Example of mathematics planning and resourcing 10

What we want children to learn (Development matters)

Objectives in bold refer to Early Learning Goals.

Mathematics objectives

• Share objects into equal groups and count how many in each group

Using and applying mathematics

• Describe solutions to practical problems, drawing on experience, talking about their own ideas, methods and choices

Related Early Learning Goals

• Have a developing awareness of their own needs, views and feelings and be sensitive to the needs, views and feelings of others (PSED)
• Recognise the importance of keeping healthy and those things which contribute to this (PD)

Possible contexts

• Provide resources such as number lines, tracks and staircases and interactive displays using numerals.
• Engage in practical activities that are underpinned by children's developing communication skills.
• Set sharing and grouping activities that are imaginative and enjoyable and that follow children's interests.
• Give children sufficient time, space and encouragement to use new words and mathematical ideas, concepts and language during child-initiated activities in their own play.
• Exploit problem-solving opportunities, for example with 'small world' play.
• Provide collections of objects for children to sort, match and count.
• Share, recite and encourage joining in with number rhymes and stories using games and books involving sharing and grouping.
• Use photographs in the learning environment to ask, for example, how many children at the water?
• Share out objects within the group, for example fruit.
• Develop interactive displays of objects with prompts for 'more' or 'less'.

Example of adult-led activity

Context: Sorting fruit

Collect an assortment of fresh and dried fruit (choose small fruit like cherries and raisins that won't need cutting) and one small paper cake case for each person.

Explain that everyone will want an equal share of fruit and that you need to decide how many of each fruit to put in each case. Give pairs of children responsibility for working out how they can share equally one of the kinds of fruit. Suggest that they don't touch the fruit too much but after counting it together the children could then use beads and pots for sharing out and paper and pencils for mark making.

Count (together and out loud) each type of fruit as you place it in a paper bag. Write the number on each bag.

Encourage their different strategies and mark making, and support them in finding a solution. They may need to alter their strategy. Help them talk and think through their problem and possible solutions. Ask them for suggestions if they have some fruit left over. They may show this in their mark making. Allow the children to share out the fruit equally into paper cake cases to hand out to each child.

Adult role

• Provide practical real-life activities that are underpinned by children's developing communication skills.
• Model mathematical vocabulary during the daily routines and throughout adult-led activities.
• Encourage children to explore objects and groups and provide resources to encourage mark making and representation, for example adding up tally marks of scores in a game.
• Provide help for those children who use a means of communication other than spoken English in developing and understanding specific mathematical language.
• Exploit opportunities for sorting, matching and then counting groups and totals, for example counting fruit at snack time, registering children, organising games.
• Share books and exploit the number potential for using vocabulary of addition and subtraction.
• Encourage children to choose numbers for problems and to make up their own story problems for other children to solve.

Opportunities for children to explore and apply

• Add trays with small compartments for sorting to the making area. Add collections of things: bottle tops, sequins, threads, tiny pieces of fabric, etc. Model sharing out the objects equally. For example: do you all want sequins? I'll put 5 each on your trays. Can you give everybody the same number of these? Have you got the same?
• Add objects into role-play that fit back into sets when tidying up. For example: each cot has 2 blankets and 1 sheet. Each pet has 3 biscuits in its bowl, and so on.
• Hang up 3 bags outside for making collections. Put a number 2 on each bag. Encourage the children to collect 2 of any treasured object in each bag, for example fir cones or smooth pebbles. The collections could be used inside and outside in the learning environment for different purposes, for example as a gallery of natural objects or for adding to the making area.
• Tidy up the pencil pots, making sure each pot contains the same number of pencils of each colour.
• Encourage the children to hand out things to others, for example enough pencils for each group.

Adult role

• Provide practical real-life activities that are underpinned by children's developing communication skills.
• Model mathematical vocabulary during the daily routines and throughout adult-led activities.
• Encourage children to explore objects and groups and provide resources to encourage mark making and representation, for example adding up tally marks of scores in a game.
• Provide help for those children who use a means of communication other than spoken English in developing and understanding specific mathematical language.
• Exploit opportunities for sorting, matching and then counting groups and totals, for example counting fruit at snack time, registering children, organising games.
• Share books and exploit the number potential for using vocabulary of addition and subtraction.
• Encourage children to choose numbers for problems and to make up their own story problems for other children to solve.

Look, listen and note

• How do children find the sum of two numbers? Adeola picked up as many conkers as she could, working out how many she had altogether: 'Five and four - nine! That's my best go.'
• Observe the variety in responses when children work out a calculation from a story. For example: Merrie said, 'If two more come there will be seven, because five and two make seven.'
• How do children count in steps/groups of, for example, 2 or 10 from given numbers and make use of this when solving problems?
• How do children use the language associated with sharing out quantities into different groups?
• How do children solve practical problems and puzzles and respond to questions such as 'How did you do that?' or 'Why have we got in a muddle with this?'

Assessment opportunities

• Observe how children use everyday objects, for example counting pennies in the role-play and seeing how many there are altogether and how many are left when some are spent.
• In outdoor activities with small apparatus are children able to solve practical problems, describing their solutions, for example sharing a number of objects equally into a given number of groups? Do they use appropriate strategies?

Related Profile scale points

C 4, 5, 6

Example of mathematics planning and resourcing 6

What we want children to learn (Development matters)

Objectives in bold refer to Early Learning Goals.

Mathematics objectives

• Sort familiar objects to identify their similarities and differences
• Count how many objects share a particular property, presenting results using pictures, drawings or numerals

Using and applying mathematics

• Sort objects, making choices and justifying decisions

Related Early Learning Goals

• Explore colour, texture, shape, form and space in two or three dimensions (CD)

Possible contexts

• Provide plenty of experience of sorting and classifying groups according to their own criteria to allow recognition of properties of regular shapes and other objects.
• Sort and classify leaves, fruit, clothing, recycled materials and natural objects according to their properties.
• Use computer programs to enable this information to be represented pictorially, for example charting eye colour, pets, favourite food or favourite colour.
• Provide collections of resources and clipboards, large pieces of paper and mark-making tools or large chalkboards.
• Use everyday activities such as snack time as a vehicle for encouraging mark making and sorting according to preference. For example: who would like apple and who would like banana?
• Use an interactive whiteboard with a variety of clip art pictures or photographs that can be moved to show the similarities and the differences between groups.
• Use collections of shapes and hoops for children to classify.

Example of adult-led activity

Context: Collecting leaves

Rake up leaves together in autumn or visit a local park. Make a collection of leaves with a variety of colours and shapes.

Sort the leaves with the children, asking about their reasons for grouping certain leaves together.

Describe and compare their leaves, noticing similarities of properties. Notice whether there are groups of more or fewer leaves with a particular property - count to make sure - and ask them why they think that might be. Let them select a set according to its shared property.

Ask them if they would like to draw their leaves, spray paint over them or make leaf prints. Make a pattern of the leaves and display these alongside the leaves and photographs of the trees. They could attach lines matching their leaves to the trees they come from.

Adult role

• Exploit everyday opportunities for sorting, matching and categorising things in everyday life by involving children in organising and labelling equipment, organising games, monitoring attendance, and voting to make decisions.
• Observe children making collections of objects in their freely chosen activities and make use of these opportunities by encouraging mark making and representing the situation pictorially.
• During real-life problems, encourage children to consider how objects may share particular properties. For example: how many children are wearing red?
• Encourage children to explore problems, to make patterns and to count and match together.
• Provide help for those children who use a means of communication other than spoken English in developing and understanding specific mathematical language.

Opportunities for children to explore and apply

• Provide model-making and pattern-making materials and work alongside children as they build. Encourage children to talk about sorting the objects for use. Discuss their reasons for choice, noticing the properties they choose.
• Provide activities that encourage children to describe and explain, for example a 'feely bag'.
• Make collections of natural objects for children to sort, match and describe, for example leaves, cones, shells and stones. Help them to make comparisons, and introduce mathematical language through modelling.
• Provide a rich range of materials for pattern making both inside and outside in the learning environment.

Adult role

• Exploit opportunities for sorting, matching and then counting groups, for example counting fruit at snack time, registering children, organising games.
• Observe children making collections of objects in their freely chosen activities and make use of these opportunities by encouraging mark making and representing the situation pictorially.
• During real-life problems, encourage children to consider how objects may share particular properties. For example: how many children are wearing red?
• Encourage children to explore problems, to make patterns and to count and match together.
• Provide help for those children who use a means of communication other than spoken English in developing and understanding specific mathematical language.

Look, listen and note

• How do children show curiosity and observation by talking about shapes, identifying how they are the same or why some are different? For example: Danny decided to make a box for his model. He chose a piece of card that was an appropriate shape for the base and different shapes for the sides.
• Can children match shapes by recognising similarities and orientation? For example: when Stevie looked at a rhomboid she said 'It looks like a boat.' She picked up a triangle and observed, 'This one's different. It's only got three points.'

Assessment opportunities

• Use events such as snack time to observe how children can sort out items, for example numbers of children wanting apple or banana.
• Observe how children begin to make pictorial representations of collections of objects.
• During events such as snack time, do children successfully sort out items, for example for the number of children wanting apple or banana?
• Can children identify appropriate properties and use these to sort and classify collections of objects, describing what they have done?
• Can children sort a collection of shapes/objects according to one property and then re-sort them using a different property?

Related Profile scale points

SSM 2, 8

NLC 8p

Example of mathematics planning and resourcing 8

What we want children to learn (Development matters)

Objectives in bold refer to Early Learning Goals.

Mathematics objectives

• Select two groups of objects to make a given total of objects

Using and applying mathematics

• Use developing mathematical ideas and methods to solve practical problems

Related Early Learning Goals

• Interact with others, negotiating plans and activities and taking turns in conversation (CLL)
• Work as part of a group or class, taking turns and sharing fairly, understanding that there needs to be agreed values and codes of behaviour for groups of people, including adults and children, to work together harmoniously (PSED)
• Investigate objects and materials by using all of their senses as appropriate (KUW)
• Find out about, and identify, some features of living things, objects and events they observe (KUW)

Possible contexts

• Establish role-play that has a focus on groups of objects, for example in a shop context with collections of fruit or groceries.
• Use everyday opportunities, such as snack time, to pose problems.
• Use self-registration opportunities to ask the children a variety of questions. For example: how many are there altogether? How many more than yesterday?
• Provide collections of objects for children to sort, match and count.
• Share, recite and encourage joining in with number rhymes and stories using games and books.
• Provide tapes and CD-ROMs of number rhymes and songs for children to listen to.

Example of adult-led activity

Context: Planting bulbs

Give the children a box of 15 daffodil bulbs and a box of 15 tulip bulbs. Ask them to plant up 6 containers in as many different ways as possible. Suggest that they can plan different ways of putting the daffodils and tulips together first so they have arrangements that they like. Provide mark-making materials. The children may like to group the bulbs into different combinations or they may draw possible arrangements.

Ask them to record how they have planted the containers to help them remember which bulbs are in each. Provide clipboards and pens. They may need some modelling or support with questions. For example: this container has 3 daffodils and 2 tulips; how could we show that?

Share their recordings and ask questions: so have you got the same number in each? Do you prefer the colour of the tulips? Will more of those look better in the pot, or more daffodils? Which would you prefer? Did you run out of any bulbs or did you plan carefully? So you've got 3 in here altogether; how many daffodils are there?

Adult role

• Model saying and using number names in a variety of contexts, for example collections of objects and games (indoors and outdoors), 'small world' figures, construction equipment and blocks.
• Exploit opportunities for sorting, matching and then counting groups, for example counting fruit at snack time, registering children, organising games.
• Scaffold children's learning by identifying where they are in understanding of number and then planning for next steps.
• Observe children and note possible next steps, for example: begins to sort and group and then moves to be able to select groups of objects for a given total.
• Share books and exploit the number potential.
• Model using the language of addition and subtraction including 'more', 'and', 'add', 'make', 'altogether', 'total', 'take away', 'how many left', etc.
• Look for situations where you can use words such as 'add', 'take away', 'altogether', 'more than' and 'fewer' and try to show what you mean by counting to demonstrate it.

Opportunities for children to explore and apply

• Model mathematics games and provide for spontaneous play. For example: roll a dice and put that number of toys (bears, shells, etc.) in one of 3 containers. Children throw the dice until they have the number they need to make 5 toys in each container.
• Provide collections of objects for children to use for sorting, matching, combining and pattern making.
• Encourage children to be curious. For example: in cooking, cut open fruit and count the number of seeds. (The children may need to use a magnifying glass or a digital microscope.) Is there the same number of seeds on each side of the fruit?
• Use real-life problems. For example: we've got 28 children altogether and lots of different fruit. Which fruit shall we choose? How many pears? Does that give us the number we need? Do we need more or less?

Adult role

• Model finding totals of objects in a variety of contexts, for example collections of objects and games (indoors and outdoors), 'small world' figures, construction equipment and blocks.
• Exploit opportunities for sorting, matching and then counting groups, for example counting fruit at snack time, registering children, organising games.
• Talk about outcomes, for example 4 red bricks and 2 yellow bricks makes 6 bricks altogether.
• Observe children and note possible next steps, for example: begins to sort and group and then moves to be able to select groups of objects for a given total.
• Share books and exploit the number potential.
• Encourage children to make marks to record their findings, for example drawing their towers or making marks to show their outcomes.

Look, listen and note

• How do children find the sum of two numbers? Adeola picked up as many conkers as she could, working out how many she had altogether: 'Five and four - nine! That's my best go.'
• Observe the variety in responses when children work out a calculation from a story. For example: Merrie said, 'If two more come there will be seven, because five and two make seven.'
• How do children use different methods to find a total?

Assessment opportunities

• See how children tackle problems such as putting 2 kinds of animal in a stable designed for 6 animals, or making a tower of 6 bricks using 2 colours.
• Are children able to respond to the request, for example, to take more conkers or cotton reels or to put some back?
• Observe the children in practical contexts using objects or by modelling with objects or apparatus. Can the children make 10 in a variety of ways by combining two or more amounts? What numbers up to 10 can they make correctly using two groups of objects?

Related Profile scale points

C 4, 5

Example of mathematics planning and resourcing 9

What we want children to learn (Development matters)

Objectives in bold refer to Early Learning Goals.

Mathematics objectives

• Begin to relate addition to combining two groups of objects and subtraction to 'taking away'
• In practical activities and discussion begin to use the vocabulary involved in adding and subtracting

Using and applying mathematics

• Describe solutions to practical problems, drawing on experience, talking about their own ideas, methods and choices

Related Early Learning Goals

• Handle tools, objects, construction and malleable materials safely and with increasing control (PD)
• Express and communicates ideas, thoughts and feelings by using a widening range of materials, suitable tools, imaginative and role-play, movement, designing and making, and a variety of songs and musical instruments (CD)

Possible contexts

• Establish role-play that has a focus on groups of objects, for example in a shop context with collections of fruit or groceries.
• Use everyday opportunities such as snack time to pose problems.
• Use self-registration opportunities to ask the children a variety of questions. For example: how many are there altogether? How many more than yesterday?
• Provide collections of objects for children to sort, match and count.
• Share, recite and encourage joining in with number rhymes and stories using games and books.
• Provide tapes and CD-ROMs of number rhymes and songs for children to listen to.
• Encourage children to make up number stories and represent them pictorially.

Example of adult-led activity

Context: Minibeasts

Look at a caterpillar and other minibeasts with children. Carefully examine them with magnifying glasses or a digital microscope. Look at their features, numbers of antennae, legs, etc. Draw or paint the minibeasts indoors and outdoors using clipboards where necessary.

Introduce the idea of designing bugs made out of playdough. The children could draw their own design or use a computer paint program to make the design. Comment on numbers of sets in their bugs: how many legs are you going to add? It could have lots of eyes couldn't it? Will it have the same number on each side? Will it be able to balance?

Make the bugs based on their designs. Provide a number of colours of playdough. Introduce adding and subtracting, and model the language. For example: shall I help you make the antennae? How many do you have? How many more will you need? Whoops that's too many; how many do we need to take away? Keep number lines on the table to help with adding and subtracting.

Adult role

• Provide practical real-life activities underpinned by developing communication skills.
• Model mathematical vocabulary during the daily routines and throughout adult-led activities.
• Encourage children to explore objects and groups and provide resources to encourage mark making and representation, for example adding up tally marks of scores in a game.
• Help those children who use a means of communication other than spoken English to develop and understand specific mathematical language.
• Exploit opportunities for sorting, matching and then counting groups and totals, for example counting fruit at snack time, registering children, organising games.
• Share books and exploit the number potential for using vocabulary of addition and subtraction.
• Encourage children to choose numbers for problems and to make up their own story problems for other children to solve.
• Model the use of vocabulary such as 'add', 'addition', 'altogether', 'and', 'total', 'take away', 'subtract', 'one more', 'one less', 'how many are left/gone', 'make', 'sum', 'is the same as', 'difference between', 'how many more than', 'count', 'group', 'count out', 'share out', 'left over'.

Opportunities for children to explore and apply

• Work alongside the children at 'small world' and construction play. Add and subtract pieces while using the language of addition and subtraction. For example: it might fit if we take some away. How many do you think we'll need to take away? Shall we put the people on the bus? Can we add any more? If 3 people get off here; how many passengers will be left? Have we got space for any more?
• Use systems for self-registration and ask the children: how many are here today? If x still come in how many will be here? Now 3 people have gone out; how many are left?
• Model mathematics games. For example: have 10 beans and a pot and work with a friend. One person decides how many to take away and the other guesses how many are left. Then they check together and swap over.
• Model using addition and subtraction with cooking, or role-play with money, sand and water. For example: we need 3 of these and 2 of those; how many have we got altogether? Have we got too many? How many will you need to take away?

Adult role

• Provide practical real-life activities underpinned by developing communication skills.
• Model mathematical vocabulary during the daily routines and throughout adult-led activities.
• Encourage children to explore objects and groups and provide resources to encourage mark making and representation, for example adding up tally marks of scores in a game.
• Help those children who use a means of communication other than spoken English to develop and understand specific mathematical language.
• Exploit opportunities for sorting, matching and then counting groups and totals, for example counting fruit at snack time, registering children, organising games.
• Share books and exploit the number potential for using vocabulary of addition and subtraction.
• Model the use of vocabulary such as 'add', 'addition', 'altogether', 'and', 'total', 'take away', 'subtract', 'one more', 'one less', 'how many are left/gone', 'make', 'sum', 'is the same as', 'difference between', 'how many more than', 'count', 'group', 'count out', 'share out', 'left over'.

Look, listen and note

• How do children find the sum of two numbers? For example: Adeola picked up as many conkers as she could, working out how many she had altogether: 'Five and four - nine! That's my best go.'
• Observe the variety in responses when children work out a calculation from a story. For example: Merrie said, 'If two more come there will be seven, because five and two make seven.'

Assessment opportunities

• Assess children's understanding when they are using everyday objects, for example counting pennies in the role-play area and seeing how many there are altogether and how many are left when some are spent.
• In outdoor activities with small apparatus, observe how children are able to combine groups and find the total by counting on.
• Can children solve practical problems such as: we ate 2 of our 8 jellies, so how many are left? There are 4 cars in the car park and 3 more arrive. How many are there now?

Related Profile scale points

C 4, 5, 6