35
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Percentages through the Key Stages
Catherine van Saarloos
@CoreMathsCat
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Where do these questions
appear?
In pairs, consider the collection of
questions on your table. At which stage
would you expect these questions to
appear in assessments?
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KS2: Year 5
Percentages first appear
recognise the % symbol
per cent relates to ‘number of parts per 100’
write as a fraction with denominator 100 and as
a decimal fraction
solve problems which require knowing
percentage and decimal equivalents
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study
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KS2: Year 6The Goal:
Pupils should be fluent in working with fractions,
decimals and percentages.
solve problems e.g. 15% of 360 and the use of
percentages for comparison
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study
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99% of 200 =
KS2 SATS
2018 Paper 1
A cat sleeps for 12 hours each
day
50% of its life is spent asleep.
Fill in the missing percentage
A koala sleeps for 18 hours each
day
_____% of its life is spent asleep.
KS2 SATS 2017 Paper 2
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How would you support
students with the cat and koala
problem?
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KS3: What’s new?
Interpret percentages and percentage changes
Express 1 quantity as a percentage of another
Compare 2 quantities using percentages
Work with percentages greater than 100%
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study
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KS3 ProblemsPercentage change:
percentage increase, decrease and original
value problems
simple interest in financial mathematics
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study
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5% of a number is 31
1% of the same
number is 6.2
Work out 13% of the
number
5% of a certain number
is 35.
What would 10% of the
number be?
What was the number?
AQA Foundation
Paper 1 2017
KS2 SATS practice
paper
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KS4: What’s new?
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Key Stage 4Solve Problems
interpret and solve problems, including in
financial contexts and evaluate outcomes
make and use connections between different
parts of mathematics
model situations mathematically and reflect on
solutions
select appropriate techniques to apply to
unfamiliar and non-routine problems; interpret
their solution.
https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study
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Jack and Sadia work for a company that sells boxes of
breakfast cereal.…
By what percentage does she need to reduce the
price?
Edexcel 2018 Higher
Edexcel 2018
Foundation
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Compare these two problems
What makes the Higher question more
challenging?
What can we take from this to both support
and stretch students?
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AQA A level Psychology 2017 Paper 2
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AQA A level Psychology 2017 Paper 2 Mark Scheme
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Despite 36% of students not having
the mathematical skills to answer
this question appropriately and 3%
not even attempting it, those who did
have the knowledge answered it
well. Some missed or did not
understand the requirement for three
significant figures.
AQA A level Psychology 2017 Paper 2 Examiner Report
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KS5: Sample L3 Core Maths
Content (OCR)
Do calculations IN CONTEXT
Financial: VAT, inflation and compound interest for
savings or loans.
Comparison of an annual % depreciation model with
actual values over time.
Work out an average annual % growth rate
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Which has seen the most significant
change?
Compare chocolate bars in this bbc news
article:
https://www.bbc.co.uk/news/uk-42864685
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20% of the population
are smokers. The rest
are non-smokers.
22% of smokers get
the disease.
10% of non-smokers
get the disease.
AQA level 3 core
maths Paper 2B 2017
A factory buys 10% of its
components from supplier
A, 30% from supplier B and
the rest from supplier C. It
is known that 6% of the
components it buys are
faulty.
Edexcel AS
Paper 2 2018
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Year 6 and Year 13 Approaches
to the same problems
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99% of 200
How long do you think it took Year 6 to answer
this question?
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99% of 200
I have not included the videos because I don’t
want them to be taken out of context – particularly
the Year 13 video. But I am happy to re-run this
session at some AMSP/MEI events and other
conferences in the future so you have the
opportunity to see them. Happy for you to contact
The next few slides show the written work by Year
6 and Year 13
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Year 13 Approaches
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5% of a certain number is 35 by
Year 6
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5% of a certain number is 35.
What is 10% of the number?
What is the number?
How long do you think it took Year 13 A level
Maths students to answer this question?
Year 13 Approaches
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Is this a problem?
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About MEI Registered charity committed to improving
mathematics education
Independent UK curriculum development body
We offer continuing professional development
courses, provide specialist tuition for students
and work with employers to enhance
mathematical skills in the workplace
We also pioneer the development of innovative
teaching and learning resources
Question Level
5% of a number is 31 1% of the same number is 6.2 Work out 13% of the number
AQA Foundation Paper 1 2017
Jack and Sadia work for a company that sells boxes of breakfast cereal. The company wants to have a special offer. Here is Jack’s idea for the special offer: Put 25% more cereal into each box and do not change the price Here is Sadia’s idea: Reduce the price and do not change the amount of cereal in each box. Sadia wants her idea to give the same value for money as Jack’s idea. By what percentage does she need to reduce the price?
Edexcel Higher 2018
Here is some information about smoking and a common disease.
20% of the population are smokers. The rest are non-smokers.
22% of smokers get the disease.
10% of non-smokers get the disease.
a) What percentage of the population are smokers that get the disease?
b) What percentage of those who get the disease are smokers?
c) A media report on the disease makes the following statements:
AQA level 3 core maths Paper 2B 2017
Statement 1 Most of those who get the disease are smokers Statement 2 Smokers are more than twice as likely as non-smokers to get the disease. Comment on each of these statements. You should refer to the information given at the beginning of the question, and to your answer to part (b).
d) If the percentage of smokers in the population decreased from 20%, what would happen to the percentage of those getting the disease who were smokers?
Circle your answer It would decrease It would stay the same It would increase Impossible to tell
Edexcel 2018 Foundation Number
5% of a certain number is 35. What would 10% of the number be? What was the number?
KS2 SATS practice paper
99% of 200 = 2018 SATS Paper 1
A factory buys 10% of its components from supplier A, 30% from supplier B and the rest from supplier C. It is known that 6% of the components it buys are faulty.
Edexcel AS Paper 2 2018
Of the components bought from supplier A, 9% are faulty and of the components bought from supplier B, 3% are faulty. Find the percentage of components bought from supplier C that are faulty.
A cat sleeps for 12 hours each day 50% of its life if spent asleep. Fill in the missing percentage A koala sleeps for 18 hours each day _____% of its life is spent asleep.
KS2 SATS 2018
AQA 2017 Paper 2
