Sand - or a sunny beach
A stick or index finger

Use a stick to make marks in the sand - vertical and horizontal lines, circles and crosses are good to start with.
Encourage your child to copy you then ask him/her to make marks for you to copy.
Talk about the marks and letters you make and the movements you do to make them. “I’m starting here, then going down, then stop”. “I’m starting here then going round and round and round”. “I’m going to make M for Mummy”

This helps your child develop skills and confidence in forming and connecting the curves, vertical, horizontal and zig-zag lines that form the bias of letter shapes.
Starting big then gradually working down to smaller develops as your child’s hand and eye co-ordination skills and manual dexterity skills mature and integrate.
As your child associates the language of the mark or letter shape with the action of forming these, he/she will be getting kinesthetic feedback which is essential for any motor action.
Kinesthesia is the knowledge of where each body part is and direction in which it is moving.
It is an important component of motor control for legible handwriting.

Bean bag

Chalk

Draw your basic hopscotch grid, then the first player throws a marker, such as a bean bag, into box 1.

The player hops on one foot (or alternating feet) all the to the last box and back, stopping to pick up the marker on the way.

Players take turns trying to throw in each box in order (1, 2, 3, etc.).

A simpler way to play is to follow the instructions above, but only to hop to the first square, pick up the marker, and return.

This game encourages hand/eye coordination and balance.

Why not ask your child to draw out the hopscotch board and to write the numbers, supporting their mathematical graphics.

Use Sensory Toys/Objects

Dangle objects for your baby to touch, eg hang toys over the cot or changing table, or place little one under the play gym. This encourages their reach.

Move objects in front of them such as a toy or rattle, or blow bubbles. Try objects that make a noise, move, are colourful or are black and white. This helps develop their eye movement and strength.

Sing Songs or lullabies and nursery rhymes

Any actions songs and nursery rhymes are fine. Show them the actions, eg clap their hands, clap their feet, bicycle their legs. Encourage them to look and play with their hands and feet.

Do the actions yourself and others such as wiggling fingers, pulling funny faces, clicking fingers and waving. This encourages body awareness.

With your baby on their back, hold each hand in yours and cross their hands in front of their body (so they're hugging themselves) and then uncross their hands. Repeat several times and do the same with their legs. This is important for developing coordination.

Plastic bottles - different shapes and sizes
Plastic Jugs
Plastic Funnels

Collect up different size plastic bottles, plastic funnels and jugs for bath-time maths.
Have fun pouring water into the bottles, whilst playing talk about; Filling the bottle to the top, “Is it nearly full?”, “How many little bottles of water does it take to fill this big bottle?”, “Shall we fill it half full?”.
You can add some stretch and challenge by marking up quantities with a permanent marker pen or coloured waterproof tape. For example, marking up 250ml on a 500ml bottle, and marking up 50 ml units on a 200ml bottle.
If you have 2 different shaped bottles that hold the same amount ask your child which one he/she thinks will hold the most water. Help him/her test out to see what happens.

Playing with water in this way helps children explore capacity and volume.
Talking with your child as they fill up bottles helps them develop understanding of mathematical terms associated with capacity and volume in ways that are meaningful.
Exploring how the volume of water stays the same regardless of the size or shape of a container is an important mathematical concept to develop. This is referred to as conservation of volume; having the ability to understand that redistributing liquid does not affect its volume. Children usually master this at around the age of seven years.
Children are likely to think that a tall narrow bottle contains more liquid than an equal amount in a short fat bottle. Through playing with water and different shaped containers that hold the same amount, children will begin to explore conservation of volume.

Here are some ideas that can help your child develop their mathematical skills both in the home and out and about with the family.

Number
• Counting steps/stairs as you go up – perfect for one to one matching
• Counting red cars, telephone boxes etc on the way to nursery or the shops
• Pairing up socks and shoes
• Laying the table – how many knives will we need?
• Helping peg out the washing
• Doing up their own buttons or someone elses?
• Looking at numbers around us – on house doors, registration plates, shop windows
• Helping with the shopping – we need three oranges and two lemons. How many altogether?
• Talking about the child’s age and those of the rest of the family.
• Use ordinal numbers (first, second, third etc.) in going through steps of a recipe, having a race down the garden, or getting dressed in the morning.

Sets and Sorting
• Sorting the washing
• Tidying away toys – getting the toys in the right boxes
• Talking about similarities and differences between objects or people
• Sorting everyday objects in the kitchen.

Pattern
• Following different sequences e.g. laying the table, getting dressed, in the same way each time
• Singing songs or telling stories with a clear pattern, sequence of repetition, e.g. Old MacDonald, Three Blind Mice, Three Billy Goats Gruff
• Looking at the patterns on curtains, wallpaper, wrapping paper. Children can print their own wrapping paper to wrap a friend’s birthday present
• Looking at patterns on buildings e.g. bricks in wall, windows
• Building with blocks and different construction toys – using one piece after another.

Shape and Space
• Describing different containers and packets in the kitchen and at the supermarket
• Finding shapes in the child’s own environment e.g. road signs, post-boxes, windows and doors, books
• Doing jigsaw puzzles (looking at the shapes of the pieces and the ‘holes’ where they could go, and keeping the overall shape of the puzzle develops spatial awareness)
• Playing with car mats, train sets, or outside on tricycles.

Measuring
• Estimating how much is needed, for example, how much bread to make 4 sandwiches, how much icing to ice the cake
• Playing in the sand pit using different containers
• Bath time or washing up time – pouring from one container to another, filling different containers, using containers with holes
• Talking about events throughout the day in order of sequence
• Drawing child’s attention to the clock – e.g. we’ll have tea when the big hand is on the 6
• Handling money at the shops. Role playing ‘shops’ at home using coins and counting out the right number
• Tidying things away into different boxes and containers – will we fit them all in?
• Comparing different lengths (dog’s lead, socks, shoelaces), weights (shopping bags, toys), areas (footprints of child and adult), sizes (teddies, chairs for child and adult) and capacity (child’s beaker and adults’ glass, bottles of squash).