Fractions Percentages
3-5
60 minutes
60 marks
Page 1 of 42
Q1.
Some children work out how much money two shopkeepers get from selling fruit.
They use pie charts to show this.
Mrs Binns gets £350 selling bananas.
Estimate how much she gets selling oranges.
1 mark
Mrs Binns gets a total of £1000 and Mr Adams gets a total of £800.
Estimate how much more Mrs Binns gets than Mr Adams for selling peaches.
1 mark
Page 2 of 42
Q2.
The Year 6 children in a school were asked to choose a musical instrument.
This is a pie chart of their choices.
Estimate what fraction of the children chose a drum.
1 mark
There are 80 children in Year 6.
Estimate the number of children who chose a violin.
1 mark
Explain how you decided.
...............................................................................................................................
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1 mark
Page 3 of 42
15% of the 80 children chose a guitar.
How many children is this?
2 marks
Q3.
Here are some number cards.
Use two of the cards to make a fraction which is less than
.
1 mark
How much less than 1 is your fraction?
...............................
1 mark
Page 4 of 42
##
This diagram shows the proportions of waste by weight a family throws away in one year,
Estimate what fraction of the waste is organic.
1 mark
The family throws away about 35 kilograms of plastic in a year.
Use the diagram to estimate the weight of glass and metal they throw away.
kg
1 mark
Page 5 of 42
The family throws away 130 kg of paper and card.
70% of this is newspapers.
What is the weight of newspapers?
2 marks
Q5.
Kelly chooses a section of a newspaper.
It has 50 words in it.
She draws a bar chart of the number of letters in each word.
What fraction of the 50 words have more than 6 letters?
1 mark
Page 6 of 42
Kelly says,
23 of the 50 words have less than 5 letters.
This shows that nearly half of all the words used in the newspaper have less than 5
letters in them.
Explain why she could be wrong.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
1 mark
Q6.
Calculate 24% of 525
1 mark
Q7.
Here is a shaded shape on a grid made of squares.
Draw the line of symmetry of the shaded shape.
You may use a mirror or tracing paper.
1 mark
Page 7 of 42
What fraction of the area of the grid is shaded?
1 mark
Measure angle x in degrees.
Use an angle measurer (protractor).
1 mark
Q8.
Draw one line to join two fractions which have the same value.
1 mark
Page 8 of 42
Q9.
Here is a grid made of squares.
Shade 10% of this grid.
1 mark
Q10.
Calculate
of 5000
1 mark
Q11.
Shade
of this shape.
1 mark
Page 9 of 42
Q12.
Emily makes 250 grams of a snack mixture.
15% of the weight is raisins, 25% is banana chips and the rest is peanuts.
How many grams of peanuts does she use?
2 marks
of this square is shaded.
Q13.
Page 10 of 42
The same square is used in the diagrams below.
What fraction of this diagram is shaded?
1 mark
What fraction of this diagram is shaded?
1 mark
Page 11 of 42
Q14.
Here is a grid of 20 squares.
What percentage of the grid is shaded?
%
1 mark
Q15.
Stefan has a bag that contains 3 blue marbles and 5 red marbles only.
What fraction of the marbles in the bag are blue?
1 mark
Page 12 of 42
Stefan adds one blue marble and one red marble to the bag.
What fraction of the marbles in the bag are blue now?
1 mark
Q16.
Two of the fractions below are equivalent.
Circle them.
1 mark
Q17.
A fraction of each shape is shaded.
Match each fraction to the correct place on the number line.
One has been done for you.
1 mark
Page 13 of 42
Q18.
Calculate
of 288
1 mark
Q19.
These diagrams are all made of squares.
Look at each diagram.
Put a tick ( ) if exactly
of it is shaded. Put a cross ( ) if it is not.
2 marks
Page 14 of 42
Q20.
Sarah has a packet of balloons.
The contents of the packet are
5 red balloons
5 blue balloons
10 yellow balloons
Sarah says,
‘One-quarter of the balloons are red’.
Is Sarah correct?
Circle Yes or No.
Yes / No
Explain how you know.
1 mark
Page 15 of 42
Q21.
If you know 40% of a number, explain how you could work out the original number.
1 mark
Q22.
Circle the fraction that is greater than
but less than
1 mark
Q23.
Here are five number cards.
Use three of the number cards to make this calculation correct.
1 mark
Page 16 of 42
Q24.
All the children in Class 6 vote to pick a class captain.
The choice is Holly or Dev or Joe.
Vote
once
Holly
Dev
Joe
Dev gets 10% of the votes.
Joe gets twice as many votes as Holly.
What percentage of the votes does the winner get?
%
1 mark
Page 17 of 42
Q25.
This diagram shows a shaded rectangle surrounded by squares.
What fraction of the diagram is shaded?
1 mark
Q26.
Here is part of a number line.
Write in the missing fraction.
1 mark
Page 18 of 42
Q27.
Holly says,
‘One-third of this shape is shaded’.
Is Holly correct?
Circle Yes or No.
Yes / No
Explain how you know.
1 mark
Page 19 of 42
Q28.
Seb goes on a sponsored walk to collect money for charity.
His aunt promises to pay 75p for each kilometre he walks.
She pays him £6.75 at the end of the walk.
How many kilometres does Seb walk?
km
1 mark
15% of the people walk 5 km or less.
40% of the people walk 8 km or more.
What percentage of the people walk between 5 km and 8 km?
%
1 mark
Page 20 of 42
Q29.
Here are three shapes made from regular hexagons.
Write the fraction of each shape that is shaded.
2 marks
Page 21 of 42
Q30.
In a class, 18 of the children are girls.
A quarter of the children in the class are boys.
Altogether, how many children are there in the class?
2 marks
Q31.
Write these in order of size, starting with the smallest.
0.34
0.7
43%
smallest
1 mark
Page 22 of 42
Q32.
This pie chart shows the ingredients to make
a food mixture for wild birds.
Estimate the percentage of mixture that is suet.
%
1 mark
Mina uses 100 grams of millet in the mixture.
Estimate how many grams of sunflower seeds she should use.
g
1 mark
Shade
of this shape.
Q33.
1 mark
Page 23 of 42
Q34.
Megan asked children from two different schools,
‘How do you travel to school?’
Here are her results.
Foxwood school
80 children
Midtown school
240 children
Megan says,
‘The number of children walking to Foxwood school is
more than the number walking to Midtown school.’
Is she correct?
Circle Yes or No.
Yes / No
Page 24 of 42
Explain how you know.
1 mark
At Midtown school, one third of children travel by car.
The number of children who cycle is the same as the number who go on the bus.
How many children cycle to Midtown school?
2 marks
Page 25 of 42
Q35.
Megan asked children from two different schools,
‘How do you travel to school?’
Here are her results.
Foxwood school
80 children
Midtown school
240 children
Megan says,
‘The number of children walking to Foxwood school is
more than the number walking to Midtown school.’
Is she correct?
Circle Yes or No.
Yes / No
Page 26 of 42
Explain how you know.
1 mark
At Midtown school, one third of children travel by car.
The number of children who cycle is the same as the number who go on the bus.
How many children cycle to Midtown school?
2 marks
Page 27 of 42
M1.
(a)
Award ONE mark for an answer in the range £85 to £125, inclusive.
1
(b)
Award ONE mark for the correct answer of £50.
Accept any estimate in the range £45 to £55, inclusive.
1
[2]
M2.
(a) The answer is approximately 1/7. Accept any fraction, percentage or decimal
in the range:
•
1/9 to 1/5, inclusive
•
11% to 20%, inclusive
•
0.11 to 0.2, inclusive
1
(b)
The correct answer is 10. Accept any number in the range 8 to 12, inclusive.
1
(c)
The explanation should make reference, in some form, to appropriate
fractional estimates, eg:
•
“Because it looks like a quarter of a half and that’s 10.”
•
“I thought the violin looked like half the trumpet and that was about a quarter.”
•
“I decided this because 1/4 was 20 children, so I halved 20 and made it 10.”
Explanations which lack specific reference to appropriate fractions
should not be awarded the mark, eg:
• “Because it’s a bit less than the trumpet.”
• “Because there are 6 parts to the pie chart.”
1
(d)
Award TWO marks for the correct answer of 12, even if there
are errors in the working.
Award ONE mark if the answer is incorrect, but there is evidence of an attempt to
calculate 15% of 80 by any method, eg:
•
15/100 × 80 = (incorrect answer given)
•
10% of 80 = 8, 5% is 4, so 15% of 80 = (incorrect answer given)
•
1% of 80 = 80/100 = 4/5, so 15% = 4/5 × 15 = (incorrect answer given)
The writing of “15/100 × 80” (or equivalent) alone is not sufficient
evidence of an attempt to calculate.
Up to 2
[5]
Page 28 of 42
M3.
(a)
Accept only fraction formed by the cards given.
1
(b)
consistent with part (a).
If part (a) is incorrect, accept working of 1 – (answer to part (a))
provided the numbers used are on the cards.
Accept decimals.
If answer to part (a) is greater than 1, answer to part (b) must be
negative.
1
[2]
M4.
(a) An answer in the range 1/5 to 3/10 OR 20% to 30%
OR 0.2 to 0.3 INCLUSIVE.
Numbers in range 20 to 30 must have % sign, eg:
• Do not accept ‘25’
1
(b)
An answer in the range 15 to 25 kg INCLUSIVE.
1
(c)
Award TWO marks for correct answer of 91 kg.
If answer is incorrect, award ONE mark for appropriate calculation, eg:
•
70/100 × 130 = wrong answer;
•
10% is 13 so 70% 7 × 313 = wrong answer.
•
H + 2H + H + 2H = 126
•
20 + 40 + 20 + 40 = 120
A calculation MUST be performed for award of one mark.
‘70/100 × 130’ alone is insufficient for award of one mark.
Up to 2
[4]
M5.
(a)
1
10
/5 OR /50
20
Accept other equivalent fractions, eg: /100
1
Page 29 of 42
(b)
Explanations which imply that the results from a small sample cannot safely
be applied to a large one, eg:
•
‘You could be wrong because every section is different’
•
‘The article is only a small proportion of the whole newspaper’
•
‘The rest could be different’
•
‘You can’t judge a whole newspaper by one article’
Do not accept vague or arbitrary explanations such as:
‘She might not have counted right’;
‘The words in the newspaper might be big’;
‘There are more bigger words than small’.
1
[2]
M6.
126
[1]
M7.
(a)
Line of symmetry drawn as shown.
The length of the line is unimportant, provided the intention is
clear.
Accept slight inaccuracies in drawing provided the intention is
clear.
1
(b)
1
/5 OR 0.2 OR 20%
5
Accept equivalent fractions, eg /25
1
(c)
Answer in the range of 140 to 146 inclusive.
1
[3]
Page 30 of 42
M8.
joined to
The line need not touch the fractions, provided the intention is
clear.
Do not award the mark if more than one pair of fractions are
joined.
[1]
M9.
Any three squares shaded, eg
Shaded squares need not be joined in any way.
Shading may be in terms of part squares, eg
Accept slight inaccuracies in shading provided the
intention is clear.
[1]
M10.
4375
[1]
Page 31 of 42
M11.
Any two squares shaded, eg
Accept part shapes shaded provided the intention is clear.
Accept inaccuracies in shading provided the intention is clear.
[1]
M12.
Award TWO marks for the correct answer of 150
If the answer is incorrect, award ONE mark for evidence of
appropriate working, eg:
•
15 + 25 = 40
100 – 40 = 60
10% of 250 = 25
25 × 6 = wrong answer
OR
•
100% – 40% = 60%
60% of 250 = wrong answer
OR
•
15% of 250 = 37
25% of 250 = 62
250 – 37
– 62 = wrong answer
Working must be carried through to reach an answer for the award
of ONE mark.
Up to 2
[2]
M13.
(a)
Accept equivalent fractions or decimals.
1
Page 32 of 42
(b)
Accept equivalent fractions or decimals.
U1
[2]
M14.
30%
Do not accept equivalent fractions or decimals.
[1]
(a)
M15.
Accept equivalent fractions or decimals.
1
(b)
OR
Accept equivalent fractions or decimals.
1
[2]
M16.
Two fractions circled as shown:
Do not award the mark if additional incorrect fractions are circled.
Accept alternative unambiguous indications, eg fractions ticked,
crossed or underlined.
[1]
Page 33 of 42
M17.
Diagram completed correctly as shown:
Do not award the mark if additional incorrect lines are drawn.
Lines need not touch the shapes or number line provided the
intended accuracy is clear.
[1]
M18.
126
[1]
M19.
Award TWO marks for diagrams ticked or crossed as shown:
Accept alternative unambiguous indications, eg
Y or N.
For TWO marks, accept:
If the answer is incorrect, award ONE mark for three diagrams ticked or
crossed correctly.
Up to 2
[2]
Page 34 of 42
M20.
An explanation which recognises that 5 is a quarter of 20, the total number
of balloons, eg:
•
‘
are red,
are blue and half are yellow’
•
‘A quarter of 20 is 5’
•
‘5 out of 20’
•
‘There are 20 balloons altogether and 5 are red so she is correct’.
No mark is awarded for circling ‘Yes’ alone.
Do not accept vague or incomplete explanations, eg:
• ‘5 are red, 5 are blue and 10 are yellow so that is a quarter’
• ‘There are 20 altogether’
• ‘Add all the balloons up and divide by 4’
If ‘No’ is circled but a correct, unambiguous explanation is given,
then award the mark.
U1
[1]
M21.
An explanation which recognises that 40% of the number must be
multiplied by 2
, or equivalent, eg:
•
‘You multiply by 2.5’
•
‘Halve it and multiply by 5’
•
‘Divide by 4 to get 10% and then multiply by 10’
•
‘Divide by 40 then multiply by 100’
•
‘If you had 100, quarter of 100 is 25, then times by 10 to get 250’
•
‘Double it and add half of it’.
Do not accept vague or incomplete explanations, eg:
• ‘Start with the original number and find 40% of it’
• ‘Find 10% and multiply by 10’
• ‘Divide by 4 to find 10% and then you can find 100%’
• ‘Find 1% and multiply by 100’
• ‘If you had 20 it would be 50’
• ‘Add 60%’
U1
[1]
Page 35 of 42
M22.
Fraction circled as shown:
Accept alternative unambiguous indications, eg
fraction ticked, crossed or underlined.
[1]
M23.
OR
Numbers in brackets may be given in either order.
Accept equivalent fractions or decimals.
Do not accept use of the same card twice, eg
[1]
M24.
60%
U1
[1]
M25.
Accept equivalent fractions, eg
Accept 0.2 OR 20%
[1]
Page 36 of 42
M26.
Accept equivalent fractions or decimals.
[1]
M27.
An explanation which recognises that the shaded area is
equivalent to one-third, eg:
is shaded and that is equivalent to
‘
•
‘
•
‘2 out of 6 is the same as 1 out of 3’
•
‘2 out of 6’
•
‘
•
‘There are 3 squares, and 2 halves are shaded, and 2 halves make one whole’
•
‘The two shaded triangles are the same as one square and that is one out of three
squares’
•
’1 square out of 3’
•
‘If you add the shaded parts together it makes one square’
is shaded and
is not shaded, which is the same as
shaded and
not shaded’
•
No mark is awarded for circling ‘Yes’ alone.
Do not accept vague or incomplete explanations, eg:
•
’It’s equivalent to
•
‘
•
‘The two parts shaded add up to
is shaded and
‘
is not shaded’
‘
• ‘Half of 2 squares are shaded’.
If ‘No’ is circled but a correct, unambiguous explanation is given,
then award the mark.
U1
[1]
Page 37 of 42
M28.
(a)
9
1
(b)
45%
1
[2]
M29.
Award TWO marks for three fractions correct as shown:
AND
AND
If the answer is incorrect, award ONE mark for two fractions correct.
Accept equivalent fractions, eg
for
for
Up to 2
[2]
Page 38 of 42
M30.
Award TWO marks for the correct answer of 24
If the answer is incorrect, award ONE mark for evidence of appropriate working, eg:
•
18 ÷ 3 × 4 = wrong answer
OR
•
18 ÷ 3 = 6
6 + 18 = wrong answer
Working must be carried through to reach an answer for the award
of ONE mark.
OR
•
a ‘trial and improvement’ method, eg
18 girls + 14 boys = 32
32 ÷ 4 = 8
18 girls + 10 boys = 28
28 ÷ 4 = 7
18 girls + 4 boys = 22
22 ÷ 4 =
A ‘trial and improvement’ method must show evidence of
improvement, but a final answer need not be reached for
the award of ONE mark.
Up to 2
U1
[2]
M31.
Numbers in order as shown:
0.34
43%
0.7
Accept use of equivalent fractions, decimals or percentages, eg 0.34, 0.43, 0.7, 0.75
[1]
M32.
(a)
Answer in the range 15% inclusive to 25% exclusive
Do not accept 25%
1
(b)
Answer in the range 200g to 400g exclusive
Do not accept 200g OR 400g.
1
[2]
Page 39 of 42
M33.
Diagram completed to show three triangles shaded, or equivalent, eg
Accept inaccurate shading provided the intention is clear.
[1]
M34.
(a) An explanation that shows that one quarter
of 240 is more than one half of 80, eg:
•
‘Because only 40 are walking to Foxwood
and 60 are walking to Midtown’
•
‘Half of the people who walk is 40 and
a quarter of the people who walk is 60’
No mark is awarded for circling ‘No’ alone.
Do not accept vague or incomplete explanations, eg:
• ‘Because at Foxwood it’s a half and at
Midtown it’s a quarter’
• ‘Because there are 80 children at Foxwood
and 240 children at Midtown’
If ‘Yes’ is circled but a correct unambiguous
explanation is given then award the mark.
1
U1
(b)
Award TWO marks for the correct answer of 50
If the answer is incorrect, award ONE mark for
evidence of an appropriate method, eg
240 ÷ 3 = 80
240 – 80 – 60 = 100
100 ÷ 2
Answer need not be obtained for the award of ONE mark.
Up to 2
[3]
Page 40 of 42
M35.
(a) An explanation that shows that one quarter
of 240 is more than one half of 80, eg:
•
‘Because only 40 are walking to Foxwood
and 60 are walking to Midtown’
•
‘Half of the people who walk is 40 and
a quarter of the people who walk is 60’
No mark is awarded for circling ‘No’ alone.
Do not accept vague or incomplete explanations, eg:
• ‘Because at Foxwood it’s a half and at
Midtown it’s a quarter’
• ‘Because there are 80 children at Foxwood
and 240 children at Midtown’
If ‘Yes’ is circled but a correct unambiguous
explanation is given then award the mark.
1
U1
(b)
Award TWO marks for the correct answer of 50
If the answer is incorrect, award ONE mark for
evidence of an appropriate method, eg
240 ÷ 3 = 80
240 – 80 – 60 = 100
100 ÷ 2
Answer need not be obtained for the award of ONE mark.
Up to 2
[3]
Page 41 of 42
Page 42 of 42