Article 1: The Maximum Common Factor Evaluation Draft for Mathematics Instructors: Mr. Qi
First, evaluate the teaching content:
Fill in the first volume of fifth grade mathematics of Beijing Normal University, exercise 1, 2, P463, 4.
Second, the evaluation of teaching objectives: I think Mr. Qi's objectives are very clear and in place.
1. Let students go through the process of finding the common factor of two numbers and understand the meaning of the common factor and the greatest common factor.
2. Explore the method of finding the common factor of two numbers, and accurately find the common factor and the greatest common factor of two numbers.
Third, the evaluation of teaching focus: the focus is outstanding.
Let students understand the meaning of common factor and greatest common factor.
Fourth, evaluate the teaching difficulties: the difficulties are set reasonably.
A flexible method for finding the common factor of two numbers.
5. Evaluation of the status of teaching content: The status of teaching content is closely related.
Teacher Qi studied on the basis of finding a number factor, and also laid the foundation for learning the key knowledge points of transformation in the future.
Sixth, the evaluation of teaching process design:
The design of teaching process is reasonable. 1. Let the students go through the process of finding the common factor of two numbers and understand the meaning of the common factor and the greatest common factor. 2. Through the combination of lectures and exercises, let students explore the method of finding the common factor of two numbers, and most students can accurately find the common factor and the greatest common factor of two numbers. It has achieved the teaching goal and broken through the teaching difficulties.
(1) review
By reviewing the method of finding a number factor, we can lay a good foundation for later study and reveal the topic at the same time.
(2) Reveal the theme: Find the greatest common factor of two numbers.
(3) By filling in the contents of the textbook, let students go through the process of finding the common factor of two numbers and understand the meaning of common factor and the greatest common factor.
( 1) 12=( )×( ) =( )×( ) =( )×( )
18=( )×( ) =( )×( ) =( )×( )
(3
) 12 factor 18 factor
The common factor of two numbers is the common factor.
The greatest common factor is called their greatest common factor.
(4) Fill in through P463. Let students explore the method of finding the common factor of two numbers, which can accurately find the common factor and the greatest common factor of two numbers. At the same time, break through the teaching focus: let students understand the meaning of common factor and greatest common factor.
(5) Let the students sum up: the method of finding the common factor of two numbers.
The method of finding the common factor of two numbers ① First find the factor of each number.
(2) Find the common factor of two numbers.
③ Determine the greatest common factor.
(6) The method of finding the common factor of two special numbers through P45 exercise 1; (Two numbers are multiples, and the greatest common factor is smaller) Breaking through the teaching difficulty: the method of finding the common factor of two numbers flexibly.
1 and factors of 8:
/kloc-factor of 0/6:
Common factor of 8 and 16:
The greatest common factor of 8 and 16:
2. Observe the relationship between 8 and 16 (multiple relationship). The common factor is 1, 2, 4, 8, and the largest common factor is 8, which is the smaller of these two numbers.
4 and 8 9 and 3 28 and 7
3. Summary: When two numbers are multiples, the smaller number is the greatest common factor of these two numbers.
Count.
(7) Find out 5 and 7, 2 and 3, 1 1 and 19, 3 and 7 by factor.
The common factor of and their greatest common factor.
Summary: The greatest common factor of two unequal prime numbers is 1.
(8) Find the greatest common factor of 1 and 2, 5 and 6, 8 and 9, 15 and 16. Summary: The greatest common factor of two adjacent natural numbers (except 0) is 1.
(9) Summary: Today, we learned how to find the greatest common factor of two numbers: ① Find the factor of each number first.
③ Determine the greatest common factor.
The smaller numbers are these two.
2
The greatest common factor of two unequal prime numbers is 1.
The greatest common factor (except 0) is 1.
Seven, some teaching suggestions:
1, looking for factors to review is not in place;
For example: (1)12 = () × () = ()× () = ()× ()
18=( )×( ) =( )×( ) =( )×( )
It is necessary to make it clear how much 12 is equal to and multiplied by ... these numbers are all factors of 12.
2, the content is a little too much, I am afraid that the fifth grade students can't fully accept it.
3. There is something wrong with the arrangement of exercise questions. You can add more questions to the greatest common denominator of fractional numerator and denominator.
The second part: the draft of the greatest common factor of mathematics. 1. Analyze basic knowledge and set teaching objectives accurately.
This lesson is taught on the basis that students have understood and mastered the meanings of factors and multiples, preliminarily learned to find multiples and factors of a number, and know the characteristics of multiples and factors of a number. This part is not only an important part of the basic knowledge in the field of number and algebra, but also the basis for further learning divisor and fraction calculation. According to the characteristics of textbook compilation, Mr. Liu accurately formulated the teaching goal, that is, the knowledge goal: to understand the meaning of common factor and greatest common factor in combination with solving problems, and to learn how to find the greatest common factor of two numbers. Ability goal: First, in the process of exploring the meaning of common factor and greatest common factor, we experience mathematical activities such as observation, operation, guess and induction to further develop our preliminary reasoning ability. In the process of solving problems, we can think methodically and rationally.
Second, teach concepts in real situations and experience the formation process of concepts with the help of intuitive operation activities.
By letting the students "lay the floor tiles" on a piece of paper, Mr. Liu asked the students to put a pendulum at will, observe, analyze and think, and find the rules. It must be the same factor of two numbers to meet the teacher's requirements, draw the concept of common factor, choose which floor tile is paved fastest, and let students realize the significance of the greatest common factor in life. Give full play to students' hands-on ability, let them acquire new knowledge through full hands-on, and let every student learn new knowledge. In the past, the concept teaching of common factor was usually to find out the factors of two natural numbers directly, and then let students find that some factors are common to two numbers, thus revealing the concepts of common factor and greatest common factor. In this class, Mr. Liu pays attention to guiding students to understand the common factor and the most by drawing pictures.
The formation process of the concept of great common divisor. First of all, Mr. Liu started from "How many decimeters can the side length of a square be?" What is the longest? "Starting from this question, guide students to put square pieces of paper with different sides. Through calculation, it is found that square pieces of paper with side lengths of 1 decimeter, 2 decimeters and 3 decimeters can just fill rectangular pieces of paper, and there is no redundancy. Square pieces of paper with sides of 4 decimeters, 5 decimeters, and 7 decimeters can't be filled out, and there is surplus. Secondly, it explains the reasons why it is full and not full. Thereby revealing the meaning of common factor and greatest common factor, completing the process from image to abstraction, and upgrading perceptual knowledge to rational knowledge.
Third, grasp the connotation and extension, and accurately understand the meaning of the concept.
This lesson highlights the concepts of "both" and "public". In teaching, Mr. Liu first asked students to find out the factors of 16 and 12 in their exercise books, and then revealed the meaning of the sentence "it is both a factor of 16 and a factor of 12" with the help of an intuitive set diagram to help students further understand the meaning of the common factor and the greatest common factor. This arrangement has two advantages: first, students can understand the actual background of common factors through operational activities and deepen their understanding of abstract concepts; Second, it is conducive to improving learning methods and facilitating students to experience the learning process through operation and communication. In this class, Teacher Liu pays attention to using counterexamples to highlight the significance of common factors. When expressing the common factor of 16 and 12 with the set graph, the teacher can set such a question: Is 4 the common factor of 18 and 12? Therefore, students can understand that 4 is only a factor of 12, not a factor of 18, and 4 is not a common factor of 18 and 12, so it cannot be filled in and concentrated, thus further clarifying the concept of common factor.
Fourth, find the common factor of two numbers and advocate the diversification of thinking methods. Teacher Liu accurately grasps and determines his own teaching focus. When studying this part of knowledge, he focused on finding the common factor of two numbers and encouraged students to find the diversity of the methods of the greatest common factor.
How to find the common factor and maximum common factor of 12 and 16? At that time, students were guided to use a variety of methods, such as finding the factor of 16 from the factor of 12, enumeration, comparison, set diagram and so on. Finally, the teacher also introduced the related knowledge of prime numbers. And this knowledge textbook is only in "Do you know? Briefly introduce them respectively. . Imagine that if these closely related concepts are concentrated in a class or for a period of time and cross-contrast is adopted, it will be more beneficial for students to grasp the knowledge structure as a whole, facilitate students to use knowledge flexibly and achieve a comprehensive grasp of knowledge. After the teaching of this course, it is assumed that students may still have some confusion about the concepts of common factor and greatest common factor, and there may be some mistakes in homework after class. Therefore, while teaching new knowledge, the forms of design exercises should be diverse and the levels should be clear. In the repeated comparison and internalization of concepts, students should firmly grasp the internal meaning of common factor and greatest common factor. Let students expand their understanding of common factor and greatest common factor.