Monthly
Maths
I s s u e
Curriculum Update
A levels
New linear A levels in
Mathematics and
Further Mathematics
are being developed now for first teaching
from September
2017. Read Nick
Gibb’s 1 Dec 2014
letter to Ofqual.
4 2
A Buffet of Mathematical
Possibilities
With Thanksgiving having just taken
place in the USA, we found this activity
that you could adapt for Christmas
dinner - or indeed any celebratory
dinner. See how many combinations of
turkey dinners you can make with the
help of this video from the Worldwide
Center of Mathematics.
NEW CPD web page
Click here to view
General Core Maths
webinar recording
Click here to access
2 0 1 4
An organised list of outcomes, called a
sample space, is used to help students
to determine the total number of
possible outcomes for an event. A tree
diagram is one example of an
organised list.
All of these ideas could be adapted in a
seasonal way.
Questions that you might ask students:
How many ways can I make up my
dinner plate for my first serving?
How many ways total if I go up for
seconds?
How many ways if I want to try
everything once?
Free OCR network
twilight events
NEW CORE MATHS:
Introducing the
specification and
increasing post 16
participation.
Click here to view
available courses.
D e c e m b e r
On page 651the chapter
Permutations includes a look at
different arrangements of
students in a lunch queue, at
combinations of flavours of ice
cream, and at playing tracks on
a random shuffle.
Core
Maths
Friday 5 Dec 16:00
OCR(MEI)
Quantitative
Reasoning and
Quantitative Problem
Solving webinar.
Click here to
register
www.mei.org.uk
In this issue

Curriculum Update: Core Maths
CPD and support

December focus: Christmas and
end of term problem solving for
KS3-5
How many ways if I go up for seconds

but definitely want more turkey?

Count Outcomes
Similar problems can be found in the

Probability and Combinations
chapter, page 645 (Count Outcomes)
from the US online resource McGrawHill Connect.
Click here for the MEI
Maths Item of the Month
Angry Surds Competition
Site-seeing with... Phil Chaffé
Teaching Resource: Twelve Days
of Christmas
Monthly Maths is edited by Sue Owen, MEI’s Marketing
Officer. We’d love your feedback & suggestions!
Disclaimer: This newsletter 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.
Festive food
and seasonal soda
Chocolate Ratios
Soda Santa
JustMaths offers 5
maths based starter
questions on the
subject of sharing in a
ratio. Ideal to get the
students limbered up
and ready to learn or
as a plenary to check
understanding.
American maths teaching site
Yummymath offers a seasonal
teaching resource based on this
supermarket display of cola cans.
Themed around
chocolates, this could
easily be adapted for
festive occasions.
Why are ratios
important in cake
baking?
If you’re like me you
probably have a
recipe book with
pencil scribbles next
to the ingredients
where you have
adjusted the recipe
according to the size
of your cake tin.
The Maths Careers
site explains why it’s
useful to know ratios
in cake making:
Ratios make baking
a piece of cake.
You could show this picture to your
students (download here) and give
them 30 seconds to look at it, asking
them to take a quick guess: How many
twelve packs of soda make up the
Santa? Guess without calculating.
Come up with a reasonable range for
the number of twelve packs. Decide
which numbers are too high or too low.
This activity includes a sheet of
questions - you do need to be a
member to download the editable Word
doc and solutions. However, there are
more suggestions about using this
resource on
Graham
Fletcher’s blog
and you can
access more soda
display images
on Flickr.
GCSE Maths: Area and perimeter
activities for Xmas
This area and perimeter differentiated
activity on the tesconnect site is
based on the popular Coca Cola
Christmas truck. The activity is intended
to be completed in small groups.
Question sheets and answers are
available for download by registered
users of the site (free of charge).
Smarties Art
Alex Bellos’ Guardian article Candy
Warhol: why Smartie art is
M&Mazing shows some amazing
images and links to a new website,
Candy Art, that enables you to turn any
image into a mosaic of confectionery.
The Maths Bytes code will create a
Smarties or M&Ms Art rendering of an
image, according to your choice of
confectionery, colours and number of
sweets used. You may upload your own
image - I have candied a member of the
MEI staff in the image below!
Rich problem solving:
Santa’s journey
and more
The science of
Christmas: Santa
Claus, his sleigh,
and presents
You might like to read
this Telegraph article
that contains a rather
tongue in cheek look
at Santa’s dilemma
from a scientific point
of view.
Keith Devlin’s
Mathematical
Association of
America article (2000)
The Mathematics of
Christmas and the
Washington Times
article (2013) Yes,
Santa can deliver all
those presents on
Christmas Eve: Do
the math are two of
many such pieces
that have addressed
the Santa's journey
issue over the years!
Another take on this
subject can be found
in ThatsMaths article:
Santa’s Fractal
Journey. ‘If we
assume the route is
fractal, most of the
distance is due to the
small segments from
one house to the
next. With a billion
houses to visit, and
the typical distance
between neighbouring
houses being ten
metres, we get a
length of 10 million
km.’
Bowland Maths
has imaginative
resources for rich
problem solving in secondary school
Maths; all of the materials can be
downloaded from the Bowland Maths
website and are free for noncommercial educational use.
This collection of free resources was
designed to support rich problemsolving activities in secondary school
maths, including classroom material,
assessment tasks and professional
development resources. The material is
aimed at Key Stage 3 but can be
adapted for a wide range of ages and
abilities.
As well as longer Classroom Projects,
Bowland Maths includes over thirty
‘assessment tasks’ designed to help
you assess your pupils' achievements
and progression against the Key
Processes defined in the Key Stage 3
National Curriculum. These selfcontained tasks take between twenty
minutes and an hour.
The materials developed for these tasks
are also ideal for formative
assessment that concentrates on
providing the types of rich feedback that
have been proven to help pupils
improve their reasoning.
Here are some tasks selected from the
above that you could relate to the
festive season - click the title of each to
view its level and suggested timings,
and to access the resources, which
comprise a Word document and a PDF
of the task, also a PowerPoint starter.
Speedy Santa
Pupils determine
the amount of
time Santa can
spend at each
house in the UK
when delivering presents on Christmas
Eve. He can only start after children are
asleep and he must be finished by
daybreak.
Candle Box
Pupils design a
2D net for a box,
given a 3D
picture of the
box. What types
of flaps will need
to be included and how will you tell
which ones are to be glued?
The Z Factor
Pupils determine
how long it
would take a
panel of judges
if they saw every
act that auditioned for the “Z factor”
programme. How do they decide which
of the thousands of acts get through the
first set of auditions?
Taxi Cabs
Pupils plan a trip
for a large party
using two kinds of
taxi cab that will
charge a fixed
price for the journey. The aim is to
transport 75 people to the airport as
cheaply as possible. Pupils try to decide
how many of each cab they need to
minimise the overall transport costs.
The Twelve Days
of Christmas
The Great Carol Comeback
GCSE Maths
Activity "12 Days
of Christmas"
cost?
Available to
download from the
TES connect site. The
resource contributor
says:
‘If you were to buy
every gift in the "12
Days of Christmas"
song/carol, how much
would it cost? Where
would you buy them
from? How many
humans would you
"buy"? How many non
-living objects?
12 Days of
Construction
This TES resource
involves groups of
students developing
their own skills in
construction using
independent learning.
An excellent way to
consolidate and
practise constructions
with students, and
encourages students
to work together and
listen to each other.
The Twelve Math
Days of Christmas
- Easy As Pi!
Googol
Learning
offers 12
great ways to
combine maths with
Christmas activities.
Now in its 31st year, this year’s PNC
Christmas Price Index® is themed on
reviving the popularity of the classic
carol “The Twelve Days of Christmas”
by listing the current price of each of the
components of the song and its
percentage price increase/decrease.
Bear in mind that this is an American
site and so the prices will be in US
dollars.
The PNC team explains:
‘Dear Educators and students:
The PNC Christmas Price Index® is a
simple, yet entertaining way to
introduce basic economics to
classrooms around the country. By
picking out each gift from “The Twelve
Days of Christmas” year after year, we
are able to provider a snapshot of our
current economy, lessons on inflation
and other economic trends.
‘But there’s one small problem. This
once-beloved carol has declined in
popularity. And since we can’t have a
Price Index if the song falls off the
charts, we’ve taken it upon ourselves to
introduce The Great Carol Comeback:
12 ways to bring “The Twelve Days of
Christmas” to a new generation.’
You can view and listen to the
introduction to this year’s PNC
Christmas Price Index® from the link at
the bottom of the main page: The
Great Carol Comeback. The calendar
listing each of the twelve days of
Christmas contains links to ‘Learn’ and
‘Play’ sections. I’d suggest clicking the
‘Learn’ before the ‘Play’ tabs.
On the PNC website, tabs will give also
you access to the following resources,
on which you could base new
discussions/problems - click the links
below to go straight to those pages:

Price Index by Year

Price Index by Gift

About the PNC Index

The History of the Index

Activities from the Stock
Market Game - these self
contained activities (from the
SIFMA Foundation, a US
organisation dedicated to
providing financial education for
young people) will give you
everything you need to use the
PNC Christmas Price Index®
Maths Advent
Calendars and a
competition reminder
More End of Term
Resources
Here’s a round up of maths
advent calendars we’ve found
Click the titles to visit the web pages
and download the resources
TES connect has a
host of different KS4
problem solving
resources and
puzzles suitable for
the end of term.
You can also find
Christmas activities in
the TES Secondary
Maths Collection 8 "Maths at
Christmas".
Also listed on TES
connect are recently
recommended TES
KS4 Maths
Christmas
resources
TES connect: Advent Calendar full of
fun, engaging starters
An Advent Calendar behind which are
11 different fun & engaging starter/
plenary activities covering the full maths
spectrum of topics & abilities. Designed
to be done as a running competition
between 2 teams.
TES connect: Mathematics Advent
Calendar
Over 20 problem-solving tasks for use
in maths lessons in December. Suitable
as starter activities, they span the
difficulty range from low-attaining KS3
pupils to high-achievers at KS4.
Accompanying resources for students
are included and the calendar can
easily be adapted.
Angry Surds Competition
Last month we invited
our readers to a sneak
preview of MEI’s new
maths game hosted on
our resources site
Integral: Angry Surds.
Help the surds defeat the invasion of
the decimal approximations using
Pythagoras’ Theorem! Apparently one
teacher has set this as homework for
her students!
A maths
problem
appears on
the final
screen if you
can complete
Angry Surds in
Timed Mode on ‘Insane’ challenge
level. It’s free to play! Click here to
play Angry Surds.
nrich Advent Calendar
2014
Click on each number
on the Advent Calendar
to find one of the nrich team’s favourite
mathematical activities.
Crash Course
Our new maths and
computing puzzle
column Crash Course
(see last month’s
issue) will start in
2015 - have you
taken the first steps in
Python with your
students yet?
MathsBank
Advent Calendar
24 online A level resources for students
and teachers
2014 Plus
advent
calendar
In this year's advent calendar Plus
Magazine brings you some of their
favourite books and other mathematical
toys, so you can surprise your friends
and family or, even better, yourself!
The prize for this competition is still up
for grabs so don’t forget to send us/your
students’ answers! The first person to
email a correct answer
to that problem will win
a signed copy of Simon
Singh’s book ‘The
Simpsons and their
Mathematical Secrets’!
Click here to email your answer.
Site seeing with…
Phil Chaffé
Each month a
different member of
MEI staff will share a
couple of their
favourite resources it might be some
software, a website, a
printable download, a
book, etc.
The column is
intended to be a quick
read - but we’d love
to hear from you if
you’d like to give
feedback or tell us
how you used the
resources.
This month’s
resources are shared
by Phil Chaffé, who
is a Central
Coordinator for the
Further Mathematics
Support Programme.
Phil has particular
responsibility for
Enrichment within the
FMSP and is also
London Schools
Excellence Problem
Solving Course lead.
I’ve been working on a number of
projects to do with mathematical
problem solving recently. These have
ranged from preparing teachers for the
problem solving elements of the new
GCSE to preparing students for the
STEP and AEA examinations.
One book I always
reach for when I
want to help
people develop
problem solving
skills is George
Pólya’s How to
Solve it. Although
it was originally
written in 1945 and
the writing can feel
a bit old-fashioned, the ideas remain
relevant to mathematical problem
solving at any level. It really is an
essential guide. My edition contains a
wonderful foreword by Ian Stewart that
provides an excellent summary of
Pólya’s problem solving heuristics.
The other book I reach
for is Andrew Jobbings’
A Problem Solver’s
Handbook which
provides clear advice for
students tackling a wide
variety of problems.
Each puzzle is introduced in a short
animated video. The answers are also
available in video form.
The puzzles are not aimed at a
particular age group and are suitable for
getting a wide range of students to start
thinking mathematically.
New classroom resource
In the following pages is a teaching and
learning resource, Twelve Days of
Christmas, developed by Carol
Knights, MEI Extension and Enrichment
Coordinator. The PowerPoint and Excel
files can be downloaded from the
Monthly Maths web page.
December’s resource is a selection of
short activities and puzzles – and some
a little longer – with a slightly festive
twist to count down to the end of term.
They could be used as starter activities
I often ask teachers to analyse the sort for a wide range of students in KS3 and
of mathematical problems they use in a KS4 or as a bit of fun for Post-16
students. Some have natural
classroom. Mathematical puzzles are
extensions that would make them more
often overlooked as it is difficult to tie
these down to particular topic areas. Ian challenging. In the teacher notes are
Stewart poses some fun and interesting answers for all of the problems and
suggestions for additional questions for
puzzles that can be found on the
some of the problems.
Warwick University Podcast pages.
12
After all the arguments last year, Santa has sorted
out the sleeping quarters for the reindeer.
Rudolph, Donner, Blitzen, Dasher, Comet, Cupid,
Vixen, Dancer & Prancer are all eager to know
which pen will be theirs
1
2
3
for the festive season.
4
5
6
However, instead of
simply telling them which
pens to go to, Santa has
7
8
9
left a set of clues.
12
• Rudolph will be in pen
number 1 (of course)
• No reindeer will be in a
pen that has the same
number as the number
of letters in his or her
name.
• Dancer and Prancer
will be in pens which
are numbered with
square numbers
• Cupid is not next to
Prancer
• In each row and column
there will be a reindeer
with a 5 letter name, a
6 letter name and a 7
letter name
• Cupid’s number +
Vixen’s number =
Dasher’s number
11
• At a festive gathering, Uncle Joe is again
demonstrating his amazing mathematical abilities.
• He claims to easily be able to square numbers
ending in 5 in his head.
• Here is an example of how he does it for 752:
•
•
•
•
‘Split’ the number
Work out 7x8 and 5x5 separately
Put the answers together
752 = 5625
Does it work for these numbers: 952 1052 1952?
10
Aunt Dorothy has 17 young nieces and
nephews and she likes to put together a Christmas
stocking filled with small presents for each one.
However, she likes each child to have a different set
of presents to all the other nieces and nephews.
She needs 6 presents to fill each stocking.
She could try to find 102 different presents so that
they all have completely different sets of presents,
but this would take a very long time.
What’s the minimum number of different items
she needs to find?
9
Santa Claus is making 9 Christmas puddings.
He’s made them all of equal size and weight, and
intended to put a silver coin in each one.
Unfortunately he has one coin left over, which means
that one of the puddings is without a coin…
He needs to work quickly (whilst Mrs Claus
is feeding the reindeer) to identify the pudding,
but he only has a simple set of scales to hand.
How many times does he need to use the scales to be
sure which pudding is without its coin?
8
Frosty started life 2
metres tall.
Each time there is a
sunny day, he loses 20%
of his current height.
How many sunny days
will it be before he’s
reduced to a small pile of
snow of less than 10cm?
7
Three of the Seven Dwarves are arguing about a
restaurant bill.
They’ve worked out that Grumpy (yellow hat) owes
half the bill, Bashful (orange hat) owes a third and
Doc (red hat) owes an eighth of it.
The bill is £23, but they each only have pound
coins, The manager arrives and suggests they
round it up to £24 instead as that will be
easier to split.
They are all happy with this and the
manager gets £23… how can this be?
6
Place the
numbers 1 to 12
in the circles
(once each) so
that each row of
4 numbers adds
up to the same
total.
5
5 machines are making sweets.
They are all supposed to be making
them exactly the same size, shape
and mass.
Unfortunately, one of the machines is
making them 1 gram too heavy.
How can the operator identify which
machine it is by weighing just one
batch of sweets?
4
Two identical large
equilateral triangles
form a ‘regular’ star.
What fraction of the
star is shaded?
3
All is not well in the Claus household.
Santa wants to put up some lights…
…but Rudolph, who is obsessed with numbers and
sequences, has tinkered with them so that each
one will only light up if the number that Santa
enters appears in a certain sequence
(a different sequence for each light).
It should look like the set below.
Please help Santa!
2
In each of the word sums on the next slide replace
each letter by a digit from 0 to 9.
The same letter is replaced by the same digit within a
sum, and the sum must ‘add up’ correctly.
Each digit can only be used once in each word sum
(they’re not all the same solutions).
Notice that
Example:
‘O’ is
ON E
4 3 2
replaced by
+ O N E could be + 4 3 2
‘4’ in all
places
T W O
8 6 4
2
E A T
+ E A T
F U L L
V I X E N
+ V I X E N
C O M E T
S M I
L E
+ S M I L E
H A P P Y
+
S N O W
C O M E T
M A N
C O L D
+ C O M E T
D A S H E R
1
The numbers 1 to 15 have all been assigned a
letter. Solve the clues on the next slide to crack the
code below (dots mark the end of each word):
9 5 12 3 . 5 . 7 11 3 5 6 . 9 10 1 2 4 5 8 .
3 12 3 11 8 10 13 3 ; 14 3 3 . 8 10 15 .
5 7 5 2 13 . 2 13 . A x N x (O x E + L)
1a
2T = 12
G>I
A2 = 25
AE = U
G+I = 9
V = 3D
L2 = L
Y+T = S
N+G = 20
2G = S
3E = 9
H+1 = O
R-E = Y
1b
2N+I = 28
N+2I = 17
A2 = 25
AE = U
G= 49½
(V-D)2 = Y2
L2 = L
2G = S
R2-O2=21
(x + E)(x + Y) = x2 +11x +24
Y>E
2H-T = 12
H+T = 15
Teacher notes: Twelve Days of Christmas
This is a selection of short activities and puzzles – and
some a little longer – with a slightly festive twist to count
down to the end of term.
They could be used as starter activities for a wide range of
students in KS3 and KS4 or as a bit of fun for Post-16
students. Some have natural extensions that would make
them more challenging.
In the teacher notes are answers for all of the problems
and suggestions for additional questions for some of the
problems.
Teacher notes: Twelve Days of Christmas
12: You could print out slide 3 for students to work from
1 Rudolph
2 Cupid
3 Donner
4 Dancer
5 Blitzen
6 Vixen
7 Comet
8 Dasher
9 Prancer
Teacher notes: Twelve Days of Christmas
11: Yes, this method always works.
952 = 8125
1052 = 11025
1952 = 38025
Try for other numbers.
Additional question: why does this work?
The number ‘P’5 can be written as 10P+5
(10P+5)2
= 100P2 +100P +25
= 100P(P+1) + 25
The 100 multiplier ‘shifts’ the answer to P(P+1) into the
‘hundreds’ column and beyond, leaving space for the ‘25’
Teacher notes: Twelve Days of Christmas
10: 8 different items needed
It’s probably easiest thinking
about this in terms of what
she doesn’t put in.
If she had 7 different items,
she would have to leave 1
item out each time, so there
are only 7 ways to do this.
If she had 8 different items,
she would need to leave 2 out
of each stocking.
There would be 8C2
possibilities, which is 28; she
needs 17, so this is sufficient.
Alternative approach to 8C2
Shaded cells indicate which
pairs of presents can be left
out: & 1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
There are 28 pairs.
Teacher notes: Twelve Days of Christmas
9: Just twice.
We know that the pudding without the coin will be lighter.
Group the puddings into 3 sets of 3 (A, B & C)
Identify which set of 3 the lighter pudding is in by loading
set A on one side and set B on the other. If one side rises,
it’s within that set of 3, if they balance, it’s within set C.
From the set of 3, put one pudding on one side and one on
the other. If one side is lighter, it has been identified, if they
balance, it’s the other pudding.
Additional question: what if there were 27 puddings? (just 3
comparisons needed). Recommended to change the
initial problem to 27 puddings for more challenge.
Teacher notes: Twelve Days of Christmas
8: If Frosty is built on Day 1, then on Day 15 he drops below
10 cm.
Teacher notes: Twelve Days of Christmas
7: The Dwarves were incorrect in their initial calculations:
1
2
+
1 +
1 =
23
3
8
24
Teacher notes: Twelve Days of Christmas
6: One solution is shown.
Hint: What must the total for each
line be?
Each number is used twice, so the
sum for the whole star is
2x(1+2+3…+11+12) = 156
156 ÷ 6 = 26
This forum has a good explanation
about how to find solutions
logically.
Teacher notes: Twelve Days of Christmas
5: Sweet problem.
Take:
1 sweet from machine 1
2 sweets from machine 2
3 sweets from machine 3
4 sweets from machine 4
5 sweets from machine 5.
Weight them all together.
The number of grams over the ‘proper’ weight will tell her
which machine is malfunctioning.
Teacher notes: Twelve Days of Christmas
4: 1/48th
The middle hexagon is equal in
area to the area of the 6 outside
points.
The interior hexagon has been
divided into 6 similar shapes.
One of the sections has been
divided into 4 similar triangles.
Can you show they are similar?
Teacher notes: Twelve Days of Christmas
3: You will need the Excel file ‘Christmas Lights Sequence’; macros must be
enabled for this file to work.
The aim of this activity is to light all 4 lights simultaneously, where each light is
linked to a different sequence.
A number is entered into the yellow box and ‘checked’ if the number is in the
sequence linked to the light, the light will appear, if not it remains hidden.
Through entering a range of values, students work out what the 4 number
sequences are and find the number that will light all 4 lights.
Each sequence is linear.
Eight sets of sequences are provided: for sequences 1,3,5,& 7 it is possible to
light all 4 lights simultaneously, for sequences 2,4,6 & 8 it is not.
This activity encourages problem solving and reasoning. Giving all students time
to think and explain is important.
Teacher notes: Twelve Days of Christmas
3: This is designed as a whole class activity; mini-whiteboards could be used to
encourage participation by ‘voting’ for numbers or predicting what will happen.
Possible structure and questioning.
Explain that the intention is to make all 4 lights appear.
Ask for a value to try and check it to see which lights appear.
Ask for several more values and check each.
Ask if anyone has any ideas about what numbers and/or sequences seem to be
linked to which lights.
Ask if students to give you a number to light a specific light.
Give a number and ask students to predict which lights it will make appear. This is
helpful if sequences don’t coincide as it encourages reasoning and explanation.
Ask if anyone can give a number that will light all 4 lights.
Ask if anyone can give a different number to light all 4 lights… is it just double the
first solution? Why not? This is a very common misconception.
For sequences 2, 4, 6 & 8 ask if anyone can explain why it is not possible to make
all 4 appear..
Teacher notes: Twelve Days of Christmas
3: The file uses set 1 initially. On the ‘change values’ tab it is possible
to select a different set of values (1 to 8) – you might choose to do a
couple of sets that work and then choose one that doesn’t.
Set 1: 23
Set 2: not possible to light 2 & 3 together
Set 3: 60
Set 4: not possible to light 1 & 2 or 3 & 4 together
Set 5: 61
Set 6: not possible to light 1 & 2 together
Set 7: 86
Set 8: not possible to light 2 & 4 or 3 & 4 together
Sets 9 and 10 are left blank for you to insert your own sequences or for
students to devise their own sets to challenge their peers.
Teacher notes: Twelve Days of Christmas
2: Word Sums
The instructions for these are straightforward – and they simply
rely on the rules of addition, however, some are quite tricky to
solve, whilst some have several solutions.
A solution for each one is given on the next slide.
Teacher notes: Twelve Days of Christmas
+
E
A
T
+
E
A
T
F
U
L
L
6
7
2
+
6
7
2
1
3
4
4
S
M
I
L
E
S
M
I
L
E
H
A
P
P
Y
S
N
O
W
M
A
N
O
L
D
+
C
+
3
2
0
5
9
3
2
0
5
9
6
4
1
1
8
2
+
3
C
O
M
E
T
+
C
O
M
E
T
D
A
S
H
E
R
+
9
0
7
1
4
9
0
5
6
9
2
7
0
3
+
9
2
7
0
3
1
8
5
4
0
6
+
V
I
X
E
N
V
I
X
E
N
C
O
M
E
T
4
7
8
0
1
4
7
8
0
1
9
5
6
0
2
Teacher notes: Twelve Days of Christmas
1: Coded message.
1a and 1b both have the same solutions, but 1b is more
challenging, using quadratics and simultaneous equations.
Answers:
1L 2I 3E 4D 5A 6T 7G 8Y 9H 10O 11R 12V 13N 14S 15U
“Have a great holiday everyone; see you again in 2015”
‘Sticking points’
1a: students should be able to find 4 letters quite easily, they then
need to use G+I = 9 and realise that there is only one pair of
numbers left which add up to 9, G>I enables them to move
forward. Similarly, they will get to a point near the end when they
will need to realise that only one pair of numbers remains which
would work for V=3D
Can you make all four lights appear?
2
Check