Hunan education edition seventh grade mathematics first volume teaching plan 1
Teaching content:? 1.2 axis, reciprocal and absolute value (1)
Teaching objectives:
1, knowledge and skills
(1) Master the three elements of the number axis. A given rational number will be represented by points on the number axis, and the rational number represented will be read according to the points on the number axis.
(2) Understand that any rational number can be represented by a unique point on the number axis.
(3) Understand the mathematical thought of the combination of numbers and shapes.
2. Process and method
Through the game, you can learn the content of this lesson-number axis, and feel that the actual problem is abstracted into a mathematical problem, which stimulates students' interest in learning.
Important and difficult
1, focusing on the concept of number axis and its drawing.
2. Difficulties: the drawing of the number axis, the corresponding relationship between rational numbers and points on the number axis.
Teaching process:
First, create situations and introduce new lessons.
1. For primary school? Ray. Can you represent 1 and 2 on the ray?
2. use? Ray. Can you represent a rational number? Why?
3. What do you think? Ray. What changes can rational numbers make?
After the students answered, the teacher pointed out that this was what we were going to learn in this class.
Second, cooperation and exchange, interpretation and exploration.
Let the students observe the thermometer enlarged on the wall chart, and the teacher gives language guidance: the thermometer can be used to measure the temperature, and the thermometer has scales and readings. According to the different positions of the thermometer liquid level, different numbers can be read out, so as to get the measured temperature. 0 has a scale of 10, indicating10℃; 5 levels below 0, indicating -5℃.
Similar to a thermometer, we can also draw a scale on a straight line, mark the readings, and use the points on the straight line to represent positive numbers, negative numbers and zeros. The specific method is as follows (drawing while talking):
1. Draw a horizontal straight line, and take any point on this straight line as the origin (generally take a moderate position, if the required numbers are positive, it can also be left), and use this point to represent 0 (equivalent to 0℃ on the thermometer);
2. If the direction of the origin to the right on the straight line is positive (the direction indicated by the arrow), then the direction of the origin to the left is negative (equivalent to positive above 0℃ and negative below 0℃ on the thermometer);
3. Choose an appropriate length as the unit length, and on the straight line, from the origin to the right, take a point every other length unit, which is expressed as 1, 2,3,? From the origin to the left, take a point every other length unit, which is expressed as-1, -2, -3,?
Question: Can we use this straight line to represent any rational number? (You can list several figures)
On this basis, the definition of number axis is given, that is, a straight line with origin, positive direction and unit length is called number axis.
Then ask the students: On the number axis, a point P is known to represent the number -5. If the origin on the number axis is not selected in the original position, but re-selected in another position, is the number corresponding to P still -5? What if the unit length changes? What if the positive direction of the line changes?
Through the above questions, it is pointed out to students that the origin, positive direction and unit length of the three elements of the number axis are indispensable. Thirdly, the application of migration, integration and improvement.
1. Organize students to discuss whether the number axis drawn below is correct. If not, point out what is wrong.
Figure b
Student activities: Students discuss in groups.
Induction: The number axis drawn in Figure A lacks unit length, the number axis drawn in Figure B lacks positive direction, and the unit length of the number axis drawn in Figure D is inconsistent.
Students discuss: Do all the points on the number axis represent rational numbers?
The teacher pointed out that any rational number can be represented by a unique point on the number axis, but all points on the number axis do not necessarily represent rational numbers.
2.P9 problem 1 and 2:
Example 1. Point out which rational number the points m, p and q on the number axis represent respectively.
Example 2: Draw a number axis, and use points on the number axis to represent rational numbers 3, 1.5 and-1.5. Student activity: Complete these two questions in the exercise book and communicate with your deskmate.
Teacher's activity: Ask any student to tell the answer of example 1 and communicate with the class, and then ask another student to perform the answer of example 2 on the blackboard. Teachers and students review together to cultivate students' idea of combining numbers with shapes.
3. Classroom exercises: questions 1 0 and 2 in the textbook P 10.
Finally, guide students to draw the conclusion that positive rational numbers can be represented by points on the right of the origin, negative rational numbers can be represented by points on the left of the origin, and small origins can be represented.
Fourth, summarize and reflect.
After guiding students to read the textbook, it is pointed out that the number axis is a very important mathematical tool, which establishes the corresponding relationship between numbers and points on a straight line, reveals the internal relationship between numbers and shapes, and provides us with a new method to study problems.
This lesson requires students to master the three elements of the number axis and draw it correctly. Students should also be reminded that all rational numbers can be represented by points on the number axis, and vice versa, that is, all points on the number axis do not represent rational numbers. As for which points on the number axis cannot represent rational numbers, this problem will be studied later.
Verb (abbreviation for verb) homework after class
Textbook P 13 exercise 1.2A group 1
Seven-grade mathematics knowledge point II
Addition and subtraction of rational numbers
Rational number addition rule:
1. Add two numbers with the same sign, take the same sign, and then add the absolute values.
2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0.
When a number is added with 0, it still gets this number.
Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number.