How they enjoy games when objects are shown, then hidden away.
Talk to babies about what you are doing and what is happening.
Let babies see and hear the sequence of actions you go through as you carry out familiar routines.
8-20 Months
Have some understanding that things exist, even when out of sight.
Are alert to and investigate things that challenge their expectations.
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.
Play games such as peek-a-boo or comment when a puppet pops out of a sock.
Talk to babies about puzzles they encounter such as how to get their sock back from where it has fallen, asking whether they can do it or if they might need help.
Provide lift-the-flap books to show something hidden from view.
Provide a variety of interesting displays for babies to see when they are looking around them, looking up at the ceiling or peering into a corner.
16-26 Months
Are learning to classify by organising and arranging toys with increasing intent.
Categorise objects according to their properties.
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.
Foster children's ability to classify and compare amounts.
Use 'tidy up time' to promote logic and reasoning about where things fit in or are kept.
Putting the blocks away - In a nursery school, a small group of children work independently, together, and with the support of the practitioner to tidy away the resources.
[transcript]
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Encourage children, when helping with domestic tasks, to put all the pieces of apple on one dish and all the pieces of celery on another for snacks.
Use pictures or shapes of objects to indicate where things are kept and encourage children to work out where things belong.
22-36 Months
Begin to make comparisons between quantities.
Know that a group of things changes in quantity when something is added or taken away.
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.
Help children to organise their ideas by talking to them about what they are doing.
Play games which relate to number order, addition and subtraction, such as hopscotch and skittles.
Sing counting songs and rhymes which help to develop children's understanding of number, such as 'Two Little Dickie Birds'.
Cocoa for 50p - In the outdoor area of a pre-school on a sunny day, the practitioner supports a child in his role-play about shops and money. [transcript]
You can watch the video via modem or slow / fast / superfast broadband connections. If you are behind a network firewall, why not click here to view a flash file of the video. You do need to have the flash plugin.
Provide props for children to act out counting songs and rhymes.
Provide games and equipment that offer opportunities for counting, such as skittles.
Plan to incorporate a mathematical component in areas such as the sand, water or other play areas.
30-50 Months
Compare two groups of objects, saying when they have the same number.
Show an interest in number problems.
Separate a group of three or four objects in different ways, beginning to recognise that the total is still the same.
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.
Demonstrate language such as 'same as', 'less' or 'fewer'.
As you read number stories or rhymes, ask, for example, "How many will there be in the pool when one more frog jumps in?".
Use pictures and objects to illustrate counting songs, rhymes and number stories. This will benefit all children and be particularly supportive to children learning English as an additional language.
Create opportunities for children to separate objects into unequal groups as well as equal groups.
Provide story props that children can use in their play, for example, varieties of fruit and several baskets like Handa's in the story Handa's Surprise by Eileen Browne.
40-60+ Months
Find the total number of items in two groups by counting all of them.
Use own methods to work through a problem.
Say the number that is one more than a given number.
Select two groups of objects to make a given total of objects.
Count repeated groups of the same size.
Share objects into equal groups and count how many in each group.
In practical activities and discussion, begin to use the vocabulary involved in adding and subtracting.
Use language such as 'more' or 'less' to compare two numbers.
Find one more or one less than a number from one to ten.
Begin to relate addition to combining two groups of objects and subtraction to 'taking away'.
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.
Show interest in how children solve problems and value their different solutions.
Make sure children are secure about the order of numbers before asking what comes after or before each number.
Discuss with children how problems relate to others they have met, and their different solutions.
Encourage children to make up their own story problems for other children to solve.
Encourage children to extend problems, for example, "Suppose there were three people to share the bricks between instead of two".
Use mathematical vocabulary and demonstrate methods of recording, using standard notation where appropriate.
Give children learning English as an additional language opportunities to work in their home language to ensure accurate understanding of concepts.
Encourage children to record what they have done, for example, by drawing or tallying.
Use number staircases to show a starting point and how you arrive at another point when something is added or taken away.
Provide a wide range of number resources and encourage children to be creative in thinking up problems and solutions in all areas of learning.
Encourage children to make links between cardinal numbers (quantity) and ordinal numbers (position).
Make number lines available for reference and encourage children to use them in their own play.
Help children to understand that five fingers on each hand make a total of ten fingers altogether, or that two rows of three eggs in the box make six eggs altogether.
