1. Teaching objectives:
(1) Knowledge and skills
Let students explore and initially master "finding what fraction of a number is another number" "How many" basic methods to deepen your understanding of the meaning of fractions.
(2) Process and methods
1. Enable students to use intuition and knowledge transfer to explore and answer practical problems such as "finding what fraction of a number is another number".
2． Cultivate students' awareness of independent exploration, cooperation and communication, and improve their ability to analyze and solve problems.
(3) Emotional attitudes and values ??
Let students feel the continuity of mathematics learning, know that old knowledge can solve new problems, and appreciate the ideological value of "transformation" .
2. Important and difficult points in teaching
Teaching focus: Understand the method of "finding what fraction of a number is another number".
Teaching difficulty: Determine the quantity of the unit "1".
3. Teaching preparation
Multimedia courseware.
4. Teaching process:
(1) Review old knowledge and introduce new lessons
1. Practice review.
(1) Unit conversion.
30 centimeters = ( ) decimeter; 120 minutes = ( ) hours; 2000 kilograms = ( ) tons.
After completing the exercise, the teacher guides the students to review the method of rewriting the names of low-level units into the names of high-level units.
(2) Let’s talk about it: What is the relationship between fractions and division?
(3) Fill in the appropriate numbers in the brackets below.
24÷25=( ); =( )÷( ); ( )÷7=.
2． Reveal the subject.
In this lesson we further learn to use the relationship between fractions and division to find out what fraction of one number is another. (Blackboard writing topic)
The review questions are designed to make students feel that the knowledge they learned today is related to the knowledge they have learned, thereby enhancing students' confidence in learning new knowledge. It is not only a review of the meaning of fractions, the knowledge of fractions and division, but also provides a formal basis for understanding "finding what fraction of a number is another number" in this lesson.
(2) Create situations and explore research
1. Explore the practical problem of "finding what fraction of one number is another".
Xiaoxin’s family raises 7 geese, 10 ducks and 20 chickens. What fraction of the number of geese are there as compared to ducks? How many times more chickens are there than ducks?
(1) Reading and comprehension.
Teacher: "What fraction of the number of geese is that of ducks?" What does it mean? (Students’ independent communication and discussion)
After communication, we came to the conclusion: Find what fraction of 10 is 7.
Teacher: How do you understand "how many times the number of chickens is that of ducks"?
After communication, we came to the conclusion: Find how many times 20 is 10.
(2) Analysis and answers.
Teacher: The first question here is who can be regarded as unit "1"? (Student answer: The number of ducks is "10".)
Teacher: Based on the meaning of the fraction, we can conclude that 7 is what fraction of 10? (Students answered: .)
The courseware shows the corresponding illustrations.
Teacher’s summary: Think of 10 animals as a whole, that is, the unit "1", and divide them into 10 equal parts, each with 1 animal. The 7 animals are the whole.
Teacher: How should the formula be listed?
Guide students to conclude: According to the relationship between fractions and division, to find out what fraction of 10 is 7, you can use 7÷10.
Get the formula: 7÷10=.
Teacher: How to answer the second question in the example: "How many times the number of chickens is that of ducks?"
Guide students to recall the multiple relationship between quantities and use division to solve them. Convert the problem into how many times 20 is 10, and you get the formula: 20÷10=2.
(3) Review and reflection
Teacher: What is the relationship between the above two questions? You can compare the similarities and differences between these two issues. (Students’ feedback after exchange and discussion)
The same point: they are all calculated by division.
The difference: the quotient of the previous question is a fraction, and the quotient of the latter question is an integer.
Teacher’s summary: To find what fraction of a number is another number, and to find how many times a number is another number, use division calculations. In the above two questions, the number of ducks (that is, the unit "1") is used as the divisor. The resulting quotient indicates the relationship between the two numbers, and the name of the unit cannot be noted. The difference is that the previous question is to find out how many times one number is another number, and the quotient obtained is a number less than 1; the following question is to find out how many times a number is another number, and the quotient obtained is A number greater than 1.
Teacher: Can you ask and answer other math questions?
Default: What fraction of the number of geese is there as compared to the number of chickens? How many times more chickens are there than geese? What fraction of the number of ducks are there as compared to chickens?
Summary problem-solving method: first find the unit "1", and then use the unit "1" as the divisor to perform division calculations.
7÷20=; 20÷7=; 10÷20=.
(4) Independent practice (please refer to question 2 of "Do it" on page 50 of the textbook in the courseware.)
There are 9 elephants and 4 golden monkeys in the zoo. What fraction of the number of golden monkeys are there than elephants?
(Let students first look for the unit "1", and then calculate the formula.)
The design intention is to present life situations and guide students to observe and think "The number of geese is ducks" What fraction of it?" to enable students to quickly enter the learning state. Based on the original knowledge and experience, students are encouraged to boldly present their personalized understanding through independent thinking, group communication and other links. Through comparative analysis and communication of the connection between old and new knowledge, students are guided to draw conclusions independently and deepen their understanding of "finding what fraction of a number is another number".
2． Understand how to rewrite the names of lower-level units into the names of higher-level units expressed as fractions.
(1) Show the question 9 cm=dm.
Teacher: Based on past methods, how should this problem be solved? When dividing two numbers does not yield an integer quotient, how should the quotient be expressed?
Students try to practice independently.
After the exercises are completed, teachers and students communicate and discuss.
(2) Compare the differences between this question and Question 1 at the beginning of this lesson, and what are the similarities?
Similar points: Low-level units are converted into high-level units, and the result is obtained by dividing by the rate of advancement.
Difference: The values ??in question 1 can be divided, and the quotient is an integer. The values ??in this question cannot be divided, so they are expressed as commercial fractions.
Get the answer: You can use 9÷10= to get 9 cm= dm.
(3) Teacher: Think about it, can this example be solved using the knowledge learned today?
(Review the topic learned today, students exchange and discuss.)
Guide students to say that 9 cm=dm means to find out how many 9 cm is 10 cm (10 is the rate of progress) In fractions, you can also use 9÷10=, so 9 cm= dm.
Teacher summary: To convert the number of low-level units into the number of high-level units, use the ratio to divide. When divisible, use commercial integers to express, and when divisible, use commercial fractions to express.
(4) Independent practice.
79 dm=m; 56 cm2=dm2; 133 dm3=m3.
(Let students talk about the progress rate between each unit of each question before doing it.)
The design intention is to allow students to skillfully apply what they have learned by presenting knowledge in different ways. knowledge, thereby deepening students' understanding of "finding what fraction of a number is another number".
(3) Classroom exercises to strengthen new knowledge
1. A flower bed of 3 square meters is planted with 4 kinds of flowers. How many square meters does each flower occupy on average? What if I plant 5 kinds of flowers? (expressed as fractions)
2. Class 5(1) *** had 17 calligraphy works to participate in the school's calligraphy competition, of which 4 works stood out from the 255 entries in the school and won the prize.
(1) What percentage of the winning works of Class 5(1) account for the total class entries?
(2) What percentage of the entries from Class 5(1) account for the entire school’s entries?
(Before doing this, ask students to talk about what the unit "1" in the two questions is?)
3. Unit conversion.
53 mL=L; 23 kilograms=tons;
13 seconds=minutes; 48 hectares=square kilometers.
The design intention is to allow students to deepen their knowledge and understanding of "what fraction of a number is another number" through multi-level exercises, and to improve students' observation ability, generalization and Inductive ability. The design of the exercises is closely related to the important and difficult points of teaching. At the same time, the arrangement of the exercises reflects the hierarchy from easy to difficult. The selected materials are closely related to the students' real life and have certain practicality in life.
(4) Class summary, review the whole lesson
1. What is the solution to the problem of finding what fraction of a number is another number?
(First find the unit "1" in the question, and then use the unit "1" as the divisor to perform division calculation.)
2. If the number of low-level units is rewritten into the number of high-level units, if the integer quotient cannot be obtained, how should it be expressed?
(Ask students to pay attention to rewriting the progress rate between the two units.)
The design intention is to strengthen the understanding of the knowledge learned through review. Students are required to use expressions containing letters to express calculation methods, which well cultivates students' symbolic expression ability.