Modern mathematics: odd number, also known as odd number, is an important number, that is, an integer that cannot be divisible by 2. Odd numbers are often expressed as 2n+ 1 or 2n- 1, where n is an integer. Even number, also called even number, is an important number, that is, an integer divisible by 2. Even numbers are usually expressed as 2n, where n is an integer. The sum, difference and product of even numbers are even numbers.

Primary school mathematics: Beijing edition textbook, 2004, 10 volume, 5 1 page, puts forward that the number divisible by 2 is called even number; Numbers that are not divisible by 2 are called odd numbers. Page 12 of the fifth grade textbook 20 13 of People's Education Press puts forward that among natural numbers, numbers that are multiples of 2 are called even numbers (0 is also even numbers), and numbers that are not multiples of 2 are called odd numbers.

Two. Conceptual explanation

In natural numbers, it is either odd (also called odd) or even (also called even). Generally speaking, even numbers are represented as 2n; The odd number is 2n+ 1, and n is an integer.

In order to facilitate international communication, People's Republic of China (PRC)'s national standard "Quantity and Units" issued by 1993 stipulates on page 3 1 1 that natural numbers include 0. So 0 naturally becomes an even number. 0 is a special even number.

Primary school stipulates that 0 is the smallest even number and 1 is the smallest odd number. However, what I learned in junior high school is a negative number. When there is a negative even number, 0 is not the smallest even number. Like -2, -4, -6, -8,-10,-12 are all negative even numbers; When there are negative odd numbers, 1 is not the smallest odd number. Things like-1, -3, -5, -7, -9,-1 1 are all negative odd numbers.

Even numbers include positive even numbers, negative even numbers and 0. Odd numbers include positive and negative odd numbers.

In decimal system, you can judge whether the number is odd or even by looking at the single digits: 1, 3, 5.7 and 9 are odd; Numbers with digits 0, 2, 4, 6 and 8 are even numbers.

Some properties about odd and even numbers are as follows:

① One of two consecutive integers must be odd and the other must be even.

(2) The parity of the sum of two integers-odd+odd = even, odd+even = odd, even+even = even. Generally speaking, the sum of odd numbers is odd, the sum of even numbers is even, and the sum of any even numbers is even.

③ Parity of the difference between two integers-odd-odd = even, odd-even = odd, even-even = even, even-odd = odd.

(4) The parity of the product of two integers-odd× odd = odd, odd× even = even, even× even = even. Generally speaking, in integer multiplication, as long as one factor is even, its product must be even; If all the factors are odd, then their products must be odd.

⑤ Parity of quotient of two integers-In the case of divisibility, even divided by odd is even, even divided by even may be odd or even, and odd cannot be divisible by even.

⑥ If both A and B are integers, the parity of a+b and a-b is the same.

Except 2, all positive even numbers are composite numbers.

The sum of two adjacent integers is odd, and the product of two adjacent integers is even.

Pet-name ruby If an integer has odd divisors, then this number must be a complete square number (such as 1, 4,9,16,25, etc. If a number has an even number of divisors, then this number must not be a complete square number.

Attending the famous mathematician Pythagoras discovered an interesting odd number phenomenon: adding odd numbers continuously, and the number added each time is exactly the square number. For example:

1+3= 2 squared 2

1+3+5= 3 squared 2

1+3+5+7 =4 squared 2

1+3+5+7+9=5 squared 2

1+3+5+7+9+11= 6 squared 2

1+3+5+7+9+1+13 = 7 squared 2.

1+3+5+7+9+1+13+15 = 8 squared 2.

1+3+5+7+9+1+13+15+17 = 9 squared 2.

Four. Teaching suggestion

① For odd and even numbers, the teaching materials are arranged in the content of "Characteristics of multiples of 2". In teaching, most teachers arrange the contents of odd and even numbers and "the characteristics of multiples of 2" in one lesson.

We know that students are no strangers to odd and even numbers. They already knew the odd and even numbers as early as the first year of high school, and some students also discovered the characteristics of odd and even numbers. So it should be said that it is very easy for students to master the concepts of odd and even numbers.

(2) Some teachers arrange odd and even numbers in a single class, and the key point is to let students use the characteristics of odd and even numbers to solve some problems and feel some properties of odd and even numbers. For example, let students queue up to report 1 and 2, the first person reports 1, the second person reports 2, the third person reports 1, and the fourth person reports 2 ... If this continues, how many people will report 15? What's the number of the 24th person? For example, there is a cup with its mouth facing up. If you flip the cup with the mouth down once and the cup with the mouth up twice, keep doing this. On the 10 flip, is the mouth up or down? 15?

In this way, students can feel that the nature of odd-even numbers can help us solve problems quickly, and at the same time realize the necessity of learning odd-even numbers and understanding some of their properties.