This Quibans shows the power of some Core Maths
techniques.
Here is part of the original version of an article in the
education newspaper Schoolsweek.
Coronavirus: £2.7m cost of shredding cancelled SATs papers revealed
The government has shredded exam papers for this year’s cancelled SATs and phonics tests – writing off the £2.7m they cost to produce.
Something about this didn’t seem quite right, so I did
some Core Maths to it.
First of all: it says there were 9 million ‘test papers’
and then looked at the height of a stack of paper 9 million pages tall. My experience of exam papers is that they are
usually more than one sheet.
Here is the background knowledge I already had:
·
KS2 papers are taken by almost all Year 6 children
in state schools in England (not the UK, just England).
·
England (not the UK as a whole) has a population
of about 56 million people.
·
KS1 papers are taken by almost all Year 2
children in state schools in England.
·
The phonics screening test is taken by almost
all Year 1 children in state schools in England.
·
There are 3 maths tests and 3 English tests at
KS2, 2 maths tests and 2 English tests at KS1.
Core Mathsing it
Here’s what I did with it:
·
Life expectancy in England is about 80
years. Let’s assume that there are the
same number of people at each age (might be a dodgy assumption). 56 ÷ 8 = 7, so 56 million ÷ 80 = 700,000.
·
That would give about 700,000 children in each
year group – and I will assume they all take the relevant tests.
·
Next assumption is that each test booklet has
about 20 pages, which means the equivalent of 10 sheets of A4 paper.
·
Now it’s just multiplication and addition!
·
The six papers that the Y6 children take (3 in
maths and 3 in English) have a total of 60 sheets of paper per pupil. That gives 60 × 700,000 sheets overall.
·
The four papers that Y2 children take have a
total of 40 sheets per pupil: 40 × 700,000 sheets overall.
·
The phonics test might be 2 sheets per pupil: 2
× 700,000 sheets overall.
·
This gives a final total of 102 × 700,000
sheets, which I will happily round off to 100 × 700,000 and which gives 70
million sheets of paper. This would have
a height of about 7.3 km.
That’s nearly 8 times as much as in the article, which feels
like quite a big difference!
Let’s check my assumptions. Are any of them likely to be wildly out?
·
Number of children in each year group: If anything there are likely to be slightly
more than I estimated/calculated because of population growth.
·
I didn’t account of children who didn’t take the
test though (perhaps because they are in independent schools), so maybe this balances
out the previous point?
·
I don’t know how many pages each test has, but
the ones from previous years are stapled booklets and they last about an hour
each. Surely they can’t only be 2 or 3
sheets of paper each?
So I was fairly happy with my assumptions and with my
answer of about 70 million sheets of paper.
From the numbers in the article, it appeared that the author
had assumed each of the 9 million papers was a single sheet of paper. That seems like it might be a faulty
assumption!
Looking things up
Next I looked up some figures to see how accurate my assumptions
were.
This
article says 600,000 children took the KS2 SATS last year.
This
webpage allows you to download SATS papers (KS1 and KS2) from previous
years. Here are the figures for 2019:
KS2
English

Maths


Paper 1

32 pages

Paper 1

20 pages

Paper 2

4 pages

Paper 2

24 pages

Paper 3

12 pages (reading booklet)
20 pages (answer booklet)

Paper 3

24 pages

total

68 pages

total

68 pages

That gives 136 sides of paper, which is 68 sheets
(because each piece of paper is doublesided!).
When I checked for 2018, the numbers were almost
identical (the only difference was that the English answer booklet was 4 pages
longer).
KS1
English

Maths


Paper 1

24 pages

Paper 1

20 pages

Paper 2

12 pages (reading booklet)
12 pages (answer booklet)

Paper 2

22 pages

Total

48 pages

Total

52 pages

That gives 100 sides of paper, which is 50 sheets.
Phonics screening test
It looks like (here)
that the answer sheet is filled in by a teacher and that would mean each class
only needs one copy of the question paper.
That’s a single sheet of paper for each pupil.
Comparing my estimate
with the lookedup figures
This table shows my estimated calculations and shows a
more accurate version using the figures I looked up:
My estimate

Using the real figures


KS2 papers

60 sheets per pupil × 700,000 pupils

68 sheets per pupil × 600,000 pupils

KS1 papers

40 sheets per pupil × 700,000 pupils

50 sheets per pupil × 600,000 pupils

Phonics test

2 sheets per pupil × 700,000 pupils

1 sheets per pupil × 600,000 pupils

Total

102 × 700,000 sheets
A height of about 7.3 km

119 × 600,000 sheets
A height of about 7.4 km

I am happy with that!
Do note, that I have still made some estimates when I
used the ‘real figures’.
I have assumed there are the same number of children who
take the tests in Y1 and Y2 as in Y6. I
also haven’t accounted for the class booklets for the phonics test, and for the
teacher instructions for the other tests. (I think they provide teacher
booklets in every pack of 10 papers, so this will add a couple of pages per
pupil overall).
Finally, Wikipedia says the height
of the Eiffel Tower is 300m. So if we
divide 7.4 km by 300 metres, we get that the height of the stack of paper would
be about 25 times the height of the Eiffel Tower.
Are there better representations of the height?
(Another assumption: the paper doesn’t get compressed by
the great pile of paper above it!)
The journalist who wrote the article was kind enough to confirm
that they did assume that each test paper was a single sheet and added an extra
line to the article.
UPDATE (29 July 2020)
Well this is exciting!
Since posting this Quibans the original article has been updated and now
links here:
By the power of Core Maths!
Using this with a class
I clearly haven’t used this with a class yet. Here is one way I might use it at the start
of next term, stressing the importance of Core Maths techniques in realising
when something was misstated.
Start by showing the excerpt from the article:
Coronavirus: £2.7m cost of shredding cancelled SATs papers revealed
The government has shredded exam papers for this year’s cancelled SATs and phonics tests – writing off the £2.7m they cost to produce.
Questions: What do you think? Do these numbers seem feasible? How could we tell?
Discussion about this.
Is it reasonable that 500 sheets of paper are 5.2 cm thick, are the calculations
to get the height of a million sheets correct? (Yes to all of these.)
Are there likely to have been 9 million pieces of paper
in the tests (no), are the conversions to metres and Eiffel Towers right (yes).
Next question: There _is_ an error. What is it?
(The only thing it could be is the number of pieces of
paper.)
Question: What info do you need to work out how many
pieces of paper are involved?
In response to the students’ queries, I might give them
some of the info from earlier in this post:
·
KS2 papers are taken by almost all Year 6 children
in state schools in England (not the UK, just England).
·
England (not the UK as a whole) has a population
of about 56 million people.
·
KS1 papers are taken by almost all Year 2
children in state schools in England.
·
The phonics screening test is taken by almost
all Year 1 children in state schools in England.
·
There are 3 maths tests and 3 English tests at
KS2, 2 maths tests and 2 English tests at KS1.
·
The Eiffel Tower is 300m tall.
They could then work out estimates for the number of
children in each year group (again, as I did above), or I could tell them that about
600,000 children in each of the yeargroups took the tests.
They could also estimate the number of pages in each test,
perhaps comparing with the GCSE exams (or past papers if they didn’t get to sit
the exam), or recalling their own SATS tests.
Or I might give them this information:
KS2
English

Maths


Paper 1

32 pages

Paper 1

20 pages

Paper 2

4 pages

Paper 2

24 pages

Paper 3

12 pages (reading booklet)
20 pages (answer booklet)

Paper 3

24 pages

total

68 pages

total

68 pages

KS1
English

Maths


Paper 1

24 pages

Paper 1

20 pages

Paper 2

12 pages (reading booklet)
12 pages (answer booklet)

Paper 2

22 pages

Total

48 pages

Total

52 pages

Phonics screening test
One sheet of paper for each pupil.
It is worth checking they are clear that they need half
as many sheets of paper as there are sides.
They might get calculations that look approximately like
mine:
My estimate

Using the real figures


KS2 papers

60 sheets per pupil × 700,000 pupils

68 sheets per pupil × 600,000 pupils

KS1 papers

40 sheets per pupil × 700,000 pupils

50 sheets per pupil × 600,000 pupils

Phonics test

2 sheets per pupil × 700,000 pupils

1 sheets per pupil × 600,000 pupils

Total

102 × 700,000 sheets
A height of about 7.3 km

119 × 600,000 sheets
A height of about 7.4 km

7.5 km divided by 300 metres = 25, so the stack of paper
would be about 25 times the height of the Eiffel Tower.
Final question:
Can they think of better representations of the height?
Source: https://schoolsweek.co.uk/coronavirus27mcostofshreddingcancelledsatspapersrevealed/
[NB: Some of the article appears in screenshot form because I wanted to show it before it was updated.]