Please see below the Early Learning Goal (ELG) for Number, just one aspect of Mathematics in the Early Years Curriculum.
Children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.
The expectations regarding reliably counting numbers 1-20 are;
Recognise numerals 1-20 individually, not just in order.
Order the numbers correctly, and understand regardless of which number they use for a starting point, the counting system has a sequence, therefore the same number always follow in the same order.
Something's can be counted that you are not able to touch, such as clouds, ideas, jumping etc. Counting can be a mental process as well as a physical process where they can touch and count.
The counting such things as the dots on a dice or dominos can help to support the ability to know the number of objects just by looking at groupings. You can begin to know the number automatically. This speeds up the process of identifying quantity in number.