early mathematical skills
Early mathematical skills icon

Promoting early mathematical skills

Mathematical thinking does not just begin at school. From their earliest years, children gain playful experiences with numbers, quantities, patterns, and shapes such as circles, triangles, and squares. They discover the meaning of numbers by exploring their environment. These mathematical experiences form the basis for important thought processes in later mathematical learning at school. Everyday life is full of mathematics. Parents, in particular, have a great influence on their child's mathematical experiences when they involve them in everyday activities: »We go to the movies when the clock hand points to three. We'll stay at the playground for one more hour. The ice cream costs two euros. Put four bananas in the shopping cart.« Mathematical terms such as a lot, a little, more, small, big, long, short, right, left, up, down, today, tomorrow, and yesterday are also regularly used in everyday life: »Place the glass to the right of the plate. Would you like some more carrots?« Using such words together with an activity helps children better understand these terms. Foster early mathematical skills by engaging children with the world of numbers through practical experiences.
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A family plays a dice game together.

The path to mathematical development

Mathematical precursor skills begin to develop in the first few years of life and lay the foundation for learning mathematics in school. Some parents believe their child is particularly gifted if they can count to 20 before starting school. However, simply reciting a series of numbers does not demonstrate a true understanding of numbers and quantities. A real sense of numbers only develops when children understand the quantities associated with each number. For example, a child recognizes that the number 3 represents three fingers, three plates, or three dots on a die. A deeper understanding of quantities develops through hands-on counting activities. The more frequently children connect quantities with number words, the more confidently they will later be able to visualize numbers in their heads – without using fingers or counting cubes. Mathematical precursor skills also include distinguishing quantities as more or less, ordering objects by size, and recognizing patterns such as red-blue-red-blue. These skills later help in school with understanding number sequences, addition, and subtraction. The following suggestions offer simple, playful activities to support your child’s mathematical development in everyday life.
A smiling boy in a striped shirt against a blue background.

Support activities

Promoting early mathematical skills lays the foundation for further mathematical development in school. By handling numbers, quantities, shapes, and mathematical concepts in everyday life, such as when shopping or playing dice games, children develop a basic understanding of mathematical relationships. Through these experiences, children learn, for example, that numbers are not just abstract symbols, but that each number represents a concrete quantity.
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A house entrance with the number three on the gate.

Numbers in daily life

Children encounter numbers everywhere in everyday life: while shopping, on the calendar, on the clock, as house numbers, and in many other places. However, numbers also hold a special meaning for children. They know how old they are, when their birthday is, and how many siblings they have. Give your child the opportunity to discover and understand numbers in daily life. Use everyday situations to help your child become familiar with the meaning of numbers. For example, your child can playfully learn the number sequence when counting objects (1, 2, 3, 4, 5 horses in the meadow) or determine the number of items (put 4 plates on the table). Comparing quantities (4 sweets are more than 2 sweets) or repeating a set number of movements (clapping your hands three times) also helps to promote number understanding. Through everyday experiences, your child will begin to realize that numbers are not just symbols or words, but are used in many different ways: Tomorrow is December 6th. I need 500 grams of flour for the cake. The bag of sweets costs 2 euros. You are 1 meter tall and weigh 16 kilograms. There are 4 cars in the parking lotTalk to your child about where they encountered numbers today. Conversations about numbers help develop a better understanding of them and expand your child's skills in dealing with numbers. Encourage your child's natural curiosity about numbers and connect numbers with quantities: »Put 5 bananas in the shopping basket.« or »Place 3 cups on the table.« In this way, your child acquires number knowledge in passing by understanding numbers with their eyes, ears, and hands.
A child counts from one to ten.

Counting fortune cookies

In this number game, your child practices the number sequence in a playful way, first up to 10 and later up to 20. Sit down with your child in a cozy spot. Ask them to close their eyes and hold out one hand with the palm facing up. Now gently tap their palm with your finger, starting with one. Your child counts out loud: one, two, three ... Stop at any number, for example at four, and ask: »How many fortune cookies did you count?« This keeps the game exciting from round to round. Start with numbers between one and six so your child does not feel overwhelmed. If your child is still unsure about counting, count out loud together. By regularly hearing and repeating the number sequence up to 10 and beyond, children gradually become more confident in counting. After four or five rounds, switch roles. You close your eyes and count out loud while your child taps your hand and quietly counts along, maybe even beyond six. When your child stops, you might lose track once or twice and ask with a smile: »Oh dear, how many fortune cookies was that?« This is sure to bring lots of laughter and fun. At the end, a little reward is waiting, maybe a small treat and a warm hug for all that joyful counting.
Girl jumping rope on the street.

Confident counting

Many children can already count to ten before starting school, some even up to twenty or beyond. This skill develops through everyday counting and playful practice. Counting at home helps children internalize the number sequence with confidence and makes it much easier for them to start math lessons. Even though counting may seem simple to adults, it is a longer process for children that requires time and practice. Simply reciting the number sequence is not enough. Children also need to understand that numbers always follow a fixed order and that each number is mentioned only once. This understanding develops through practical activities and playful counting opportunities. Give your child the chance to show their counting skills. Sincere praise is the best motivation for children to engage with numbers, even if the number sequence isn’t perfect yet. Let your child make mistakes and praise their efforts. Respect your child's individual interests: some children are naturally more interested in counting, while others may need a bit more encouragement. Keep offering small counting activities without putting pressure on them. With your positive support, your child will discover the world of numbers and be well prepared to start school.

Counting stair steps
Count the steps together when you go up or down the stairs.

Playing hide and seek
Playing hide and seek outdoors or indoors helps your child practice the number sequence while having fun.

Counting steps
Count steps, trees, or passing cars. Ask your child: »How many steps are there to the next house?«

Singing
Sing counting rhymes or songs that include numbers. This is enjoyable and helps develop number memory.

Baking
Let your child count ingredients, such as three eggs or five tablespoons of flour.

Playing games
Use games like dominoes or memory, where quantities and number symbols are linked. This teaches your child to associate numbers with specific quantities.

Numbers in the surroundings
Show your child numbers in the environment, such as house numbers, clocks, or price tags in the supermarket.

Jumping rope
When jumping rope, count the jumps out loud together.

Throwing a ball
Throw the ball to each other without letting it fall to the ground, and count the number of throws with your child.
The preschool child plays dominoes.

Quantity domino

With a domino game, you playfully encourage the recognition and matching of structured quantities. The child learns to match the same number of dots on the domino cards. Games with structured quantities help children develop cognitive images of numerical quantities, which later make mental arithmetic in school easier.
Spread the domino cards face down on the table, leaving only the starting card with a single dot visible. The child turns over a card and names the number of dots shown on it, either by recognizing the quantity at a glance or by counting the dots one by one. If the number of dots matches the starting card, the child places the card next to it. Otherwise, the card is turned face down again. The child continues to turn over cards, naming the quantities displayed. Help your child recognize and name larger quantities.
A girl shows the number 10 with her hands.

Back numbers

This game playfully promotes an understanding of quantities and numbers and is usually great fun for children. Tap a specific number from 1 to 10 on the child's back with your index finger, for example, four times. The child counts quietly and then says the number 4. The numbers 5 and 10 have a natural connection to our fingers. Therefore, place one hand flat on the child's back for the number 5 and both hands for the number 10. Before starting the game, ask the child how many fingers one hand has and how many fingers both hands have. If the child does not know the answer, ask them to count their fingers. Over time, your child will internalize the finger picture of the numbers 5 and 10. These finger pictures will make arithmetic easier later in the initial lessons by helping children recognize the relationships between other numbers and 5 and 10. For example, children realize in their imagination that the number 6 is one more than 5 and the number 9 is one less than 10. The child then takes their turn by tapping numbers on your back, and you name the corresponding numbers. The role reversal increases the joy of playing together.
Boy runs up colorful stairs.

Number stairs

A good understanding of mathematics before starting school helps children experience fewer difficulties in mathematics during their elementary school years. Small number games in preschool, which are enjoyable for the child and take place without pressure, contribute to the development of mathematical understanding. Create a number staircase with the child and practice the number sequence from 1 to 10 or beyond. Write the numbers large on cardboard and draw the corresponding quantity next to each number. Attach the cards to the edge of the stairs so that the first step corresponds to the number 1 and each subsequent step has the following numbers.

Forward and backward counting
Practice counting over a longer period of time. Hold the child’s hand and walk up or down the stairs in equal steps while counting forward or backward together. After several repetitions, the child will begin to count along. Forward counting is usually easier for children than backward counting, as backward counting develops after forward counting.

Recognizing quantities
A number staircase supports the learning experience that numbers have both a predecessor and a successor. Also, draw the child’s attention to the quantity images. Encourage the child to think, so they can recognize that exactly one point is added at each stair step. For children, it is not immediately obvious that number words, numerals, and quantities belong together. The development of quantity perception is an important learning process. Only through diverse experiences do children come to understand that the number word 5, the numeral 5, and the quantity 5 all represent the same thing.
Domino cards with numbers and dots
The number two under a red fly swatter.

Fly swatter with numbers

Not only can you catch flies with a fly swatter, but you can also play a concentration game to help your child recognize numbers quickly and easily. Your child will learn to distinguish number symbols more quickly and recognize numbers effortlessly. This skill will help them work with numbers more confidently and quickly in future math lessons. The game is particularly suitable for children who already know some number symbols from 1 to 5 or more. If your child does not yet know the number symbols, it’s a good idea to start introducing them in everyday life. You can find more tips under ›Numbers in daily life‹. It's important to keep the game fun and relaxed. The joy of playing should be the focus, not the goal of getting everything right. This keeps your child motivated and helps them learn to recognize numbers quickly and confidently.

How to play
Write the numbers from 1 to 10 on small cardboard cards. It is advisable to start with a smaller selection, such as the numbers 1 to 5, so your child doesn’t feel overwhelmed. Once they can quickly recognize these numbers, you can gradually introduce more. Place the cards on the floor or table with the number side facing up. Give your child a fly swatter. Say a number out loud and show the corresponding number with your fingers. Your child should then swat the correct card as quickly as possible. Alternatively, you can just show the number with your fingers, and your child can say the number before swatting the corresponding card. Once your child has swatted the correct number, praise them and set the card aside. Then, call out another number. The game ends when there are no more »number flies« left to swat.
A child sits with their father on the couch and taps on a smartphone.

Typing phone numbers

Typing a telephone number can be a fun activity that promotes a child's mathematical understanding and memory. A telephone number is a sequence of numbers that the child gradually learns through repeated listening, pointing, repeating, and typing. This strengthens the child's understanding of the meaning and sequence of numbers. Telephone numbers demonstrate how numbers can be used as ›codes.‹ For example, if you say: »This is Auntie's phone number«, the child learns that numbers can have different meanings. Through the various applications of numbers, the child learns that numbers don’t just represent quantities (like five bananas), but can also be used as units of measurement (like four years old), to repeat actions (like hopping four times), or as contact information (like a phone number). Understanding these different applications of numbers forms an important foundation for mathematical thinking because it helps children develop a broader understanding of the meaning and functions of numbers.

Getting to know familiar numbers
Start with groups of two or three digits, which the child repeats and types on the keypad. For example: »Look, this is our phone number. I'll tell you the first two digits and show them to you on the keypad. Just repeat them and type them in.« Begin with 2 to 3 digits and add more as you go. With regular practice, your child will get used to the sequence of numbers and begin to recall them from memory. This builds the child’s confidence and independence. It can be helpful to practice with a familiar number, such as the one from home or from the grandparents. However, make sure the phone is in flight mode to avoid accidental calls. If your child already has a good command of the number sequence, it can be motivating to let the phone ring ›properly‹ once. Let the child type in the private number of home or close relatives to simulate a real call. This makes the exercise more exciting and provides an additional incentive.
A little girl puts two cucumbers into the shopping cart at the supermarket.

Shopping together

An important step toward understanding quantities is one-to-one correspondence. Children learn to assign a number word to each object they count. For example, if parents ask their child to put four bananas in the shopping basket, the child counts »one, two, three, four« and gradually understands that the last number mentioned represents the total quantity. Parents who involve their children in this way also make things easier for themselves, as the child stays busy and doesn’t get bored. Shopping also provides a great opportunity to promote spatial thinking. Terms like up, down, left, and right help children structure their environment and develop a sense of position and orientation. For example: »Place the milk to the right of the apple juice.« or »Place the two cucumbers on top of the other items so they don’t get squashed.« Such instructions foster an understanding of spatial relationships and support spatial orientation.
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