@meiconference #meiconf2019ks2 sats practice paper 99% of 200 = 2018 sats paper 1 a factory buys 10%...

@MEIConference #MEIConf2019

#MEIConf2019

Percentages through the Key Stages

Catherine van Saarloos

@CoreMathsCat

#MEIConf2019

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?

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

How would you support

students with the cat and koala

problem?

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

KS4: What’s new?

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

Compare these two problems

What makes the Higher question more

challenging?

What can we take from this to both support

and stretch students?

#MEIConf2019

AQA A level Psychology 2017 Paper 2

#MEIConf2019

AQA A level Psychology 2017 Paper 2 Mark Scheme

#MEIConf2019

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

#MEIConf2019

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

#MEIConf2019

Which has seen the most significant

change?

Compare chocolate bars in this bbc news

article:

https://www.bbc.co.uk/news/uk-42864685

#MEIConf2019

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

#MEIConf2019

Year 6 and Year 13 Approaches

to the same problems

#MEIConf2019

99% of 200

How long do you think it took Year 6 to answer

this question?

#MEIConf2019

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

me Catherine.vansaarloos@mei.org.uk

The next few slides show the written work by Year

6 and Year 13

#MEIConf2019

#MEIConf2019

Year 13 Approaches

#MEIConf2019

#MEIConf2019

5% of a certain number is 35 by

Year 6

#MEIConf2019

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

#MEIConf2019

Is this a problem?

#MEIConf2019

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