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Gallery 4

    © Copyright M. Worthington & E. Carruthers 2012

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 word-association.

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’ ‘multi-modally’, 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

  • Representing quantities that are counted

Early Operations: children’s own written methods

  • Counting continuously

See:  taxonomy of development


June 2009

The Baby Clinic Visit and role play (reception, 4-5 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 baby-weighing 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 child-initiated 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 left-hand 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 year-old.

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

  • Early explorations with marks – attaching mathematical meanings


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 (code-switching 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

  • Numerals as labels


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

  • Early written number


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 numeral-like 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:

  • Early written numerals

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:

  • Numerals as labels


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 self-initiated 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:
  • Early written numerals

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

Three-year 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.

  • Written number and quantities:
    representing quantities that are not counted


March 2008

  • Written number and quantities:
    representing quantities that are not counted

Data handling: favourite zoo animals (4-5 year-olds)

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.

  • Written number and quantities:
    representing quantities that are counted

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?

Seven-year 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 fore-finger 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 ‘meaning-full’ contexts for children’s future explorations of symbolic ‘written’ languages - such as writing and written maths.

Nadia’s symbols

 

  • Written number and quantities:
    early explorations with marks

 


Autumn 2007

Nikita’s Birthday Card

  • Written number and quantities:
    numerals as labels

 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

Child-initiated 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.

Marie-Anne 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 open-ended space, opportunities, resources and time for children to initiate their own role play. Additionally it serves to emphasise the importance of visits and first-hand



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

  • Children’s own written methods (calculations): exploring symbols

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’

  • Children’s own written methods (calculations): separating sets

This was a teacher-led 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

  • Written number and quantities:
    early explorations with marks


 

April 2007

Nursery: ‘plane tickets’

  • Written number and quantities: early written numerals; representing quantities

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

  • Written number and quantities: representing quantities that are counted

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, role-play, 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

  • Written number and quantities:
    exploring symbols

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 teacher-planned 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 self-checked 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.

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