# 40-60 months

- Recognise some numerals of personal significance
- Count up to three or four objects by saying one number name for each item
- Count out up to six objects from a larger group
- Count actions or objects that cannot be moved
- Begin to count beyond 10
- Begin to represent numbers using fingers, marks on paper or pictures
- Select the correct numeral to represent 1 to 5, then 1 to 9 objects
- Recognise numerals 1 to 5
- Count an irregular arrangement of up to ten objects
- Estimate how many objects they can see and check by counting them
- Count aloud in ones, twos, fives or tens
- Know that numbers identify how many objects are in a set
- Use ordinal numbers in different contexts
- Match then compare the number of objects in two sets
- Say and use number names in order in familiar contexts
- Count reliably up to ten everyday objects
- Recognise numerals 1 to 9
- Use developing mathematical ideas and methods to solve practical problems

**Observation 1**

Laura had been most interested in watching the class register being filled in each day. Some squared paper had been made available in the graphics area. Laura selected a piece of squared paper. She asked where the names should go on the register, and was shown the position of the names down the left side of the class register. She then began selecting children's name cards from the name pockets on the classroom wall, and copying them down the left side of her paper. She said, "I have made nine lines. The M is for Paddy, he's away".

**Comments:** Laura has observed the marks that are made in the register. We can see here that just as children have a 'Literacy set' so do they have a 'Maths set'. Children form ideas about what makes up the written word and equally they begin to acquire knowledge about what makes up the numeric world. Here Laura uses the register to both write children's names and to make marks that represent each child.

**Observation 2**

A group of children were spontaneously playing "buses". James set up a bus and was the driver. He collected tickets and as the children 'got on the bus' he asked each child "How many stops do you want to go?" Using his finger he then tapped on the ticket the correct number of times for the number of stops a child wanted to travel. He did this in a 'line' along the ticket.

**Comments:** James was using his fingers to mark out the number of stops each child was taking, perhaps this felt like an official 'record' to him and as such it's possible to see it as a pre-curser to mathematical graphics.

**Observation 3**

Lewis planned to play in the play dough and organised himself with an apron. He chatted as he squeezed and rolled the play dough between his palms. He broke off small pieces and rolled them into sausage shapes and laid them on the table, "One, two, three....". He broke off a bigger piece, rolled it into a sausage as before and put it next to the others, "That one's big and they're little". Shuma and Natasha joined Lewis and started by exploring the play dough, patting, squeezing and rolling it. Then Shuma copied Lewis by breaking off small pieces and rolling them into sausage shapes, Natasha did the same. The adult present commented on there being a huge number of sausages and wondering how many there were now. Lewis looked at the row of sausages and counted, "One, two, three, four, five, big ones and little ones". The three children continued to break pieces off the large lump of play dough, roll them into sausage shapes and add them onto the row. Each time Lewis would count them. He counted 22 sausages accurately.

**Comments:** Undertaking this network learning project resulted in a number of changes that practitioners made in the language they used to encourage mathematical thinking. One of the changes you can see here; instead of asking "how many are there?", which can make a child feel put on the spot and can close off an interaction, the practitioner wonders aloud. This can make conversation more real, rather than reduce learning to question and answer. Lewis clearly enjoyed the challenge of counting and the mere suggestion of there being many encouraged him to count. the children playing with Lewis had a chance to learn from his impressive counting skills!

**Observation 4**

The children had grown beans and they collected them from the garden. The children looked at and felt the beans inside the pods. They guessed how many beans might be in their pods before opening them. Fay felt carefully and accurately estimated how many beans were in the pod and then opened it. The children were asked to show how many they had on a piece of paper so that they could share with others how many beans they had each found in the pods they had grown. Fay placed hers carefully in a row then drew each one on her piece of paper to show how many she had. Then Fay decided to draw a face on each one.

**Comments:** The beans were important to the children because they had seen them through from seeds as they grew and ripened. They were strongly motivated to find out how many beans were in each pod and excited as they felt the beans through the pods skin. They had a purpose for recording how many beans they each found so that their success in growing beans could be shared with each other, the staff and their families. The children recorded the number of beans they found in their own ways. Fay drew each bean using a pictographic representation.

**Observation 5**

Alice was outside with a small group of friends who were playing bus journeys. They had chairs, a steering wheel, bags, hats and tickets. They were playing near to a large chalk board. Alice suggested going to the seaside. "I've got my bucket and spade, we can make sandcastles. They might have ice cream." An adult playing alongside drew an ice cream on the chalk board, and said that one was for her, and then asked who else wanted one. Alice asked everyone who wanted one and the adult suggested she might like to record how many the wanted so they didn't forget. Alice drew an ice cream for each child who wanted one. Alice then counted each ice cream accurately and wrote a number 8 on the board.

**Comments:** children will use mark-making in their play if this is regularly modelled and encouraged and if the resources are readily available.

**Observation 6**

A practitioner had been modelling different ways of recording how many children were taking part in snack time. She explained to the children that she needed to write this down so that she could see how much fruit was needed. Carol wanted to count the children sitting in her group this time. Carol drew faces to represent the girls present and drew circles for the boys. After drawing the pictures she then also added standard symbols.

Comments: Carol is beginning to represent numbers using a variety of marks including standard symbols. Modelling a variety of mark-making to record numbers encourages the children to record in their own ways which will be more meaningful to them than one prescribed format.

**Observation 7**

Michael was asked by an adult to help with the register. Michael had two boxes. He transferred a pebble from the "away" box to the "here" box. Each time he did this he made a mark in the appropriate column. At the end of "doing the register" he counted up his marks on the "away" column and wrote the number three. He totalled the "here" column but didn't want to attempt to write the numeral.

**Comments: **Michael has used iconic and symbolic marks on paper to represent amounts. He has also used developing mathematical ideas to solve this practical problem and has counted reliably up to fifteen tally marks, which represent the pebbles. Filling in registers is a purposeful and meaningful mathematical experience. It provides a real context for mark-making.

**Observation 8**

As part of healthy eating a small group of children had discussed their choice preferences for a healthy breakfast, written their name on a sticker and helped to make a class bar chart. After the activity the adult put the chart on the door and Michael looked at it, saying that most of the children had eaten cereal. The adult asked him if he would like to write the numbers on the chart so we could see how many children ate cereal. Independently, and written from memory, he wrote numbers up to twelve in the corresponding space.

**Comments: **Michael wrote numbers one to twelve from memory using symbolic and graphical representation.

**Observation 9**

Karl explored the number mats in the block area. He ordered the number mats correctly and independently from zero to ten. He copied the number of each mat on a piece of paper as he laid it down on the floor. He told the adult to look at his piece of paper so she would know which "number comes next". He continued to copy the numbers from the mats. After all the mats were laid, he counted them backwards, "number ten, number nine (and continued in this way to count down). Doing some more marks on his paper, explained to the adult "I drawed an X". When adult asked why, he explained, "Because I'm quitting the number game".

**Comments:** Writing numbers for a purpose, counting accurately and using appropriate numerical language for each numerical symbol, uses number names and number language spontaneously and accurately in play, counts reliably from zero to ten, and recognises their corresponding numerical symbols, says and uses the number names in both increasing and decreasing order, using numbers as labels and representing quantities that are counted, counting continuously.

**Observation 10**

Georgina was playing with some plastic ducks in a tray set out as a pond. With the ducks was a set of small laminated numbers, naught to ten. Georgina counted the ducks, first putting one duck in a space, and putting a number one next to it. She then put two ducks together and put a number two next to them. She worked systematically through the numbers to ten.

**Comments: **Georgina counted out from one to ten, using 1:1corespondence, and finding the correct numeral.

**Observation 11**

Elaine's mum had been in Australia for a few weeks.** **Elaine had talked about her mum's absence and knew she would be coming home in 8 more days. She recorded one stroke to represent one day (one more sleep) on a message board. She made 8 more lines and totalled them. She pointed to the numeral 8 on the movable number line.

**Comments: **Elaine used eight iconic marks to represent the eight days remaining before her mum returned from Australian. She knew that the number eight represented how many days were left all together. These marks were very important to Elaine, they were helping her to manage her separation from her mother.

**Observation 12**

Playing near the maths resources Amy took the clock jigsaw from the shelf and put it on the floor. She removed all of the numbers, put them in a line in numerical order, and then put them back in the clock.

**Comments: **Amy used developing mathematical ideas and methods to solve the practical problem of ordering numbers one to twelve independently.

**Observation 13**

Clara was playing in the graphics area. It was the day after her fourth birthday, Clara made a birthday card and wrote a four on it. She then cut out a four from a commercial birthday card and glued it on. She used a hole-punch four times on the card. Next she found the Geomec and made a birthday cake with four candles. She carried it over to another child and they sang 'Happy birthday to you'.

**Comments: **Clara identified the correct numeral for her age and was able to write the numeral. She is able to count four accurately as she showed when using the hole-punch and when making candles using Geomec.

Observation 14

Ashley moved the cursor to pop the bubbles randomly when playing Bubble Castle. He released a rabbit from a bubble and said, "Yeah, I got another one." When he had completed the game he counted all the rabbits in the tower, 1 to 5. He then counted 1 to 5 fingers and said, "Look there's 5 like this," and held up 5 fingers. He listened to the dragon counting the rabbits. "We got the same, I got 5 didn't I?"

**Comments: **Couunts up to five accurately showing 1 to 1 correspondance.