Teaching purpose: 1. Make students understand the generation and significance of fractions, the denominator and numerator of fractions, and the characteristics of fractional units, so as to read and write fractions correctly.
2. Cultivate students' abstract generalization ability.
3. Feel the view that "knowledge comes from practice and serves practice".
Emphasis and difficulty in teaching: understanding the meaning of fractions.
Teaching process:
First, reveal the topic.
1. Question: (1) Divide six apples equally to the second child. How much per person? (3 per person)
(2) Divide 1 apple to two children equally. How much does each child get? Everyone gets half of this apple.
2. Assign a student to measure the length of the blackboard with a ruler of 1 meter. (longer than 3m, shorter than 4m)
Step 3 reveal the topic
In actual production and life, people often can't get integer results when measuring and calculating, and in this case, scores are produced. What exactly is a score? In this lesson, we will learn the meaning of fractions.
Second, the new curriculum teaching
1. Point out to students: We have learned that dividing an object or a unit of measurement into several parts on average is called a score. For example:
(1) Show the moon cake map. Question: Divide 1 cake into two parts equally. How much is each part?
(2) Show a square diagram. Question: How to divide this square piece of paper? How many shares did you get? each
(3) Show the line graph and ask questions: divide a line segment into five parts on average. How much part of this line segment is this 1 part? How about making four copies like this?
If the length of 1 decimeter is divided into 10 parts, what is the score of this 1 part? seven
2. Further understand the unit "1".
All of the above regards an object or a unit of measurement as a whole, and we can also regard many objects as a whole, such as four apples, a batch of toys, a class of students and so on. For example:
(1) Show the picture of apple on page 86 of the textbook. Question: Divide four apples into four parts equally. How much is an apple?
(2) Show the panda map. Question: Take six panda toys as a whole and divide them into three parts on average. What is a part of the whole?
(3) Exercise: Say how many parts in the picture below are colored.
(4) Guide the students to sum up: All of the above are to regard an object as a whole and divide it into several parts on average, indicating that such one or several parts can also be expressed by scores.
3. Reveal the meaning of the score.
(1) Observe the blackboard writing formed in the above teaching process.
Tell students that an object, a unit of measurement or a whole composed of many objects can be represented by the natural number 1, which we usually call the unit "1". (blackboard writing: unit "1")
(2) feedback.
① In the above picture, what is regarded as the unit "1" respectively?
③ Discussion: What is a score?
(3) Summarize and write on the blackboard. Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction.
4. Exercise 18, question 1, 2, 3.
5. Name of each part of the teaching score and the unit of the score. Reading and writing scores.
(1) The teacher writes a few scores at will and asks the students to tell each part of the score.
(2) Read the last paragraph on page 86 of the textbook and think: What do the denominator and numerator in a fraction mean? (Name and answer)
(3) Understand the decimal unit and get a preliminary understanding of its characteristics.
Exercise:
(4) Think about it: What are the methods of reading and writing scores?
Third, consolidate the practice.
Fourth, class summary.
1. What is a score? How to understand the unit "1"?
2. What is a decimal unit? What are the characteristics of decimal units?
Verb (abbreviation for verb) class assignment
Do it on page 87.
Six, thinking practice
Fill in the appropriate fraction in the brackets in the figure below, indicating that each small number is a fraction of a big square.
Lesson 2 (42 in total)
Teaching content: the application of fractional meaning-pages 87-88 of the textbook, such as 1, do a problem and exercise 18, questions 4-7 and 8*.
Teaching purpose: 1. Make students further understand the meaning and unit of the score and apply it correctly. Learn to express fractions with points on a straight line. Can relate the meaning of the score, answer correctly and find out the score between one number and another.
2. Further cultivate students' abstract generalization ability.
3. The idea of combining infiltration number with shape.
Emphasis and difficulty in teaching: understanding the meaning of fractions.
Teaching process:
First, review preparation
1. Use fractions to represent the shaded parts in the chart.
2. Oral answer: What is a score? How to understand the unit "1"?
3. Exercise 18, questions 5 and 6.
4. Fill in the blanks.
Second, reveal the topic
Announce the learning content and learning objectives. Application of fractional meaning.
Third, the new teaching curriculum
1. Understand that points on a straight line represent fractions.
Fractions are also numbers, and can also be expressed by points on a straight line (number axis).
(1) Understand the method of expressing fractions by points on a straight line.
① Draw a horizontal straight line, and draw equidistant lines on the straight line to indicate 0, 1, 2.
② Divide line segments according to denominator. If the denominator is 4, divide the unit "1" into 4 parts on average.
What to draw first and how to draw it?
② How many parts should the interval from 0 to 1 be divided? What if the denominator is 8? The denominator is 10?
According to the students' answers, the teacher wrote on the blackboard:
What score does integral represent?
(3) What should I do if I want to represent a fraction with the denominator of 10 on this straight line?
What is the score represented by the seventh point between 0 and 1 on this straight line?
2. practice.
(1) The second question of "doing" at the bottom of page 87.
3. Teaching examples 1.
(1) Read the questions by name to help students understand the meaning of the questions.
(2) Show the discussion questions and discuss them at the same table.
① What is the unit "1" in this question?
② 1 person accounts for a fraction of the whole?
(3) How many students are there in the class?
(3) Report the discussion results and answer the questions on the blackboard.
(4) Summarize the analysis ideas. When answering such questions, it is generally necessary to find out what the unit "1" is according to the meaning of the fraction, that is, the denominator is divided into several parts on average, where 1 is a decimal unit, and then look at how many such decimal units are, that is, the fraction.
4. practice.
Page 88 "Do it".
Fourth, consolidate practice.
1. The question "Do it" on page 87 1.
2. Use points on a straight line to represent the following scores.
There is a batch of flour in the canteen. After eating 45 bags, there are 28 bags left. What percentage of this batch of flour have you eaten? How much is left?
Verb (abbreviation of verb) course summary
1. What's the way to express a fraction with a point on a straight line?
2. Oral answer: What is the basis for finding the score that one number is another number? How to think when solving problems?
Classroom assignment of intransitive verbs
Exercise 18 questions 4 and 7.
Seven, thinking practice
1. Exercise 18, question 8*.
2. What is the percentage of shadows in the following picture?
Lesson 3 (43 in total)
Teaching content: the relationship between fractions and division-textbook page 90 -9 1 example 2, example 3, do a problem and practice 19 1-3.
Teaching purpose: 1. Make students correctly understand and master the relationship between fraction and division, and use fraction to represent the quotient of dividing two numbers.
2. Cultivate students' logical reasoning ability.
3. Infiltrate dialectical thinking and stimulate interest in learning.
Emphasis and difficulty in teaching: understanding and mastering the relationship between fraction and division.
Teaching process:
First, review preparation
1.
2. calculation.
( 1)5÷8 = (2)4÷9 =
Second, reveal the topic
We know that when calculating integer division, we often encounter infinite division or can't get integer quotient. With the score, we can solve this problem. In this lesson, we will learn how to express the quotient of division with fractions and understand the relationship between fractions and division. (blackboard writing topic)
Third, the new teaching curriculum
1. Teaching Example 2.
(1) After reading the questions, instruct the students to list the formulas according to the meaning of integer division. Blackboard writing:
1÷3 =
(2) Discussion: What is the result of dividing 1 by 3? what do you think?
(3) Teachers draw a schematic diagram of line segments to help students understand.
(3) write back.
2. Teaching example 3.
(1) After reading the questions, guide the students to list the formulas: 3÷4 =.
(2) Instruct students to operate: Take out three circular pieces of paper with the same size, regard them as three cakes, and divide them into four cakes with scissors.
(3) Ask several students to dictate the main points and the results of each point, and the teacher will summarize several different points. And display:
(4) induction. From the above operation demonstration, we can know that the three cakes are divided into four parts on average, and there is no
Displaying this number of three servings can also be considered as dividing the whole consisting of three cakes (unit "1") into four servings on average, indicating this number of servings.
3. Understand the relationship between fraction and division.
① When two natural numbers (except 0) are divided, what number is used to represent them when the integer quotient cannot be obtained?
② What are the dividend and divisor in the division formula when the quotient is expressed by fractions?
What is the relationship between fraction and division?
(2) Teachers' summary and students' speeches can be summarized as follows:
① Fractions can represent the quotient of integer division;
② When the quotient of integer 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. (Emphasize the word "equality")
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?
(4) think about it: can b here be 0? Why?
Inspire students to say that in integer division, the divisor cannot be zero, and the denominator in the fraction cannot be zero, so here b≠0.
(5) Think again: Is there a difference between fraction and division? What is the difference?
Emphasize that a fraction is a number, but it can also be regarded as the division of two numbers. Division is an action.
4. Students read textbooks, ask questions and ask difficult questions.
Fourth, consolidate practice.
1.9 1 "Do it" in the middle of the page.
2. Answer orally.
3. Column calculation.
(1) Distribute 3 tons of chemical fertilizer to 5 villages on average. How many tons of chemical fertilizer will each village get? (expressed in fractions)
(2) Xiaoming walked in 20 minutes 1 km. How many kilometers does each branch walk on average? (expressed in fractions)
Verb (abbreviation of verb) course summary
Guide the students to review the whole class, talk about what they have learned, summarize it by themselves, and the teacher will supplement it.
Classroom assignment of intransitive verbs
Exercise 19 question 1-3.
Seven, thinking practice
Fill in the appropriate numbers in the brackets.
Lesson 4 (44 in total)
Teaching content: the application of the relationship between fraction and division-textbook page 965438 +0-92 cases 4, case 5, do a problem, practice 19 4-7 and 8*.
Teaching purpose: 1. Further understand the relationship between fraction and division, and apply this relationship to solve related practical problems.
2. Cultivate students' ability of migration and analogy.
3. Know that "things can be transformed into each other under certain conditions".
Emphasis and difficulty in teaching: finding the application problem that one number is the fraction of another number.
Teaching process:
First, review preparation
1. Oral answer:
When 30 decimeters = () meters 180 points = ()
After the exercise, guide the students to review the method of rewriting the name of the lower-level unit into the name of the higher-level unit.
2. Say: What is the relationship between fraction and division?
3. The quotient of the following formula is expressed by a fraction.
(1) 7 ÷ 9 = (2) 4 ÷ 7 = (3) 8 ÷15 = (4) 5 tons ÷8 tons =
Second, reveal the topic
This lesson is about the application of the relationship between fraction and division. (blackboard writing topic)
Third, the new teaching curriculum
1. Teaching example 4.
(1) Example 4, review questions.
(2) Question: According to the method of rewriting the low-level company name into the high-level company name, how should these two questions be calculated?
How to express the quotient when dividing two numbers can't get the integer quotient?
Let all the students try to practice.
(3) collective modification. Ask the students to talk about their thoughts during the review.
(4) What are the similarities and differences between Comparative Example 4 and the review question 1?
It is emphasized that when the integer quotient cannot be obtained by dividing two numbers, the result can be expressed by a fraction.
2. practice.
"Do it" at the bottom of 9 1 page.
3. Teaching example 5.
(1) Show the review questions on page 98 of the textbook for students to answer independently.
When revising collectively, inspire students to analyze: this question compares who with whom, and the number of chickens is several times that of ducks. What is the standard and how to calculate it? What is the formula?
Name of board: 30÷ 10 = 3
A: There are three times as many chickens as ducks.
(2) Take Example 5 and read the questions, encourage students to think from different angles, and organize students to discuss problem-solving methods.
After the discussion between teachers and students, there are two main methods to evaluate:
① Start with the meaning of the score. The number of geese is only a fraction of that of ducks, that is, 7 is only a fraction of 10. Take 10 as a whole, and divide it into 10 blocks on average, with 7 blocks each.
② Start with multiple relationships. The number of geese raised is a fraction of that of ducks, which is based on the number of ducks.
(3) Compare the similarities and differences between the review questions and Example 5.
By comparison, students can see that finding a number as a fraction of another number and finding a number as a multiple of another number are all calculated by division, and both are based on standard numbers as divisors. The obtained quotient represents the relationship between two numbers, and neither of them can be marked by the unit name. The difference is that the previous question is to find a number that is several times that of another number, and the quotient obtained is a number greater than 1. The following problem is to find the fraction of one number to another, and the quotient obtained is a number less than 1.
4. practice.
Page 92 "Do it".
Fourth, consolidate practice.
1. Fill in the appropriate score in the brackets.
8 cm = () m 146 kg = () ton
23: 00 = () days 4 1 square decimeter = () square meters
67 square meters = () hectares 37 cubic centimeters = () cubic decimeter.
2. There are 25 girls in Class Five (1), 4 more than boys.
(1) What percentage of boys are in the class?
What percentage of girls are in this class?
(3) Compared with the number of girls, what is the number of boys?
Verb (abbreviation of verb) course summary
1. Rewrite the low-level company name number to the high-level company name number. How to express it when the integer quotient cannot be obtained?
2. What is the solution to the application problem that one number is a fraction of another number?
Classroom assignment of intransitive verbs
Exercise 19 questions 4-7.
Seven, thinking practice
Exercise 19 question 8* and thinking questions.
Lesson 5 (45 in total)
Teaching content: comparison of scores-textbook page 94-95, Example 6 and Example 7, Do a problem, Exercise 20 1-4.
Teaching purpose: 1. The sizes of two fractions with the same denominator or the same numerator will be compared.
2. Further deepen the understanding of the score.
3. Cultivate students' ability to observe, compare and summarize.
4. Cultivate students' judgment and reasoning ability.
5. Guide students to explore the internal relationship between knowledge and infiltrate dialectical materialism.
Teaching emphasis and difficulty: understanding and mastering the comparison method of two scores. Understand and master the comparison method of two fractions of the same molecule.
Teaching process:
First, bedding pregnancy (microcomputer or projection display)
1. oral calculation: (one person operates in front, and the other students operate in groups)
1.53 - 0.7 = 0.75÷ 15 = 0.4×0.8 = 48÷0.0 1 = 38+6.03 =
4×0.25 = 12÷0.4 = 40×5.2 = 9.8÷ 1.4 = 70÷500 =
0.48÷ 120 = 1.5-0.06 = 0. 15×60 = 0.09÷3 = 1. 125×8 =
2. Students look at the questions and answer:
(1) Divide a cake into four parts on average, and each part belongs to it ()
Second, explore new knowledge.
1. Introduction to the new lesson: Students have a good grasp of the meaning and unit of scores, so how to compare scores? Today, we are going to learn the comparison of scores. (Comparison of blackboard writing scores)
2. Teaching example 6.
(1) Question: Compare the two scores of the following groups.
Hmm. How interesting
(2) Compare the first two scores.
(3) compare the size of the second group of two scores:
① Draw the line segment on the right of Example 6:
(4) Group discussion Example 6 What are the similarities between the scores of the two groups? How to compare their sizes? Guide the students to sum up: the denominator of the two fractions is the same, that is, the units of the fractions are the same. For two fractions with the same denominator, the fraction with larger numerator is larger.
[On the basis of students' observation and discussion, let the students summarize themselves, let the students participate in the whole process of knowledge formation, and give full play to the main role of the students. ]
(5) Feedback exercise: 94 pages of "doing".
Compare the size of two scores in the following groups.
One person does it on the demonstration platform, and the other students fill it in the notebook.
(2) Collective correction and talking about the thinking process of judgment.
3. Teaching examples 7
(1) Question: Compare the two scores of the following groups.
(2) Compare the first two scores.
① Drawing: Observe how many parts the circle is divided into by two pictures.
② Move the shadow part of two overlapping pictures. Students observe and discuss: What do you find? What is the conclusion?
With the help of advanced teaching instruments, the teaching difficulties are skillfully broken through, and the teaching concept of taking students as the main body is fully embodied.
(3) Compare the sizes of the two scores in the second group.
1 plot:
Who are the older and younger students? Why?
(4) Summary:
(1) Observe the two groups of scores in Example 7. What conclusion do you draw?
Guide the students to make it clear that the numerator of the two groups of scores is the same, but the denominator is different. For two fractions with the same numerator, the fraction with smaller denominator is larger. (blackboard writing)
(5) Feedback exercise: 95 pages of "doing".
Compare the size of two scores in the following groups.
① Students fill in books:
(2) The group exchanges the thinking process of correcting and talking about judgment.
③ Focus on the communication and thinking process.
Third, consolidate development.
1. Recall the comparison method of two scores.
2. Exercise 20 questions 1. Write the score in □ according to the picture, and fill in ">" or ".
3. Exercise 20, question 3. Use fractions to represent the quotient of two divisors in the following groups, and then compare their sizes. (Give an oral answer and explain the reasons)
2÷5 and 4÷5 4÷7 and 4÷8 5÷ 16 and 5÷ 12
4. Ask each other questions in groups of four and compare them.
Fourth, the class summarizes.
What skills have you learned in this course?
Verb (abbreviation for verb) assigns homework.
Exercise 20, questions 2 (students fill in the book by themselves) and 4.
Lesson 6 (46 in total)
Teaching content: comprehensive exercises-Exercise 25- 10 and1*, 12* on page 96-97 of the textbook.
Teaching purpose: to enable students to further master the method of comparing scores and correctly compare the sizes of more than two scores.
Emphasis and difficulty in teaching: the method of comparing two or more scores.
Teaching process:
First, basic training
1. Compare the size of each group below.
2. Oral answer: How to compare the size of two scores?
Second, practical guidance.
1. Exercise 20, question 7.
(1) Read the questions and specify the requirements.
(3) Observe the size relationship of these scores from the chart, and arrange them from small to large.
(4) Question: If there is no direct graph, can these scores be compared directly?
2. Exercise 20, Question 8.
(1) Guide students to observe the characteristics of each group's scores and compare their sizes.
Third, classroom exercises.
1. Use ">" to connect the scores of each group.
2. Exercise 20, Question 5, and talk about the reasons for right and wrong.
3. A story book, Xiaoling read it in 8 days and Xiaojun 10 days. How many books do they read on average every day? Who reads fast?
4. The distance between A and B is 300 kilometers, car A travels 50 kilometers per hour, and car B travels 60 kilometers per hour. What are the scores of the whole journey of car A and car B at each time point?
Fourth, class assignments.
1. Exercise 20, questions 6, 9, 10.
2. Guide students who have spare capacity to practice 1 1* and 12*.
2. True score and false score
1 class hour (47 class hours in total)
Teaching content: the meaning of true score and false score-textbook page 98-99: example1-example 3, doing a problem and practicing 2 1: 1-3.
Teaching purpose: 1. Know the true and false points, and master their characteristics.
2. Learn to turn fractions whose numerator is a multiple of denominator into integers.
3. Cultivate students' abilities of observation, comparison, analysis and logical thinking.
4. Infiltrate the mathematical thought of classification and transformation to inspire students' dialectical materialism.
5. Stimulate students' interest in exploring new knowledge and promote the cultivation of students' good learning quality.
Emphasis and difficulty in teaching: understanding the concepts and characteristics of true points and false points. Understanding two practical meanings of false scores.
Teaching process:
First, pave the way for pregnancy