Teaching design of preliminary understanding of negative numbers

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"Preliminary Understanding of Negative Numbers" 1 Teaching Design of Teaching Objectives

1. Let students know negative numbers and the reading and writing methods of negative numbers and positive numbers in familiar life situations, and know that 0 is neither positive nor negative, positive numbers are greater than 0 and negative numbers are less than 0.

2. Make students learn to use positive and negative numbers to describe some simple quantities with opposite meanings in real life, and further deepen their understanding of negative numbers.

3. Let students experience the process of creating symbols to express the opposite meaning, experience the process of mathematicization, enjoy the fun of creative learning, and develop students' sense of symbols through cameras.

4. By introducing the understanding and use of negative numbers in ancient China, let students realize the outstanding contribution of ancient China civilization to the development of mathematics and inspire national pride.

Teaching emphases and difficulties

Understand the meaning of negative numbers and further establish a sense of numbers.

teaching process

Talk before class: In order to express the number of objects in life, natural numbers appeared; In specific operations, when the measurement of a unit is less than one unit, decimals appear again. In order to express two quantities with different meanings but the same value, a new problem of number and blackboard writing appears.

First, independent creation produces new numbers.

1. Teacher: The new term has started. The students in our class have changed, and so has the school. Please look at the teacher's information:

(1): Class members have also changed. Our class has transferred three students to one student this semester.

(2): The school library borrows new books 100 and lends books 100.

(3) Xiaoming deposited the lucky money 800 yuan in the bank and took out 100 yuan as pocket money.

Teacher: Students, what are these quantities? (It is a quantity with opposite meaning). Is there any good way for students to distinguish between quantities with opposite meanings?

In order to clearly distinguish between 100 books and 100 books, the students came up with various methods. You are really creative, very creative.

2. How to express the quantity with opposite meaning? Mathematicians in history have also conducted long-term exploration and research on this issue. (Show the fourth page of the history of mathematics textbook "Do you know?" )

Second, learn to read and write as soon as you know negative numbers.

1. Discuss quantities with opposite meanings at the same table, and then add "+"or "-".

Communicate and report.

2. Introduce "Do you know" on page 4 of the textbook. And reading and writing methods of positive and negative numbers.

Can you name a positive number and a negative number again? Anything else? How many?

Students, due to the needs of production and life, people have created negative numbers again. Let's go into life together and further understand negative numbers.

4. To sum up, just now, we met a new friend: negative numbers are used to represent quantities with opposite meanings. If one quantity is specified as positive, the other quantity is negative. Please give an example.

Give birth to a quantity with opposite meaning.

6. Write on the blackboard according to the students' answers, and read and write positive and negative numbers on the blackboard.

Third, communicate and enrich understanding.

1. Teaching examples 1

The TV station broadcasts the weather forecast every day. Do you know what to use to measure the temperature? (courseware shows thermometer)

Observe the regularity of the number arrangement on the thermometer.

(Courseware highlights two scales: 10) Are the temperatures of two 10 the same? Why?

Will you use the positive and negative numbers you learned today to represent the temperature indicated by these two scales respectively?

(The courseware shows that the thermometer shows the temperatures in Shanghai, Nanjing and Beijing) Will you use the positive and negative numbers you learned today to represent these temperatures?

Who is the key to distinguish between temperatures above zero and temperatures below zero?

What is zero degrees Celsius, that is, above zero temperature and below zero temperature?

What is the temperature above zero? What about the temperature below zero? What are the zeros of positive and negative numbers?

2. Teaching Example 2

(1) Show Page 3 Example 2 Please tell me what the items in the passbook mean? (Answer by name)

(2) Explain the meaning to the teacher according to the students' answers.

(3) deskmates talk about the meaning of positive and negative numbers.

(4) Is 0 a positive number? Is it negative? What are positive and negative numbers?

Summary: 0 is neither positive nor negative.

Fourth, contact life and internalize understanding.

In addition to temperature and altitude, negative numbers are used in many places in life.

1. Negative number in the elevator: Uncle Wang and Aunt Li both take the elevator from the ground floor of the office building. Uncle Wang went to the fifth floor for a meeting, and Aunt Li went to the second floor to get the car. Which button should they press separately in the elevator?

2. Shenzhou VII and negative numbers: The temperature of the Shenzhou VII spacecraft to be launched in China will reach above () in space, while the temperature on the back will be lower than (). But through heat insulation and control, the temperature in the capsule can be kept at () all the time, which is very suitable for astronauts to work.

( 1)2 1℃(2) 100℃(3)- 100℃

3. Negative number in the product description: the food packaging bag is marked with "500+2g". After taking out five bags, the quality inspector weighed them and recorded them as +0. 1g,-1g, 0g, +0.5g and -3g.

What do you mean by +0. 1g,-1g, 0g, +0.5g, -3g? What does 500+2g mean?

Five, the class summary, extracurricular extension.

Say and say what you learned today.

Teaching Design Part II "Preliminary Understanding of Negative Numbers" Teaching Content

Page 120 of the textbook, examples 3 and 4, classroom activities 1~3, exercise 25, questions 3, 6, 7 and 8.

Teaching objectives

1. In familiar life situations, if we further understand the meaning of negative numbers, we will use positive numbers and negative numbers to represent quantities with opposite meanings.

2. Feeling the wide application of negative numbers in life will explain the practical significance of some negative numbers in life.

teaching process

First of all, this game is very exciting.

Teacher: Let's play a game to relax. This game is called "I object, I object, I object". Rules of the game: If the teacher says something, please say something with the opposite meaning. Who will have a try first?

① Look up (look down); ② Go ahead 200 meters (walk back 200 meters); ③ The elevator goes up15th floor (down15th floor).

Let's take the more difficult one and see who responds fastest.

I deposited 500 yuan in the bank. (500 yuan takes it out)

(2) knowledge contest, class five (1)20 points. (Deduct 20 points)

(3) 10, the school canteen earned 500 yuan. (Thanks to 500 yuan)

④ Above zero 10 diopter. (-10 photos)

Students at the same table play interactive games.

Second, review old knowledge.

We have studied negative numbers. Can you give some examples of negative numbers?

What else do you know from the study of the previous content?

Third, learn new knowledge.

1. Teaching Example 3.

Example 3: Xiaoming walks 200 meters east and Xiaojun walks 200 meters west.

The teacher asked: How are you going to express these two quantities with different meanings?

Student 1: Go 200 meters east, marked as +200 meters, and go 200 meters west, marked as -200 meters.

Student 2: Walking 200 meters west is marked as+200m, and walking 200 meters east is marked as-200m.

Teachers should give affirmation to these two symbols.

Students try independently:

(1) If the car is driving due north for 50m, and it is marked as +50m, how should the car go due south 100m?

(2) If the weight loss of 2kg is recorded as -2 kg, what does +5kg mean?

After the students finish, they collectively modify the summary: in this way, we can use positive numbers and negative numbers to represent quantities with opposite meanings.

(3) Exercise: Question 2 in class activities.

After reading the question, ask: What are the two opposite quantities in the question? What quantity does a positive number represent?

Ask the students to independently use positive and negative numbers to indicate the situation of goods entering and leaving. Final collective revision.

2. Teaching example 4.

Teacher: Actually, positive numbers and negative numbers are widely used in life. For example, an agricultural shopping mall made a profit and loss statement for the second half of the year: (Example 4)

July, August, September, 65438+ October, 165438+ October, 65438+ February.

Profit and loss (RMB)+6500-27000-750+9500+16700

Teacher: What do the positive and negative numbers in the table mean?

Student: A positive number means profit, and a negative number means loss.

Teacher: What information did you get from the form?

Communicate in groups and then report to the class.

Student1:July +6500 means a profit of 6500 yuan in July.

Student 2: August -2700 means a loss of 2700 yuan in August.

Student 3: ...

Teacher: Profit and loss are also two quantities with opposite meanings. We use positive and negative numbers to represent it, which is concise and accurate.

Fourth, classroom exercises.

1. Problems in classroom activities 1. Let the students talk about the meaning of positive and negative numbers. Let the students speak first, then communicate in groups.

2. Classroom activities 3. Students complete independently, teachers patrol, individual counseling and collective correction.

3. Think back to the game we played just before class. Can these phenomena also be described by positive numbers and negative numbers? Show them randomly according to the students' answers:

(1) I deposited it in 500 yuan in the bank as (); Then take out 500 yuan as ().

(2) In the knowledge contest, the score is 50 points, marked as (); Then deducting 50 points is ().

(3) The school canteen earned 800 yuan, which was recorded as (); So I lost 500 yuan as ().

(4) elevator up 15 floor, recorded as (); Then go down to 15 floor and record it as ().

4. Discuss negative numbers in life.

The teacher shows the negative numbers in the passbook and the elevator map, and asks the students to say what they mean.

Teacher: What does -800 in the passbook mean?

Student: Take out 800 yuan as-800; Deposit in 1200 yuan as 1200 yuan or as+1200 yuan.

What do 1 and-1 in the elevator mean? (bounded by the ground, the ground floor is 1 or+1, and the underground floor is-1. )

What number should the teacher press to go to the 33rd floor now? Go to the third basement?

5. Teach yourself "Do you know?"

Students read the textbook page 124. What did you get?

Classroom assignment of intransitive verbs

1. Exercise 25, question 3. Students speak independently first, and then the whole class speaks together.

2. Exercise 25, question 6. Students finish the book independently, teachers patrol, individual counseling, and then the whole class corrects it collectively

3. Exercise 25, question 7.

Teacher's inspiration: What does it mean based on 30kg per box? What does this mean? What about +4 and 1

Students complete the two questions independently, and the teacher gives individual guidance and corrects them collectively.

Seven. Course summary

What did you gain from today's study? What do you know about negative numbers?

Teaching Design Part III "Preliminary Understanding of Negative Numbers" Teaching Content;

People's Education Edition, Mathematics, a Standard Experimental Textbook for Compulsory Education Curriculum, Volume II of Grade 6, pages 2-4, examples 1 and 2.

Teaching objectives:

1. Guide students to know negative numbers in familiar life situations and read and write positive numbers and negative numbers correctly; Know that 0 is neither positive nor negative.

2. Make students learn to express some practical problems in daily life with negative numbers and experience the connection between mathematics and life.

3. Carry out patriotic education for students in combination with negative history; Cultivate students' good mathematics emotion and attitude.

Teaching emphases and difficulties:

The meaning of negative numbers.

Teaching process:

First, talk and communicate.

Dialogue: Students, as soon as class begins, everyone will do a set of opposite actions. What is that? (Stand up and sit down. ) Today's math class begins with this topic. (On the blackboard: On the contrary. There are many natural and social phenomena around us that have the opposite situation. Please look at the screen: (Play the picture. The sun rises in the east and sets in the west every day; Someone got on and off at the bus stop; There are buying and selling in the bustling market; There are losers and winners in the fierce competition ... can you name some such phenomena?

Second, the teaching of new knowledge

1. quantities with opposite meanings.

(1) Introduce an example.

Dialogue: If you continue to "chat" along the topic just now, you will naturally enter mathematics. Let's look at some examples together.

(1) The sixth grade was transferred to six students last semester and six students this semester.

② Aunt Zhang made a profit 1500 yuan in February, and lost money in 200 yuan in March.

③ Compared with the standard weight, Xiaoming weighs 2.5 kg and Xiaohua is light 1.8 kg.

④ The water level of the reservoir rises by meters in summer and drops by meters in winter.

It is pointed out that when these opposing words are combined with specific quantities, they become a group of "quantities with opposite meanings". (Supplementary blackboard writing: quantity in the opposite sense. )

(2) try.

How can these quantities with opposite meanings be expressed mathematically?

Please choose an example and try to write a statement.

……

(3) show communication.

……

2. Know the positive and negative numbers.

(1) introduces positive and negative numbers.

Let's talk about it: Just now, some students wrote "+"in front of 6, which means 6 people are transferred, and adding "-"means 6 people are transferred (blackboard writing: +6-6), which is completely in line with mathematics.

Introduction: Numbers like "-6" are called negative numbers (blackboard writing: negative numbers); The number is: minus six.

"-"has a new meaning and function here, which is called "minus sign". +is a plus sign.

Like "+6" is a positive number, pronounced as: plus six. We can add "+"before 6 or omit it (blackboard writing: 6). In fact, many of the numbers we used to know were positive.

(2) Give it a try.

Please use positive numbers and negative numbers to represent another set of quantities with opposite meanings.

After writing, communicate and check.

Teaching Design of "Preliminary Understanding of Negative Numbers" Part IV I. Teaching Objectives

Knowledge and skills

Let students know negative numbers in familiar life situations and read and write positive numbers and negative numbers correctly. Know that 0 is neither positive nor negative.

(2) Process and method

Understand the specific meaning of negative numbers according to the actual situation, and learn to use positive numbers and negative numbers to represent quantities with opposite meanings in life.

(3) Emotional attitudes and values

Let students know the history of negative numbers, feel the connection between positive numbers and negative numbers and life, and carry out patriotic education with historical materials.

Second, the difficulties in teaching

Teaching emphasis: understand the different meanings of negative numbers in combination with the real situation.

Difficulties in teaching: Understanding the different meanings of negative numbers according to the actual situation.

Third, teaching preparation.

Courseware.

Fourth, the teaching process

(A) exciting conversation, the introduction of new lessons

1. Students, have you ever seen negative numbers in your life? Do you know what it means?

2. What exactly is a negative number? What's the difference? In this class today, let's get to know negative numbers (reveal the theme).

The design intention is to get straight to the point, understand the students' cognitive basis in the dialogue and activate their life experience.

(B) combined with the situation, understand the meaning

1. Preliminary perception of negative numbers

(1) courseware shows the second page of the textbook.

The following is the temperature forecast of six cities at 20121(1201265438+20: 00 on October 22nd) issued by the Central Meteorological Observatory.

Teacher: Please observe carefully and tell me what you find.

Preset: ① The highest temperature in Harbin is-19℃ and the lowest temperature is-27℃; Haikou is the hottest, with the highest temperature of 23℃...②- 12℃ means MINUS 12 degrees Celsius (pronounced MINUS 12 degrees Celsius); Add "-"before the figure of the temperature below zero. ...

(2)-3℃ and 3℃ are the same meaning? Please show it on the thermometer.

Preset: ①-3℃ means three degrees below zero and 3℃ means three degrees above zero; (2) They have opposite meanings; (3) First find 0℃, three squares from the bottom mean -3℃, and three squares from the top mean 3℃.

(3) What does 0℃ mean?

Preset: ①0℃ means the weather is very cold; ②0℃ indicates the temperature at which fresh water begins to freeze; ③0℃ is the dividing line between the temperature above zero and the temperature below zero.

Summary: The temperature below 0℃ is called sub-zero temperature, and the number is usually preceded by "-"(minus sign). The temperature above 0℃ is called the temperature above zero. Add "+"(plus sign) before the number. In general, the plus sign can be omitted.

(4) Please indicate-18℃ on the thermometer, which temperature is lower than -3℃ or-18℃?

The design intends to introduce negative numbers with the temperature that students are familiar with, get a preliminary understanding of the reading and writing methods of negative numbers, realize the particularity of 0, and ask the question "Does 3℃ mean the same as -3℃?" Guide students to perceive two quantities with opposite meanings expressed by positive numbers and negative numbers.

2. Know positive and negative numbers

(1) courseware shows example 2 on page 3 of the textbook.

Teacher: After studying the temperature, let's look at the numbers in the passbook. What did you find? What do these numbers mean

Default: ①2000.00 means to deposit 2000 yuan; (2) the meaning of 500.00 and -500.00 is just the opposite, one is to save 500 yuan and the other is to spend 500 yuan.

(2) Teacher: There are many quantities that mean two opposite meanings, such as above-zero temperature and below-zero temperature, income and expenditure. Can you give an example of this?

Default: the water level rises by 2 meters and falls by 2 meters; When getting on the bus, 5 people, 6 people; Goods are transported in 200 tons and shipped out 150 tons. ...

(3) How can you express two quantities with opposite meanings in this way?

Teacher: In order to represent two quantities with opposite meanings, two numbers are needed. One is the number we learned before, such as 3500, 4.7,

These figures are positive numbers; The other is to add the minus sign "-"before these numbers, such as -3, -500, -4.7,-and so on.

Wait, these numbers are negative. So what is 0? (0 is neither positive nor negative, it is the dividing line between positive and negative numbers. )

(4) Basic exercises (the courseware shows the second question of "doing" on page 4 of the textbook)

Let the students think independently about what is positive and what is negative, and fill in the corresponding circles.

The design aims to make students realize the necessity of negative numbers in concrete life examples, understand positive numbers and negative numbers, and initially establish the concepts of positive numbers and negative numbers. There are also -7, -5.2,-

Let students perceive that there are negative integers, negative fractions and negative decimals in negative numbers.

(3) Return to life and expand application.

Teacher: In daily life, people still use positive numbers and negative numbers many times. Let's have a look!

1. Courseware shows page 6 of the textbook, exercise 1, question 1.

(1) Students finish independently and give feedback collectively.

(2) How do you feel after reading this information? How many degrees is the difference between the average temperature of the moon surface during the day and the average temperature at night?

2. Courseware shows page 6 of the textbook, exercise 1, question 5.

(1) Read the question carefully. What information did you get? What don't you understand? (Introduction: Sea level is the average height of the ocean; Altitude is the vertical distance above sea level at a certain point on the ground. )

(2) Independent completion and collective feedback.

Do you know the altitude of your city? Tell me about its specific meaning.

3. The courseware shows the exercise 1 on page 6 of the textbook, question 2.

(1) Read the question carefully and tell me what you know.

(2) Please indicate the time in Sydney and London. What time is it in Beijing?

(3) Based on Beijing time, the time in Dhaka, the capital of Bangladesh, is -2. Do you know what time it is?

(4) Do you know the time in other time zones at this time? Try to show it.

4. Courseware shows exercises.

The words "(120 5) g" are printed on the outer packaging of 120 g instant noodles produced by a food factory. Xiaoming bought a bag of such instant noodles and weighed it and found117g. Did the manufacturer cheat? Why?

(1) What information do you know?

(2) What does "1205" mean?

(3) If 120 grams is recorded as 0 grams, how many grams can 1 17 grams be recorded?

The design intention is to let students learn to use positive and negative numbers to represent two quantities with opposite meanings through the information in life, which enriches the understanding of positive and negative meanings.

(d) Understand the history and summarize it in class.

1. Courseware shows page 4 of the textbook "Do you know?" Content.

In fact, the generation and development of negative numbers have a long history. Let's have a look.

(1) What's your new understanding of negative numbers after reading the introduction?

(2) How do you feel?

The design aims to introduce the history of negative numbers to students through the combination of pictures and texts, so that students can experience the development of negative numbers and China's contribution to the development of negative numbers, stimulate students' national pride and further enrich their understanding of negative numbers.

2. What did you learn from this course?

Teacher: There is more knowledge about negative numbers in life waiting for us to explore. As long as students are good at observation, they will gain more in their future life and study.