Seventh Grade Mathematics Lesson Plan for Positive and Negative Numbers
The main knowledge point of this module "Positive and Negative Numbers" is to understand numbers and negative numbers, and to know under what circumstances positive and negative numbers are used to represent them. Next is the lesson plan for positive and negative numbers in seventh-grade mathematics that I compiled for you. I hope you like it!
Teaching plan for positive and negative numbers in seventh-grade mathematics 1
Background of the lesson plan
Junior high school students love to play and are active. They are in the transition stage from image thinking to abstract thinking. Students often find overly abstract problems boring and puzzled. Multimedia has the characteristics of image and intuition. Use it to build a platform for students' thinking and imagination, create a good learning atmosphere, fully mobilize students' enthusiasm and consciousness for learning, and achieve the purpose of pursuing knowledge in a happy form; new courses Standard requirements: Classroom teaching should be conducive to students' active participation in mathematical activities such as observation, experimentation, guessing, verification, reasoning, and communication. The content should be presented in different ways of expression to meet diverse learning needs. during the teaching process. It is necessary to strengthen students' awareness of hands-on practice, independent exploration, cooperation and communication, and focus on cultivating students' ability to solve practical problems.
1.1 "Positive and Negative Numbers" Teaching Design Plan
(Lesson 1)
People's Education Press Ninth Grade Mathematics Volume 1
Geng Xinhua, Beicheng Middle School, Binbei Street Office, Bincheng District, Binzhou City, Shandong Province
Postcode: 256651 Contact number: 15865403584
Analysis of teaching materials:
1. Location of teaching materials The status and function of: "1.1 Positive and Negative Numbers" section is the content of the first section of the first chapter of the seventh grade volume of the People's Education Press. The content of this section is mainly about learning the definitions and connections of positive numbers, negative numbers and zero. It is the basis for the study of rational numbers in this chapter.
2. Teaching Objectives
Knowledge and skills: Understand the meaning of rational numbers with the help of examples in life, be able to judge whether a number is positive or negative, and be able to use positive and negative numbers to express features in life Quantity in the opposite sense.
Process and methods: 1. Understand the necessity of introducing negative numbers, feel the widespread application of rational numbers, understand that mathematical knowledge comes from life, and understand the connection between mathematical knowledge and the real world.
2. Ability to present and raise mathematical problems in specific situations, and explain the rationality of the results.
Emotional attitudes and values: Willing to be exposed to mathematical information in the social environment, willing to talk about mathematical topics, and play an active role in mathematical activities.
3. Teaching is important and difficult
Key points: Understand the necessity of introducing negative numbers and the widespread application of rational numbers, and be able to use positive and negative numbers to represent quantities with opposite meanings in life. .
Difficulty: Be able to use positive and negative numbers to express quantities with opposite meanings in life, and develop the habit of applying mathematics to practical problems in life.
Teaching method: Adopt the teaching method of "phenomenon-problem-goal", and strive to embody the teaching concept of "subject participation, independent exploration, cooperation and exchange, and guidance and exploration"
Teaching process
The teacher demonstrates the multimedia courseware with the first picture as the main body in the relaxed and cheerful music.
Design intention of teacher activities and student activities in the link
Creating situations to introduce new lessons
Autonomous learning
Teacher-student interaction
Collaborative inquiry
Standard testing
Learning summary
The teacher shows pictures to illustrate the generation of natural numbers and fractions. Then
Question
Question 1 Weather forecast: The temperature on a certain day in Binzhou City in winter is -3~3℃. What does it exactly mean? What is the temperature difference in our city on this day?
Question 2 2. In 2010, my country's peanut production increased by 1.8% compared with last year, and rapeseed production increased by -2.7% compared with last year. What does the -2.7% increase here mean?
The -3 and -2.7% in the two questions are There are new numbers that we have not learned before. This shows that with the development of life and labor, the numbers we have learned before are no longer enough, and new numbers need to be introduced. To serve our lives. Thus introducing a new lesson
1. Present the learning objectives of this lesson
1. Recognize the necessity of introducing negative numbers through examples in life.
2. Know what negative numbers, zero, and positive numbers are.
3. Can you judge whether a number is positive or negative?
4. Can use positive and negative numbers to express quantities with opposite meanings in real life
2. Show the self-study outline for this lesson
1. Knowledge point 1: The concepts of positive and negative numbers ---------Read page 2 of the textbook, like 3, 2, 0.5 , 1.8% is called a number larger than 0. If necessary, sometimes add "+" in front of the positive number, such as +5, , , ,... The "+" in front of a positive number is generally omitted: numbers like -3, -2, -3.5% with a "-" sign in front of a positive number are called .
Such as -6, ,…. "-6" is pronounced as .
2. Knowledge point 2: Understanding of "0" -------- Read page 2 of the textbook
0 is neither a number nor a number, it is a positive The watershed between numbers and negative numbers. Its meaning is very rich, it can mean "nothing" or other specific meanings.
3. Knowledge point 3: Use positive and negative numbers to represent quantities with opposite meanings -------- Read the textbook on page 3
Quantities with opposite meanings must have Two elements: one is their meaning; the other is that they all have quantity, and they must be quantity.
1. Instruct students to exchange results within their own group, collect problems that each group does not know, and try to let other groups solve them.
2. The teacher collects problems that the whole class does not know and helps solve them.
Do it: (show slides)
Teaching Plan for Positive and Negative Numbers in Seventh Grade Mathematics 2
1.1 "Positive and Negative Numbers" Teaching Design Plan< /p>
(Lesson 1)
Analysis of teaching materials:
1. The status and role of teaching materials: The section "1.1 Positive and Negative Numbers" is the The content of the first section of the first chapter of the seventh grade textbook is mainly about learning the definitions and connections of positive numbers, negative numbers and zero. It is the basis for the study of rational numbers in this chapter.
2. Teaching objectives
Knowledge and skills: Understand the meaning of rational numbers with the help of examples in life, be able to judge whether a number is positive or negative, and be able to use positive and negative numbers to express features in life Quantity in the opposite sense.
Process and methods: 1. Understand the necessity of introducing negative numbers, feel the widespread application of rational numbers, understand that mathematical knowledge comes from life, and understand the connection between mathematical knowledge and the real world.
2. Able to present and raise mathematical problems in specific situations, and explain the rationality of the results.
Emotional attitudes and values: Willing to be exposed to mathematical information in the social environment, willing to talk about mathematical topics, and play an active role in mathematical activities.
3. Teaching is important and difficult
Key points: Understand the necessity of introducing negative numbers and the widespread application of rational numbers, and be able to use positive and negative numbers to represent quantities with opposite meanings in life. .
Difficulty: Be able to use positive and negative numbers to express quantities with opposite meanings in life, and develop the habit of applying mathematics to practical problems in life.
Teaching method: Adopt the teaching method of "phenomenon-problem-goal", and strive to embody the teaching concept of "subject participation, independent exploration, cooperation and exchange, and guidance and exploration"
Teaching process
The teacher demonstrates the multimedia courseware with the first picture as the main body of the first section.
Design intention of teacher activities and student activities in the link
Create situations to introduce new lessons
Autonomous learning
Teacher-student interaction
< p> Collaborative inquiryStandard testing
Learning summary
The teacher shows pictures to illustrate the generation of natural numbers and fractions. Then
Question
Question 1 Weather forecast: The temperature in Beijing on a certain day in winter is -3~3℃. What does it exactly mean? What is the temperature difference in our city on this day?
Question 2 In a football match involving three teams, the red team beat the yellow team (4:1), the yellow team beat the blue team (1:0), and the blue team beat the red team (1:0). How to determine the scores of the three teams? Goal difference and ranking order?
Question 3 The length of a certain machine part is designed to be 100mm, and the size marked on the processing drawing is 100 0.5 (mm). What does 0.5 here mean? The length range of qualified products How much is it?
Among the three questions, -3 and 0.5 are new numbers that we have not learned before. This shows that with the development of life and labor, the numbers we have learned before are no longer enough. New numbers need to be introduced. To serve our lives. Thus introducing a new lesson
1. Present the learning objectives of this lesson
1. Recognize the necessity of introducing negative numbers through examples in life.
2. Know what negative numbers, zero, and positive numbers are.
3. Can you judge whether a number is positive or negative?
4. Can use positive and negative numbers to express quantities with opposite meanings in real life
2. Show the self-study outline for this lesson
1. Knowledge point 1: The concepts of positive and negative numbers ---------Read page 2 of the textbook, like 3, 2, 0.5 , such numbers larger than 0 are called. According to needs, sometimes "+" is added in front of the positive number, such as +5, , , ,... The "+" in front of a positive number is generally omitted: numbers like -3, -2, -0.5 with a "-" sign in front of a positive number are called . Such as -6, ,…. "-6" is pronounced as .
2. Knowledge point 2: Understanding of "0" -------- Read page 2 of the textbook
0 is neither a number nor a number, it is a positive The watershed between numbers and negative numbers.
Its meaning is very rich, it can mean "nothing" or other specific meanings.
3. Knowledge point 3: Use positive and negative numbers to represent quantities with opposite meanings -------- Read the textbook on page 3
Quantities with opposite meanings must have Two elements: first, their meaning; second, they all have quantity, and they must be quantity.
1. Instruct students to exchange results within their own group, collect problems that each group does not know, and try to let other groups solve them.
2. The teacher collects problems that the whole class does not know and helps solve them.
Do it: (show slides)
Within one month, Xiao Ming’s weight increased by 2kg, Xiaohua’s weight decreased by 1kg, and Xiaoqiang’s weight remained unchanged. Write down their weight this month. Growth Value
Seventh Grade Mathematics Lesson Plan Three for Positive and Negative Numbers
Teaching Objectives
Knowledge and Skills:
To enable students to understand positive numbers And negative numbers arise from actual needs.
Process and method:
In the process of introducing negative numbers from specific examples, students will understand the concepts of positive and negative numbers, and be able to judge whether a number is positive or negative. Preliminary Be able to use positive and negative numbers to represent quantities with opposite meanings, and understand the meaning of 0.
Emotions and attitudes:
In the process of forming the concept of negative numbers, students’ abilities of observation, induction and generalization are cultivated, and students’ enthusiasm for learning mathematics is stimulated.
Academic Analysis
1. Understand the background of negative numbers (the generation and development of numbers are inseparable from the needs of life and production), and understand the importance of using negative numbers in production and life sex. 2. Students go through the process of introducing negative numbers: examples in production and life (quantities with opposite meanings) - not enough numbers - introduction of negative numbers - representation of mathematical symbols - problem solving and other processes to initially cultivate Students develop a sense of mathematical symbols and understand the status and role of mathematical symbols in mathematics learning. Cultivate students' ability to actively explore the essence of problems in the process of cooperation and communication with others, and to be good at observation, induction, generalization and discovery of methods to solve problems.
Key points and difficulties
Correctly understand positive and negative numbers, and understand the meaning of the quantity represented by 0.
Teaching process
Teaching activities
Activity 1 Import Import
Review and review, and do a good job in connecting students to what they have been studying for six years Mathematics experience, numbers are no stranger to every student. I believe that students have realized that the emergence and development of numbers are inseparable from the needs of production and life. First, let us review: the production of natural numbers and the production of fractions. Demonstrate courseware, display pictures, and visually explain the generation and expansion of numbers: (Show pictures to illustrate the generation of natural numbers and fractions. Let students understand the benefits of the generation of number symbols) Teacher-student activities (guide students to observe the pictures and try to explain them Meaning): We know that in order to express the number of objects (such as hunting counts in primitive societies) or the order of things, 1, 2, 3,... are produced; in order to express "no" (such as when the prey is divided), 1, 2, 3,... are introduced; Number 0; sometimes the results of distribution and measurement (measuring land) are not integers and need to be expressed as fractions (decimals). In short, numbers are developed to meet the needs of production and life.
Design Intention : The emergence and development of numbers are inseparable from the needs of life and production.
Activity 2 Import Activity 2
Demonstrate courseware, display questions and corresponding pictures.
Question (1) The temperature on a certain day in Beijing in winter is -3~3. What does it exactly mean? What is the temperature difference in Beijing on this day?
Question (2) In a football match involving three teams, the red team beat the yellow team (4:1), the yellow team beat the blue team (1:0), and the blue team beat the red team (1:0). The goal differences of the three teams were respectively It is 2, -2, 0. How to determine the ranking order?
Question (3) In 2006, my country's peanut production increased by 1.8% over the previous year, and rapeseed production increased by -2.7% over the previous year. Here is the increase - What does 2.7% mean?
Teacher-student activities: The teacher demonstrates the courseware and explains the background of the problem:
For example, in the question of goal difference, first introduce the determination of football match rankings Order regulations:
If two teams have different points, the team with higher points will be ranked first;
If two teams have the same points, the team with higher goal difference will be ranked first;
Both teams have the same points and goal difference, and the team with more goals is ranked higher.
Next, the points calculation rules are introduced: 3 points for a win, 1 point for a draw, and 0 points for a loss. From this, it is easy to know that the points of these three teams are 3+0=3.
Finally, the calculation rules for the goal difference are introduced: the red team beats the yellow team (4:1), which means that the red team scores 4 goals and concedes 1 goal, or the yellow team scores 1 goal and concedes 4 goals, and the goal difference is Just scored a few more goals in the game. Here goals scored and goals conceded are opposite quantities. We stipulate that goals scored are represented by "+" and goals conceded are represented by "-". In this way, the number of goals scored and the number of goals conceded can be represented by adding "+" or "-" in front of the number of goals scored and the number of goals conceded respectively.
Goal difference is the sum of goals scored and goals conceded in the game. For example, taking the red team as an example, the goals scored are 4 and the goals conceded are 2 (one goal conceded in each of the two games) are recorded as -2, so the goal difference of the red team is 4+(-2)=2. It can be calculated similarly The yellow team's goal difference is -2 (the goals scored are 2 goals less than the goals conceded, which is equivalent to a net loss of 2 goals, so it is recorded as -2), and the blue team's goal difference is 0.
In the teacher Under the guidance of the students, students thought about -3~3, the order of goal difference and ranking, the significance of -2.7% growth, and the four arithmetic operations that must be performed on these new numbers when solving these problems.
Design intention: Through the example of temperature - the emergence of a new number -3 also involves the subtraction of rational numbers; in the example of goal difference, negative numbers also appear, determining the goal difference involves the addition of rational numbers to determine the ranking The sequence involves the comparison of the sizes of rational numbers; in the example of output growth rate, using positive and negative numbers to describe changes in the specified direction and other issues lead to the use of various symbols to represent numbers, allowing students to try to explain them and stimulate their curiosity. At the same time, explain the problems, find out their essence, and reveal the essence of the problem (a quantity with opposite meaning).
Representation of quantities with opposite meanings
Teacher-student activities: In view of the above analysis and discussion, under the guidance of the teacher, let students try to summarize the representations of quantities with opposite meanings:
For example, in the problem of temperature, above zero and below zero (zero is the dividing point) are quantities with opposite meanings. We stipulate that above zero is positive and below zero is negative; in the example of goal difference, The ball and the goal conceded (the opponent's goal) are also quantities with opposite meanings. We stipulate that a goal scored is positive and a goal conceded is negative... Generally speaking, for quantities with opposite meanings, we can define one of the quantities as meaning. is positive, and a "+" (pronounced as "positive") is written in front of it to indicate it; a quantity with the opposite meaning is defined as negative, and a "-" (pronounced as "negative") is written in front of it. ") to represent (except zero)
Design intention: to summarize the expression methods of quantities with opposite meanings through examples, to cultivate students' awareness of cooperation and communication and the ability to understand the essence of problems from the specific to the general.
Seventh Grade Mathematics Lesson Plan 4 for Positive and Negative Numbers
[Teaching Objectives]
1. Knowledge and Ability
With the help of the experience in life The example will determine whether a number is positive or negative, and can use positive and negative numbers to represent quantities with opposite meanings
2. Process and method
1. Process: introduce negative numbers through examples, so as to Instruct students to identify positive and negative numbers and their representations, and to use positive and negative numbers to express quantities with opposite meanings.
2. Methods: discussion method, inquiry method, teaching method, and observation method.
3. Emotions, attitudes, and values
Willing to be exposed to mathematical information in the social environment, willing to talk about mathematical topics, and play an active role in mathematical activities
Key Points and Difficulties] The focus of this lesson is to understand how 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 be able to accurately cite typical examples of quantities with opposite meanings and to clarify the criteria for classifying rational numbers.
There are various ways to introduce positive and negative numbers. The material is introduced by two examples familiar to students: temperature and altitude. 5 degrees Celsius higher than 0℃ is recorded as 5℃, 5 degrees Celsius lower than 0℃ is recorded as -5℃; 8848 meters higher than sea level is recorded as 8848 meters, and 155 meters lower than sea level is recorded as -155 meters. From these two examples, it is natural to call numbers greater than 0 positive numbers, and numbers with a "-" sign as negative numbers; 0 is neither a positive number nor a negative number, but a neutral number, representing the "benchmark" of measurement. . The introduction of positive and negative numbers in this way will not only help students correctly use positive and negative numbers to express quantities with opposite meanings, but will also help students understand the magnitude properties of rational numbers. Think of negative numbers as numbers less than 0. In the textbook, the concept of "quantity with opposite meaning" does not appear. This is a deliberate attempt to avoid or downplay the concept. The purpose is to reveal the properties of positive, negative numbers and zero in a profound way from the beginning of the introduction of positive and negative numbers, and to help students correctly understand the concepts of positive and negative numbers.
What should be clear about the classification of rational numbers is: different classification standards lead to different classification results. The classification results should be non-repeated and not omitted, that is, each number must belong to a certain category and cannot belong to different categories at the same time. Two categories.
Teaching suggestions
This lesson is based on the numbers learned in elementary school, and introduces negative numbers from quantities that represent opposite meanings. In terms of content, negative numbers are better than non-negative numbers. Negative numbers should be abstract and difficult to understand. Therefore, in the selection of teaching methods and teaching languages, we should pay as much attention as possible to the connection between primary and secondary schools, which does not violate scientific nature and is consistent with the principle of acceptability. For example, when explaining the concept of rational numbers, let students clearly understand the fundamental difference between rational numbers and arithmetic numbers. Rational numbers are composed of two parts: the symbolic part and the numerical part (that is, arithmetic numbers). In this way, on the basis of understanding arithmetic numbers and negative numbers It is much easier to understand the concept of rational numbers.
In order to enable students to master the necessary mathematical ideas and methods, when clarifying the classification of rational numbers, they can consciously penetrate the thinking methods of classification discussion and understand the classification. standards, classification results, and their interconnections.
By unifying both positive and negative numbers into rational numbers, the dialectical thought of the unity of opposites can be gradually established and penetrated into daily teaching.
1. The introduction of negative numbers
We know that numbers arise from people’s actual production and life needs. [Projection 1~3: Figure 1.1-1] People produced the numbers 1, 2, 3... through counting and sorting; the number 0 was introduced to express "nothing" and "vacancy"; sometimes integers cannot be obtained in measurement and distribution results, for which fractions and decimals are produced.
In life, production, and scientific research, we often encounter problems with number representation and number operations.
[Projection] 1. The temperature on a certain day in Beijing in winter is -3~3℃. What does it exactly mean? What is the temperature difference in Beijing on this day?
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