m e i . o r g . u k
Curriculum Update
GCSE
Ofqual has
announced the
publication of revised
GCSE maths sample
assessment materials
by AQA, OCR,
Pearson and WJEC
Eduqas.
Commenting on the
announcement,
Glenys Stacey, Chief
Regulator, said:
“The new sample
papers are now
judged to be very
similar, in terms of
expected difficulty,
and also likely to
differentiate across
the full range of
students. They meet
our requirements.
We appreciate that
teachers will want to
choose a specification
that best suits their
students and the way
that they teach, with
the assurance that,
whichever board they
choose, standards will
be comparable when
students sit their
exams in 2017 and
beyond.”
I s s u e
J u l y
4 8
2 0 1 5
End of term update
We have a different format of M4
magazine this month as we know that
the end of the term is nigh!
We recently held our annual
conference and wanted to share some
of it with you, especially if you were
unable to attend, so on the next page
you’ll find a few photos from the threeday event, and an adapted version of
the Delegate Challenge for you to use
with students (or to try yourself!). This
was devised by Carol Knights, the MEI
Extension and Enrichment Coordinator.
The original activity, targeted at
teachers, included QR codes for
participants to scan to find more
information related to the questions.
The QR codes (and resources) were
available on each of the exhibition
stands on the Friday of the conference.
Overall winner of the Delegate
Challenge was a team from Peter
Symonds College, with Howard Fay
coming a very respectable second. The
winning team shared a prize of two
Dynakars to add to their existing one!
You can read more in
the Ofqual press
release.
Click here for the MEI
Maths Item of the Month
Howard was presented
with a prize of a Casio
Edifice men’s watch by
Tatiana Bowskill,
Education Project
Manager of Casio UK.
We also
awarded
other
prizes:
some
delegates
spotted a gold label on a leaflet in their
delegate bag, which won them a prize
from that organisation.
In this issue
You can see
the Dynakar
in action on
YouTube.

Curriculum Update: New GCSE
specimen assessments available
on exam boards’ websites

July focus: End of term update

KS3-KS5 Teaching Resource:
Summer Challenge
M4 is edited by Sue Owen, MEI’s Marketing Manager.
We’d love your feedback & suggestions!
Disclaimer: This magazine provides links to other Internet sites for the convenience of users. MEI is not responsible for the availability or content of these
external sites, nor does MEI endorse or guarantee the products, services, or information described or offered at these other Internet sites.
Delegate ideas
Delegate Ideas
We asked MEI Conference Delegates
to share what ideas they would take
away from the conference and share
with their colleagues back at their
school/college. The response to this
was great: some delegates Tweeted
their #MEIConf2015 #Ideas (follow the
link to read these), while others wrote
their ideas onto sheets and pinned
them onto a
noticeboard.
We will put all
of these ideas
together onto a
document and
upload these to
our MEI
Conference
2015 archive,
where in due
course some of our session resources
will also be uploaded.
You can read more about
the conference by
searching for
#MEIConf2015 on Twitter.
MEI Conference 2015
New end of term
resource
The final teaching and
learning resource of
the academic year is
a replica of the
delegate challenge
from MEI’s Annual
Conference.
There are 15
challenges, presented
in approximate order
of difficulty, for you
and your students to
enjoy. You should
find some questions
are suitable for KS3
students whilst others
will challenge A level
students.
Some hints are
provided after the
relevant question and
all answers are given
in the teacher notes
at the end of the
resource.
The PowerPoint
version of the
resource can be
downloaded from the
Monthly Maths web
page - you can then
remove the teacher
notes and solutions
before sharing it with
your students!
Have fun!
M4 Magazine will return next term, when it will change to a half-termly issue.
Challenge 1
Arrange all the digits 1 to 9, using
them once each only, to form a
fraction equivalent to 1/3
Challenge 1 Hint
What could the 2 numbers end in?
What could the first digit of the
bottom number be?
Challenge 2
A handywoman is going to fix numbers onto
bedroom doors in a very large hotel. The
numbers are supplied as individual digits.
There are 1000 rooms, how many 7’s does she
need?
Challenge 3
Why is the number 8,549,176,320 special?
Challenge 4
What are the smallest integer values of A, B and
C such that the product of any two of the values
added to the third gives a square number?
Challenge 5
Find the three 4 digit numbers that equal the
square of the sum of the two 2-digit numbers
formed from the 1st and 2nd digits and 3rd and
4th digits.
e.g. one that doesn’t work:
1546 ≠ (15+46)2
Challenge 5 Hint
Can you use a spreadsheet to help you find
them?
Challenge 6
.-- .... .- - -.. --- -.-- --- ..--. . - .. ..-. -.-- --- ..-- ..- .-.. - .. .--. .-.. -.-... .. -..- -... -.-- -. .. -. .
Help here
Challenge 7
A set of 15 dominoes (all combinations of 1 to 5)
is placed on a square grid as shown – except that
the outlines haven’t
2 2 3 5 4 3
been given…
What number is on the
2 1 3 2 5 4
other half of the domino 4 1 5 5 3 4
with the ‘1’ highlighted? 3 3 2 2 4 1
4 5 1 5 1 1
Challenge 7 Hints
What are all the possible dominoes?
Are there any dominoes
that have to be in a
certain place?
2
2
4
3
4
2
1
1
3
5
3
3
5
2
1
5
2
5
2
5
4
5
3
4
1
3
4
4
1
1
Challenge 8
Cherries are naturally 80% water.
Dried cherries are made by leaving them in the
sun until they have lost 75% of their water.
What is the percentage water content
of dried cherries?
Challenge 9
Mia uses an escalator at a railway station.
If she runs up 8 steps of the escalator, then it
takes her 55 seconds to reach the top. If she runs
up 15 steps of the escalator, it takes her 37.5
seconds to reach the top.
How many seconds would it take
Mia to reach the top if she did not
run up any steps at all?
Challenge 10
Each side of the triangle ABC is divided into 5
equal parts.
What is the ratio of the area of the blue triangle to
the area of ABC?
B
A
C
Challenge 10 Hints
B
C
A
A
B
C
Challenge 11
A boat carries rocks on a small, still lake making
the depth of water in the lake D.
The rocks are released and sink to the bottom of
the lake.
Is the level of water in the lake now greater than,
less than or the same as D?
Challenge 11 Hint
Think about a small marble made of gargantuan –
a (fictitious) metal which is 1000 times as ‘heavy’
as lead.
Challenge 12
A large number of sweets need to be eaten.
Eating alone, it takes Hannah an hour to eat a jar
of them, Mike 3 hours, Nat 5 hours and Oscar 7
hours.
Eating together, how long, to the nearest
minute, does it take them to eat their
way through 3 jars of sweets?
Challenge 12 Hints
In 15 hours, Mike will have eaten 5 jars and Nat
will have eaten 3 jars.
Can you find a whole number of hours in which
they will all have eaten full amounts of jars?
Challenge 13
A symmetrical yellow crescent is formed from two
circles as shown with O being the centre of the
larger circle.
AB = 5cm and CD = 9cm
What are the diameters of
the two circles?
Challenge 14
The circumference of a circle is divided into n
equal arcs and semi-circles constructed as
shown.
Can the blue shapes at the edge ever be equal in
area to the orange petals?
If so, what should n be?
Challenge 14 Hint
Try looking at just one blue shape and orange
petal.
Challenge 15
What is the internal side length of the smallest
hollow cube which can wholly contain 4 identical
spherical chocolates, each of diameter 10cm?
Challenge 15 Hint
Think about how the chocolates could be
arranged. Some ping pong balls or tennis balls
might be helpful.
Teacher notes: Summer Challenge
The final edition of the academic year is a replica of the delegate
challenge from MEI’s Annual Conference.
There are 15 challenges, presented in approximate order of difficulty,
for you and your students to enjoy. You should find some questions
are suitable for KS3 students whilst others will challenge A level
students.
Some hints are provided after the relevant question and all answers are
given in the teacher notes below.
Enjoy!
Teacher notes: Summer Challenge
Challenge 1
5832
17496
or
5823
17469
Challenge 2 300
Challenge 3 All the digits are in alphabetical order
Challenge 4 1, 7 and 9
Teacher notes: Summer Challenge
Challenge 5 2025 3025 9801
Sample spreadsheet columns below, searching for zero values in
column G.
For this solution it helps to work ‘backwards’ through the problem.
Start with a number (A) and square it (B), split the square numbers into
first pair and second pair (C leading to D&E), add them together (F),
compare with original number (G).
A
B
C
D
E
F
G
44
1936
19.36
19
36
55
11
45
2025
20.25
20
25
45
0
n
n^2
B/100
int( C )
(C-D)*100
D+E
F-A
Teacher notes: Summer Challenge
Challenge 6 What do you get if you multiply six by nine? 54
Challenge 7 4.
Challenge 8 50%
Challenge 9 75 seconds
Challenge 10 8:25
look for triangles of equal base and height.
Challenge 11 Less than D.
When the rocks are in the boat, the mass of water displaced is equal to
the mass of the rocks, when in the water, the volume of water displaced
is equal to the volume of the rocks.
Since the rocks sink, their density is greater than 1, hence more water
is displaced when the rocks are in the boat than when they are in the
water.
Teacher notes: Summer Challenge
Challenge 12 1 hour and 47 minutes
Find the lowest common multiple of the number of hours for each
person to eat a jar.
In 105 hours, Hannah eats 105 jars, Mike 35, Nat 21 and Oscar 15.
That’s 176 jars between them.
176 jars in 105 hours (6300 minutes), so use proportional reasoning to
find how long it takes to eat 3 jars.
Challenge 13 50cm and 41 cm
Teacher notes: Summer Challenge
Challenge 14 8
Consider the circle to have a radius of 2r, then the
area of the circle is 4πr2
Looking at a single sector and ‘petal’,
blue area=orange area
only if
area of sector = area of semicircle
Area of semicircle is 0.5πr2
Area of sector = 0.5πr2
when there are 8 sectors
Teacher notes: Summer Challenge
Challenge 15 10+5√2 or an equivalent expression
The chocolates should be arranged as a tetrahedron with each
chocolate nestling in a vertex. This means that 2 chocolates will sit
diagonally at the bottom of the box and 2 at the top. Use this 2d
diagram to calculate the size of the square.