Teaching objectives
1. Make students understand the concepts of positive and negative numbers and judge whether a given number is positive or negative;
2. Positive numbers and negative numbers will be initially applied to represent quantities with opposite meanings;
3. Let students understand the meaning of rational numbers and classify them;
4. Cultivate students to gradually establish the idea of classified discussion;
5. Through the teaching of this lesson, the dialectical thought of unity of opposites is infiltrated.
Teaching suggestion
I. Analysis of key points and difficulties
The focus of this lesson is to understand that positive and negative numbers are generated by actual needs and what numbers are included in rational numbers. The difficulty is the necessity of learning negative numbers and the classification of rational numbers. The key is to accurately cite typical examples of quantities with opposite meanings and clarify the criteria for rational number classification.
There are many ways to introduce positive and negative numbers. The textbook introduces two familiar examples: temperature and altitude. 5℃ higher than 0℃, 5℃ lower than 0℃ and-5℃; It is 8848m higher than the sea level, and it is 8848m lower than the sea level155m, and it is-155m. From these two examples, it is natural to call a number greater than 0 a positive number, plus? -? The number of symbols is called negative number; 0 is neither positive nor negative, but a neutral number, indicating measurement? Benchmark? . Introducing positive and negative numbers in this way will not only help students correctly use positive and negative numbers to represent quantities with opposite meanings, but also help students understand the size nature of rational numbers. Understand negative numbers as numbers less than 0. Did not appear in the textbook? A quantity with opposite meaning? The concept of. This is to avoid or dilute this concept. The purpose is to reveal the nature of positive and negative zeros and help students understand the concept of positive and negative numbers correctly.
With regard to the classification of rational numbers, it needs to be clear that different classification standards have different classification results, and the classification results should be neither heavy nor leaking, that is, each number must belong to a certain category and cannot belong to two different categories at the same time.
Second, teaching suggestions
This lesson introduces negative numbers from quantities with opposite meanings on the basis of numbers learned in primary school. In terms of content, negative numbers are more abstract and difficult to understand than non-negative numbers. Therefore, in the choice of teaching methods and teaching languages, attention should be paid to the connection between primary schools and secondary schools as much as possible, which is neither scientific nor in line with the principle of acceptability. For example, when explaining the concept of rational number, let students clearly understand the fundamental difference between rational number and arithmetic number. A rational number consists of two parts: a sign part and a number part (that is, an arithmetic number). In this way, it is much easier to understand the concept of rational number on the basis of understanding arithmetic numbers and negative numbers.
In order to enable students to master the necessary mathematical ideas and methods, we can consciously penetrate the thinking method of classification discussion when defining the classification of rational numbers, and understand the classification standards, classification results and their relationships. If all positive and negative numbers are unified into rational numbers, the dialectical thought of unity of opposites can be gradually established and infiltrated into daily teaching.
Third, the understanding of the concepts of positive and negative numbers.
1﹒ The concepts of positive and negative numbers cannot be simply understood as: use? +? The number of the symbol is positive, use? -? The number of the symbol is negative.
After introducing negative numbers, the range of numbers is expanded to rational numbers, and the extensions of odd numbers and even numbers are also expanded from natural numbers to integers. Integers can also be divided into odd and even numbers, and the number divisible by 2 is even, for example? -6,-4,-2,0,2,4,6? Numbers that are not divisible by 2 are odd numbers, such as? -5,-4,-2, 1,3,5?
So far, there are five kinds of subdivision of numbers we have learned: positive integer, positive fraction, 0, negative integer and negative fraction, but when studying problems, rational numbers are usually divided into positive number, 0 and negative number for discussion.
4. Generally, positive numbers and 0 are called nonnegative numbers, negative numbers and 0 are called nonpositive numbers, and positive numbers and 0 are called nonnegative integers; Negative integers and 0 are collectively referred to as non-positive integers.
Fourthly, the classification of rational numbers.
Integers and fractions are collectively called rational numbers. 1) Positive integers, zero and negative integers are collectively called integers; Positive and negative scores are collectively called scores.
2) Integers can also be regarded as fractions with denominator of 1, but for the convenience of research, the fractions in this chapter refer to fractions without integers.
3) What is used in the concept? Collective? This word, does it still have a meaning? Are integers and fractions rational? The meaning of is different. The former avoids the question of whether the score contains integers, even if the integers are included in the score range, saying? Collective? It's not bad, but the latter statement is not appropriate.
4) The difference between fractions and decimals:
Fractions (reduced fractions) can be expressed in decimals, but not all decimals can express the number of components.
5) Numbers learned so far (except? ) are rational numbers.