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Teaching content: People's Education Press fifth grade mathematics prime number and composite number.
Teaching objective: 1. Understand the concepts of prime number and composite number, judge whether a number is prime number or composite number, and classify natural numbers according to the number of factors.
2. Cultivate students' abilities of careful observation, comprehensive generalization, accurate judgment, independent exploration, independent thinking and cooperative communication.
Teaching emphasis: Can accurately judge whether a number is a prime number or a composite number.
Teaching difficulty: finding prime numbers within 100.
Teaching process:
First, review the introduction (deepen the understanding of previous knowledge and pave the way for new knowledge)
Let's count who is whose factor, who is whose multiple, who is even and who is odd.
3 and 15 4 and 24 49 and 7 9 1 and 13.
Answer by roll call.
Second, study the concepts of prime numbers and composite numbers in groups.
Divide the class into two groups and write the factor of 1~20.
1, observe the characteristics of factor number.
2. Fill in the form submitted by the division to the board of directors.
There is only one factor.
There are only two factors: 1 and itself.
There are other factors besides 1 and itself.
3. Teacher's summary: There are only two factors, 1 and oneself. Such numbers are called prime numbers. There are other factors besides 1 and itself, and their numbers are called composite numbers. (blackboard writing: prime numbers and composite numbers)
4. Give an example.
Can you give some examples of prime numbers?
Can you give some examples of composite numbers?
Exercise: Who is the smallest prime number? Who is the smallest composite number? How many factors does a prime number have? How many factors are there in a composite number?
5。 Explore whether "1" is a prime number or a composite number.
As I said just now, there is another category that has only one factor. Think about it: Besides 1, are there any other numbers with only one factor? (No,) 1 Is it a prime number? Why? Is it a composite number? Why? (No, because it doesn't conform to the characteristics of prime numbers or composite numbers. )
Guide students to make it clear that 1 is neither a prime number nor a composite number.
Exercise: Are natural numbers composite except prime numbers?
Third, classify natural numbers.
1, think about it
Teacher: Divide natural numbers into odd and even numbers according to whether they are multiples of 2. According to the number of factors, what are the non-zero natural numbers?
Health: prime number, composite number, 1.
2. Tell me about it.
Now that we know what a prime number is and what a composite number is, what is the key to judge whether a number is a prime number or a composite number?
Guide students to make it clear that the key is the number of factors. If a number has only 1 and its own two factors, it is a prime number; If there are more than two factors, it is a composite number.
Fourth, teachers and students learn 24 pages of examples 1.
Teacher: Besides finding factors to judge whether a number is prime or composite, you can also use the method of looking up the prime table.
1, the teacher instructs students to find prime numbers within 30.
Question: There are prime numbers, composite numbers and 1 among these numbers. Now, if you want to keep the prime number within 30, what should you do with other numbers? (Cross out 1 first,) Then what? (Cross out even numbers other than 2) What was finally crossed out? (Finally, multiples of 3 and 5 were crossed out, but 3 and 5 themselves were not crossed out.) What are the remaining numbers? (The rest are prime numbers within 30. )
(especially remember prime numbers within 20, because they are commonly used. )
2。 This group studies prime numbers within 100.
3。 Report prime numbers within 100. Teachers and students * * * collate the quality table within 100.
4。 Application of quality table in 100:
Exercise: (1) Are all odd numbers prime? (2) Are all even numbers composite?
Fifth, thinking training.
There are two prime numbers whose sum is an odd number less than 100 and a multiple of 17. Find these two numbers.
Sixth, class summary.
What did you learn in this class? (Prime number and composite number) What is a prime number? (A number has only two factors, 1 and itself. Such numbers are called prime numbers. ) What is a composite number? A number has other factors besides 1 and itself. Such numbers are called composite numbers. ) Can you judge prime numbers and composite numbers? What is the key to judgment? Look at the number of factors in this number. )
Reflection: In the class of designing prime numbers and composite numbers, I put the main line of "careful observation, comprehensive generalization and accurate judgment" through the whole class. And design a small exercise at the back of each new knowledge. In order to consolidate and deepen the understanding and memory of new knowledge in time. The final thinking training is to improve the thinking of the students who learn well in this class. Summary also summarizes new knowledge for the whole class.
When students are looking for factors within 20, I should pay attention to exploration and show autonomy. That is, let students try to find out the factors of each number in the shortest time, and under my guidance, classify them according to the logarithm of the number of factors, and finally get the concepts of prime number and composite number. In the future study, I should advocate more independent and exploratory learning and pay attention to the "learning process" instead of rushing to see the results. Let students become independent and automatic thinkers. When learning new knowledge, they can choose, judge, explain and use it according to accumulated knowledge and experience, so as to discover and create something.
extreme
Teaching objectives:
1. Understand the concepts of prime number and composite number, judge whether a number is prime number or composite number, and classify natural numbers according to the number of divisors. 2. Cultivate students' ability of independent exploration, independent thinking and cooperative communication.
3. Cultivate students' spirit of daring to explore scientific mysteries and fully display the charm of mathematics itself.
Teaching focus:
1, understand and master the concepts of prime numbers and composite numbers.
2. Learn to judge whether a number is prime or composite.
Teaching difficulties: distinguish odd numbers, prime numbers, even numbers and composite numbers.
Teaching process:
First of all, explore and find, summarize the concept:
1, Teacher: (Show three identical small squares) The side length of each square is 1. How many different rectangles can you spell by using these three squares to make a rectangle?
Students think independently, and then the whole class communicates.
2. Teacher: How many different rectangles can these four small squares spell?
Students think independently, raise their hands and answer after imagination.
3. Teacher: Students, think again. If there are 12 such small squares, how many different rectangles can you spell?
Teacher: I think many students already know it without drawing. (Name it)
4. Teacher: Students, what do you think will happen to the number of different rectangles if more squares are given?
The students almost said with one voice: the more the better.
Teacher: Are you sure? Guide the students to discuss. )
5. Teacher: Students, sometimes a small square can only spell one rectangle, and sometimes it can spell multiple rectangles. Do you think you can only spell one when the number of small squares is what? When can you spell more than one rectangle? And give an example.
Let the students discuss in groups first, and then communicate with the whole class. The teacher writes on the blackboard according to the students' answers.
Teacher: Students, like the numbers above (3, 13, 7, 5, 1 1), we call them prime numbers in mathematics, and the numbers below (4, 6, 8, 9, 10,/kloc).
After students think independently, communicate in groups, and then communicate with the whole class.
Guide students to summarize the concepts of prime numbers and composite numbers, and write them on the blackboard with students' answers: (omitted)
6. Let the students illustrate which numbers are prime numbers and which numbers are composite numbers, and give the reasons.
7. Teacher: What do you think "1" is?
Let the students think independently and then discuss.
Second, hands-on operation, quality table.
1, the teacher shows: 73. Ask the students to think about whether it is a prime number.
Teacher: It is not easy to know what 73 is at once. It would be convenient if there is a quality table to check. (The students all say "Yes". )
Teacher: Where did this watch come from?
(The teacher shows the number table within 100) This number is 1 to 100, not a prime number table. Can you find out the prime numbers within 100 and make a prime number table? Who wants to talk about their ideas? Let the students fully express their ideas. )
2. Let students make high-quality forms by hand.
3. Collective communication.
Third, practice to consolidate:
Complete Exercise 4, Questions 1 and 2.
Four. Topic overview:
What have you gained from the heated discussion in this class?
Tisso
Teaching purpose:
1. Make students understand the concepts of prime number and composite number, and correctly judge whether a number is prime number or composite number.
2. Cultivate students' ability of observation, comparison, abstraction and generalization.
3. Cultivate students' spirit of independent inquiry and ability of independent thinking. Teaching emphasis: the concepts of prime number and coordination.
Teaching difficulties: the difference between prime number, set number, economic number and even number
Teaching process:
Talk before class:
Classify people in the classroom. Experience: According to the classification standard of "don't ask", the same thing can be classified in many ways. Clarity: The accuracy of classification is very important.
First, review the old knowledge.
Say, what numbers can you get in our study space? (Don't repeat what you said to your classmates)
Classify these natural numbers. Natural numbers can be divided into new numbers and even numbers according to whether they are divisible by 2.
Set the chart corresponding to the blackboard writing.
natural number
(Is it divisible by 2?)
Fill in the numbers listed by the students in the corresponding circles.
Q: What do you want to say after reading the assembly drawing? Look at the picture and say what you think. Review the knowledge about odd and even numbers.
Description: This is a valuable classification method, which is very useful in future research.
Q: Do you want to learn a new classification method? What do you want to know about the new classification method?
Second, implement the new curriculum.
Today we will classify natural numbers by looking for divisors.
Review: What is divisor? How to find a divisor that can be counted completely?
Work at the same table. Find all the divisors of the listed numbers. (simultaneous performance)
Guide students to observe: observing the number of numbers contained in the above numbers can be divided into several situations!
Write on the blackboard according to the students' answers.
natural number
(divisor)
(There are only two divisors) (There are three or more divisors)
Guide students to think: If there are only two divisors, what are the characteristics of these two divisors? Introduce the concept of divisor.
Define the concept of composite number. Question: How many divisors does a composite number have? Think about it: 1 What are the divisors? Is it a prime number? Is it a composite number?
Clear: This is a new classification method. Look at the factory assembly circle. What are you going to say? Look at the pictures, say what you think and consolidate the knowledge of temples and balconies. )
Guess: How many odd numbers are there? What about the composite number?
Clear: Because the number of natural numbers is infinite, so is the number of new positive even numbers. Solve problems with new knowledge.
Give the following numbers of the example 1, which are prime numbers? What is a composite number?
15 28 3 1 53 77 89 1ll
Students do it independently.
Q: How do you judge?
Clarity: you can find all the divisors of each number, and then judge according to the meaning of prime number and composite number; Only when a number finds 1 and the third constraint other than itself can it be judged whether it is a composite number or a prime number. It is not necessary to find all the divisors, which can improve the judgment efficiency.
Note: You can also look up a table to determine whether a number is a prime number. Commonly used prime numbers within 100. See the table of prime numbers within 100 in the book. Check whether the judgment of example 1 is correct with prime number table.
After practice.
Third, practice consolidation.
1, stick to the divisor of the following numbers, point out which ones are prime numbers and which ones are composite numbers, and then check with the prime number table.
22 29 35 49 5 1 79 83
2. Display numbers from 2 to 50. Cross out the multiples of 2 first, and then cross out the multiples of 3, 5 and 7 in turn (but 2, 3, 5 and 7 themselves are not crossed out. )
After the students operate, they ask: What's left?
Tell the students that ancient mathematicians used this method to find prime numbers.
Fourth, the class summary
Have you mastered this new classification method? Students answer: the camera reveals topics, prime numbers and composite numbers.
Discussion: What is the relationship between prime numbers, composite numbers, odd numbers and even numbers?
Verb (abbreviation of verb) homework (omitted).