Developing number sense at an early age is critical for children to understand math in later years. While children encounter math concepts such as pattern recognition since infancy, most initial number sense is developed in the Pre-K, K, and 1st grade. In order to effectively develop number sense, children need lots of practice counting numbers.

**Pre-Counting**

Pre-counting is an understanding of the math concepts such as ‘more’, ‘less’ and ‘the same’, and the relationship between these topics. Children at this stage develop these concepts by comparison; no actual counting is involved. Pre-counting is important because it lays the foundation of counting, and develops an understanding of the ways that numbers are related to each other. For example, five is two more than three, and one less than six.

Parents may teach their children the concept of pre-counting by preparing two sets of candies with different quantities, and comparing them side by side. Using one-to-one matching helps children figure out which of the two sets contains more or less candies.

**One-to-One Counting**

One-to-one counting helps develop children’s ability to count. Children with the ability to do one-to-one counting can both say the standard list of counting words in order, and match each spoken number with only one object. This stage of counting for kindergarten is important because all other number concepts are based on the meaning attached to counting.

Similar to the pre-counting activity, parents can use their children’s favorite snack to teach one-to-one counting. Parents may have their children put the snack onto some disposable plates with sticker dots. As the children repeatedly match the snack to the sticker dots, they can gradually develop the idea of one-to-one counting.

**Counting Sets**

The key point of counting sets is to develop children’s understanding of cardinality (the size of a set). Children who understand counting sets can tell when you count the items in a set, with the last number counted tells the size of that set. They will also know that numbers in a set remain constant as long as no items are added to the set, or taken from the set. Cardinality is important because it allows children to use numbers to describe and compare sets. Later, the concept of combining and separating sets of items will transform into addition and subtraction.

Parents may teach their children about counting sets by placing a group of objects in a line on a table and ask them the question, “How many?”. To ensure that a child has fully understood the concept, parents can say a number and have the child show the correct amount of objects. Manipulatives are usually a great starting point for teaching this concept.

**Counting from One to Solve Number Problems**

Children entering this stage of counting are able to solve addition and subtraction problems with the use of play materials to keep track of their counting. For example, children will combine 3 and 2 by first counting out “1, 2, 3” for the first set and “1, 2” for the second set, then physically join the sets and count them all together – “1, 2, 3, 4, 5”. Children will come to understand that the count gets bigger when groups are combined, and the count gets smaller when groups are separated.

A great way to train children about ‘counting from one’ would be physically counting two different types of toys. For example, parents can use marbles and car toys, then have their children count the amount of car toys right after they finish counting the amount of marbles. This activity will help children develop the number sense that two sets can be combined even if they do not share the same traits (colors, shapes, etc.)

**Counting On to Solve Number Problems**

Once children understand cardinality and the forward and backward number sequences, they can count on or back to solve number problems. Unlike counting from one to solve number problems, children can now add or subtract by counting from the largest number. This practice builds children’s math skills in operations of addition and subtraction.

Parents may practice this type of counting by creating a path game. During the game, children will roll a game die and count the amount of spaces to move their game piece. Parents should encourage their children to count on from the current spaces their game piece is in.

Whether children have number sense in kindergarten or older, the key point is that their learning is hands-on and conceptual in nature. Through practice, children efficiently and flexibly acquire the skills to use number words and sequences, allowing them to smoothly solve more complex arithmetic tasks at a later age.

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**Citations:**

When and How to Teach Numbers to Kindergarten – https://parenting.firstcry.com/

The Importance of Number Sense in Early Learning – https://thewritestuffteaching.com/

Number: Early Learning Progression – https://nzmaths.co.nz/

How to Teach the Concepts of More and Less (Freebies) – https://justaskjudy.net/

Ways to Teach Counting – https://www.prekinders.com/

Teaching Counting: Considerations for Instruction – https://intensiveintervention.org/