Tisch
Teaching objectives:
Knowledge and skills
Through guessing, verification and application, students are guided to explore and understand that the law of integer multiplication is also applicable to decimals.
Process and method objectives
Can correctly, reasonably and flexibly use the multiplication law to perform simple operations related to decimal multiplication.
Emotional attitudes and values goals
Let students communicate and cooperate to experience the joy of success.
Teaching focus:
Exploring, discovering and understanding the law of integer multiplication is also applicable to fractional multiplication.
Teaching difficulties:
Simple calculation of decimal multiplication by algorithm.
Analysis of learning situation:
Most fifth-grade children have developed good study habits and can express their opinions boldly in class. Therefore, in the teaching of this class, I fully mobilize students' enthusiasm, improve students' participation in classroom activities, and let students master what they have learned through personal exploration and experience. At the same time, I feel the mystery in mathematics and increase my interest in learning mathematics.
Teaching rules:
In this class, I mainly use teaching methods such as "independent inquiry, cooperation and communication, report verification". Stimulate students' thirst for knowledge by creating vivid teaching scenes. Let students discover through observation, communicate through inquiry and solve problems through cooperation. Specifically, it is divided into the following methods: 1, scenario creation method. 2. Activity inquiry method. 3. Collective discussion method.
Teaching process:
Create scenarios, introduce new lessons-independent inquiry, problem solving-careful topic selection, multi-layer training-question summary, reflection and evaluation.
The first link: create situations and introduce new lessons.
At the beginning of the class, I will throw a question to the children: classmates, we have learned some operation rules of integer multiplication. Who can tell us what is the arithmetic of integer multiplication?
Students will answer: multiplicative commutative law, multiplicative associative law and multiplicative distributive law.
Then I will ask my children to express these three laws with numbers, letters or symbols. After the students showed me, I made a summary: We know that the laws of multiplication can make some calculations easier in integer multiplication, so can these laws be applied to fractional multiplication? Today we will study this problem in this class. Write on the blackboard at the same time.
In this link, let the children express the three laws in their favorite way, on the one hand, stimulate their interest in learning, on the other hand, review and consolidate what they have learned and prepare for learning new lessons. Introduce the old into the new, stimulate children's inquiry, and let children think with goals.
The second link: independent exploration and problem solving.
I designed the following teaching activities in this section.
(A) team cooperation, speculation and verification
1. Show the following topics with slides.
0.7× 1.2○ 1.2×0.7
(0.8×0.5)×0.4○0.8×(0.5×0.4)
(2.4+3.6)×0.5○2.4×0.5+3.6×0.5
Let the children guess, what is the relationship between each group of formulas? (Of course, because it is a guess, the students' answers are likely to be different. )
2. Students explore and verify by themselves.
Ask the students to divide into groups and draw a conclusion through calculation. It turns out that the results of each set of formulas are equal.
Then I guide the students to observe each set of formulas carefully. What are their characteristics?
Students will draw the following conclusions through observation: the first set of formulas uses multiplicative commutative law, the second set uses multiplicative associative law, and the third set uses multiplicative distributive law.
3. Example verification.
I asked the children: through the above set of examples, can it be explained that the law of multiplication also applies to fractional multiplication?
Children may have two opinions: yes or no.
In view of different viewpoints, let me guide you: yes, a simple set of examples is not convincing, and we need to cite more examples to verify it. Let's take the first group as an example and write three such formulas in groups to verify whether they are equal.
Give children enough time to write, let them report after verification, and try to let several groups of students report, so that there are more examples and the conclusions are more convincing. )
At the same time as the students report, I will purposefully write several groups of formulas on the blackboard for students to observe and find that the law of multiplication is also applicable to fractional multiplication.
After everyone's communication, I guided them like this: Just after that group of students communicated with each other, can you sum up your findings in one sentence? Guide the students to draw the conclusion that the operation law of integer multiplication is also applicable to decimal multiplication. )
In this session, I first let students guess and perceive the relationship between the formulas in their minds, then verify and further understand the relationship between the formulas, and inspire students to verify with examples again, so that they can use their own hands and brains and listen to other students' speeches to draw conclusions. In this link, the teacher's role is only to guide the instructions, and never impose the rules on the students, but to let the students guess, discover and verify themselves.
(B) flexible application to solve problems
Display example 8
Teacher: Students, observe the following two questions carefully and see if you can work them out in a simple way.
0.25×4.78×4 0.65×20 1
(1) Let the students think independently, and then try to write it in the exercise book.
(2) roll call students to perform.
Then I will make children think: the first question, why do you multiply 0.25 and 4? What algorithm is used here?
The child will naturally answer: the multiplication exchange law is used.
Then ask them: what do you think is the key to solving the second problem?
According to the previous knowledge, students will answer: divide 20 1 by 200+ 1, and then use the law of multiplication and distribution to complete it. (Because the multiplication distribution rate was a difficult point in last semester's study, I also want to emphasize here that children should realize that special numbers must be decomposed before they can be simplified. )
Then continue to ask questions: what should be paid attention to in decimal multiplication in order to make the calculation simple? Inspire students to think, carefully examine questions and observe the characteristics of numbers. )
In this link, let children use what they have learned to solve problems, which is the purpose of mathematics learning. By using their own brains, students try to use multiplication algorithm to make calculation simple, which stimulates them to use knowledge to solve problems, and at the same time makes students realize the simplicity of using multiplication algorithm and experience the happiness of success.
The third link: careful topic selection and multi-layer training.
In this link, according to the teaching objectives and the problems existing in students' learning, I designed targeted and clearly defined practice groups (basic questions, variant questions, extended questions and open questions).
The exercise is designed as follows
Through various forms of practice, students' interest in learning is further improved and their cognitive structure is more perfect. At the same time, strengthen the teaching focus of this course and break through the teaching difficulties.
The fourth link: question summary, reflection and evaluation.
Show the following two questions with slides.
Let the students speak in groups, and each student can exchange what he has learned. In evaluation: let students evaluate themselves first, and then let them evaluate each other. Finally, I will praise the whole class to enhance students' self-confidence and sense of honor and make them love mathematics more.
In this link, through the exchange of learning income, children's confidence in learning mathematics knowledge is enhanced, and their spirit of questioning and innovation is cultivated.
extreme
Teaching objectives:
1. Let students know that the operation law of integer multiplication is also applicable to fractional multiplication, and can use the operation law of multiplication to calculate fractional multiplication correctly, reasonably and flexibly.
2. Cultivate students' observation ability, analogy ability and the ability to use what they have learned flexibly to solve problems.
3. Let students communicate and cooperate, and experience the joy of success.
Teaching focus:
1. Understand the operation law of integer multiplication, which is also applicable to fractional multiplication.
2. Simply calculate decimal multiplication by using the algorithm.
Teaching difficulties:
Simple calculation of decimal multiplication by using algorithm.
Prepare teaching AIDS: computer projection, cards
teaching process
First, introduce a conversation
Teacher: Students, last class, we learned that the order of integer mixing operation is applicable to decimals. Besides, what else applies to decimals? In this lesson, we will discuss whether the law of integer multiplication applies to decimals (a teacher's blackboard topic).
Second, explore new knowledge.
1, the arithmetic of integer multiplication is also applicable to fractional multiplication.
Teacher: Who can tell me what operation rules you have learned in integer multiplication and how to express them with definite mother?
Student: The commutative law of multiplication: a b = b a, the associative law of multiplication (a b) c = a (b c) The distributive law of multiplication: (a+b) c = AC+BC. (blackboard writing)
0.7× 1.2= 1.2×0.7
(0.8×0.5)×0.4=0.8×(0.5×0.4)
( 1.4+3.6)×0.5=2.4×0.5+3.6×0.5
Teacher: (Finger expression) What do these expressions mean?
Sheng 1: the first line of the formula uses the commutative law of integer multiplication;
Health 2: the second line applies the associative law of integer multiplication;
Health 3: The formula in the third line applies the distribution law of integer multiplication.
Teacher: Who can sum up what these formulas mean in one sentence?
Health 4: It shows that the operation law of integer multiplication is also applicable to decimal multiplication.
2, teaching how to use the law of multiplication:
Teacher: (blackboard writing) 0.25×4.78×4
Please observe carefully and see if this problem can be worked out simply and conveniently, and how it can be worked out simply. Please exchange your ideas with each other in the group.
Students observe, think and communicate in groups, and teachers patrol, participate and discuss together. Let the students talk in class.
Teacher and students sum up the blackboard together: look, think and count.
Teacher: Now, please use the method just summarized to calculate this problem and see how to calculate it simply.
Teacher: (blackboard writing) 0.65×20 1
Study group discussion, exchange ideas, teachers participate, prompt and guide in time, and then students calculate. After the students finish, the teacher extracts representative homework and shows it by computer projection. 0.65×20 1
=0.65×(200+ 1)
=0.65×200+0.65× 1
= 130+0.65
= 130.65
Teacher: (can you tell the students about your problem-solving ideas?
Health 1: I'll find a special number 20 1 first, because 20 1 can be written as 200+ 1, and then multiply 200 and 1 by 0.65, and calculate it by multiplication and division and distribution.
(The teacher writes on the blackboard while talking, and makes a simple calculation after decomposition. )
Teacher: Just now we discussed two simple calculation skills together. Some students also have many simple calculation skills, and students can learn from each other. Please look at the following two questions again, how to calculate reasonably and simply (let students do it independently).
(computer projection) 32× 1.25 (4+2)×0.9
Third, expand the practice.
Teacher: Here are three numbers 4, 0.8, 1.25. Please fill in the questions according to the algorithm of multiplication and talk about how to make the calculation simple by using the algorithm.
Fourth, the whole class summarizes and reflects on their experiences.
Teacher: Students, what did we learn today? What did you get?
Verb (short for verb) homework
Please use the correct and reasonable method for simple calculation.
1, required question:
( 1) 102×0.45 (2)0.34×0.5×0.6 (3) 1.25×0.7×0.8
(4) 1.2×2.5×+0.8×2.5 (5)(0.8+0.2)×6.7
2, choose to do the problem
( 1) 99× 1.45 (2)99× 1.45+ 1.45
(3)99× 1.45+3× 1.45- 1.45×2 (4)99× 1.45+2× 1.45- 1.45
Tisso
Teaching content: the law of integer multiplication is extended to fractional multiplication (P. 12, Example 8 and "Do it", Exercise 2, Question 2. )
Teaching requirements: make students understand that the operation law of integer multiplication is also applicable to decimals, and simply calculate some decimals by using the operation law of multiplication.
Teaching emphasis: the application range of numbers (including integers and decimals) in the law of multiplication.
Teaching difficulty: using the operation law of multiplication to perform simple operation of decimal multiplication.
Teaching aid: a few slides.
Teaching process:
First of all, inspire:
1, calculation:
25×95×4 25×32 4×48+6×48 102×56
2. What operation rules have we learned in integer multiplication? Please indicate it in letters.
According to the students' answers, write on the blackboard:
Multiplicative commutative law ab=ba
The law of multiplicative association a (BC) = (ab) c
Multiplication and distribution law a(b+c)=ab+ac
2. Let the students illustrate how to apply these laws to simplify the calculation. Pay attention to the numbers used by students when giving examples. )
3. Show three groups of formulas on page 9 of the textbook: Are the left and right results of each group of formulas equal?
0.7× 1.2○ 1.2×0.7
( 0.8×0.5)×0.4○0.8×(0.5×0.4)
(2.4+3.6)×0.5○2.4×0.5+3.6×0.5
Let the students see if each set of formulas is equal.
It is concluded that the commutative law, associative law and distributive law of integer multiplication are also applicable to fractional multiplication.
4. Discard the topic and write it on the blackboard: the operation law of integer multiplication is extended to fractional multiplication.
Second, try
1, the problem of Example 8 (1):0.25×4.78×4.
2. Guide students to change their thinking: Can you imitate the simple calculation method of similar problems in integer multiplication to calculate this problem? Please try to do it and say the name of the blackboard.
Can you tell me which algorithm should be used in each step? According to the students' answers, the blackboard is 0.25×4.78×4.
= 0.25× 4× 4.78 Multiplicative Commutation Law
= 1× 4.78 multiplicative associative law
=4.78
It is pointed out that the part surrounded by dotted line can be omitted.
4. Practice after trying:
50×0. 13×0.2 1.25×0.7×0.8 0.3×2.5×0.4
Students finish independently, and teachers patrol and coach students with difficulties. Name the board and perform in groups.
5. Demonstration: Question (2) of Example 7: 0.65×20 1
What do you think is the key to this problem? (Replace 20 1 with 200+ 1 and use multiplication and division. )
Can you do it? Who will talk about the solution to this problem? (Name the stage to explain the demonstration) 0.65×20 1
=0.65×(200+ 1)
=0.65×200+0.65
= 130+0.65
= 130.65
Step 6 practice:
0.78× 100.5 1.5× 102 1.2×2.5+×0.8×2.5
Students finish independently, and teachers patrol and coach students with difficulties. Name the board and perform in groups.
Third, use
Do it on pages 1 and 12: simply calculate the following questions.
0.034×0.5×0.6 102×0.45
2、
The picture on the right shows the playground plan of Hong Guang primary school.
Figure. The length and width in the figure are calculated by the following formula
Decrease by 1000.025m according to the actual length and width.
Double-sided painting. Seek the truth of this playground
International zone. 0.048 m
On the basis of careful examination, let the students talk about what they plan to do and their own ideas first. Give praise to students who can solve problems by simple methods, and then let them calculate independently and correct collectively.
Fourth, experience:
What did you gain today?
Verb (abbreviation of verb) homework p 13 page 4 questions.