99 + 99 you only get a three-digit number’;
•    ‘If you add any 2 two-digit numbers, you will get a three-digit number or a
two-digit number’.
No mark is awarded for circling the ‘Yes’ alone.
Do not accept vague or arbitrary explanations such as
•    ‘The numbers aren’t big enough’;
•    ‘It doesn’t work’.
If ‘No’ is circled but a correct unambiguous explanation is
given then award the mark.
[1]

 

M10.          Any two numbers such that Sara’s number is thirteen greater than Leon’s, eg
          Leon 10    Sara 23
Accept decimals, fractions, negative numbers and zero.
[1]

 

M11.          (a)     Award TWO marks for the correct answer of 192 OR £192.00
          If the answer is incorrect award ONE mark for evidence of an
appropriate method, eg
£8.50 × 12 = £102
£4.50 × 20 = £90
cost = £102 + £90
Accept for TWO marks £192.00p OR £192 00
Accept for ONE mark £192p OR £19200 OR £1.92 OR £19.20 OR £1920 as evidence of an appropriate method.
Answer need not be obtained for the award of the mark.
Up to 2
(b)     16
1
[3]

 

M12.          Award TWO marks for the correct answer of £2.47
          If the answer is incorrect, award ONE mark for evidence of appropriate working,
eg (4 + 6 + 7) –14.50 = 2.50
250 – 3 = wrong answer
Accept for TWO marks £2.47p OR £2 47
Accept for ONE mark £247p OR £247 OR 2470 OR 24.7 as evidence of appropriate working.
Calculation must be performed for the award of ONE mark.
Up to 2
[2]

 

M13.          (a)     Award TWO marks for the correct answer of £21.80
Accept £21.80p OR £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
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.
Up to 2

(b)     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’.
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’.
1
[3]

 

M14.          (a)     
Laura	£17.10	

Accept £17.10p OR £17 10 OR £17 10p OR 1710p written outside the box.
Do not accept £1710 OR £1710p OR £17.1
1
(b)     
Carl	£10.50	

The above guidance on notation applies also to this mark.
1
[2]

 

M15.          An explanation that recognises that Asim paid 20p more than Mike, eg
•    ‘Asim paid £3.60 and Mike paid £3.40 so Asim paid 20p more’;
•    ‘Asim paid only 20p more for 3 lots of 4 cans’;
•    £3.60 is 20p more than £3.40, not 50p’;
•    ‘Mike paid 20p less than Asim’.
OR
An explanation that recognises that Asim paid £3.60 and Mike paid £3.40,
eg
•    ‘Asim paid £3.60 and Mike paid £3.40’;
•    ‘Because 50p more would mean that Asim spent £3.90 but he spent £3.60’;
•    ‘£3.60 is not 50p more than £3.40’.
Award the mark if either NO is circled OR if neither ‘Yes’ or ‘No’ is circled, provided a correct unambiguous explanation is given.
Do not award the mark for circling ‘No’ alone.
Do not accept an explanation which makes comparisons between incorrect amounts of money, eg
•    ‘Asim’s only cost him £3.40 and Mike’s cost him £3.80’;
•    ‘Because 2 × £1.70 = £2.40 and 3 × £1.20 = £3.60 and £3.60 is 120p more than £2.40 not 50p more than £2.40’.
Do not accept an explanation which makes comparisons between the price of one of each pack, eg
•    ‘Because 4 cans cost £1.20 and 6 cans cost £1.70 so take the cost of £1.20 – £1.70 = 50p’.
Do not accept an explanation which is vague or ambiguous or merely restates the question, eg
•    ‘I know that Mike must be wrong because Mike’s costs a lot more than 50p more’;
•    ‘I know Mike paid 50p more’.
U1
[1]

 

M16.          
Accept equivalent fractions or decimals, eg 0.375
[1]

 

M17.          10
U1
[1]

 

M18.          Award TWO marks for the correct answer of 16
If the answer is incorrect, award ONE mark for evidence of appropriate
working which involves a complete and correct method, eg
12 × 5 = 60
11 × 4 = 44
60 + 44 = 104
120 – 104 = wrong answer
An answer must be given for the award of ONE mark.
Up to 2
                U1
[2]

Examples of responses
We can assume from Kate’s first sentence that she correctly calculated 12 multiplied by 5 to equal 60 then added it to 44. So her explanation makes clear how she worked out that 104 pencils were used. In her attempt to subtract 104 from 120, she made an error but she describes a complete and correct method. Kate can be awarded the mark. In contrast, Bill attempted to explain how he worked out the total number of pencils used. However, as he has not recorded this total, we cannot assume that his answer of 20 was the difference between 120 and the total he calculated. His written description does not describe a complete method. Bill cannot be awarded the mark.
Kate                                                        Bill

1 mark                                                    0 marks

Ashley has made one calculation error when working out 11 groups of 4. Although he has not recorded the method that he used to obtain his answer of 18, we can assume that his method was correct since 120 subtract 102 equals 18. There is sufficient evidence for us to assume that Ashley’s method was complete and correct. Ashley can be awarded the mark. Paula also has calculated incorrectly 11 groups of 4 but, unlike Ashley, her follow-up working does not provide an appropriate method for calculating the number of pencils left. Her method is not complete or correct. Paula cannot be awarded the mark.
Ashley                                                  Paula

1 mark                                                    0 marks

Sumila has used a counting back method that shows that she recognised the need to subtract twelve groups of 5 and eleven groups of 4 from 120. She made one error in calculating 12 multiplied by 5. However, the method she used was complete and correct. Sumila can be awarded the mark. Michael also has used a counting back method but since he subtracted only one lot of 5 then one lot of 4 from 120 to obtain his answer, his working shows that he failed to identify a complete or correct method. Michael cannot be awarded the mark.
Sumila                                                  Michael

1 mark                                                    0 marks

 

M19.          50
Accept –50
[1]

 

M20.          Award TWO marks for the correct answer of 73p OR £0.73
          If the answer is incorrect, award ONE mark for evidence of appropriate method, eg
•    195 + 38 + (70 × 2) = 373
•    373 – 300
Accept for ONE mark £73p OR 0.73p OR £73 as evidence of appropriate method.
Answer need not be obtained for the award of ONE mark.
Up to 2
[2]

 

M21.          Award TWO marks for the correct answer of 250
          If the answer is incorrect, award ONE mark for evidence of appropriate working, eg
•    150 × 5 = 750
•    1000 – 750 = wrong answer
Calculation must be performed for the award of ONE mark.
Up to 2
[2]

 

M22.          (a)     42
1
(b)     11
1
[2]

 

M23.          (a)     £200
1

(b)     Award TWO marks for the correct answer of 37p OR £0.37
OR
for finding the correct difference between £199.63 and the answer given for 13a
Answer to (a) must be a multiple of £10 for the award of TWO follow-through marks.
If the answer is incorrect, award ONE mark for evidence of appropriate method, eg
74.68 + 65.90 + 59.05 = 199.63
200 – 199.63
OR
          for evidence of an appropriate method to find the correct difference between £199.63 and the answer given for (a).
Answer need not be obtained for the award of ONE mark.
Accept for ONE mark £37p OR 0.37p OR £37 as evidence of appropriate method.
Up to 2
[3]

 

M24.          Award TWO marks for the correct answer of 384
If the answer is incorrect, award ONE mark for evidence of appropriate method, eg
          7 + 5 + 4 = 16
          16 × 24
OR
          7 × 24
          5 × 24
       + 4 × 24
Answer need not be obtained for the award of ONE mark.
Up to 2
[2]

 

M25.          (a)     £2.86
1
(b)     Award TWO marks for the correct answer of £2.02 OR 202p
If the answer is incorrect, award ONE mark for evidence of appropriate working, eg
4.69 + 3.29 = 7.98
10 – 7.98 = wrong answer
Accept for ONE mark £202p OR £202 OR 2.02p as evidence of appropriate working
Calculation must be performed for the award of ONE mark
Up to 2
[3]

 

M26.          Sapna                              Robbie         
U1
[1]

 

M27.          29
[1]

 

M28.          Award 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 answer
Calculation must be performed for the award of ONE mark.
Up to 2
[2]

 

M29.          An explanation which correctly compares two percentages or two scores, eg:
•    ‘40 out of 80 is 50%’
•    ‘50% is more than 40%’
•    ‘40% of 80 is 32’
•    ‘40 out of 80 is better than 40 out of 100’
•    ‘40 out of 80 is more than 32 out of 80’
•    ‘Kate has less than half marks’.

No mark is awarded for circling ‘Hassan’ alone.
Do not accept vague or incomplete explanations, eg:
•    ‘Hassan has half marks’
•    ‘Percentages are bigger’
•    ‘Hassan has more than 40%’
•    ‘Kate has less than 40 out of 80’.
If ‘Kate’ is circled but a correct unambiguous explanation is given, then award the mark.
U1
[1]

 

M30.          Award TWO marks for the correct answer as shown:
Kate had  Jamie had 
If the answer is incorrect, award ONE mark for evidence of appropriate method, eg
150 ÷ 2 = 75
(75 + 10) AND (75 – 10)
OR
a ‘trial and improvement’ method, eg
•    55      35
     65      45
     75      55        (a difference of 20p)

OR
•    70      80
     90 60
     80 70        (a total of £1.50)
Accept for ONE mark:
Kate had  Jamie had 
OR
Kate had  Jamie had 
Answer need not be obtained for the award of ONE mark.
A ‘trial and improvement’ method must show evidence of improvement.
Up to 2 (U1)
[2]

 

M31.          11
[1]

 

M32.          Award TWO marks for the correct answer of 55p OR £0.55
          If the answer is incorrect, award ONE mark for evidence
of appropriate working, eg 8.75 – 7.65 = 1.10
1.10 ÷ 2 = wrong answer
Accept: for ONE mark £55 OR £55p OR 0.55p as evidence of appropriate working.
Working must be carried through to reach an answer for the award of ONE mark.
Up to 2
[2]

 

M33.          Award TWO marks for the correct answer of £33.75
          If the answer is incorrect, award ONE mark for evidence of appropriate
method, eg:
•    Ben: £15
Nisha: £15 – £7 = £8
Emily: £8 + £2.75 = £10.75
£15 + £8 + £10.75
          OR
•    15 + (15 – 7) + (15 – 7 + 2.75)
Accept for ONE mark £3375 OR £3375p as evidence of appropriate method.
Answer need not be obtained for the award of ONE mark.
Up to 2
[2]

 

M34.          (a)     7
Accept 7 r 55p.
Do not accept 7 r 55
1

(b)     Award TWO marks for the correct answer of £4.11
          If the answer is incorrect, award ONE mark for evidence of appropriate
method, eg
4 × 3.79 = 15.16
8.95 + 15.16 = 24.11
24.11 – 20
Accept for ONE mark £411 OR £411p as evidence of appropriate method.
Answer need not be obtained for the award of ONE mark.
Up to 2
[3]

 

M35.          (a)     7
Accept 7 r 55p.
Do not accept 7 r 55
1

(b)     Award TWO marks for the correct answer of £4.11
          If the answer is incorrect, award ONE mark for evidence of appropriate
method, eg
4 × 3.79 = 15.16
8.95 + 15.16 = 24.11
24.11 – 20
Accept for ONE mark £411 OR £411p as evidence of appropriate method.
Answer need not be obtained for the award of ONE mark.
Up to 2
[3]

 

 

E1.          No comment available.

E2.          The 1996 Standards report identified a weakness in children’s understanding of multiplication and division and the relationship between them. There is some evidence that children have made progress. For example, in this question the children were given a situation to interpret and all children achieving Level 4 or 5 overall, together with most children achieving Level 3, showed that they knew to multiply or divide when each was appropriate.

E3.          The 1996 Standards report identified a weakness in children’s understanding of multiplication and division and the relationship between them. There is some evidence that children have made progress. For example, in this question the children were given a situation to interpret and all children achieving Level 4 or 5 overall, together with most children achieving Level 3, showed that they knew to multiply or divide when each was appropriate.

However, although children knew that multiplication was required, more were successful in their calculation when a calculator was available than when it was not. Children’s ability to handle the mechanics of multiplication using a paper and pencil method were not strong, particularly at the lower levels. Where children tried to apply a standard algorithm they often went astray. For example, in this question, which required a multiplication of 24 by 12, Ben (who achieved Level 5 overall) became confused by the place value aspect.

More commonly children used a non-standard approach, for example a staged approach, shown here by Alex (who achieved Level 4 overall), or the application of knowledge, as demonstrated by Gavin (who achieved Level 4 overall).

However, non-standard approaches depend on understanding, and it is when they do not work that the limits of children’s understanding is revealed, as in this example by Gemma (who achieved Level 3 overall).

Children’s informal methods can also be highly inefficient, even though successful, as Holly shows. Holly’s approach is based on multiplication as repeated addition, and many children who achieved Level 3 overall used this approach.

E6.          No comment available.

E9.          Children working at level 3 found this question difficult. Children achieving level 4 overall performed better, with about half answering correctly, and this figure rose to about 80% at level 5. Omission rates were unusually high for the location of the question in the middle of the test.

About two-thirds of children agreed with Nadia when she said If you add a two-digit number to a two-digit number you cannot get a four-digit number. This response was given by about 40% of children working at level 3 overall, about 65% of those working at level 4 and about 85% of those working at level 5. Of these children, only about 5% of those working at level 3, just over 35% of those working at level 4 and about 75% of those working at level 5 were able to give a creditworthy explanation to justify their answer.

E10.          There was substantial improvement in performance from children working at level 3 overall to children working at level 5. Omission rates were rather high for this question, given its position in the test.
The majority of incorrect responses reflected not even partial understanding of the question.

E11.          This question assesses children’s ability to identify and use the correct operations required to solve number problems set in a context involving money. Children are asked to record the method that they used to answer the first part of this question.
In the first part of the question, about three-quarters of children at level 4 were given both marks. A further 15% received one mark for recording a correct method. Ninety-five per cent of children at level 5 received both marks. More than half of children at level 3 were also given both marks, with a further 15% receiving one mark.

Nearly 10% of children at level 4 gave answers with correct digits but ambiguous or incorrect units, such as £192p, £19200, or £1.92. This error was rarely seen at the other levels. Other errors were varied, with no common trends.
Standard vertical multiplication and addition algorithms were the most common methods recorded. These were used by 40% of children at level 3, increasing to over three-quarters of children at level 5. It is pleasing to note that few children at any level gave only one stage of the method required to answer the question. The nature of the methods recorded suggested that about a third of children at each level did not use a calculator to answer.

The second part of the question was answered correctly by 80% of children at level 4, and 95% of those of level 5. Children at level 3 found this difficult with only one-third answering correctly and 10% failing to give an answer.
The most common mistake was to attempt to multiply, rather than divide, £24 by £1.50. Thirty per cent of children at level 3 made this error, as did nearly 10% at level 4.
 * Two marks awarded for fully correct answer

E12.          This question assesses children’s ability to solve a number problem involving addition and subtraction of amounts of money. Children are asked to record their working.
Of children at level 4, 60% worked through to the correct answer for the award of two marks, as did 15% of children at level 3. With children at level 5 the proportion was over 90%. Girls were more successful than boys. Those children who showed a complete method, totalling the cost of the three books and subtracting £14.50 from the answer, but made arithmetical errors were awarded one mark. This was the case with more than 10% of children at level 3 and over 15% at level 4.

Nearly 40% of children at level 3 showed only one stage of the working, typically finding the cost of the three books but failing to continue this to find how much had been saved. Since this is an incomplete method such responses received no mark. Such errors were also made by more than 15% of children at level 4.

Of those who gave a complete method the most common approach was to use vertical methods of addition and subtraction. These were used by 30% of children at level 3, rising to over 80% at level 5. At all three levels there were about 10% of children who used compensation methods, for example, adding £3.99, £5.99 and £6.99 as £4, £6 and £7 and subtracting 3p from the result.
Two marks awarded for fully correct answer

E13.          The first part of this question assesses children’s ability to identify and use appropriate operations to solve number problems set in a context involving money and length. Children are asked to record their working,
For the first part of the question, nearly 90% of children at level 5 gave a correct answer for two marks; nearly all remaining children at level 5 were awarded one mark for recording a correct method. About half of those at level 4 were also correct for two marks, as were nearly 30% of children at level 3. A further third of children at levels 3 and 4 gained one mark for recording a correct method.
Incorrect responses were varied and few trends were seen.

Children working at levels 4 and 5 were most likely to use a method involving standard vertical multiplication and addition calculations. More than one-third of children at level 3 used a standard multiplication and addition method and just as many used an informal method. Informal methods were less common at levels 4 and 5.
Of those children at any level who showed working and reached the correct answer, more used standard vertical calculations than informal written methods.
It is pleasing to note that few children recorded only a partial method.
The second part of the question assesses children’s ability to explain their reasoning regarding whether a statement is correct.

Only one-fifth of children at level 4, increasing to nearly two-thirds of those at level 5, answered the second part of the question correctly. Of children at level 3, very few were awarded the mark and 20% omitted this part of the question. In addition 10% of children at level 4 omitted this part of the question. The most common error, at all levels, was to give an explanation saying it would cost more if only square slabs were used, without comparing this to other costs. This response was given by 15% of children at level 5 and over one-quarter of children at levels 3 and 4.
 * Two marks awarded for fully correct answer

E19.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/2c)
This question assesses children’s ability to find the difference between a positive integer and a negative integer, set in the context of temperature.

Performance
More than 75% of children working at level 4 gave the correct answer, as did nearly all of those working at level 5 and over one-third of those working at level 3.

Common errors and misconceptions
•    A common error made by over 15% of children working at level 4 and one-third of those working at level 3 was 10, which was reached by subtracting 20 from 30 rather than –30.
•    Almost 10% of children working at level 3 gave –10 as their answer, which was reached by subtracting 30 rather than –30 from 20.

E20.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/3a, 4a)
This question assesses children’s ability to identify and use the appropriate operations required to solve number problems set in a context involving money. Children are asked to record the method that they use to solve the problem.

Performance
More than 70% of children working at level 4 were awarded two marks for the correct answer, as were almost 90% of those working at level 5 and over half of those working at level 3.
A further 10% of children working at level 4 were awarded one mark for demonstrating a correct method, with an incorrect answer.

Common errors and misconceptions
•    A common answer given by over 5% of children working at level 4 and over 10% of those working at level 3 was £3.73, which demonstrated an incomplete method where the second stage of the problem was omitted.

Methods
•    A standard written addition and subtraction method was used successfully by over 20% of children working at level 4 and 65% of those working at level 5.
•    Of those children who reached a correct answer, over 60% of those working at level 4 and almost 30% of those working at level 5 recorded one stage of their working and carried out the other stage mentally.
•    Over 15% of children working at level 4 and one-third of those working at level 3 completed only one stage of the method.
•    Children working at levels 4 and 5 were more likely to use standard written methods in this question and were generally successful.

E21.          Target Level: 4
Curriculum Coverage (POS ref: Ma3/4a; Ma2/4a)
In this question children are required to identify and use the correct operations to solve the word problem set in the context of capacity. The question draws on their knowledge that one litre is equivalent to 1000 millimetres. Children are asked to record their working.

Performance
Fifty-five per cent of children working at level 4 gave the correct answer for two marks. Ninety per cent of those working at level 5 were also awarded two marks for a correct answer, as were over 10% of children working at level 3.
A further 5% of children at each level failed to give the correct answer but were awarded one mark for recording a correct method.

Common errors and misconceptions
•    An answer of 850 was given by over 10% of children working at level 4, which suggested they subtracted the amount for one glass rather than five.

Methods
•    Over 70% of children working at level 4 and 85% of those working at level 5 who reached a correct answer, used multiplication and subtraction in their working.

E22.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/4a)
This question assesses children’s ability to identify and use the appropriate operations to solve word problems set in a context involving length.

Performance
Two-thirds of children working at level 4 gave the correct answer for the first part, as did 90% of those working at level 5 and over one-third of those working at level 3.
On the second part, success rates improved slightly for children working at levels 4 and 5. Three-quarters of children working at level 4 answered correctly as did nearly all of those working at level 5. Children working at level 3 were less successful on the second part than the first part with less than 30% answering correctly.

Common errors and misconceptions
•    For the first part, nearly 15% of children working at level 3 gave the incorrect answers 30 or 60, which suggests that they ignored the orientation of the bricks in the tower and instead multiplied the height or length of one brick by five.
•    For the second part, 5% of children working at level 4 and over 10% of those working at level 3 gave the answers 12 or 13, which were close to the correct answer of 11.

E23.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/2i, 4a, 3i, 3k)
The focus of this question is to identify and use the correct operations required to solve number problems set in the context of money. For the second part of the question children are asked to record the method used to find the difference between two amounts of money.

Performance
For the first part, nearly 70% of children working at Level 4 were successful as were nearly 90% of those working at Level 5 and over one-third of those working at Level 3.
For the second part, over half of children working at Level 4 were awarded two marks for a correct answer as were over 80% of those working at Level 5 and nearly 15% of those working at Level 3.
Almost 20% of children working at Level 4 who failed to reach a correct answer were awarded one mark for recording a correct method. About 10% of children working at Levels 3 and 5 were also awarded one mark.
Common errors and misconceptions
•    Nearly 5% of children working at Level 4 and 15% of those working at Level 3 gave an answer of £199.63, suggesting that they only completed one stage of their working.

Methods
•    Over one-third of children working at Level 3 and nearly 70% of those working at Level 5 used a standard written addition and subtraction method.
•    One-quarter of children working at Level 4 and over 15% of those working at Level 5 recorded one stage of their working and carried out the second stage mentally.
•    Of those children who reached a correct answer, over one-third of children working at Level 4 and 70% of those working at Level 5 used a standard written addition and subtraction method.

•    Of those children who reached a correct answer, over 15% of children working at Level 4 used informal methods.
•    Of those children who reached a correct answer, 30% of children working at Level 4 and 20% of those working at Level 5 recorded one stage of their working and carried out the other stage mentally.
•    The most common method used was standard written addition and subtraction: about three-quarters of children who used this method were successful.
•    Of children who recorded only one stage of their working, about two-thirds were correct.
•    Of children who used personal methods or jottings, about 60% were correct.

E24.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/4a, 3k, 3j)
This question assesses children’s ability to identify and use the correct operations required to solve number problems set in a ‘real life’ context. Children are asked to record their method.

Performance
Over three-quarters of children working at Level 4 were awarded two marks for a correct answer as were 90% of those working at Level 5 and over half of children working at Level 3.
A further 10% of children working at Levels 3 and 4 who failed to give a correct answer were awarded one mark for recording a correct method. Five per cent of children working at Level 5 were also awarded one mark for a correct method.
Common errors and misconceptions
•    Over 5% of children working at Level 4 gave an answer of 168, suggesting that they worked out only the number of tomato soup tins and ignored the other soup tins.

Methods
•    Over 65% of children working at Level 4 used a standard written multiplication method. Over 80% of children working at Level 5 and one-third of those working at Level 3 also used this method.
•    Nearly 10% of children working at Level 4 and 15% of those working at Level 3 used informal methods.
•    Nearly 10% of children working at Level 4 and over 10% of those working at Level 3 recorded one stage of their working and carried out the other stage mentally.
•    Of those children who reached a correct answer, over three-quarters of those working at Level 4 and over 80% of those working at Level 5 used a standard written multiplication method.

•    Of those children who reached a correct answer, 10% of those working at Levels 4 and 5 and 15% of those working at Level 3 used informal methods.
•    Of those children who gave a correct answer, 10% of children working at Level 4 and 20% of those working at Level 5 recorded one stage of their working but carried out the other stage mentally.
•    The most common method used was standard written multiplication and addition: about 90% of children who used this method were successful.
•    Of children who recorded only one stage of their working, about 90% were correct.
•    Of children who used personal methods or jottings, about three-quarters were correct.

E25.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/4a, 3e, 3i)
This question assesses children’s ability to identify and use the appropriate operations to solve number problems set in a context involving money.
For the first part of the question, children are required to find the difference between two amounts of money.
For the second part of the question, children are asked to record the working that they used to complete a two-step problem.

Performance
For the first part, nearly 70% of children working at Level 4 gave a correct answer, as did over 90% of those working at Level 5 and almost 30% of those working at Level 3.
For the second part, almost 70% of children working at Level 4 gave the correct answer for two marks. Nearly 90% of those working at Level 5 were also awarded two marks for a correct answer, as were almost one-quarter of children working at Level 3.
Thirty per cent of children working at Levels 3 and 20% of those working at Level 4 were awarded one mark for recording a correct method. Nearly 10% of children working at Level 5 were also awarded one mark.

Common errors and misconceptions
•    Over 5% of children working at Levels 3 and 4 gave an answer of £3.14 for the first part, suggesting that they may have incorrectly subtracted the smaller digit from the larger digit in each column when subtracting £2.99 from £5.85.
•    Over 5% of children working at Level 4 and nearly 10% of those working at Level 3, incorrectly subtracted £7.98 from £10, giving an answer of £3.98 or £3.02 for the second part of the question.
•    Over 10% of children working at Level 3 gave an answer of £7.98 reached by adding £4.69 and £3.29, suggesting that they only completed one stage of the problem.

Methods
•    Of those children who were awarded two marks for a correct answer, over 75% working at Level 4 and over 85% working at Level 5 used addition and subtraction in their working.
•    More than three-quarters of all children who wrote down an addition and subtraction method for the second part of the question successfully calculated the correct answer.
•    Around 15% of children working at Level 4 who were awarded two marks for a correct answer used informal methods.
•    Around 15% of children working at Level 4 who were awarded two marks for a correct answer recorded only one stage of their working.

E26.          Target Level: 4
This question assesses pupils’ ability to use and apply their mathematics to solve a number problem set in a ‘real life’ context.
Performance
•    Fifty-five per cent of pupils working at level 4 gave the correct answer. More than 85% of pupils working at level 5 and 20% of those working at level 3 were also correct.

Common errors and misconceptions
•    The most common incorrect response was to give the numbers nine and five. These were given by more than one-quarter of pupils working at level 4, more than one-tenth of pupils working at level 5 and almost one-quarter of those working at level 3. These pupils probably began by dividing the 14 biscuits equally to give seven each, and then misinterpreted ‘Sapna has 2 more’ as Robbie giving two biscuits to Sapna.
•    Over 5% of pupils working at level 4 and nearly 20% of those working at level 3 gave an answer of nine and seven. These pupils probably began by giving Sapna and Robbie seven biscuits each and then misinterpreted ‘Sapna has 2 more’ to give two more biscuits to Sapna.

E27.          Target Level: 4
This question assesses pupils’ ability to solve a number problem that requires understanding of number operations, including inverses.
Performance
•    Over 70% of pupils working at level 4 gave the correct answer. More than 90% of pupils working at level 5 and almost one-third of those working at level 3 were also awarded the mark.

Common errors and misconceptions
•    Almost 5% of pupils working at level 4 and more than 5% of those working at level 5 gave an incorrect answer of 23. These pupils probably made one error, starting by subtracting instead of adding 9 and then carrying out the rest of the inverse operations correctly.
•    Over 20% of those working at level 3 omitted this question.

E28.          Target Level: 4
Curriculum Coverage (POS ref: Ma2/4a, 3h)
This question assesses pupils’ ability to identify and use the appropriate operations to solve a number problem set in a ‘real life’ context involving length. Pupils are asked to record their working.

Performance
Almost three-quarters of pupils working at level 4 gave the correct answer for the award of two marks. More than 95% of pupils working at level 5 and almost 30% of those working at level 3 also gained two marks.
Fewer than 5% of pupils at any level were awarded one mark for a correct method without the correct answer.

Common errors and misconceptions
•    The most common incorrect answer was 7, given by nearly 5% of pupils working at level 4 and more than 10% of those working at level 3. These pupils did not engage with all the information needed to solve the problem, and probably subtracted 5 (the number of lengths David swam) from 12 (the number of widths Rosie swam).
•    Other errors were varied.

Methods
Almost 10% of pupils working at level 4 failed to follow the instruction to show their working. This was also true of nearly 15% of those working at level 3.
Almost all pupils working at level 5 recorded some working.
A method involving multiplication was recorded by more than 55% of pupils working at level 4 and nearly 90% of those working at level 5.
A method involving repeated addition but not multiplication was used by more than 10% of pupils working at levels 3 and 4 but was rarely seen among those working at level 5.
Of those pupils who gave the correct answer, more than three-quarters used a method involving multiplication, with about 10% recording a method involving repeated addition but not multiplication.

 
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