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Numbers as Labels and for Counting |
Calculating |
Shape, Space and Measures |
| Birth-11 Months |
- Responses to people and objects.
- The attention that young babies give to changes in the quantity of objects or images they see, hear or experience.
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- How they enjoy games when objects are shown, then hidden away.
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- Babies' explorations of space through their movements, for example, by rolling from back to front.
- How babies begin to be aware of distance, as they grasp and reach out.
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| 8-20 Months |
- Preferences for particular rhymes and action songs that relate to number.
- The pictures of familiar things, in books, that babies recognise and point to, such as a ball or a teddy.
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- Babies' interest in looking for things that disappear from sight.
- Babies' persistence in trying to achieve something they have managed before, such as lifting the lid on a box that has previously popped open.
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- Instances of babies' investigation of objects and space such as looking for hidden objects or putting things in and taking them out of containers.
- How they hold out their arms wide to gather up a big teddy and bring hands together to pick up a small ball.
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| 16-26 Months |
- Awareness of number during play, such as the number words used and when and why they use them.
- How children notice or choose a larger quantity.
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- Occasions when young children gather things together, such as collecting several books or lining up cars.
- Children's interest in helping when an adult sorts the fruit at snack time, for example, putting all the apples together.
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- Children's strategies as they select and fit shapes in a puzzle or balance blocks on one another.
- Children's interest in and familiarity with the shapes of everyday objects.
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| 22-36 Months |
- How young children show their understanding of number labels such as 1, 2, 3.
- The contexts in which young children use marks and symbols.
- Situations that prompt children to talk about numbers.
- The numbers children recite spontaneously in their games.
- Children matching one thing with another, for example, glasses and straws.
- Children putting things in order of 'turn'.
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- The deductions children make about whether there is some juice left, or whether it is 'all gone'.
- Children's attempts at estimation and their efforts to check by counting.
- How children engage with simple counting songs and games, for example, 'Five Currant Buns'.
- When children begin to know about dividing things equally into two groups.
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- Observations made by children relating to shapes or patterns.
- When children begin to use some words that describe time, amount and size, for example, when children say things like "me bigger" to a smaller friend.
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| 30-50 Months |
- Children knowing that different numbers have different names.
- Children using the names for numbers accurately.
- The range of numbers that children refer to, and why they use certain numbers.
- Children's guesses about numbers of things and their ability to check them.
- Accuracy in the use of ordinals (first, second, third and so on).
- The strategies that children use to match number and quantity, for example, using fingers or tallying by making marks.
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- The strategies children use that show they are working out whether a group of objects is the same or different.
- How children work out a solution to a simple problem by using fingers or counting aloud.
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- Children's skills in matching shapes and in completing puzzles.
- Children's recognition of shapes in the environment, for example, that a roof has a triangle at one end.
- Children's ideas about why something is the correct size, for example, a piece of paper to wrap a gift.
- How children apply their understanding of shape and space, for example, knowing they need one flat shape and one that is 'pointy'.
- Children's use of mathematical names for shapes, such as 'circle' and 'triangle'.
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| 40-60+ Months |
- The personal numbers that children refer to, such as their age, house number, telephone number or the number of people in their family.
- Instances of children counting an irregular arrangement of up to ten objects.
- Children's methods of counting out up to six objects from a larger group, for example, when children do a jigsaw together and share out the pieces, counting to check everyone has the same number.
- How children begin to represent numbers using fingers, marks on paper or pictures.
- Children's recognition of numerals.
- How children use their developing understanding of maths to solve mathematical problems, for example, solving a debate about which of two piles of pebbles has more in it.
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- Methods children use to answer a problem they have posed, for example, "Get one more, and then we will both have two".
- How children find the sum of two numbers.
- The variety in responses when children work out a calculation.
- The ways children count repeated groups of the same size, for example, counting the number of socks in five pairs.
- How children share objects, for example, sharing eight crayons equally among four children and knowing that each child has two crayons.
- Children working out what remains if something is taken away.
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- Children's interest in and observation of shapes, such as how some are the same or different.
- How children match some shapes by recognising similarities and orientation, for example, Stevie looked at a rhomboid, saying, "It looks like a boat". Picking up a triangle, she says, "This one's different... it's only got three points".
- How children select a named shape for a particular purpose.
- Children's use of positional or directional clues, for example, "We had to come round the park and past the shops".
- Children's ordering of two items by length or height, for example, comparing the length of zips on coats: "Too long for your coat".
- Children's identification of a mathematical problem involving shape, space or measures and the ways they solve them.
- Children's use of positional language, for example, "I'm near the end of the path".
- Words children use to describe comparisons and measures such as 'greater', 'smaller', 'heavier' or 'lighter'.
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