2. Three Hundred and Forty-Two Add Seven Hundred and Eighty Nine

ONE SOLUTIONS

1. 23 x 51 (I’ve provided the grid for you!)

2. three hundred and forty-two add seven hundred and eighty nine.

3. Half of 127

Half of . . .

100 50

20 10

7 3 ½

TOTAL 63 ½

1.(a)Gives a correct method to show that1
9 × 28 = 252
eg

 28
×9
252 [with evidence of the 7 tens]
7



so 72 + 180

(b)7562

The most common correct methods:
Use the relationship between 27 × 28 and 9 × 28
eg

3 × 252 (or their incorrect value from (a))

252 + 252 + 252

Calculate 27 × 28 directly
eg

10 × 27 = 270, 270 × 3 = 810,
810 – 54



so 400 + 160 + 140 + 56

[3]

2.Multiplication grid

Table correct, ie

2

orOnly one error or omission1

TWO SOLUTIONS

1. 234 ÷ 3 (I’ve provided the table for you!)

Answer; 78

2. five hundred and forty seven take two hundred and eighty five.

3. Quarter of 246

Half is 123

Half again 61½

1.Coins

(a)9.41

(b)1.851

(c)16.81

[3]

THREE SOLUTIONS

Complete these three multiplications using the grid each time.

1

2.

3.

£30

£ 6

£36

Name the shapes

THRE

1.(a)Indicates 78.491

Accept rounded or truncated values eg:

78: 78.5; 78.4

(b)Indicates 261

Ignore any further working after 26 has been shown eg

(c)For 2m shows correct processing relating to the dive rating chosen and2
a correct interpretation, hence showing one of the following:

ProcessingInterpretation

......

102.69 ÷ 3.26Total mark would have to be at least 31.5,

(= 31.5)which is not possible / more than 30.

......

31.5 ÷ 3Each judge would need to give 10.5 which

(= 10.5)is not possible / greater than 10.

......

30 × 3.26Even with full marks the maximum score

(= 97.8)would be 97.8.

......

102.69 – 97.8He is still short of winning.

(= 4.89)

......

102.69 ÷ 30If full marks (or 30) are given the rating

(= 3.423)needs to be at least 3.423.

......

Accept equivalent words or phrases.

Do not accept responses which offer no, incomplete or invalid processing relating to the dive rating chosen eg:

He cant get more than 30.

He got 34, but 30 is the maximum.

Even if he gets 10 each time its not enough.

Its impossible for him to win.

He cant score 102.69 with that dive rating.

He should have done a higher rating.

[4]

FOUR SOLUTIONS

1.What number is six less than minus two?

2.I have a fair six-sided dice, numbered one to six. I roll the dice.
What is the probability that I roll a number greater than two?

There are 4 numbers greater than two, so the probability is 4 or 2

6 3

3.What is five per cent of three hundred pounds?

10% of 300 = 30

5% is half of 10% so is £15

4.Write the number that is halfway between a half and one.

¾

5.What is the area of a rectangle with a width of six centimetres and a length of seven centimetres?

6 rows of 7 = 42 so 42 cm2

1.Museum

(a)2882

orFor only 1 Digits 288 seen

(b)5002

orFor only 1 Gives an answer of 5 followed only by one or more zeros, eg

5000

50

[4]

FIVE SOLUTIONS

1. 2x + 7 = 21 2. 6x – 6 = 24

2x = 14 6x = 30

x = 7 x = 5

3. 5f + 3 = 18 4. 10y – 3 = 17

5f = 15 10y = 20

f = 3 y = 2

1.(a)for 2m indicates the correct use of a non-calculator method, obtaining2
(£)123.50(p) or (£)123 50(p)

26 × £5 = 130, 26 × 25p = £6.50, so £123.50

4 × 26 = £104, 75p × 20 = £15,

75p × 6 = £4.50 total is £123.50p

Acceptable evidence of non-calculator working would include any of the following sets of numbers (note that units must be consistent in £ or pence, hence 950 with 2850 would not be acceptable)....
95(.00), 28.5(0)
9500, 2850
04(.00) 18.2(0), 1.3(0)
0400, 1820, 130

Award only 1m for all working shown correctly but with the answer given as 12.35, 123.5, (£)12350(p) or other error in the final stage (for example in the final addition, eg:



.

(b)For 2m shows in working the correct use of a non-calculator method,2
indicating 15 as the number of kites that can be made,

[4]

SIX SOLUTIONS

Using the methods you know you should . . .

1. 245 + 377

2. 472 – 258

3. 342 x 96

30 780

2 052

32 832

1.(a)For 2m indicates £33.25’, eg:2

33.25

33.25p on answer line.

For only 1m shows a correct method with only one computational error, eg:

Shows 3325 with the decimal point omitted or incorrectly placed, or with units incorrectly stated.

Evaluates 35 × 5p and subtracts the answer from £35 making only one error throughout.

Shows in working 2850 and 475 (or 3150 and 175) incorrectly totalled with their answer correctly converted to pounds.

For 2m do not accept 33.25p other than on the answer line.

For 1m do not accept inconsistent units
eg:

‘285 and 475’

‘315 and 175’

(b)For 2m indicates 142

For only 1m shows a complete correct method with no errors other than in the
remainder, but the total number of trees is not stated

[4]

SEVEN SOLUTIONS

1. £196 ÷ 7 = £28

2. £976 ÷ 8 = £122

1.(a)For 2m indicates 142

For 2m accept any number under 16 given or implied as the number of extra booklets eg:

‘14, 3 booklets left over.’

‘14 r 4’

For only 1m uses a correct method with only one error, and states the correct
number of packs for their result

(b)For 2m shows the correct number of grams eg:2

10560 (g)

For 3m accept the correct total in kilograms eg:

‘10.56’ in the answer space.

‘10.560 kg’ elsewhere.

[5]

2.86022

or

Shows a complete correct method with not more than one computational error1
eg

3740 + 3740 + 374 × 3 = 7480 + 1122



EIGHT SOLUTIONS

1.Ninety-seven per cent of the Earth’s water is salt water. The rest is fresh water.
What percentage of the Earth’s water is fresh water?

100% in total so 100 – 97 = 3%

2.What number is four less than minus seven?

3.What is the next prime number after seven?

Prime numbers have only two factors. After 7 is 11

4.I have a fair six-sided dice numbered one to six.
I am going to roll the dice.
What is the probability that I will roll an odd number?

3/6 or a half

5.Forty-four people paid twenty-five pence each to go into a book sale.
How much money is that altogether?

Four 25p’s is £1, so 44 lots will be £11

1.Trip

(a)121682

or1

Shows a complete correct method with not more than one computational error

(b)131

[3]

2.Indicates the village shop
and
gives a correct justification, based on 2
correctly calculating a pair of comparable valuesU1
eg

At the supermarket 6.25 × 6 = 37.5(0)
At the village shop 7.20 × 5 = 36

6.25 × 6 – 7.2 × 5 = 1.5

6.25  5 = 1.25,
7.20  6 = 1.2(0)

£75 for 60 or £72 for 60

For £1 you get of a pen or of a pen

You pay 95p extra for 1 more pen, but they’re at least £1.20 each so it
must be a better deal

[2]

NINE SOLUTIONS

Look at the number cards below;

Using the cards above, write down;

(i)the square numbers 1 25

(ii)the prime numbers 7 2 11 3 17

(iii)the factors of 50 1 2 25 50

(iv)multiples of 3 3

1.Calculators

£ 27.502

or
Shows the digits 2751
eg

27.5

2750

2.75

[3]

2.Travel to work

(a)£729(.00)2

orShows the digits 729, eg1

72900

72.90

orShows a complete correct method with not more than one computational error, but with the decimal point correctly positioned, eg

20 × 45 = 900
16 × 45 = 8 × 90 = 720
720 + 9

(b)£ 141

[3]

TEN SOLUTIONS

1. 4e + 3 = 19 2. 6k – 10 = 26

4e = 16 6k = 36

e= 4 k = 6

3. 4f - 9 = 27 4. 6g + 6 = 9

4f = 36 6g = 3

f = 9 g = ½ (or 0.5)

1.Water

(a)82

orShows a complete correct method, eg1



1.8 ÷ 0.225

225 × 2 = 450
450 × 2 = 900
900 × 2 = 1800
2 × 2 × 2

orShows the value 1800 or 0.225

Accept value qualified, eg

About 8

(b)481

[3]

2.(a)Indicates why 9 × 19 must be less than 2000, eg:1

Thats enough for 10 stamps.

For stamps 1p more its still less than £2.

Make them 20p each..

9 × 20 = 180

10 × 19 = 190

20 × 10 = 200

20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 = 180

All the 10s in 19 is only 90p, and all the 9s is less than that.

9 × 10 = 90 and 9 × 9 = 81, both less than £1.

Accept working with rounded numbers even if there is a numerical error, eg 20 × 9 = 189

Do not accept partial working with no explanation
eg 9 × 10 = 90, 9 × 9 = 81

Ignore any reference to units

(b)States 171(p) and indicates use of a correct non-calculator method, eg:1

Units are not required.

Accept 171 or 1.71 with any units.

Do not accept 17.1

[2]

ELEVEN SOLUTIONS

1(a)For 2m indicates use of a suitable no-calculator method, obtaining 52920g
for the weight,

Award only 1m if there is an error in multiplication or addition of one pair of digits,

Award 1m for 2520 and 50400 shown in working.

(b)Correctly compares 50kg and 52920g., eg:1

52920g is more than 50kg.

50kg is only 50000g.

The tins are 2920 too heavy.

About 2kg over.

(c)Correctly converts between metres and centimetres before or after calculation, eg:
1.24m to 124m, 14cm to (0).14m or 112cm to 1.12m1

For 2m indicates use of a suitable non-calculator method, obtaining 8 for the number of layers of tins, eg:

states 8 and shows:2

[6]