The fifth grade elementary school mathematics "fraction and division" courseware one.
Teaching content:
Page 49~50 and exercise 12: 1~ 12.
Teaching objectives:
1. Knowledge and ability: The quotient of dividing two numbers is expressed by a fraction, and it is clear that the quotient of dividing two numbers can be expressed by a fraction.
2. Process and method: Through observation and inquiry, we can understand the relationship between score and division and experience the inquiry process of the relationship between score and division.
3. Emotion, attitude and values: Stimulate students' interest in learning by observing, exploring and infiltrating dialectical thinking.
Teaching focus:
Master the relationship between fraction and division, and use fraction to represent the quotient of division of two numbers.
Teaching difficulties:
Understand that you can divide two numbers by fractions.
Teaching aid preparation:
courseware
Teaching process:
First, check the import.
1. What does this mean? What is its decimal unit? How many decimal units does it have?
2. Cut a wire into three sections on average, and the length of each section is a fraction of this wire. Who is the unit "1"?
3. Introduction: What is the quotient of 5 divided by 9? Blackboard writing: 5÷9
If the quotient is not expressed in decimals, is there any other way? You can solve this problem by learning the relationship between fraction and division. Fraction and division.
Second, the new teaching
1. Teaching examples 1: Show the topic.
(1) Lists the formulas. (Blackboard: 1÷3=)
(2) Discussion: What is the result of dividing 1 by 3? what do you think?
(3) The teacher draws a schematic diagram. Divide a cake into three parts, one of which should be cake, that is, "1".
Blackboard: 1÷3= 1/3 (pieces)
2. Teaching Example 2: Show the theme
(1) Hands-on operation. Take out three circular pieces of paper with the same size as three cakes and divide them into four cakes with scissors.
(2) The teacher summed up several differences in oral methods and the results of each assignment.
(3) Summary: As can be seen from the above operation, the three cakes are divided into four parts on average. No matter how you divide it, each part is three cakes, that is, three cakes. Three cakes add up to 1 cake, which is a cake. Therefore, 3÷4=3/4 (block).
In this way, not only can it be understood that 1 cake (unit "1") is divided into four parts on average, indicating such three parts, but also the whole consisting of three cakes (unit "1") is divided into four parts on average, indicating such 1 part.
The students discuss the meaning of this expression with each other.
3. The relationship between teaching scores and division.
(1) observation 1÷3=3÷4= these two formulas.
Think about it.
① When two (non-0) natural numbers are divided, what number can be used to represent it when the integer quotient cannot be obtained?
(2) When the quotient is expressed by fractions, what are the dividend and divisor in the division formula?
What is the relationship between fraction and division?
(2) Summarize three points
The (1) score can represent the quotient of division.
② When the quotient of division is expressed, the divisor should be used as the denominator and the dividend as the numerator.
The dividend in division is equivalent to the numerator in the fraction, and the divisor is equivalent to the denominator in the fraction (emphasizing the word "equivalent"). The relationship between fraction and division can be expressed in the following form.
(3) If A stands for dividend and B stands for divisor, how to express the relationship between fraction and division?
Blackboard: a÷b=a/b(b≠0)
(4) Can b here be 0? Why?
Clear: When two integers are divided, the quotient can be expressed by a fraction. Conversely, can a fraction be regarded as the division of two integers? (Yes, the numerator of a fraction is equivalent to the dividend in division, and the denominator is equivalent to the divisor. )
(5) Is there a difference between fraction and division? What is the difference?
Fraction is a number, but it can also be regarded as the division of two numbers. Division is an operation.
4. Teaching Example 3: Show the theme
(1) Lists the formulas. Blackboard: 7÷ 10
(2) How to calculate? 7÷ 10=
Third, consolidate practice.
1. Do: do it independently and modify it collectively.
2. Exercise 12, questions 1 and 2: Complete independently. When revising, talk about how to calculate.
Questions 3 and 4: Write it in a book and revise it collectively.
Questions 5 and 6: Complete independently. When revising, talk about your own ideas.
3. Homework: Exercise 12 7- 1 1, select 12.
Fourth, class summary.
What did you learn and gain in this class?
Blackboard design:
Fraction and division
Example 1: 1 ÷ 3 = 1/3 (pieces)
Example 2: 3 ÷ 4 = 3/4 (each)
Example 3: 7 ÷ 10 = 7/ 10
Grade five mathematics "fraction and division" courseware II
Teaching objectives:
1. By observing, comparing, discovering and understanding the relationship between score and division in a specific situation, the commercial score of dividing two numbers is expressed.
2. Using the relationship between score and division, explore the method of mutual transformation between false score and score, preliminarily understand the algorithm of mutual transformation between score and score, and carry out mutual transformation correctly.
Teaching focus:
1, grasp the relationship between fraction and division, and express the quotient of division with fraction.
2. Using the relationship between fraction and division, we can correctly realize the mutual transformation between false fraction and fraction.
Teaching methods:
In order to achieve the above-mentioned teaching objectives, highlight key points and break through difficulties, I mainly adopt teaching methods such as creating situational method, guiding inquiry and discovery induction. Give appropriate inspiration, guidance and inspiration when exploring the essential laws of knowledge, and help students complete the process of exploring knowledge.
Teaching process:
First, the introduction of situations leads to new knowledge.
The situation of courseware playing "dividing cakes" Students observe and say the corresponding division formula, and express the number of blocks each person gets with scores. This link follows the familiar situation of sharing cakes in last class, and leads to the protagonists of "division" and "fraction".
Second, explore and discover, and summarize cognition.
1, the relationship between fraction and division. At this time, the teacher will develop the students' thinking of sharing cakes in time and practice quickly.
(1). Divide cake A into 8 pieces on average. How many pieces per piece?
(2) Divide the cake A into b blocks on average. How many pieces per piece?
Students write the division formula first, and then express the result with fractions. The teacher writes on the blackboard.
12 =1/2.
9÷4=9/4
a \8 = a/8。
A÷b=a/b block
Through this exercise, the transition from individual to general thinking is completed, which creates conditions for fully discovering the relationship between fraction and division.
2. Induce cognition and clarify the relationship.
(1), students observe and think: What is the relationship between fraction and division?
(2) Report the survey results.
Blackboard writing: divided by dividing line =
(3) Guiding ideology: In division, the divisor cannot be 0, so what should be specified in the score?
The denominator of student discussion cannot be 0.
Blackboard: (divisor is not 0).
3. Try to use letters.
4. Practice in time.
2÷3=、8÷7=、 16÷5=、 10÷ 12=
5/6=()÷()、 13/ 15=()÷()
12/7=()÷()、 100/6=()÷()
(2) False scores and scored scores are exchanged.
How to turn 7/3 into a fraction? How to turn 2 into a false score?
1. Students study in groups. Teachers show warm tips to guide students to cooperate in learning.
2. Test the effect of cooperative learning.
3. The teacher makes targeted comments.
4. Practice in time.
Question 2 on page 40 of the textbook. This link guides students to explore the method of interaction between false scores and scores, and adopts the form of learning and practicing, so that knowledge can be consolidated in time.
Fourth, the class summarizes and the students talk about the gains.
Students summarize the knowledge points of this lesson and form a complete understanding of this lesson.
Blackboard design:
The blackboard writing is the epitome of a class, and my blackboard writing is designed by grasping the relationship between the teaching key scores and division in this class.
The third part of the courseware of "fraction and division" in fifth grade primary school mathematics
Teaching objectives:
1. Let the students understand that the quotient of the division of two integers can be expressed by fractions.
2. Make students master the relationship between fractions and division.
3. Cultivate students' awareness of application.
Teaching focus:
1. Understand the relationship between inductive fraction and division.
2. Understand the meaning of fractions with the meaning of division.
Teaching preparation:
Courseware and CDs
Teaching process:
First, review the introduction.
Teacher: Students, last class we learned about the generation and significance of scores. When measuring, dividing things or calculating, we often can't get accurate integer results. At this time, we often use scores to express it. So what is a score? (Students answer the meaning of scores)
Courseware shows exercises.
(1) Cut a wire into three sections on average. How long is each part? Who does this question take as the unit "1"?
(2) Divide the nine bananas into three parts equally. How much are these bananas for each part? How many are there in each serving?
(3) Distribute 1 packet of biscuits to two people equally, and each person will get (1/2) packets.
Introduction: There are many close relationships between knowledge and knowledge. In this lesson, let's learn the relationship between fraction and division. (blackboard writing topic)
Second, explore new knowledge.
Courseware demonstration exercise
(1) Divide 18 cake among three people equally. How many cakes does everyone have? (column calculation)
(2) Divide the six cakes among three people equally. How many cakes does everyone have? (column calculation)
Teacher: These two problems are solved by division. Calculation is to divide the whole into three parts on average and figure out how much each part is. Let's look at this problem again.
Example 1: Divide 1 cake among three people. How many cakes does everyone have?
Teacher: How should this question be formulated? (Student formula, teacher's blackboard writing: 1÷3)
Teacher: What does 1÷3 mean?
Health: 1÷3 means to give a cake to three people equally and ask how much one person gets.
Teacher: OK, this question is also a question of dividing a whole into three parts on average. How much is one part? It is also a question of average score, so division is also used. So, do you know how much each person has?
Health: 1/3. (Teacher writes on the blackboard)
Teacher: Does everyone think so? Who can tell me what you think?
The teacher shows the courseware, and the students demonstrate while talking: We regard this circle as this cake, and divide it into three parts on average, and each person gets one of them, which is 1/3 of this cake.
Teacher: Look, each copy is 1/3. How many cakes does everyone get?
Health: 1/3.
Teacher: In division, we can't get the exact integer result, so we can express it by fractions. So everyone's share of the cake is one.
Teacher's Note: 1÷3 means that a cake is distributed to three people equally. How many cakes do you want each person to get? We know by demonstration that everyone gets 1/3. So the result of 1÷3 is 1/3. (Write on the blackboard "=") (Read the formula together)
Teacher: A cake is divided equally among three people. We know that everyone gets 1/3. Now we are going to share some other projects. Would you? (Courseware gives example 2)
Read the title by name
Teacher: Who can list the formulas?
Health: 3÷4 (teacher writes on the blackboard)
Teacher: This problem is to divide a whole into four parts on average, and how much each part is also calculated by division. How many moon cakes does everyone get? The teacher prepared school tools (3 CDs) for each group. Now, please share one point with your school tools and see how many moon cakes each person gets.
Group operation, teacher patrol guidance.
Teacher: Everyone has reached a conclusion. Which group of students would like to tell you what your group's conclusion is?
(The group will report and demonstrate)
1 team report: our team scored one point each. We divide a circle into four parts, and each person gets 1, which is 1/4.
Teacher: Can it be expressed in a formula?
Group 1: 1 ÷ 4 = 1/4.
Teacher: Good. Please continue to report.
1 group: Next, we divide the other two circles in the same way. Finally, everyone got three pieces 1/4, which is 3/4.
Teacher: Do you think their method is ok? (Yes) Let's recall their methods again. (The teacher tells the method and demonstrates the courseware. )
Teacher: Is there any difference in this method?
The second group report: our group put three circles together and divided them into four on average. Everyone got 1 and put them together to get 3/4 pieces.
Teacher: (Courseware demonstration method 2) This method is to put three moon cakes together, regard them as a whole, divide them into four parts on average, and each person gets one, that is, 1/4 of the three moon cakes. Together, it is 3/4.
Teacher: Through everyone's operation, we know that everyone got 3/4 pieces of moon cakes (3/4 pieces of blackboard writing). Some students are divided piece by piece, and some students are divided into three pieces together, but these two different methods get 3/4 pieces, which means that the result of 3/4 is 3/4.
Teacher: Please have a look. What are the results of these two division formulas today? Please think about it. What is the relationship between fraction and division?
Student group discussion
Health: We find that the dividend is the numerator and the divisor is the denominator.
Teacher: Can you try to express it?
Student: Divider = Divider/Divider (blackboard writing)
Teacher: If A is the dividend and B is the divisor, can letters be used to indicate the relationship between fraction and division?
Health 1: a ÷ b = a/b (blackboard writing)
Health 2: Teacher, I think we should also write b≠0.
Teacher: Why b≠0?
Student: Because B stands for divisor, the divisor cannot be 0.
Student: The denominator of the score cannot be equal to 0.
Teacher: Good. Through observation and thinking, we know that there is such a relationship between fraction and division (the relationship between fraction and division)
Teacher: We know that when two integers are divided, the quotient can be expressed by a fraction. On the other hand, can fractions represent the division of two integers?
Students observe the formula and think.
Health: Yes. For example, 3/4=3÷4.
Courseware presentation and simultaneous reading: when two integers are divided, quotient can be expressed by fraction, divisor should use denominator, and dividend should use numerator. Conversely, a fraction can also be regarded as the division of two numbers. The numerator of a fraction is equivalent to the dividend in division, and the denominator is equivalent to the divisor.
The fractional line is equivalent to division.
Teacher: We already know the relationship between fraction and division through study. What's the difference between fraction and division?
Please observe the formula on the blackboard and discuss it with your classmates.
Students report, the teacher summarizes: division is the same operation as addition, subtraction, multiplication and division we have learned; A fraction is a number, and a fraction can also represent the division of two numbers.
Third, consolidate the practice.
1. Use fractions to express the quotient of the following formula.
7÷ 13=、3÷ 1 1=、8÷5=
9÷ 16=、m÷n=
have a try
()÷7=4/7、 1÷()= 1/3
7/9=()÷9、5/8=()÷()
3. Put 1kg raisins in two bags on average. How much does each bag weigh? Three packs on average?
4. Fill in the blanks (exercise 12, question 3)
5. Cut the 5m-long rope into 8 sections, each section is (5/8) m long and each section is (1/8).
Fourth, the class summary