Unit 3 Division of Fractions
Teaching content:
Understanding of 1 and reciprocal
2. Decimals
Step 3 solve the problem
Teaching material analysis:
This unit is to learn the understanding of reciprocal on the basis that students have mastered fractional multiplication; Fractional division and fractional division knowledge solve practical problems. The main contents include: the significance and calculation of fractional division; Solve the problem. Three-dimensional target:
Knowledge and skills:
1, let the students understand the meaning of reciprocal and find the reciprocal of a number.
2. Make students understand the meaning of fractional division, master the calculation rules of fractional division, and be skilled in calculation.
3. Enable students to solve the application problem of "knowing a fraction of a number". Find this number by equation or arithmetic, and further improve students' ability to solve application problems.
Process and method:
Hands-on operation, through intuitive understanding, enables students to understand integer divided by fraction, guides students to correctly summarize the calculation rules, and can correctly calculate by using the rules.
Emotions, attitudes and values:
Let students be further inspired by the dialectical materialism that things are interrelated. Teaching methods and learning methods:
Practice, independent exploration and cooperative exploration
Teaching emphases and difficulties:
The meaning and calculation method of dividing a number by a fraction will solve related problems with fractional division. Master the operation sequence of fractional elementary arithmetic, and be able to skillfully apply calculation rules to calculate.
Derivation of calculation rules for dividing a number by a fraction. Understanding of quantitative relationship in fractional division application problems. The total amount of work is expressed in the unit "1", and the meaning of work efficiency.
Chapter 2: The latest teaching plan of fractional division in grade 6 of 20xx People's Education Press.
Unit 3 Fractional Division
Unit teaching content: textbook 28-47 pages, understanding the reciprocal, meaning and calculation of fractional division and solving related practical problems.
Unit teaching objectives:
Knowledge and skills:
1. Make students understand the meaning of reciprocal and master the method of finding the reciprocal of a number.
2. Make students understand the significance of fractional division, understand and master the calculation method of fractional division, and calculate fractional division.
3. Let students solve some practical problems related to fractional division.
Process and method: Through observation and reasoning, cultivate the ability of reasonable reasoning and summary. Mastering the calculation method of fractional division can comprehensively apply the knowledge of fractional division to solve problems in real life.
Emotional attitude and values: enable students to understand the close relationship between mathematics and life, and understand and master mathematical ideas such as models, equations, and the combination of numbers and shapes.
Unit teaching material analysis: This unit is to learn fractional division on the basis that students have mastered the calculation method of fractional multiplication. Through the study of this unit, on the one hand, students have completed the learning task of addition, subtraction, multiplication and division of scores, systematically mastered the four operations of scores, and mastered the methods to solve related practical problems; On the other hand, it further deepens the understanding of the relationship between multiplication and division, recognizes the internal relationship between mathematical knowledge and methods, and provides more support for solving practical problems related to fractions; At the same time, it also lays a solid foundation for the later study of ratio, proportion and percentage. Key points of unit teaching: the significance and calculation method of fractional division and solving practical problems by division. Difficulties in unit teaching: exploration and understanding of the calculation method of fractional division.
Unit teaching measures: 1. Make full use of teaching materials to promote learning transfer. The textbook of this unit has made great efforts in revealing the internal relationship of relevant knowledge and providing analogical thinking materials. In teaching, we should make full use of these resources, activate students' existing knowledge and experience, guide students to make analogies and promote the positive transfer of learning. 2. Strengthen intuitive teaching, explore and understand the calculation method by combining practical operation and graphic language. 3. Provide rich problem situations and cultivate students' learning ability.
Understanding of reciprocity of the first kind
Teaching content: understanding of reciprocal (content on pages 28 and 29 of the textbook)
Teaching objectives:
Knowledge and skills: through observation, research, analogy and other mathematical activities, guide students to understand the meaning of reciprocal and summarize the methods of finding reciprocal.
Process and method: Through exploration and discovery activities, let students understand the meaning of reciprocal and master the method of finding reciprocal.
Emotional attitude and values: cultivate students' awareness of independent exploration and innovation through self-designed programs.
Teaching emphases and difficulties:
Key points: understand the meaning of reciprocal and master the method of finding reciprocal.
Difficulty: Find the reciprocal of the decimal with reciprocal meaning. .
Teaching preparation: courseware
Teaching process:
First, preview before class
Second, create a situation
1, Teacher: Let's play another word game. The teacher said, "Qin is my deskmate." What else can I say? Health: You can also say "it's Qin's deskmate." Teacher: Can the teacher understand that Qin and he are deskmates? Health: I was a little hesitant at first, and then I answered "yes". The blackboard writing is mutual. Students, our national language is so beautiful, in fact, there is such beauty in the mathematics kingdom, so we might as well give it a try. .
2. Reveal the topic. Today, we will learn such a number-reciprocal.
Third, independent inquiry.
1. Show the following exercises.
×=2 ×= 5×=× 12=
(1) Name the students to answer.
(2) What are the characteristics of students observing these formulas?
(3) Intra-group communication.
(4) Each group reports the communication.
(5) Teacher's summary: ① The product of these formulas is 1. The numerator and denominator in these formulas are reversed.
Blackboard: Like this, two numbers whose product is 1 are reciprocal.
Read the concept of reciprocity and understand the conditions of reciprocity.
3. Special numbers: 0 and 1. Blackboard: 0 has no reciprocal, and the reciprocal of 1 is itself.
Fourth, cooperation and exchanges.
1, find the reciprocal of a number' method:
We just know the concept of reciprocal, how to find the reciprocal of a number?
Example 1. Which two numbers are reciprocal?
How to find the reciprocal of a number?
×=
=
X = So, the reciprocal of is and the reciprocal of is.
(2) Induction: How to find the reciprocal of a number? Blackboard writing: numerator and denominator exchange positions.
Fifth, expand applications.
(1) Complete "Doing" on page 28 of the textbook. Students answer independently and teachers patrol.
(2) Complete exercise 6 1-5 on page 29 of the textbook.
Summary and evaluation of intransitive verbs
three
The Significance of Fractional Division in the Second Classroom
Teaching content: the significance of fractional division and the teaching goal of fractional division into integers (the content on page 30 of the textbook);
Knowledge and skills: 1. Make students experience the process of exploring the method of fractional division, and understand and master the calculation method of fractional division. 2. Can correctly calculate the score divided by integer questions. Process and method: Hands-on operation, through intuitive understanding, enables students to understand the division of fractions into integers, guides students to correctly summarize the calculation rules, and uses the rules to correctly calculate.
Emotional attitude and values: cultivate students' observation ability, comparative analysis ability and language expression ability, and improve their computing ability.
Teaching emphasis: understand the meaning of fractional division and master the calculation method of fractional division by integer. Teaching difficulty: master the calculation method of dividing score by integer.
Teaching preparation: courseware, a rectangular piece of paper.
Teaching process:
First, preview before class
Second, create a situation
Third, independent inquiry.
1, give an example of 1.
2, adapt to the conditions and problems, according to the division calculation.
3. Understand the significance of fractional division. The teacher asked: If a box of fruit weighing one kilogram is divided into five parts on average, how many kilograms is one part? How to calculate?
Students try to list formulas.
Guided observation: What is the relationship between these formulas? What kind of operation is fractional division? Does it have the same meaning as integer division?
4. Summarize the significance of fractional division.
4 58
Fourth, cooperation and exchanges.
1, fraction divided by integer.
(1) Give an example of 1. Guide students to analyze and show quantitative relations with charts.
The teacher asked: How much do you want each paper to be?
(2) Column calculation.
The teacher asked: What was the result? How did this result come about? The students in the group get a 10% discount, so do the math.
(3) clear your mind. Idea 1: divide the average into two parts, that is, divide four parts into two parts, each part is two parts, that is. Idea 2: Divide the average into two parts and find out how much each part costs.
(4) Summarize the calculation method of dividing fraction by integer. A fraction divided by an integer equals a fraction multiplied by the reciprocal of this number.
Fifth, expand applications.
1, consolidation exercise. Complete the "do" on page 30 of the textbook.
2. Fill in the blanks.
The meaning of (1) fractional division and integer division () are known () and () and the operation of finding ().
(2) Fraction divided by integer (except 0) equals integer fraction ().
(3)÷5=×()=( )
3. Calculate and check. 65 1 1 15÷3= ÷ 10= ÷ 1 1= ÷30= 1 128 13 1289894545 12 152545 1545
Summary and evaluation of intransitive verbs
1. What did we learn today? (The meaning of fractional division and the calculation rules of fractional division by integer)
five
The third part: the score division of the first volume of the sixth grade mathematics teaching plan published by People's Education Press.
[Unit teaching material analysis]: Based on students' knowledge of integer multiplication and division, solving simple equations and fractional multiplication, this unit learns the preliminary knowledge of fractional division and ratio. This knowledge lays a foundation for students to learn fractional division. Learning this unit will play a very good role in deepening students' understanding of calculation methods and improving their calculation ability. The content of the textbook includes: fractional division, problem solving, the application of ratio and proportion. This knowledge is an important foundation for students to further study. Through the study of this unit, on the one hand, students have basically completed the learning task of adding, subtracting and dividing fractions, and the system has mastered the four operations of fractions; On the other hand, I began to learn the preliminary knowledge of ratio, which provided the foundation for later learning percentage and proportion. These two achievements will play an important role in further research.
[Unit Teaching Objective]: 1. Make students feel the significance of fractional division in specific situations, master the calculation method of fractional division, and correctly calculate fractional division through oral or written calculation. 2. Let students use fractional division to solve practical problems and find the score of a given number. 3. Understand the meaning and basic nature of ratio, know the relationship between ratio, fraction and division, correctly find and simplify ratio, and use the relevant knowledge of ratio to solve practical problems.
4. Let students feel the value of learning mathematics in concrete and vivid situations.
[Key points of unit teaching]: 1, calculation of fractional division; 2. The solution of fractional division problem; 3. Understanding and application of the meaning and basic nature of ratio.
[Difficulties in Unit Teaching]: Understand the arithmetic of fractional division; Application of ratio.
first kind
Teaching content: Divide fractions by integers (example 1, example 2)
Teaching objectives:
1, to guide students to understand the meaning of fractional division and master the calculation method of fractional division with the help of existing experience in specific situations, and to correctly calculate fractional division of integers.
2. Guide students to actively participate, think independently, cooperate and communicate through inspiring problem scenarios and exploratory learning activities, and form computing skills.
3. Infiltrate the idea of transformation in teaching, so that students can fully feel the beauty and charm of transformation.
Teaching emphasis: 1, understand the meaning of fractional division; 2. Research on integer division algorithm.
Teaching difficulty: research on fractional divisibility algorithm.
Teaching preparation: teaching wall chart of example 1; A rectangular piece of paper is divided into five parts on average.
Teaching process:
First, create a scene import:
1, students, have you ever been shopping in the supermarket? What did you buy? Have you ever bought several of the same things? Can you give me an example? Give an example and ask the students to find the total price of the example with an expression. )
Second, the exploration of new knowledge:
(A) the significance of fractional division
1, give an example of the teaching wall chart of 1, let the students look at the picture to observe the meaning, say the export type and answer the meaning and how to arrange it.
2. Can the above question be adapted into the problem of division calculation? (Students think independently and answer questions orally, forming)
3、 100g=？ Kg, can you change the above question to kg? (Guide students to transform integer multiplication and division application problems into component multiplication and division application problems)
4. Guide students to observe and compare the problems of integer multiplication and division with those after rewriting, and analyze the problems of integer division and fractional division.
The connection and significance of fractional division.
5. Exercise: (Consolidate and deepen the understanding of meaning) Do it on page 28 of the textbook. Students practice independently and ask them to explain why they should fill in this form when correcting.
(2) Divide the score by an integer.
1, group learning activities:
Activity (1) Divide 4/5 of this paper into 2 parts equally. How much is each part of this rectangular paper?
Activity (2) Divide 4/5 of this piece of paper into 3 pieces on average. How much is each piece of this rectangular piece of paper?
[Activity Requirements] Finish independently first, and then communicate in the group: What laws have you found through origami operation and calculation? Do you have any questions to ask?
2. Report the learning results:
Activity 1 student a, divide 4/5 by 2, that is, divide 4 1/5 by 2, 1 is 2 1/5, that is, 2/5; The formula is: 4/5÷2=(4÷2)/5=2/5.
Student B, divide 4/5 into 2 parts, each part is 4/5 of 1/2, that is, 4/5×1/2; Expressed by the formula: 4/5×1/2 = 4/10 = 2/5;
Student C, I found that the numerator 4÷2 can be used when calculating 4/5÷2, and the denominator remains the same;
Ding, I found that dividing a fraction by an integer may be converted into multiplication, that is, multiplying the reciprocal of this integer;
Activity 2: Students A and 4 should be divided into three parts equally, but not directly. I first find the least common multiple of 4 and 3, divide 4 into 12, and then divide 12 into three parts on average. The formula can be expressed by 4/5÷3, and 4 is not divisible by 3. I don't know how to calculate this problem.
Student B, my division is the same as that of the previous students. The difference is that when I calculate 4/5÷3, I convert 4/5÷3 into 4/5× 1/3, because dividing 4/5 into 3 parts on average is to find out what 4/5 1/3 is.
Discussion:
1. From the origami experiment and calculation, how to find the calculation score divided by an integer?
2. Can an integer be 0?
Summary and consolidation: a fraction divided by an integer not equal to 0 equals a fraction multiplied by the reciprocal of the integer.
Third, consolidate and improve.
3. Divide 3/5 into 4 parts on average, and how much is each part; What number multiplied by 6 equals 3/20?
4. If A is a natural number not equal to 0, what is 1/3÷a? What is 1/a÷3? Can you use a specific figure to test the above results?
Fourth, homework exercises
Blackboard design:
Fractional division-divide a fraction by an integer.
Example: 1 weight of each box of fruit candy 100g, how many grams do three boxes weigh? Example 2 Divide 4/5 of a piece of paper into 2 parts, and each part is100× 3 = 300g →110× 3 = 3/10g.
Three boxes of fruit candy weigh 300g, how much g does each box weigh? 4/5÷2 =(4÷2)/5 = 2/5 4/5÷2 = 4/5× 1/2 = 2/5 300÷3 = 100g→3/65438+。 Which part of this paper?
300÷ 100=3 (box) → 3/10 ÷/kloc-0 = 3 (box) 4/5 ÷ 3 = 4/5× 1/3.
Dividing by an integer that is not equal to 0 is equal to multiplying the score by the reciprocal of the integer.
Second lesson
Teaching content: a number divided by a fraction (Example 3)
Teaching objectives:
1. Guide students to analyze and summarize the calculation law of dividing a number by a fraction by drawing a line segment.
2, can use the law, correctly and quickly calculate the division of fractions.
3. Cultivate students' abstract thinking ability.
4. Let students acquire knowledge by exploring knowledge, experience the joy of success and establish self-confidence in learning. Teaching focus:
Analyze and summarize the calculation law of dividing a number by a fraction.
Teaching difficulties:
Understand the arithmetic of dividing a number by a fraction.
Teaching process:
First, check the import.
1, calculation: 5/6 ÷103/5 ÷ 315/16 ÷ 2040/39 ÷ 26.
Say, how do you avoid mistakes in calculation? What should I pay attention to in calculation? )
2. The length of Shengli Road is1000m, and it took Dongdong 20 minutes to walk the whole distance. How many meters does Dongdong walk per minute on average?
(Answer independently and explain the basis for solving the problem)
3.2/3 hours has () 1/3 hours, 1 hour has () 1/3 hours.
Second, the exploration of new knowledge:
1, teaching example 3: Xiaoming walked 2 kilometers in 2/3 hours, and Xiaohong walked 5/6 kilometers in 5/ 12 hours. Who walks faster? Teacher: What is known?
Health: Xiaoming and Xiaohong's respective time and corresponding distance are known.
Teacher: What's the problem?
Health: Who can walk faster?
Teacher: Who can walk faster? Just comparing what?
Health: Just compare who is faster.
Teacher: Can you list the formulas according to the meaning of the question?
Health: 2÷2/3 5/6÷5/ 12
2. Research on the calculation method of division with divisor as fraction;
On guiding students to draw line segments
：
Teacher: How many are there in two thirds 1/3? Walked 2 kilometers in 2/3 hours. Can you find out how many kilometers I walked 1/3 hours?
Health: There are two in 2/3 1/3. Find out how many kilometers you walked in 1/3 hours, and you can use 2km2, which is 2km2×1/2; Teacher: What exactly does 1km from 2 km÷2 mean? Which segment on the line graph is it?
Health: ellipsis
Teacher: 1 hour. How many 1/3 hours? Can you find out how many kilometers 1 hour has traveled?
Health: 2× 1/2×3=2×3/2=3 km.
Instruct students to observe: 2÷2/3=2× 1/2×3=2×3/2=3 (hint: observe the step size of 2÷2/3=2×3/2) Teacher: What is the division converted into to calculate? Divided by 2/3=?
Student: The method of converting division into calculation. Divided by 2/3 equals 3/2.
Teacher: Can you describe the calculation method of integer divided by fraction in your own language?
There are narratives in the language, which can be expressed by letters. As long as it is correct, the students' conclusions will be affirmed. )
Teacher: Please follow the summation formula above. How to convert division into multiplication for calculation? Can you tell the main points of transformation? Health: 1, the dividend has not changed; 2. Divide by the symbol and multiply by the symbol; 3. The divisor becomes its reciprocal.
3. Students independently calculate 5/6÷5/ 12 to modify and merge books.
：
4. Ask students to test and answer according to the meaning of fractional division.
Third, consolidate and improve:
On pages 1 and 3 1, do the last two small questions of question 1 and question 2.
(After completing the 1 question, ask students to read each formula completely, and then complete the second question, ask students to write out the calculation process. )
2. Exercise 8, the last four small questions of Question 2.
After the students finish this problem, the teacher instructs the slow-thinking students to calculate the product of multiplication formula first, and then find out the relationship between the two problems.
Fourth, the class summary:
1 What did we learn together today?
Can you say the main content of today in complete sentences?
What do you think you should do to avoid mistakes when you finish your homework?
5. Homework exercises: Exercise 8, Questions 3 and 4. (Question 3: After the students finish the questions, guide the students to change 4/5 of the questions into decimals and verify them by fractional division. )
Six. Teaching reflection:
The third category
Exercise content: Calculation of fractional division
Practice goal:
1 Calculate the fractional division correctly and skillfully on the basis of understanding the fractional division operation;
Use the learned knowledge of fractional division to solve the corresponding practical problems.
Practice process:
First, the basic knowledge exercise:
1, calculation:
⑴2/ 13÷2 8/9÷43/ 10÷3 5/ 1 1÷522/23÷2
⑵3/ 10÷223/24÷26 17/2 1÷5 18/9÷7 13/ 15÷4
Students calculate independently, and teachers patrol and guide. When reviewing, let the students talk about how to calculate.
By calculating the following questions, please think about it. What are the similarities between division with integer divisor and division with fraction divisor?
Guide the students to sum up: dividing by a number that is not equal to 0 is equal to the reciprocal of the number H.
Second, in-depth practice.
1. Calculate the following problems and compare their calculation methods.
5/6+2/35/6-2/35/6×2/35/6÷2/3
2、
Ask the students to discuss in groups after calculation: What laws have you found? Please tell us the rules you completely found. According to the students' answers, the teacher wrote the following on the blackboard:
When a number is divided by a number less than 1, the quotient is greater than the dividend;
When a number is divided by 1, the quotient is equal to the dividend;
When a number is divided by a number greater than 1, the quotient is less than the dividend.
Third, solve the problem:
Exercise 8, questions 7 to 8.
Question 7 is answered by the students independently.
When answering question 8, remind the students that they need a unified unit first.
Summarize the * * * characteristics of the three problems: all are to find out how many other quantities a quantity contains, and all are calculated by division.
Fourth, homework exercises:
Questions 5 and 9+0 and 33 on page 65438.
2. A store packed 120kg fruit candy in plastic bags. If each bag is 1/4kg, how many bags can these fruit candies be packed?
Five, teaching reflection:
the fourth lesson
Teaching content: Example 4, Exercise 9, Question 1-4.
Teaching objectives:
1, correctly answer four mixed questions of fractions calculated in two or three steps.
2. Use what you have learned to solve the problem of simple score application in two-step calculation.
3. Cultivate and train students' ability to think, analyze and answer questions.
Teaching focus:
1 and the correct calculation of two or three steps.
2. Cultivate and train students' ability to solve problems by using what they have learned.
Teaching process:
One: Review and pave the way