We use mathematics every day of our lives. We use math when we read a recipe and measure out the ingredients, when we go shopping and when we garden.

It is important to introduce numeracy concepts within the preschool years as we are forming essential lifelong skills. By providing learning experiences that are fun and play-based we are forming positive attitudes to numeracy.

The games and activities included here address a range of essential mathematical and pre-math concepts:

• Noticing and studying shape is an important foundation for geometry. Straight, curved and bent are about shape and are used in everyday conversation. Children will gradually understand the concept of triangle, square and circle.
• Up, down, next to and upside down are all helpful for understanding position and direction
• Grouping something together: identifying same and different, and eventually how something is different
• Big and little are about measurement
• Sorting is about classifying, for example color, size or packing away the groceries in a logical way
• There are patterns in the way we say numbers and when numbers begin to be repeated (for example, 21, 22, 23). When children notice the pattern in the numbers they will know what comes next
• Half and quarter, or splitting something into equal amounts, introduces the concept of fractions
• Sharing is about division
• High and low are measurements and comparisons, as are full and empty
• Heavy and light are about mass. Later, children will notice that the big things are not always heavy and the small things are not always light
• Numbers explain how much, how long and how many
• Top, bottom and edge relate to the concept of area

The activities suggested below allow children to work at their own pace and extend on their own ideas. The activities offer opportunities to expose children to mathematical language in everyday situations.

1. Collection of shoes

This activity explores the topic of recycling. Families can be involved by bringing in old shoes. Take prints of the shoes by using paint, wet sand or the mud pit and look at the lines and patterns with the children.  Other activity ideas are:

• Shoes can be added into the sandpit, allowing for the shoes to be filled with sand so that the children can consider concepts of heavy and light, full and empty
• Shoes can be arranged in order of size
• Shoes can be grouped according to different attributes; for example, shoes with laces or buckles.

2. Dough

Dough is a sensory experience that children love and which allows them to explore a variety of numeracy concepts:

• Make dough balls of different sizes; this activity can introduce the concept of sequencing. You can also introduce scales to enable a discussion about mass
• Counting the balls to learn names of numbers
• Also use dough to make ‘snakes’ for the concepts of long and short, thick and thin etc. Compare sizes and weights and look at length and relative length
• Use dough placemats to explore shapes and numbers. You can find my Number and Shape Play Dough Placemats here.

3. Graphs

Make basic graphs with the children to introduce graphs as a pre-math concept. Use a survey to gather the information – I usually do this on a big piece of cardboard so it’s an interactive experience. Grouping things together is about noticing objects that are the same or different and counting them. Sorting things teaches the concept of classifying.

Once you have tallied up the results, you can look at comparisons.

You could, for example:

• Compare favorite colors
• Compare the color of family cars
• Compare the pets that children have.

4. Heights

Measure children’s heights using strips of receipt paper. Children lay down and work together to take the measurements. The child can then paint or decorate their strip of paper.  Children order the lengths from shortest to tallest. You now have a visual representation of height. When comparing heights with the children, work from left to right as a reading comprehension strategy.

5. Belts

I recycled my son’s martial arts belts from his first grading as a young boy until his late teens. These were perfect as they presented a variety of lengths and colors. Other belts can be substituted; for example, men’s, women’s, children’s, leather or cloth belts.

Work with the children to order the belts according to length.  Cloth belts can be made into shapes. Make a big circle using a longer belt, and compare it with a little circle, made using a shorter belt.

6. Block Construction

Children plan and design using construction blocks, while also identifying different patterns, lines and heights. The children can recognize shapes and lengths as well as measure and balance. Children love to build tall towers. I like to print out photos of famous towers from around the world, such as the Eiffel Tower, Leaning Tower of Pisa and Empire State Building. Look for patterns, curves etc. You can also do this for a tower in your local city. Use a variety of mathematical language when discussing the towers.

Children can also follow instructions for building that introduce math concepts such as: build a tower as tall as your knee / hip / chin. Introduce concepts of relative height (taller, shorter) and discuss differences too. Alternatively, you can use number cards up to 10. Children then build using the number of pieces on the card.

You can also set the children a project – building a road with 2 bridges, for example.

7. Sand

The sand pit is a fun way to explore many pre-math concepts:

• Children can dig tunnels of different lengths and build castles of different shapes
• Turning a bucket of sand upside down to make a castle is about position and direction
• You can count how many scoops are needed to fill up a bucket or how many shovels of sand are required to make a castle
• The children can follow instructions to bury themselves in the sand; for example, one leg and two arms
• You can consider the weight of a bucket full of sand compared to an empty bucket
• Children can problem solve, “How will we lift this container full of sand?”, “Will we empty half or get 3 friends to help?”
• Use dry and wet sand to look at different concepts, for example, which is heavier? Why do footprints look different?
• Different sized buckets and scoops
• ‘Full, half, empty’.

8. Water Play

Use jugs and measuring cups to explore concepts such as empty, half and full. Use boats to explore big and little, patterns and sequencing through lining up the boats – and then count the boats. Sharing the boats with your friends explores the concept of division. The concepts of floating and sinking can also be introduced. On a warm day add ice cubes. How many ice cubes will fill a jug? It’s amazing to watch children make their own mathematical discoveries without them even realizing.

9. Cooking

Cooking is a fun activity for pre-math concepts. Children have to follow the sequence of events and count (How many spoons? How many eggs?). Bowls can be used to demonstrate the concept of full and empty. Different sized bowls, spoons and cups are used and many different shapes of cooking tins. If cooking a cake or pizza, when it comes time to eat, fractions are introduced by cutting it into halves, quarters etc.

10. Painting

Fill a ketchup bottle with paint to allow children to experiment with size, color, shape and patterns. Add a little water to the paint and test to make sure you have the right consistency so when you tip the bottle the paint runs slowly down the paper on the easel. Working from the top of the page, children squeeze the paint from the bottle. Children continue to do this along the paper, moving from left to right. We then watch the paint run down the paper. Use language such as 1^st, 2^nd, 3^rd, fastest, top and bottom, long and short in your conversations.

11. Collage

To do collages with your children you will need a variety of natural and recycled materials with various shapes/sizes and textures. They should include items collected from your outside environment as well. For example: different shaped and colored leaves, acorns, flowers, tree bark, various sized boxes, wrapping paper, ribbons, yarn and greeting cards. Children can consider children can consider measurement, size, color, shape, patterns, comparison, sorting, classification and grouping.

Collage is very hands-on and involves all the senses. Collage can be created anywhere, inside or outside – for example, we did a great big collage on sustainability, using recycled items brought in by families and collected outside by children (each child had a container).

Alternatively you can do a more structured activity. When one of my classes was researching life in the sea we made an octopus from a paper bag. We crumbled pieces of newspaper and placed them inside the bag until it was ‘big, round and full’. We made 8 legs from different lengths of paper – count the legs for accuracy.

12. Outdoors

The outdoor play area is full of activities to address pre-math concepts, for example:

• Big and little balls/hoops – compare size and weights
• Going up and down a ladder
• Under and over
• High and low
• Using a see-saw for heavy and light
• Obstacle courses
• Walking along straight and curved lines and shapes
• Counting how many goals were made
• Sorting the sandpit toys into containers
• Gardening, digging small holes for flowers and big holes for bushes.

13. Songs and finger plays

Engaging songs and finger plays never fail to get children involved and counting without any pressure. Some of my favorites for this purpose include:

Going on a Bear Hunt

This traditional song explores concepts of over, under, through, position and direction.

The echo is in brackets.

5 little ducks

The children act these songs out, which introduces the concept of subtraction and addition.

Five little ducks
Went out one day
Over the hill and far away
Mother duck said
“Quack, quack, quack, quack.”
But only four little ducks came back.

Four little ducks
Went out one day
Over the hill and far away
Mother duck said
“Quack, quack, quack, quack.”
But only three little ducks came back.

Three little ducks
Went out one day
Over the hill and far away
Mother duck said
“Quack, quack, quack, quack.”
But only two little ducks came back.

Two little ducks
Went out one day
Over the hill and far away
Mother duck said
“Quack, quack, quack, quack.”
But only one little duck came back.

One little duck
Went out one day
Over the hill and far away
Mother duck said
“Quack, quack, quack, quack.”
But none of the five little ducks came back.

Sad mother duck
Went out one day
Over the hill and far away
The sad mother duck said
“Quack, quack, quack.”
And all of the five little ducks came back.

5 Elephants went balancing

One elephant went balancing
Step by step on a piece of string
He/she found it such tremendous fun
That he called for another elephant to come

[Another child joins the first child and holds on to his/her shoulder]

Two elephants went balancing …

[Another child joins the children and holds on to the second child’s shoulder]

Three…

Four …

Five elephants went balancing
Step by step on a piece of string
They found it such tremendous fun
But the string went SNAP [clap]
And they all fell down

What’s the time Mr Wolf?

What’s the time Mr Wolf is great for learning the names of numbers and the concept of “how many”.

The children step out the numbers and increase awareness of numbers and time.

This game reinforces 1 to 1 correspondence, where the children count out the steps; for example, for three o’clock you step 3 times, counting each step aloud.

14. Social Play Areas

One of my favorite social play areas to set up for my preschool children for math concepts is a shop environment, as this play situation can involve:

• Checking out with coins and notes
• Making a price list
• Sorting and organizing food items
• Creating a shopping list
• Using names of numbers and recognising written numerals

15. Pasta Threading

Preschool children love to thread colored pasta to make necklaces and wristbands. Children can sequence the pasta, count, make it long or short and make comparisons of length.

Please be aware of any children with celiac disease before undertaking this activity; if you have any, use gluten-free pasta.

16. Sewing Hessian

Sew around a piece of hessian to make a placemat by threading string of different lengths and colors. Introduce concepts of in and out, over and under when sewing. The placemats can be of different shapes; for example, square, rectangle, triangle or circle. Refer to the ‘straight and curved’ sides. When talking about the ‘top’ and ‘edge’, we are introducing the maths concept of ‘area’.

17. Make your own puzzles

Children draw or paint a picture to be used as a puzzle. Make 2 to 4 pieces from the picture and then the children assemble it back together into a whole picture. When cutting the picture into halves and quarters, we are considering a basic introduction to fractions.

18. Tapping sticks

Rhythm sticks have always been popular with children. This can be a standing or sitting activity or you can even alternate between the two.

The children can tap on the floor, end to end, or parts of the body, etc.

Routines should be simple, repetitive and fun. There are various CDs available that can accompany tapping stick games, which are available in a variety of languages.

They introduce the concept of comparing fast and slow, which is a pre-math activity. They can also count the number of taps in a phrase or tap the sticks high and low and follow patterns

This game can also be a great opportunity to expose the children to different styles of music.

19. Let’s go fishing

I like to cut out the children’s painted hand prints and turn them into fish. Draw a face with the fingers horizontal for the fish’s tail. Number each fish, having a pair of fish with the same number. Laminate them and attach a paper clip to each fish.

Use a magnet tied to a string as a fishing rod to go fishing. Children can try to catch a pair of fish with the same number or see how many fish they can catch. They can name the number or count the total of their catch.

20. Musical shapes

Scatter a number of different shaped carpet cut-offs or chalk different shapes onto the carpet. Play some music for children to move and dance to. When the music stops, name 1 or 2 shapes for children to find and stand at. Use this game to introduce shapes with more complex attributes.

21. I wrote a letter

Children can draw, paint or write a letter to someone special. Have a variety of big and little envelopes available. Children can place their finished letter inside an envelope by folding the letter in half or maybe even in quarters to make it fit (how many times do you need to fold it?). Then an address can be written on the front ready for posting.

22. Electrical tape roads

Use brightly colored electrical tape on a table to make a road. Use four colors, each representing a separate road. Children use a matching colored car to push along the corresponding colored road. They will follow the straight, curved or bent pattern of the road. By using the whole surface of the table, we can talk about the ‘top’, ‘bottom’ and ‘edge’ which is the ‘area’ of the table.