Children's Mathematical
Graphics of Past Months 
April 2010 
Melanie’s 'ladybird'

Transforming signs
and meanings
Melanie made marks on a
piece of paper  then taking some scissors, made
cuts at the bottom at the top and removed portions
of paper. She lifted the paper and moving it across
the table called happily to the other children
‘She’s dancing!’ Adding more marks she explained
‘She’s got a pretty dress’ and then explained that
this was ‘A lady dancing’.
By the next day Melanie
had altered what she had done, making several cuts
across the paper. Now she explained that it was a
‘ladybird’. Her teacher thought that the change of
meaning to ‘ladybird’ might have been through
wordassociation.
Referring to children
cutting out something they have drawn, Kress
explains the ‘makers’ shifting interest… while it is
on the page I can do “mental things” with it… when
it is off the page I can do physical things with
it,’ (1997: 27). Melanie explored her ideas about a
‘lady’ and ‘ladybird’ ‘multimodally’, with the help
of paper, crayons and scissors, enabling her to
express and communicate personal meanings.



July 2009 
Karl's Tables
Karl’s teacher told the children that
the headteacher had to do an audit and count everything in the
school! She wondered if the children would be interested in helping
– and choose something to count in their class.
The children were very excited. Karl (4
years 9 months) decided to count the tables in the classroom. He
noticed the many legs tucked beneath the tables and showed something
of the appearance of ‘lots of legs’ as he drew each of the ten
tables.
When he’d finished Karl counted and
recounted, putting a mark with his pen on each table he’d drawn.
Checking (without being asked suggests reflection and mature
behaviour. Finally, at the top Karl wrote his approximation of ‘10’
and his teacher wrote ’10’ in pencil beneath. 

Written number and
quantities
Early Operations:
children’s own written methods
See:
taxonomy of development 


June 2009 
The Baby
Clinic Visit and role play (reception, 45 years) 
Visiting the local Baby Clinic, the children watched as Health
Visitors weighed babies and recorded their weights on charts and in
books, and listened to discussions about their progress. On their
return to school some rich, symbolic play developed spontaneously,
supported by a real set of babyweighing scales their teacher had
borrowed.

Over several days, a piece of paper on which one child made marks
was added to by others. Their graphics show that:
 They understood that adult use written marks and symbols for
specific purposes
 They drew on their knowledge of symbols, including approximations of
letters and numerals they have seen.
Some children used the initial letter of their name or their age
number to stand for what they said.
During their play the children freely used language of measurement
such as ‘heavy’, ‘this big’, ‘three long’ and ‘getting bigger’ and
general comments and questions such as ‘How’s your baby doing?’ as
they weighed dolls and teddies. The conversations between health
professionals and mothers and their purposeful writing had made an
impression and the children were able to integrate their experiences
into their play. 
Written number and quantities

Early written numerals

Numerals as labels



May 2009 
Catherine’s fractions
This example was on Catherine’s first whole day at school in the
Reception class. Catherine was quiet and reserved and initially
hesitant about what she wanted to do during the children’s extended
period of childinitiated play. As she talked quietly to her
teacher, Catherine explained that her sister was 2½ years on that
day and decided to draw a picture of her.
After a while she brought her drawing to her teacher. She had
written a ‘C’ in the top lefthand corner to represent her name and
added a similar symbol that appeared to be a ‘c’ with a line beneath
it (or perhaps a reversed numeral of ‘2’. I wondered if she would
add something to signify ½ and smiling, she wrote the ‘c’ symbol
next. Was this her way of representing approximately a half
of a numeral ‘2’?
The
next day as soon as she arrived at school Catherine confidently went
to the writing area and wrote some more symbols explaining ‘I’m 4½
years old!’ She had written a numeral ‘4’ followed by her
approximation of a half of a numeral 4. 
These invented symbols were ingenious solutions that enabled
Catherine to communicate specific mathematical meanings and show
considerable insight for a young four yearold. 
Written number and quantities

Early written numerals (exploring fractions)



March 2009 
John  Subtracting
Grapes 

John (5 years)
represented the total quantity of grapes he had and crossed out the
2 he had eaten. He then added 2 arrows to reinforce his
understanding about ‘taking away’ (and perhaps to help communicate
to others, what he had done).
John has represented his calculation as narrative action, in
which there is a strong sense of sequenced narrative and conclusion
(answer). John began by writing across the page but (due to the
orientation of his paper) decided to curve the string of numbers in
order to fit it on the page. 
Early operations: the development of children’s own written methods

Counting Continuously;

Exploring symbols.



February 2009 
Matt's Marks 
Matt had just had his third birthday. At home he sat on the kitchen
floor near his aunt who was writing postcards. Matt announced that
he was ‘drawing’. He rapidly covered many sheets of scrap paper with
a range of marks, some which he names as ‘drawings’ and others were
written messages, which he explained.
Showing this piece to his aunt, he ‘read’ it as ‘I spell 80354’.
This was the first time that he had attached mathematical meanings
to any marks he had made. Matt is growing up in a family in which
his marks and early representations are encouraged and valued. At
home reading books, using the computer and writing are all daily
events and part of everyone’s experience.
This example shows that Matt understands that marks can carry
meanings and are sometimes be used to represent numerals. Perhaps he
was thinking about a phone numbers he’d heard, as a reference point
for
his number string. Talk about how to ‘spell’ may also be something
he’s heard discussed with regard to spelling his brother’s name or
his own..


The
development of written number and quantities



January 2009 
John – adding grapes: teacher
led group activity


John (5 years 3 months) was
adding the grapes that he had selected and put in two small dishes.
He decided to represent his ideas on paper. Using a combination of
narrative (words), pictures and numerals. He read what he had done:
‘2 grapes, there is two; 4 grapes, there is four’. Finally he wrote
the total ‘6’ (on the left).
When children choose to represent ideas to support their
mathematical thinking, they choose a graphic response that they feel
most comfortable with that suits the maths in which they are
engaged. On this day John chose a combination of words, numerals and
pictures (codeswitching between the different ways of representing)
to help him think about this operation. 
Early operations:
development of children’s own written methods

Separating sets
and

Exploring symbols



December 2008 
Jessica's Clocks

Many homes and early years settings have
wall clocks and children often choose to draw them in the graphics
area. Selecting a piece of paper Jessica (4 years, 6 months),
thought hard about how she would fit in all 12 numerals on the dial
she had drawn and managed to include almost all on her third drawing
(in the centre). She was pleased with her drawing and told the adult
‘It’s nearly milk time’.
Jessica drew on her knowledge that there
are 12 numbers on a clock face. She was persistent with her learning
and challenged herself, getting the feel for layout, use of space
and shape. ON this occasion she was playing with a piece of
knowledge and connecting it to a real and personally meaningful
context of milk time in her nursery. Jessica carried her sign around
to show the other children in the nursery. Woods (1988) talks about
children being the ‘architects of their own learning’.
Written number and quantities



November 2008 
Carl's Car Park Tickets  small world
play

Carl (4 years and 5 months) had
built a ‘car park’ and arranged rows of toy cars inside it. Suddenly
he announced ‘You have to have a ticket or you get done!’ Reaching
out to a nearby tray of paper, pens and scissors in the small world
play area, he wrote his own symbols and then cut out his tiny
‘parking tickets’. He placed each ticket on a car, reading them as
he did so: ‘40p, 40p, 40p, 50p, 70p, 80p, 90p’.
Carl’s dad was a lorry driver and Carl
knew a lot about road transport. Having ready access to pens and
paper triggered further ideas and he went on to make a sign that he
read as ‘NO PARKING’; a £50’ sign on one of the cars and a ‘CLOSED’
sign that he put by the entrance to his car park. His play continued
for over half an hour and drew several of his friends who joined in.
Their talk developed into a discussion about car registration plates
(about which Carl was very knowledgeable).
Finally Carl became a salesman,
explaining the merits and cost of various vehicles in his car park
to his friends and to his teacher who had been observing this rich
play.

The development of
written number and quantities



October 2008 
Barney – subtracting beans

This was the first occasion that
Barney had used paper to help his thinking about subtraction.

Early in the term at the beginning of
Y1, Barney’s teacher introduced a game with flowerpots and beans.
The children played in pairs, one child counting (out loud) a small
handful of beans before adding them to a pot. The other child then
removed several beans (without counting) and hid them. Together the
children worked out how many had been subtracted by checking how
many remained. Barney first
wrote ’10 take 1 is 9’ at the top and then represented the
flowerpots with the beans inside, using an arc of arrows to
represent the physical action of ‘taking away’. This was the first
instance we have of this personal, invented sign for subtraction.
During the same lesson, Barney then moved to a more efficient form
by omitting the drawings of flowerpots and beans. Finally he
explored another child’s idea of representing a hand with a numeral
on it, to signify the quantity that he had removed (not shown
here). 
Early operations: the development
of children’s own written methods
 Separating sets
 Exploring symbols
Barney also explored
‘narrative action’ and ‘code switches’ in this example 


September 2008 
Molly's Numbers

Molly (3 years, 11 months) was
playing in the graphics area. She made a string of marks that are
both letter and numerallike symbols and are written from left to
right. These symbols share some features of emergent writing
(see Clay, 1975). Molly referred to her symbols as ‘seven, six and
number eight’.
The development of written number
and quantities:



August 2008 
Making ‘Dinner Registers’
One day when her teacher called the dinner register, Natasha brought
a piece of paper and a pen to make her own. Natasha focused on the
concept of a list and included some ticks and circles as she’d seen
her teacher do. 



Natasha (4 years, 6 months): Representing quantities
that are not counted 
Gemma (4 years, 4 months): Early explorations with
marks 
Alice (5 years, 3 months): Representing quantities
that are counted 

Gemma wanted to join in and used marks
with some approximations of circles and crosses (to denote either
packed lunches or school dinners) and Alice represented the
children’s responses in two columns, in a way that was easy to check
when she’d completed it (she also drew her own packed lunch box in
the centre). Each example shows
the child’s current thinking as she used ways of representing to
help her think about the data. Their interest led many other
children to choose to make their own registers during the term.
The development of written number
and quantities:
See:
taxonomy of development



July 2008 
Tommy and the Elephant

When he was playing, Tommy (4 years: 10
months) chose to copy the numbers on a ‘hundred square’ on the door
of the classroom. He was very engrossed in what he was doing and
carefully copied the numbers to ‘60’. He then drew a hamster by the
numeral ‘1’; and drew himself by the numeral ‘4’. Finally he drew an
elephant next to the number ‘60’.
The previous day Tommy’s class had been
for a visit to the zoo. When he showed his teacher what he had done,
he explained that hamsters don’t live very long and that he was four
years old, finally adding ‘elephants live a long time’.
Tommy had made a significant step in
relating his knowledge about ages and animals’ life expectancies.
He had combined his knowledge with what he had just learnt at the
zoo and devised his own system of labelling. 
The development of
written number and quantities:



June 2008

Alex's Numbers (small numerals
were written by the teacher following Alex's explanation)


Adults sometimes refer to a child ‘not
knowing his numbers’. In this example, Alex (4 years 11
months) decided to write his own symbols for numbers he wanted to
write. This was selfinitiated and did not appear to relate to
anything he had been counting at that moment.
Alex used elements of standard letters
(for example, ‘2’, 5’, ‘6’ and ‘7’) and numerals (e.g. ‘3’ and ‘4’)
that he knew. He used the initial letter ‘A’ from his name and was
consistent when writing ‘5’. There are a number of other positive
aspects in the symbols Alex used that show just how much he already
knows about written numbers – it’s just that he does not yet know
our numbers!

The development of written number and
quantities:



May 2008

Louisa’s strawberries
Five year old Louisa was calculating how
many strawberries she had altogether in two small dishes. She decided to use some paper and a pen
to help her think about the operation, and read this as ‘Two
strawberries and four more – altogether there’s six.’
Using words appeared to help her
think about the signs ‘+’ and ‘=’ and finally Louisa ate her
strawberries!
Early operations: development of
early written calculations:
 Separating sets
 Exploring symbols



April 2008

Joe’s Spider
Threeyear old Joe had been playing with
some toy spiders and told his teacher that spiders have 8 legs.
Later he decided to draw a spider.
Joe’s drawing gives his sense of a
spider and he represented his idea of many legs. At this age Joe’s
drawing was lively and dynamic since he was unrestricted by
influences of school. When children represent quantities that they
do not count it is their personal sense of quantity that they
represent.




March 2008


Data handling: favourite zoo animals
(45 yearolds) The children in
this class had visited the local zoo the previous day and when they
arrived at school were engaged in heated discussions about the
‘best’ animals they had seen.
Their teacher capitalized on their
interest by suggesting they might find out what their friends’
favourites were. Several children chose to represent their own
preferences. Bianca drew a tiger, lion, giraffe and  and
then decided to write her friends’ names at the foot of her paper as
each of them told her which their favourite animal was from those
she had drawn. 
Tommy drew his favourite animals
(left to right) – a lion, a crocodile, a giraffe and a tiger. Each
time he asked one of the children to name their choice, Tommy marked
a cross beneath the animal they had selected.
Later when we looked at the children’s
findings it became clear that some were easier to interpret than
others and this led to a discussion of possible ways of representing
findings so that others could readily interpret and understand the
data.
For young children data handling is
far more meaningful if they can make personal decisions such as
these and come to shared understanding through dialogue. These
examples show individual’s thinking at the time (rather than one
that is ‘better’ than the other) and are equally important in the
children’s development.


Building on what the children already
understand has much more meaning to them than (for example) being
told to colour in squares on a block graph. It will help them to
understand the value of certain layouts and to make effective
choices about how to represent their data. 


February 2008

Miles and the nectarines
Miles was 7.5 years old. The children in
Miles’s class were about to go on a residential trip and were
planning to stop for a picnic on the way. Their teacher used the
opportunity this provided for the children to solve problem, showing
them a pack of three nectarines she had bought and inviting them to
work out:
How many packs of
nectarines will we need to buy so that all 26 children
can have one each at the picnic? 
Sevenyear old Miles decided
to use pen and paper to help him think about how to calculate the
total number of packs they would need.
He chose to orientate his paper in
‘portrait’ format (thereby limiting the length of the empty number
line he drew) but quickly understood that he would run out of space.
His highly adaptive solution was to double several of the jumps that
he made as he worked from right to left.
Providing a real context for
mathematics helps young children’s understanding and leads to
increased levels of involvement. After the children had discussed
how they had worked out their calculations and their findings, their
teacher bought 9 packs of nectarines to add to the food for their
picnic the next day – and the additional nectarine was enjoyed by
their teacher!
Early operations: development
of children’s own written methods
 Calculating with larger
numbers supported by jottings


January 2008

Charlotte’s
‘hundreds and pounds’

Charlotte
(4 years, 2 months)
was with her friend Jessica in the nursery. They had each selected a
piece of paper and chosen coloured pens, holding as many as they
could in each hand and covering their paper with dots. As they
excitedly made marks, Charlotte told her teacher, ‘Look! I’m doing
hundreds and pounds!
Charlotte’s
reference to ‘hundred’s and pounds' meant that she was making
connections with the quantity of dots which seemed a lot to her.
Both a ‘hundred’ and ‘pounds’ fits into her thinking about a lot.
Charlotte used spoken language to express what the marks she made on
paper suggested to her, attending to the link between her marks and
the mathematical vocabulary of quantity in a general sense.
Written
number and quantities:
§
early explorations with marks
§
representing quantities that are not counted



December 2007

Nadia (4 years 7 months) found some
squared paper in the technology area and chose to explore symbols in
her own way, using one square for each. It was the abstract symbols
themselves – their appearance and form; their potential functions
and the meanings that she attached to them that interested her.
When she showed this to me, Nadia ‘read’
the ‘E’; several ‘Js’; ‘a star’; ‘T’ ; ‘round’ (gesturing in the air
with a her forefinger to make a circular movement); ‘umbrella’ (in
the centre of the paper) and ‘square’ (lower right).
Thus, while some symbols she named as
standard letters, for others she focused on the shape or form (i.e.
the circle and square) and two symbols suggested pictorial
representations (the star and umbrella).
The ‘stuff’ that children use to
explore meanings within their play, offers ‘meaningfull’ contexts
for children’s future explorations of symbolic ‘written’ languages
 such as writing and written maths. 
Nadia’s symbols


Autumn 2007

Nikita’s Birthday Card

Nikita (3 years and 4
months) Birthdays are
something with which young children identify and that excite them:
the changing of their age is important to them.
To enhance the graphics area in the
nursery we asked the children to bring in old birthday cards from
their family. We discussed with each child the card they had brought
in and provided additional materials.
Children chose to go to this area if
they wished and adults carefully observed and noted down findings.

Nikita made a birthday card for herself.
She looked through a box of cardboard numerals and selected a ‘3’
which was her age at the time, then glued the numeral on the paper.
She made some marks with blue and black pens. Nikita was very quiet
whilst she did this and whispered to her teacher ‘This card is for
me – I am three’. Nikita knew
her own age and recognized the numeral ‘3’. Her marks look very much
like early writing and the crosses may have been kisses, although
she did not say. Nikita had showed a great deal of understanding of
birthday cards. 


August 2007

Marina (5 years 0 months) and
the Library Van
Childinitiated role play can be wonderfully rich! On this
occasion we had visited the city library, and then two weeks
later had exchanged a box of books at the mobile library van
that had called in the village  that our class had borrowed.
This visit coincided with
Marina’s enclosing and containing schema, and on our
return to school she spontaneously created a narrow, enclosed
space for a ‘library van’. A number of children were also drawn
to this play and explored their understanding about libraries
over a period of several ways.
The children’s role play was rich
in both literacy and mathematics – including using money and
giving change; using a calculator, completing forms and writing
letters.
MarieAnne made a road safety
poster and attached it to the front of the counter (as she had
seen in the city library). Marina was especially interested in
what she had heard about library fines at the city library and
now drew on this knowledge for her library van role play. She
wrote endless letters to library visitors demanding huge sums
for their overdue books! During this letter writing she chose to
use a calculator and real coins to work out monies owed and to
give change, and also added stamps to the envelopes.
This role play was entirely the
children’s and points to the value of staff providing openended
space, opportunities, resources and time for children to initiate their own
role play. Additionally it serves to emphasise the importance of
visits and firsthand 
experience to support schemas
(see
Athey, 2006) and role play.
Commenting on Marina's role play,
Wood and Atfield (2005) emphasize
how ‘this vignette shows how literacy and numeracy are social
and cultural practices that children observe in their everyday
environments, and subsequently initiate in their play’ (p.79). 
 Written
number and quantities: early written numerals;
numerals as labels; representing quantities that are counted


July 2007
Jack: adding
grapes
We were using grapes
to explore addition (they would eat the grapes later). Jack
(4 years 11 months): chose two separate amounts of grapes to
add for each of his calculations and decided to use paper and
pen to help him explore the use of symbols.
He left a gap
between the two sets of grapes in each calculation so that it
can be read as ‘4 + 3’ (and below) ‘6 + 6’. We term this use of
a space between two sets to be added or subtracted implicit
symbols, since whilst the child has not at this stage
represented the addition symbol, his layout – and when he reads
it out, shows he has implied the symbol and recognized that an
operant is needed.
Finally Jack drew a
line in each calculation before writing the total: this line
functioned as an equals sign for Jack at this point in time,
helping him move towards a deep understanding of standard
symbols (see the Taxonomy
and exploring symbols)

June 2007

Kamrin’s ‘Tweedle
birds’

This was a
teacherled lesson in a Reception class: problem solving –
division by sharing
Kamrin (5 years 7 months) invented his own system to
check if 8 could be shared equally between two. He wrote a
question mark by the numeral 8 and then a cross, as at first he
thought it could not be divided equally between two. Then he
invented ‘Tweedle birds’ and shared eight ‘eggs’ equally between
the two birds, adding a tick to show that eight could be divided
equally. Kamrin then went on to explore several other ways to
find if other numbers could be dividing equally in two, finding
increasingly efficient methods of doing this – or using
‘successive shorthand’.



May 2007

Julie  Weighing Babies This was
freely chosen play in the ‘baby clinic’ role play area. Julie
(4 years and 3 months) weighed her baby on the scales and
made a mark on her booking sheet in the appropriate space; she
repeated this after using a tape measure to check the baby’s
length. When she wrote the baby’s age Julie said ‘6’ and made 6
distinct tally marks (iconic).
Julie understands that quantity
(representing mass) and numerals can be represented with
symbols. She used her own early explorations with marks
and represented quantities that are counted to
represent her personal meanings as she weighed her baby.
You can see more of the Cambridge
Nursery children’s graphics in Gallery 3




April 2007

Nursery: ‘plane tickets’
These 3 and 4 year old
children in the nursery had been playing aeroplanes and the
Nursery Teacher made some ‘tickets’ to which the children could
add their seat numbers.
In these examples Louis, Sarah
and Joe were exploring early marks and using their own early
written numerals. You can see more of the children’s plane
tickets in the Teachers’ Gallery.


March 2007

Chloë's Dinner Register
Chloë (5 years) had
brought her own exercise book from home to play with in the
graphics area. She said she was “making register”. She wrote the
names down (as squiggles) for the children in the class and then
counted them to see if she’d made the right number of marks. She
counted to 4 and then counted random numbers to 20. She used
number strips to check and count how many children were in the
class. She chose to use tallies to represent the number of
children who were away.
Chloë has a statement of special
needs and finds articulating language difficult: this was the
first time that she had shown any interest in the graphics area.


February 2007

Louisa’s dial
 Written number and
quantities: numerals as labels

In the
graphics area, Louisa, 4.9 years, made what at first
glance appears to be a clock. In this class the teacher gave
each group of children certain options for them to choose for
play. When Louisa showed me her dial she assigned an activity to
the numerals 1 – 5: bricks, puzzles, roleplay, reading and
painting. She paused with her finger on ‘6’, and unable to think
of other play possibilities in her class she smiled and
explained ‘you have to sleep’. As she moved the hand of the dial
she stopped at the letters ‘fo’ (off) and explained ‘this is
where you turn it off’.
Louisa had related what she knew about analogue clocks to that
of her classroom culture: perhaps she was also making links with
her home culture too, where after playing at the end of the day
she goes to sleep.



November 06

Sam’s marks
Spontaneous marks that young children choose to make within
their play provide powerful and meaningful contexts.
Bradley (3.5 years) had been playing
in the writing area with the calculator for about 15 minutes,
making marks as he looked at the buttons on the calculator. He
told his teacher ‘my dad’s got one of these’. Sam (3. 6 years
old) was nearby, watching as Bradley used the calculator and
made his own marks on paper as he did so (above). Marks such as
these are an important feature of young children’s early
mathematical development concerning symbols. 
 Written number and
quantities:
early explorations with marks



October 06


Mark’s crosses Some of the boys
were very excited about playing in the garage role play area
(next to the graphics area). Mark (4 years) chose a
corner of the playground explaining that this was a ‘no entry
area’ (for cars). He was exploring a sign that children see in
many contexts, in a way that was personally meaningful to him at
the time. Later in school, he will meet ‘+’ and ‘x’ as signs in
mathematics.
We chose this lovely photo for
the cover of our second edition
and would like to thank Louise Glovers, Nursery Teacher at
the Robert Owen Children’s Centre in Greenwich for this lovely
photo of Mark.



July/August 2006

Jessica’s Number Line
 Written number and
quantities: early explorations with marks
In the nursery the children had
created a number line together with giant numerals that they had
chosen. Jessie (4 years and 3 months). Jessie was one of
several children who chose to make her own number line on a
strip of paper.
Jessie centred on the letter ‘J’
that was the most important letter to her and used it to stand
for number and written symbols. Jessie’s dots may be
representations of other numerals and ‘line’ may be a literal
translation of the line she had often heard referred to in the
‘number line’.


June 2006

Amelie’s Dice game
 Written number and
quantities: numerals as labels; representing
quantities that are counted
 Children’s own written
methods (calculations): exploring symbols
This was a teacherplanned
activity that provided open opportunities for children to
explore their thinking. Each pair of children had two dice
between them and were invited to ‘put something down of paper’
to show what they got each time they rolled the dice.
Amelie (4 years 6 months)
counted the dots each time she rolled the dice and carefully
made the same number of dots with her pen on the right side of
her paper. She has also used letters from her own name
(particularly the capital ‘A’) and her age number ‘4’. She
noticed the marks and symbols that some of her friends used and
added several ‘+’ signs and also a ‘=’ sign at the top of the
paper, with some numerals written within boxes. She ‘read’ the
‘e’ as ‘eight’ (a similar shaped symbol).
Amelie was very proud of this piece – it is dynamic and full of
energy and spontaneity of a young child.


May 2006

Frances
and the train
 Children’s own written
methods (calculations): representing quantities that
are counted; counting continuously & calculating with larger
numbers

Our
class of 4 – 6 year olds had travelled by train to visit an old
‘pannier’ market in a town in the north of the county and on the
return journey our carriage was very crowded. The following day
Aaron commented “I bet there were a million people on the
train!”
After some discussion about how we might find out, Aaron phoned
the railway station. Returning to the class he told his friends
that there had been 7 carriages on our train and 75 seats in
each carriage. A number of children were intrigued by this large
quantity and wanted to find out how many there were altogether.
Each chose their own ways to work this out (with resources or
through representing their thinking on paper).
Frances (6 years 1 month)
explored a number of ways before drawing representations of the
seats in one carriage (below). She selfchecked and found that
she had drawn one too many and crossed it out (above). In order
to represent the remaining 6 carriages, Frances asked if she
could photocopy her first carriage – an interesting solution
using repeated addition. 
