Teaching plan design of "factor and multiplication" in the second volume of fifth grade mathematics in the new curriculum standard primary school

# Lesson Plan # Introduction The number of factors of a number is limited, and there are countless multiples of a number. The following content is ready for your reference!

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I. Teaching content

1. Factor and multiple

Characteristics of multiples of 2.2, 5 and 3

3. Prime numbers and composite numbers

Second, the teaching objectives

1. Make students master the concepts of factor, multiple, prime number and composite number, and know the connections and differences between related concepts.

2. Make students master the characteristics of multiples of 2, 5 and 3 through independent exploration.

3. Gradually cultivate students' mathematical abstract ability.

Third, the arrangement characteristics

1. Simplify concepts and reduce students' memory burden.

Three aspects of adjustment:

A. The concept of "divisibility" no longer appears, and the concepts of factor and multiple directly come from the multiplication formula.

B. "prime factor decomposition" is no longer formally taught, but only introduced as reading materials.

C. Common factor, common factor, common multiple and minimum common multiple are moved to the unit of "Significance and Properties of Fraction" as the knowledge basis of reduction and total score, highlighting its application.

2. Pay attention to the abstraction of mathematics.

Number theory knowledge itself is abstract. Students should also pay attention to cultivating abstract thinking in senior three.

Fourth, specific arrangements.

1. Factor and multiple

Concepts of factors and multiples

In the past: use ÷ = to indicate separability, and use ÷ = to indicate separability.

Now: use = to directly introduce the concepts of factor and multiple.

The concepts of (1) factor and multiple are given by 2× 6 = 12.

(2) Use 3× 4 = 12 to further consolidate the above concept.

(3) Let students use the concepts of factor and multiple to independently discover other factors of 12.

(4) Students can be guided to sum up the concepts of factors and multiples with the general multiplication formula × =.

(5) Explain the research scope of this unit.

Please note the following points:

(1) Although the word "divisibility" does not appear, it is essentially based on divisibility. So the multiplier and product in the multiplication formula must be integers.

(2) Factor and multiple are a pair of interdependent concepts and cannot exist independently.

(3) Pay attention to the relationship and difference between the "factor" in the names of each part of multiplication and the "factor" in this unit.

(4) Pay attention to distinguish the connection and difference between "multiple" and "multiple" learned before.

Example 1 (the solution of the factor of a number)

(1) We can find the factor of 18 in different ways (list the multiplication formula with the product of 18 or the division formula with the dividend of 18), but we should guide students to think in an orderly way.

(2) The set circle is used to represent the factor, which paves the way for finding the common factor of two numbers later.

Characteristics of factors of numbers

(1) factor itself, the minimum factor is 1.

(2) The number of factors is limited.

(3) This conclusion is obtained through the example of 1 and the special case of "doing one thing" by incomplete induction, which embodies the idea from concrete to general.

Example 2 (Solution of Multiple of a Number)

(1) Solution: The product obtained by multiplying this number by any non-zero natural number is a multiple of this number.

(2) Use set circle to represent multiples, paving the way for finding common multiples of two numbers later.

Do it.

Combined with the example 1, multiples of 2, 3 and 5 are provided, which prepares for discussing the characteristics of multiples of 2, 3 and 5 later.

Characteristics of multiples of numbers

(1) The minimum multiple is itself, and there is no multiple.

(2) The number of factors is infinite.

(3) This conclusion is obtained through the example of 1 and the special case of "doing one thing" by incomplete induction, which embodies the idea from concrete to general.

Characteristics of multiples of 2.2, 5 and 3

Because the characteristics of multiples of 2 and 5 are reflected in single digits, and multiples of 3 are related to the sum of digits, which is more complicated, so the characteristics of multiples of 3 are arranged in the back. This part plays an important role in mastering the four operations of reduction, total score and fraction.

Characteristics of multiples of 2

(1) is introduced from the "even number" of life situations.

(2) Observe the single digits of the multiple of 2 and summarize the characteristics of the multiple of 2.

(3) Introduce the concepts of odd number and even number.

(4) Students can find some numbers to verify at will, but they don't need strict proof.

Characteristics of multiples of 5

The arrangement of (1) is similar to the arrangement of multiples of 2.

(2) We can further summarize the characteristics of multiples of 2 and 5, that is, multiples of 10.

Characteristics of multiples of 3

(1) emphasizes independent exploration, allowing students to experience the process of observation-guess-* guess-observation-guess-verification.

(2) You can choose any number to further verify the conclusion with positive and negative examples.

(3) You can also change the position of each digit of any multiple of 3, so as to understand the characteristics of multiple of 3 more deeply.

3. Prime numbers and composite numbers

Concepts of prime numbers and composite numbers

(1) According to the number of factors with each number less than 20, the numbers are divided into three categories: 1, prime number and composite number.

(2) You can choose any number, so that students can judge whether it is a prime number or a composite number according to the concept.

Example 1 (find prime numbers in 100)

(1) There are various methods. You can judge one by one according to the concept of prime numbers, or you can use screening method.

(2) Grasp the teaching requirements: know the prime numbers within 100 and be familiar with the prime numbers within 20.

Suggestions on teaching verbs (abbreviation of verb)

1. Strengthen the connection between concepts, guide students to understand concepts in essence, and avoid rote learning.

Understand other related concepts from the meaning of factors and multiples.

2. Pay attention to cultivating students' abstract thinking ability.

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Teaching content:

Compulsory Education Curriculum Standard Primary School Mathematics Grade Five Volume II Chapter II "Factor and Multiplication" Section 1 Example 1 (textbook page 13) and Exercise 2 Part I Question 4.

Teaching material analysis:

On the basis of students mastering the concepts of factor and multiple, under the guidance of teachers, this teaching section allows students to try to explore the method of "finding the factor of a number" by using multiplication formula and division. At the same time, through various forms of training, students can skillfully find the factors of Quan Yi number. In addition, by guiding students to express the factor of a number in the form of set, on the one hand, we can infiltrate the idea of set into students, and more importantly, we can prepare for later teaching to find the common factor of two numbers.

Teaching objectives:

1, the application of trial teaching method encourages students to explore the methods and regular characteristics of finding the factors of a number independently, and can skillfully find the factors of a whole number;

2. Gradually cultivate students' thinking methods of abstract induction from individual to whole and from concrete to general.

Teaching focus:

Explore the method and characteristics of finding the factor of a number.

Teaching difficulties:

By finding the factor of a number, we can find the factor of a whole number skillfully.

Teaching aid preparation:

Projector, small blackboard, card

Teaching hours: one class hour.

Teaching philosophy:

Using the method of trial lecture, starting from the students' existing knowledge and experience, through the guidance of teachers and the students' self-study of the example 1, this paper tries and explores the method of finding the factor of a number independently, and can use the obtained method and experience to find the factor of a whole number.

Teaching process:

First, review the old knowledge.

Teacher: Students, we have learned the concepts of factor and multiple before. The teacher would like to test how you are doing, can you?

Health: (default) Yes!

Teacher: Show me the small blackboard.

1, use the interdependence of factors and multiples to talk about the interrelationships of the following groups.

2 1 and 72× 7 = 1430 ÷ 6 = 5

2. Judges.

(1) 12 is a multiple and 2 is a factor. ( )

(2) 1 is a factor of 14, and 14 is a multiple of 1. ( )

(3) Because 6× 0.5 = 3, 6 and 0.5 are factors of 3, and 3 is a multiple of 6 and 0.5. ( )

Teachers give appropriate praise and encouragement according to the completion of students' exercises, and at the same time enter the new class teaching: …

Second, the new curriculum teaching

Process 1: Try training.

(A) Show the problem

Teacher: Students, the teacher has a new problem and wants to ask you to help solve it, okay?

Health: OK! (Default)

Question: What is the factor of 14?

(2) Students solve problems, teachers patrol, and provide timely guidance to students with learning difficulties according to the actual situation.

(3) Information feedback.

Blackboard writing:

1× 14

14 2×7

14÷2

The factors of 14 are: 1, 2,7, 14.

Process 2: Teaching materials for self-study (P 13 cases 1).

(1) Examples of students' self-study 1.

Teachers put forward self-study requirements (projection):

What are the factors of 1 and 18?

2. How did the children find the factor 18? Have they finished reading it? If not, please help them finish.

3. Do you have any other way to find it? Please try to write all the factors of 18 in your favorite way.

(2) Information feedback

1, feedback self-study requirements;

Blackboard writing:

1× 18

18 2×9

3×6

The factors of 18 are 1, 2,3,6,9, 18.

It can also be expressed as a factor of 18.

2, knowledge comparison, explore and discover the law.

(1) Teacher: Students, based on the experience gained in finding the factors of 14 and 18, think again about the following questions:

Projection presentation questions:

Thinking 1: How to find out?

(2) Students think and teachers guide them in time.

(3) Share your thoughts at the same table.

(4) Interaction between teachers and students. Summarize the method and point out the topic.

The way to find the factor of a number is to calculate it by multiplication or division.

Process 3: Try to practice.

(1) Show exercises on the blackboard.

1, what are the factors that found 30? What is the factor of 36?

2. Combined with the number of factors of 14, 18, 30, 36, what are the characteristics of a number's factors? [Hint: The minimum factor of a number is (), and the factor of is (). 〗

(B) Information feedback: the characteristics of teacher-student interaction.

Blackboard writing:

The number of factors of a number is limited. Its minimum factor is 1, and its factor is itself.

Third, class assignments.

Exercise 2, question 2 and the first half of question 4.

Fourth, classroom extension.

Guess: Who is the number with only one factor?

Verb (abbreviation of verb) course summary

Teacher: Did you learn how to find the factor of a number today? Do you know the factor characteristics of a number?

Health: ...

Blackboard design:

The method of finding the factor of a number

1× 14

14 2×7 method: calculate by multiplication or division (divisible).

14÷2

The factors of 14 are: 1, 2,7, 14.

1× 18

18 2×9

3×6

The factors of 18 are: 1, 2, 3, 6, 9, 18 Features: The number of factors of a number is limited.

It can also be expressed as:

Its minimum factor is 1, and its factor is itself.

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Teaching objectives:

1, students master the method of finding the factor and multiple of a number;

2. Students can understand that the factor of a number is limited and the multiple is infinite;

3. Be able to skillfully find out the factors and multiples of a number;

4. Cultivate students' observation ability.

Teaching focus:

Master the method of finding the factor and multiple of a number.

Teaching difficulties:

Can skillfully find the factor and multiple of a number.

Teaching process:

First, introduce new courses.

1. Show the theme map and ask the students to do a multiplication formula.

2. Teacher: See if you can read the following formula.

Display: Because 2×6= 12.

So 2 is a factor of 12, and 6 is also a factor of 12;

12 is a multiple of 2 and 12 is also a multiple of 6.

3. Teacher: Can you talk about another formula in the same way?

(Name the students)

Teacher: Do you understand the relationship between factor and multiple?

Then can you find other factors of 12?

4. Can you write a formula to test your deskmate? Students write formulas.

Teacher: Who will work out a formula to test the class?

5. Teacher: Today we are going to learn factors and multiples. (Exhibition theme: factor multiple)

Pay attention to watch p 12 together.

Second, new funding.

(A) looking for factors

1, example 1: 18 What is the factor?

From the factor of 12, we can see that there is more than one factor of a number, so let's find the factor of 18 together.

Students try to finish: report

(The factors of 18 are: 1, 2, 3, 6, 9, 18).

Teacher: Tell me how you found it. (Student: By division,18 ÷1=18 ÷ 2 = 9, 18 ÷ 3 = 6, 18 ÷ 4 = by multiplication.

Teacher: What is the minimum factor of 18? What is this? When we write, we usually arrange it from small to large.

2. In this case, please look for the factor of 36 again.

The factors of Report No.36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Teacher: How did you find it?

Give examples of errors (1, 2, 3, 4, 6, 6, 9, 12, 18, 36).

Teacher: Is this ok? Why? No, because you only need to write one repetition factor, you don't need to write two sixes. )

Take a closer look, what is the smallest factor among the 36 factors, and what is the real one?

It seems that the smallest factor of any number must be (), and the smallest factor must be ().

3. Which factor are you looking for? (18, 5, 42 ...) Please write down one of them in your exercise book and report.

4. In fact, in addition to writing a number factor in this way, it can also be expressed by a set, such as

/kloc-factor of 0/8

1、2、3、6、9、 18

Conclusion: We have found so many factors. How do you think to find them so as not to miss them easily?

Start with the smallest natural number 1, that is, start with the smallest factor and find all the way. In the process of searching, one by one, from small to uppercase.

(2) Multiply

1. We found the factor of 18 together. Can you find a multiple of 2?

Reports: 2, 4, 6, 8, 10, 16, …

Teacher: Why can't I find it?

How did you find these multiples? (Health: Just multiply 2 by 1, 2 by, 3 by, 4 by …)

So what is the minimum multiple of 2? Can you find it?

2. Ask the students to finish the questions 1 and 2: Find multiples of 3 and 5.

The multiples of Report 3 are: 3,6,9, 12.

Teacher: Is this ok? Why? How should I change it?

Rewritten as: multiples of 3 are: 3, 6, 9, 12, ...

How did you find it? (Multiply 1, 2, 3, ... by 3 respectively)

The multiple of 5 is: 5, 10,15,20, ...

Teacher: To express multiples of a number, besides this method of literal narration, it can also be expressed by sets.

Multiples of 2, multiples of 3 and multiples of 5.

2、4、6、8…… 3、6、9…… 5、 10、 15……

Teacher: We know that the number of factors of a number is limited, so what is the multiple of a number?

The number of multiples of a number is infinite, the smallest multiple is itself, and there is no multiple.

Third, the class summary

Let's recall, what did we focus on in this class? What did you get?

Fourth, work independently.

Complete Exercise 2, Question 1 ~ 4.