Teaching plan of "rational number subtraction" in seventh grade mathematics

Teaching objectives

1. Understand and master the law, and convert the operation into addition operation;

2. Infiltrate students' thoughts by transforming subtraction operation into addition operation, and cultivate students' computing ability through operation.

3. By revealing the law, the dialectical materialism thought of universal connection and mutual transformation between things is infiltrated.

Teaching suggestion

(A) Analysis of key points and difficulties

The focus of this section is to skillfully use the law for subtraction. Solving the calculation problem of rational number subtraction requires strict mastery of two steps: first, the subtraction operation is converted into addition operation, and then the sign and absolute value of the result are determined according to the rational number addition law. It is difficult to understand the law, and the key to the breakthrough is the transformation and change from subtraction to addition. In learning, we should pay attention to our experience: the problem that decimal minus large number will not be reduced has been solved, and the difference between decimal minus large number is negative, so subtraction can always be realized within the scope of rational number.

(B) knowledge structure

(3) Suggestions on teaching methods

1. After guiding the students to read the textbook, the teacher emphasized that subtraction turned into addition because subtraction became its inverse. Addition and subtraction of rational numbers can be solved by addition when negative numbers are introduced.

2. Whether the subtraction is positive, negative or zero, it conforms to the rational number subtraction rule. When using rules, be careful that the minuend will never change.

3. Because any subtraction operation can be unified as addition operation, we don't need to specify several algorithms by subtraction, which is beneficial to the consolidation and memory of knowledge.

4. Note that after introducing negative numbers, you can subtract decimals from large numbers and express the difference with negative numbers.

Example of instructional design

First, the goal of quality education

(A) the main points of knowledge teaching

1. Understand and master the law.

2. You can perform the operation.

(2) Key points of ability training

1. Transform subtraction into addition, and infiltrate students' thoughts.

2. Cultivate students' logical thinking ability through the deduction of rational number subtraction rules.

3. Cultivate students' computing ability through operation.

By revealing the law, the dialectical materialism thought of universal connection and mutual transformation between things is infiltrated.

(D) the starting point of aesthetic education

In elementary school arithmetic, subtraction can't be realized forever. After learning this lesson, I know that subtraction can be realized forever within the scope of rational numbers, which embodies the complete beauty of knowledge system.

Second, the guidance of learning methods

1. Teachers try to guide students to analyze and summarize, with students as the main body and teachers and students participating in teaching activities together.

2. Students' learning rules: explore new knowledge → summarize conclusions → practice and consolidate.

Three. Key points, difficulties, doubts and solutions

1. Key points: rational number subtraction rules and operations.

2. Difficulties: the deduction of the rational number subtraction rule.

Fourth, the class schedule

1 class hour

Verb (abbreviation for verb) Prepare teaching AIDS and learning tools.

Computer, projector, homemade film.

Sixth, the design of teacher-student interaction activities.

Teachers ask practical questions, students actively participate in exploring new knowledge, teachers show exercises, and students discuss and solve them in various ways.

Seven, teaching steps

(A) the creation of situations, the introduction of new courses

1. Calculation (oral answer) (1); (2)-3+(-7);

(3)- 10+(+3); (4)+ 10+(-3).

2. The pictures in the introduction of this chapter on page 42 of the textbook are displayed by physical projection. It's a winter day in Beijing. The maximum temperature during the day is 10℃, and the minimum temperature at night is -5℃. How much is the highest temperature higher than the lowest temperature on this day?

Teachers guide students to observe:

Health: 10℃ is higher than -5℃ 15℃.

Teacher: Can you list the formulas?

Health: 10-(-5).

Teacher: How to calculate?

The teacher concluded: This is what we are going to learn today.

Teaching method guidance

1 topic not only reviews and consolidates the addition rule of rational numbers, but also lays the foundation for the subtraction operation of rational numbers.

Question 2 is a concrete example. Teachers create problem situations to stimulate students' cognitive interest and abstract concrete examples into mathematical problems, thus pointing out the theme of this lesson.

(2) Explore new knowledge and teach new lessons.

1. Teacher: As we all know, 10-3 = 7. Who can complement the attribute symbol in the formula 10-3 = 7?

Health: (+10)-(+3) =+7.

Teacher: Calculation: (+10)+(-3) How much?

Health: (+10)+(-3) =+7.

Teacher: Let the students observe the results of the two formulas, from which we can draw the following conclusions.

(+ 10)-(+3)=+ 10)+(-3).( 1)

Teacher: Through the above questions, can students observe whether subtraction can be converted into addition calculation?

Health: Yes.

Teacher: How did it change?

Health: Subtracting a positive number (+3) equals adding its inverse (-3).

The teaching method shows that teachers play a leading role, pay attention to students' participation consciousness, fully develop students' thinking ability, and let students know that subtraction can be transformed into addition calculation by trying.

2. Look at another question and calculate (-10)-(-3).

Teacher's inspiration: To solve this problem, according to the significance of rational number subtraction, it is required to add a number with (-3) to get-10. Then who is this number?

Health: -7 means: (-7)+(-3) =- 10, so (-10)-(-3) =-7.

The teacher gave another question: Calculate (-10)+(+3).

Health: (-10)+(+3) =-7.

Teachers guide students to observe the results of the above two questions, so as to draw:

(- 10)-(-3)=(- 10)+(+3).(2)

Teachers further guide students to observe formula (2); What conclusion can you draw?

Health: Subtracting a negative number (-3) equals adding its inverse number (+3).

Teacher's summary: From (1) and (2), we can see that subtraction can be converted into addition.

The teaching method shows that students are unfamiliar with rational number subtraction. In order to face the whole people, the second question gives students an opportunity to further observe and compare, and students can summarize, summarize and think for themselves. At this time, students are active in thinking, easy to play their initiative in learning, and at the same time cultivate students' ability to analyze problems, so as to achieve the purpose of ability training.

Teacher: Through the above two questions, please think about the law of subtraction between two rational numbers.

Student activities: students think and ask their deskmates to tell each other, correct and supplement each other, and then raise their hands to answer. Other students think and prepare to correct or supplement.

Teacher: Show me the law of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number. (blackboard writing)

The teacher emphasized the rule: (1) subtraction should be converted into addition, and subtraction should be converted into inverse number. (2) This rule is applicable to the subtraction of any two rational numbers. (3) The general form expressed by letters is:

The explanation of teaching methods, combined with the example of introducing thermometer into the new class, further verifies the rationality of this law, points out the practical significance of rational number subtraction to students, and makes students realize that mathematics comes from reality and serves them.

4. Examples:

[Display projection 1 (for example, 1, 2)]

Example 1? Calculate (1) (-3)-(5); (2)0-7;

Example 2? Calculate (1) 7.2-(-4.8); (2)()-.

Example 1 is the process of students' oral problem solving. The teacher writes on the blackboard, emphasizing the standardization of problem solving, and then teachers and students summarize the steps of problem solving: (1) transformation, (2) addition.

Two questions are done by two students, the others are written in exercise books, and then the teachers and students comment.

Teaching method explains the process of students' oral problem solving, and teachers demonstrate on the blackboard to cultivate students' rigorous style of study and good study habits. Example 1(2) is 0 minus a number, so students who have just started classes are prone to make mistakes. Here is an example to attract students' attention. Example 2 is a simple variant topic, which is intended to show that rational number subtraction is not only applicable to integers, but also to fractions and decimals, that is, rational numbers.

Teacher: Organize students to make up their own questions and answer them.

The teaching method is that teachers and students participate in teaching equally, so that students can freely compile the topic of rational number subtraction, with the aim of consolidating the knowledge that students are afraid of learning. Doing so, on the one hand, can activate students' thinking and cultivate their expressive ability; On the other hand, students' initiative and sense of participation can be enhanced by giving questions, answering questions and correcting each other. At the same time, teachers can get students' feedback information about knowledge mastery and feedback the existing problems in time.

Teacher: Let's look at a set of questions together.

[Display Projection 2 (Calculation Problem 1, 2)]

1. Calculation (oral answer)

( 1)6-9; (2)(+4)-(-7); (3)(-5)-(-8);

(4)(-4)-9 (5)0-(-5); (6)0-5.

calculate

( 1)(-2.5)-5.9; (2) 1.9-(-0.6);

(3)()-; (4)-().

Student activities: Ask students to answer the question 1, ask four students to act out question 2, and the other students do it in their exercise books.

This teaching method shows that students are already familiar with rational number subtraction. When doing exercises, students should be guided to pay attention to the law of rational number subtraction, instead of simply converting subtraction into addition mechanically, so as to prepare for gradually omitting the intermediate steps of addition in the future.

Show the picture on page 45 of the textbook with physical projection.

The highest mountain in the world is Mount Qomolangma, which is 8848 meters above sea level. The lowest place on land is the Dead Sea Lake in West Asia, with an altitude of -392 meters. What's the difference between two heights?

Answer: 8848-(-392) = 8848+392 = 9240.

So the height difference between the two places is 9240 meters.

The teaching method shows that this topic is practical problems, which echoes the practical problems introduced in the new curriculum, implements the teaching syllabus's stipulation that "students should abstract practical problems into teaching problems and gradually form the consciousness of using mathematics", and transforms practical problems into rational number subtraction, which shows that mathematics comes from reality and is applied to practice.

(4) class summary

Question: What did you learn from this lesson? A: A little.

Teacher: The subtraction rule of rational number is a transformation rule, which requires students to master and apply its calculation. It is not a problem that the primary school can't solve the problem of insufficient subtraction such as 2-5. In other words, within the scope of rational numbers, subtraction can always be realized.

Eight, in-class exercises

( 1)3-(-3)=____________; (2)(- 1 1)-2=______________;

(3)0-(-6)=____________; (4)(-7)-(+8)=____________;

(5)- 12-(-5)=____________; (6)3 is greater than 5 _ _ _ _ _ _ _ _;

(7)-8 is _ _ _ _ _ _ smaller than -2; (8)-4-( )= 10;

(9) If, then the symbol is _ _ _ _ _ _ _ _;

(10) is expressed by the formula: Mount Everest is 8848 meters above sea level, and Turpan Basin is-155 meters above sea level. What's the difference between these two heights _ _ _ _ _ _ _.

2. True or false

(1) When two numbers are subtracted, the difference must be less than the minuend. ()

(2)(-2)-(+3)=2+(-3).( )

(3) Zero minus a number equals the reciprocal of this number. ()

(4) The equation has no solution within the range of rational numbers. ()

(5) If,,,. ()

Nine, homework

(1) Required questions: 2. Even number problem, 3. Even number problem, 4. Even the question on page 83 of the textbook.

(2) Multiple choice questions: 5 and 8 on page 84 of the textbook.

X. Blackboard Design

Practice your answers in class.

1.( 1)6; (2)- 13; (3)6; (4)- 15;