Mathematical development

To give all children the best opportunities for effective mathematical development, practitioners should give particular attention to:

• many different activities, some of which will focus on mathematical development and some of which will draw out the mathematical learning in other activities, including observing numbers and patterns in the environment and daily routines;
• practical activities underpinned by children's developing communication skills;
• activities that are imaginative and enjoyable;
• help for those children who use a means of communication other than spoken English in developing and understanding specific mathematical language;
• opportunities to observe, assess and plan the next stage in children's learning;
• relevant training to improve practitioners' knowledge, skills and understanding.

Aspects

Numbers as Labels and for Counting
Calculating
Shape Space and Measures

Included below are short articles on -

A list of resources to help develop mathematical understanding.
Mathematical language
Questions to ask to help develop mathematical understanding and problem solving
Some games and activities to help develop mathematical understanding and language
Good books for Maths Ideas

A list of resources to help develop mathematical understanding.

Try to vary the materials, equipment, resources and environments (e.g. indoors/outdoors) you use and how you use them as much as possible. This will help to maintain interest, develop learning, extend opportunities and develop mathematical language.

Counting, numbers and sorting

• Real objects and materials e.g. shells, conkers, pebbles, leaves, fir cones, feathers, pasta shapes
• Different sized, coloured and shaped objects
• Sorting trays
• Pegs
• Numbers made out of different materials e.g. plastic, foam, sand paper, wood
• Buttons and beads
• Cotton reels
• Cars and other small toys
• Keys
• Calculators
• Abacus
• Pegged number line
• Telephones
• Calendars and diaries
• Computers, keyboards, tape recorder, programmable toys
• Telephone directory
• Counting and number books and puzzles
• Catalogues
• Recipe books and menus

Shapes and patterns

• Shapes made from different materials
• Pegboards
• Tap a shape games
• Beads of different shapes, sizes and colours
• Magnetic shapes
• Linking games e.g. multi-link, unifix
• Construction sets
• Playdough, clay, Plasticine & cutters
• Collage/junk modelling materials

Measuring and weighing

• Sand/water timers
• Rulers
• Tape measures
• Sets of hand and foot prints
• Balances and scales
• Real objects and natural materials
• Graded containers
• Stop clocks
• Thermometers
• Sand and water

Time

• Calendars
• Diaries
• Stop clocks
• Timers
• Clocks
• Time line

Money and shopping

• Real coins
• Tills
• Purses
• Baskets and bags
• Real items for use in a shop
• Bills, order forms and receipts
• Notepads and pens
• Clip boards
• Calculators
• Catalogues
• Scales
• Menus

Games

• Track games
• Dice games
• Matching, sorting, colour, shape and size games
• Shape, number, colour and texture dominoes
• Card games and lottos
• Puzzles
• Large and small pieces
• Sequencing puzzles
• Inset puzzles
• Shape puzzles

Mathematical language

This is crucial to the development of mathematical thinking. Use mathematical language to help children name, describe, talk about comparisons, explain relationships (e.g. between size, shape, position), question, predict and solve problems.

Some mathematical language to use: -

• More/less
• Bigger/smaller
• Longer/taller/shorter
• Higher/lower
• Full/empty
• Heavier/lighter
• Wider/narrower
• Faster/slower
• Too much/too little
• Same/different
• Before/after
• Balance
• Both
• All together
• Add/take away
• Share
• In/out/on/under/beside/above/between/behind/in front
• Names of numbers, shapes, days/months of year, coins
• Round, flat, straight, curvy
• Corner, line
• Does fit/doesn't fit

Questions to ask to help develop mathematical understanding and problem solving

• How much/many?
• How do you know how much/many?
• Are there enough?
• What can you tell me about...?
• How do you think you could...?
• Is there another way you could...?
• What's different/what's the same?
• Why did you choose this?
• What can you say about...?
• What might happen if...?
• Which of these go together?
• What comes next?
• What comes before?
• How did you guess?
• Why do you think...?
• Suppose...what do you think might happen then?
• What do we do now?
• Can you find one the same?
• Do you think this will fit/be enough?
• Which/who has more/less?
  Can you make it smaller/bigger/longer/shorter...?
• What/who is first/second/last...?
• What could we use to help us?
• Why doesn't this work?
• What have you done so far?
• What else could we do to...?
• How did you work that out?

Some games and activities to help develop mathematical understanding and language

Number recognition and counting

• Use a pegged number line for counting, matching, missing number and jumbled up number games.
• Make a moveable number line using yoghurt pots. Label the pots with numbers. Children choose correct number of objects to put inside each pot and place in order.
• Make a vertical number line, using the children's handprints.
• Make a tactile number line using materials such as sandpaper, fur, cord, velvet etc. for a multi-sensory approach.
• Label attractive boxes with different numbers. Children place correct number of natural objects in each box e.g. shells, fir cones, conkers, feathers
• Place a few wooden/plastic numbers in a feely bag. Can children pull out a given number by feel only?
• Place wooden/plastic numbers in separate envelopes. Slowly pull them out one by one to reveal a small part of the number. How soon before the children can guess what the number is?
• Hang number cards on a mug tree. Can children hang the correct number of objects on each mug peg? Use scrunchies, rubber bands, bracelets, curtain rings
• Hang numbered pockets on the wall. Children place correct number of items in each pocket.
• Thread correct number of cotton reels/beads on to numbered laces.
• Hold a small number of marbles in your hand and slowly drop one by one into a covered container. Children listen carefully and tell you how many you dropped in.
• Show a number of objects on the floor. Cover them up. Can the children remember how many?
• Go for a number walk with a number card. See how many times the children can see that number e.g. on a bus, shop, menu, house, car
• Go for a number walk and take photos of numbers in the environment. Make a display of the photos.
• Collect examples of numbers on packaging, magazines, labels etc. from the environment and set up a display.
• Stick a number on each side of a box/tin. Children clip the correct number of pegs to each side of the container.
• Hide pieces from a number jigsaw around the room. Children have to go and find the pieces, bring them back to a central point and help put the jigsaw together.
• Label bikes and create numbered 'parking bays'. See if the children can park their bikes in the correct bays.

Music

• Play musical instruments behind a screen a certain number of times. Can children tell you how many bangs on the drum, shakes of the maracas etc?
• Play an instrument a certain number of times. Can the children play their instrument the same number of times?
• Sing and act out number rhymes and songs.

Sand, water and malleable materials

• Find foam numbers in water or sand
• Make numbers out of playdough
• Draw numbers with fingers in shaving foam/paint/gloop
• Catch given numbers of floating objects in nets.
• Fill and empty a variety of containers (tall, short, thin, wide, large, small etc.) with water, sand or materials such as lentils and rice.

Creative Area

• Make models with different sized, shaped, coloured and textured boxes and materials.
• Print with different shaped objects.
• Collage large numbers and shapes.

Cooking and snack time

• Make number shaped biscuits
• Stick certain number of currants/chocolate drops etc. on cakes/biscuits
• Make a recipe book using pictures and numbers of cupfuls/spoonfuls needed for each recipe.
• Make menus with prices, for the role-play cafe.
• Cut up fruit into segments and portions. Talk about halves, quarters and shapes.
• Encourage children to pour drinks for themselves.
• Share out biscuits/fruit together with the children.
• Count out fruit, biscuits, drinks

Physical

• Knock over numbered skittles
• Throw large dice and clap, jump, hop catch ball etc. correct number of times
• Throw correct number of beanbags into numbered containers
• Jump along numbered carpet tiles in order from 1-5/10
• Use large chalked shapes on the ground. Throw a shape dice, children run to correct shape. A harder version would be to add colours so children have to run to the red square, the green circle etc.
• Throw correct number of quoits over numbered cones.

Measuring and time

• Draw round hands and/or feet and cut out. Use for measuring activities and games.
• Give children a length of string, fabric or a ruler. How many things can they find that are longer/shorter?
• Place some pegs in a line on a pegboard. Can children add or take away pegs to make the line longer/shorter?
• Give children different sized containers. See how many conkers, cones, shells etc. they can fit inside them.
• Use role-play to encourage the children to find things to fit e.g. the right sized hat, belt, bag, container etc.
• Make a time line with photos of what the children do in the day e.g. register, snack, outdoor play ... encourage them to refer to it during the session.
• Use a sand timer at tidying up times in order to help children learn about the concept of time.

Shapes

• Collect flat and 3D shaped items from the environment and make a display e.g. tins, food packets, money
• Stick a large favourite picture on to a piece of card. Cut into two or more shapes according to the ability of the child and see if they can put the picture together again.
• Carefully cut/break for example a toothpaste box, a flowerpot (watch edges) into pieces. Can the child put the item back together again?
• Play with flat shapes on the floor and find which are the same and which fit together.
• Cut sponges into different shapes and use to print shape pictures.
• Place shapes into a bag. Ask children to pull out a circle, a square, a curvy shape, a straight shape etc. by feel only.
• Go on a shape walk. Take a shape with you and look for that shape in the environment.
• Use shapes freely to make own pictures and patterns.
• Make shape biscuits.
• Make shapes with playdough.
• Mark out large shapes on the floor. Children run round to music and go and stand inside a given shape when the music stops.
• Children march/dance round to music. When the music stops, they make a shape with their body.

Good books for Maths Ideas

Featherstone Educational Publications -

The Little Book of -

• Cooking from Stories ISBN - 1-904187-04-8
• Sand and Water ISBN - 1-904187 52 8
• Small World Play ISBN 1-905019-35-1
• Colour, Shape and Number ISBN 1-905019 27 X
• Of Clay ISBN 1-905019 26 2
• Maths from Stories 1-905019 25 4
• Cooking Together 1-905019 13 0
• Of Dough 1-905019 10 6
• Maths Activities
• Maths Songs and Games
• Outside in All Weathers

Lawrence Educational Publications -

• The Small World Recipe Book 50 Ideas ISBN 1-903670 39 X
• 50 Exciting Ways to use a Builders Tray ISBN 1-903670 15 2
• Plant An Idea ISBN 1-903670 24 1
• 50 Exciting Things to do Outside ISBN 1-903670 07 1

Belair Early Years Publications

• Water play ISBN 0-94788 252 9
• Shape, Space and Measures ISBN 0-94788 270 7
• Number and Calculating