The concept of a natural number is introduced as a member of the initial segment of a natural sequence of numbers. Therefore, it is important for each student to learn what each number is called and how it is designated by a printed and written digit.
In this case, it is necessary to achieve the assimilation of the following:
– each number is formed during counting from the previous number and one, as well as from the number following it and one;
– each number is greater than the number immediately preceding it by one and less than the number immediately following it when counting by one;
– what place each number occupies in the series of numbers from 1 to 10, after what number and before what number it is called when counting.
The acquisition of this knowledge allows one to form an understanding that each number does not act separately, but in connection with other numbers. All this forms an idea of the natural series of numbers. At the same time, one should prepare for studying the actions of addition and subtraction, as well as comparison of numbers and designation of relations “more”, “less”, “equal” with the corresponding signs (>, <, =). This gives initial information about equalities and inequalities.
At the same time, students become familiar with a point, a straight line, a straight segment, learn to measure segments with a centimeter and draw segments whose length is expressed as a whole number of centimeters.
The teaching method at this point has the peculiarity that several consecutive numbers are considered simultaneously, and not individual numbers. They study segments of the natural series from one to the number that was introduced last: 1, 2; 1, 2, 3; 1, 2, 3, 4, etc.
When studying the first ten, children are introduced to the number zero. This is done by performing exercises to count objects one by one until there are none left. For example, they pick leaves one by one from a tree branch, take apples from a vase, etc. Zero is obtained when there are no objects left.
Then the number zero is compared with 1. The result of the comparison is written as an inequality: 0 < 1. As a result of performing a number of such exercises, it is established that 0 must stand in a series of numbers before the number 1.