Teaching content:

Jiangsu Education Publishing House, the first volume of fifth grade primary school mathematics, page 1-2, example 1, example 2, "Try it", page 5, "Exercise 1", question 1-4.

Analysis of learning situation:

The initial understanding of negative numbers (known as negative numbers before the 20 1 1 version of the curriculum standard) only appears on the first volume of the fifth grade primary school mathematics textbook of Jiangsu Education Press, page 1-5. Throughout the content of the textbook 12 for primary school mathematics published by Jiangsu Education Publishing House, the knowledge of negative numbers is not involved before and after, and only five pages form a thin independent unit. Before the fifth grade, students were exposed to positive numbers and zeros, which is a very strange concept for negative numbers. But the seeds of "negative number" have been buried in students' lives, such as the-1 floor in the elevator, and how many degrees Celsius will be negative in winter.

Teaching objectives:

1. In the process of counting a number and measuring a quantity, it is meaningful to initially perceive the background of negative numbers and realize the existence of negative numbers in real life; ?

2. Understand the meanings of positive numbers, negative numbers and "0", master the expression methods of positive numbers and negative numbers, and describe the phenomena in real life with positive numbers and negative numbers, such as temperature, altitude and other quantities with different meanings, and use "0" as the intermediate quantity; ?

3. Experience the close relationship between mathematics and life, mathematics and culture, and stimulate students' interest in learning mathematics.

Teaching emphases and difficulties:

1. Understand the meanings of positive numbers, negative numbers and "0";

2. Use positive numbers, negative numbers and "0" to describe the phenomena in life. ?

Teaching process:

Introduction: In the process of "counting" and "measuring", negative seeds are bred.

Teacher: Students, please look at the projection. (Showing photos to Hua) Do you know him? (Some students said they knew, while others said they didn't know)

Teacher: He is a famous mathematician in our country. (The word "Hua" is displayed) His name is ... You tell me (the student says). What's his last name? Zi (Hua) is a polyphonic word. When it is used as a surname, it should be pronounced Hu. He once said a sentence, many people mispronounced it because of polyphonic characters (showing that "number comes from number, quantity comes from quantity"). Who will try it? (looking for students who raise their hands)

Teacher: (Turn two numbers into red) Look at these two same words. Do they sound the same? The first word should be read? What about the second one? (According to the students' answers, display the pinyin of these two words accordingly.)

Teacher: (Turn the two "quantities" into red) Are these two words pronounced the same? (According to the students' answers, display the pinyin of these two words accordingly.)

Teacher: OK, let's read this sentence together! What do you want to say after reading it?

Health 1: Pay attention to polyphonic words when reading!

Student 2: number (shù) gives number (), quantity (Li) gives quantity (Li)!

Teacher: It seems that learning mathematics is inseparable from "number" shǔ and "quantity Liang"! ("Quantity" and "Quantity" are shaded)

[Comment: The mathematician Hua's surname is disyllabic, and there are disyllabic words in one of his famous mathematical sayings. It seems to be unintentional coincidence, but it is actually designed with heart. By guiding students to read polyphonic words correctly, students can feel that concise language contains profound mathematical truth from famous Chinese sentences, and take this as a starting point to find the feeling of mathematics learning, and extend it from famous mathematical sentences to the teaching and learning of new courses! In this process, students not only feel the charm and taste of mathematics culture, but also grow and develop themselves, reflecting the growing taste. ]

Teacher: Let's count first, shall we? (good)

Teacher: (showing a circle) Can you count? Count together (1) (show another disk) and then count (2) (show 10 disks in succession, let the students continue to count). Will you finish counting like this? What should I do? (Students say ellipsis and display ellipsis)

Teacher: Now let's start with 10 and count backwards (reduce the number of discs in turn so that there are more students, when 1 appears). Is there a number less than 1 (0, there is no CD in the courseware) What does 0 mean?

Teacher: 0 means there is no object at all. It seems that 0 is the smallest number when expressing the number of objects!

Teacher: OK, we counted them together just now. Let's measure it again!

Teacher: (showing a blue ribbon) This is a blue ribbon. Can you measure its length? (Will) I believe everyone will test! (Take out a ruler to measure the length of the strip) Is this the amount? Its length is ... (4 cm). What does the 0 here mean except that it has no length? (Guide students to say the starting point of measurement, and a "starting point" appears)

Teacher: A blue ribbon of the same length (moving the blue ribbon down), a classmate measured it like this. Do you think it's okay? (Let the students say)

Teacher: The teacher also thinks this quantity is ok, but the starting point of measurement has been changed from 0 to 1 (red line is displayed). What should the number 5 on the ruler become? (The student's answer is 4) What numbers do 2, 3 and 4 on the ruler become respectively? (Students answer 1, 2, 3) What about 6, 7, 8, 9? (Students answer 5, 6, 7, 8)

Teacher: OK, what number should the 0 on the ruler become? Please write the answer in your exercise book! (Students write by hand, teachers patrol, and students with different writing methods write on the blackboard)

Teacher: Did you write it? Do you want to know how mathematicians express this number? (Think about it) Mathematicians express this number like this (-1 appears). Raise your hand if you write like a mathematician! (Some students wrote-1) The teacher gave you a word: You have the potential of a mathematician, which is amazing! Please put it down!

Teacher: Mathematicians put a small bar in front of 1 to indicate this number. This small bar is not a minus sign, but a minus sign. This number is the negative number we want to know today (part of the topic: negative number).

Teacher: How do you pronounce this number? (Show "negative one") Read together! (Students read and the teacher writes on the blackboard-1) Read it again! (Students read again)

Teacher: Now, the teacher moves the ruler to the left 1cm. What number should be used to represent zero at this time? Please write it in your exercise book. Please raise your hand if you write the same thing! (The whole class writes -2) Read together. If you translate 1cm to the left, what number should you use to represent 0? (-3) What if you pan to the left again?

Teacher: (There is a straight line in the courseware) This is a straight line. If this point on a straight line is represented by 0 and these points are represented by 1, 2, 3, 4, 5 respectively, what numbers should these points be represented by? (Students answer:-1, -2, -3, -4)

Teacher's summary: Well, students, we found in the process of counting just now that 0 is the smallest number when representing the number of objects; In the process of measurement, we found that 0 can also represent the starting point of measurement, and at the same time we know a new number called (pointing to the "negative number" on the blackboard) ... (negative number) Now let's think about it together. Have you ever seen negative numbers in your life? (The student said that the teacher asked you in real time what the negative number you saw meant? )

[Comment: The understanding of "negative number" is not simply that the number less than 0 is called negative number. The design of this link makes students feel that 0 is the smallest number when expressing the number of objects in the process of "counting"; In the process of "measuring a quantity", 0 not only means nothing, but also means "starting point". I changed the starting point from 0 to 1 in real time, and the other numbers on the ruler changed in turn, making students think: how to express 0 at this time? Students try to express this number. Although only some students use-1, in view of the present situation that all students in the next class use -2, the concept of negative number is established. Students have an intuitive perception of negative numbers in the unconscious process. This design conforms to children's age characteristics and cognitive laws, and has a strong flavor of children's growth and knowledge, as well as a touch of culture. ]

Second, the key point: feel the existence of negative numbers in the process of understanding "temperature" and "altitude"

Teacher: (showing thermometer) What is this? Know (thermometer)? Who will introduce it?

Health 1: There is red liquid in the middle of the thermometer. When the temperature is high, it will rise, and when the temperature is low, it will fall!

Health 2: The thermometer has a scale of 0, which means 0 degrees Celsius.

Health 3 supplement: if it is higher than 0 degrees Celsius, it is called how many degrees Celsius above zero; What is below 0 degrees Celsius is called how many degrees Celsius below zero.

Teacher: A thermometer is an instrument for measuring temperature! There is a small circle with an F in the upper right corner of the thermometer, indicating the temperature in Fahrenheit. This is used in other countries, but we generally don't use it in China. There is a small circle C in the upper left corner to indicate the temperature in degrees Celsius, which we often use in China to measure the temperature. Just now, a classmate said 0 degrees Celsius. Does 0 degrees Celsius mean there is no temperature? (No) What temperature does 0 degrees Celsius represent? People set the temperature of the ice-water mixture at 0 degrees Celsius. (Showing pictures of ice-water mixture) Can you feel 0 degrees Celsius?

Teacher: This is the lowest temperature in Nanjing, Sanya and Harbin on a certain day. (Example 1 picture)

Teacher: Let's take a look at the lowest temperature in Nanjing first. (Enlarge the temperature in Nanjing) Who will read it? (Display 0℃) (Enlarge the temperature in Sanya) What is the lowest temperature in Sanya on this day? (20℃ above zero) 20℃ above zero, we can also use -20℃ to represent (show -20℃) this number is read as +20℃, read it together (students read it on the blackboard: -20), (enlarge the temperature in Harbin) (show -20℃ and \ according to the students' answers.

Teacher: Which do you think is better than 20℃ above zero or -20℃, -20℃ and -20℃ here? Tell me your reasons! (Students say) That's true. (20℃ above zero and 20℃ below zero disappear)

Teacher: What's the difference between "-20 degrees Celsius" and "-20 degrees Celsius"? (Guide students to say that numbers greater than 0 are represented by positive numbers, and numbers less than 0 are represented by negative numbers)

Teacher: It seems that the students already know the temperature indicated by the thermometer. would you like to have a try？

Teacher: (Show "Try") This is the highest mountain in the world-Mount Everest! Its peak lies on the border between China and Nepal. (Showing the temperature map) This is the lowest temperature of Mount Everest on a certain day. Who will read it? (Students will show it after answering-17℃, blackboard writing-17)

Teacher: This is the lowest basin in the world-Turpan Basin. This is the highest temperature in Turpan basin on a certain day. Who will read it? (According to the students' answers, it shows -35℃ and blackboard writing +35). This is the lowest temperature in Turpan basin on this day. Who will read it? (According to the students' answers, it shows -5℃ and writes it on the blackboard -5)

Teacher: Please think it over. What is the temperature difference in Turpan basin on this day? Do you know what "temperature difference" means? (Student says) What's the temperature difference? What is the temperature difference (40℃)? Why is the temperature difference so big? In fact, the reason for the large temperature difference in Turpan basin is related to its unique geographical location!

Teacher: What is the unique geographical location of Turpan Basin? Do you want to know? (thinking)

Teacher: If we imagine that Mount Everest, the highest peak in the world, and Turpan Basin, the lowest basin in the world, move together. (Example 2 is shown)

Teacher: The word "altitude" appears everywhere. Who can tell me what altitude means? (Students say first) Altitude is the vertical height of altitude! Usually we stipulate that the average height of sea level is 0 meters. What about Mount Everest above sea level and Turpan Basin below sea level? Please discuss it with two people at the same table!

Teacher: Mount Everest is 8844.4 meters above sea level, which we call 8844.4 meters above sea level. It can be written as "+8844.4 meters" (+8844.4 meters, blackboard writing: +8844.4). How to express the height of Turpan basin? (Students answer that the altitude is-155m,-155m, and the blackboard is-155).

Teacher: Do you want to know the average altitude of Huai 'an? (Thinking) (Showing the elevation of Huai 'an) Do you know what the elevation of Huai 'an is?

Teacher: OK, class, look at the blackboard together. Are all the numbers on the blackboard negative? (No) So what are negative numbers? (Student) Numbers like-1,-17.5, -20,-155 are called negative numbers. Can you say another negative number? Is that all you got to say What shall we do (ellipsis)

Teacher: Numbers like +20, +35, +8844.4,+14.5 are called … (positive numbers, marked as "positive numbers"). Can you say another positive number? Is that all you got to say

[Comment: The introduction of thermometer laid a good foundation for the teaching of 1. Only when students know and understand the components and functions of the thermometer can they consciously read the temperature indicated by the thermometer. The trial practice after example 1 not only checked whether the students correctly read the temperature indicated by the thermometer, but also laid a natural foundation for the teaching of example 2, and realized the natural connection between "temperature" and "altitude". From students talking about negative numbers in life to finally revealing the concept of negative numbers, the process shows the taste of life. ]

3. Immersion: Experience the simplicity of mathematical symbols in the historical evolution of negative numbers.

Teacher: Actually, the generation and development of negative numbers have a long history. Let's get to know each other.

(There appears "Do you know?" Play the recording: China is the first country to recognize and use negative numbers. According to the "Nine Chapters of Arithmetic", as early as more than two thousand years ago, the ancients in China had "the grain in the warehouse is positive, and the grain out of the warehouse is negative; The idea that the money earned is positive and the money spent is negative. 1700 years ago, China mathematician Liu Hui first put forward the concepts of positive and negative numbers. More than 400 years ago, French mathematician Gillard first used "+"to represent positive numbers and "-"to represent negative numbers. This method has been used to this day. )

Teacher: Students, what have you read in the long history of negative numbers? Health 1: China is the first country to recognize and use negative numbers! (Real-time guidance: As China people, we should be proud)

Born 2: 1700 years ago, there were concepts of positive numbers and negative numbers.

More than 3400 years ago, "+"was used to represent positive numbers and "-"was used to represent negative numbers.

Teacher: Has the negative number changed during its generation and development? What changes have taken place?

Health: From appearance to Chinese characters to symbols, it is getting more and more concise!

Teacher: The students speak very well! Some people say: Mathematical language is the simplest language in the world! It seems that this sentence has some truth.

[Comment: For "Do you know?" In our teaching, the general design is to put this part at the end of class for students to understand. I would say, "You know what?" Teaching should be carried out in the middle and before practice, highlighting mathematical culture as an important part of teaching, and digging it out to truly show the taste of mathematical culture. This cultural history not only makes students feel proud that they are from China, but also makes them realize that "negative number" has gradually become concise in the process of production and development, trying to present symbolic thoughts. ]

Fourth, perspective: enter the world of negative numbers from a mathematical point of view and improve the understanding of negative numbers.

Teacher: Let's walk into the "negative world" from the perspective of mathematics!

Teacher: (show "one point") Fill in the following numbers in the appropriate circle (students answer together when asked about 8) What is 8? (Positive numbers) Positive numbers are preceded by a+sign, and 8 is not preceded by a+sign. Why is it also positive? (Students try to explain why) In order to further simplify the positive number, the "+"in front of the positive number can also be omitted. Of course, adding "+"before positive numbers is to be consistent with negative numbers in form. Can the "﹣" sign before the negative number be omitted?

Student: No, if the symbol before the negative number is also omitted, it will be confused with the positive number!

Teacher: (Put 8 blackboard books in the range of positive numbers) +20, +35, +8844.4,+14.5 are all positive numbers, and the preceding "+"can also be omitted! What about 0? Is it a positive number? Is it negative? Please discuss with two classmates at the same table! (Paste "0", which is neither positive nor negative, and it is the dividing point between positive and negative numbers)

Teacher: (Show "Lianyilian" for students to observe first) What is the temperature when the water boils? (100℃), which company is it from? (2) What is the temperature when water freezes? (0℃) Which company is it? The lowest temperature on the earth's surface is at the South Pole, which can reach ... (-89.2℃).

Teacher: (Show "Fill in") Use positive or negative numbers to indicate the altitude below. First photo, who's here? (Please raise your hand to answer) The second picture.

Teacher: (showing "practical activities") This is a food packaging bag. (Click to see larger image) There is such a mark on the packaging bag (flashing 500 2g, click to see smaller image). What does 500 2g mean here? Discuss at the same table! (Students report after discussion) Here, 500 refers to the standard weight, and food packed in packaging bags with more than 500 2g or less than 500 2g is qualified. Why? Because there are generally errors in packaging, more than 2g, 500 or less than 2g is a reasonable error, and beyond this range, it is not a reasonable error, understand?

Teacher: Here are five bags of such food that the quality inspector took out for inspection. The test results are as follows: (Show the form) Do you think these bags of food are all qualified? Why? (Students say)

Teacher: Well, students, we only have a preliminary understanding of negative numbers today (the whole topic: "Preliminary understanding of negative numbers"), and we will learn step by step in the future!

Teacher: Tell me what you got today.

[Comment: The teaching that the "﹢" in front of the positive number in the textbook can be omitted is a direct notice. For such knowledge points, I practice "one point". Should the number 8 be placed in a positive circle or a negative circle? Let students be clear in the cognitive conflict, and let students feel the simplicity of mathematics further. ]