The ratio of sugar to water in syrup is 1: 10.
The gold ratio is 1: 0.6 18.
Height and weight: 5: 1
The ratio of male to female employees in a certain unit is 2: 1.
National Flag of China: 3:2
Instructional design of "the meaning of comparison"
Teaching content: Nine-year compulsory education, six-year primary school mathematics, volume 1 1, pages 55 ~ 56, corresponding to "doing one thing", exercise 14, question L ~ 4, supplementary exercise problem.
Teaching purpose:
1. Make students understand the meaning of ratio, correctly write the corresponding ratio of the relationship between two multiples, and use the meaning of ratio to ask and solve problems.
2. Learn the reading and writing methods of comparison, and know the first item, the comparison number and the last item of comparison.
3. If you master the method of calculating the ratio, you will calculate the ratio correctly.
4. Understand the relationship between ratio and division and fraction, understand that the latter term of ratio cannot be zero, and understand that things are interrelated.
Emphasis and difficulty in teaching: understanding the meaning of ratio is both important and difficult. The difference between comparison and division and fraction is another difficulty in teaching.
Preparation of teaching AIDS: red flags with a length of 3 cm and a width of 2 cm, slides, etc.
Teaching process:
First, talk about inspiration and introduce new courses.
Teacher: In our daily work and life, we often compare two quantities. If the teacher holds a red flag 3 cm long and 2 cm wide, see who is the smartest and compare the length and width of this red flag. How does he ask questions and compare them with what methods he has learned before?
Inspire the students to ask questions, and then the teacher answers and writes on the blackboard.
Comparison relation: subtract 3-2 = L (decimeter).
Proportional relationship: divided by 3 ÷ 2 = = 1.
2÷3=
Teacher: (pointing to the blackboard) From the comparison of the length and width of the red flag, we can see that there are two ways to compare quantities: one is to find how much one quantity is more than another by subtraction, and the other is to find how many times or fractions one quantity is another by division. In today's lesson, we will learn a new mathematical comparison method-ratio based on comparing two quantities by division.
(blackboard writing: proportion)
Teacher: What do you mean by comparison? How does it read and write? What are the names of its parts? What is the relationship between ratio and division and fraction? These are all the things we will learn in this class. Let's learn the meaning of comparison first.
(complete blackboard writing theme)
Second, the new curriculum teaching
Significance of length teaching ratio.
The teacher asked: 3÷2 Compared with which quantity is the red flag? (length and width comparison)
The teacher said: with the new mathematical comparison method, the length is several times the width, and it can be said that the ratio of length to width is 3 to 2. (blackboard writing: the length-width ratio is 3 to 2)
Ask for help and release inspiration: Please think about it and imitate the above example. What about 2÷3?
The aspect ratio is 2 to 3.
Summary: From the multiple ratio of the length and width of the red flag, we know: who is several times or a fraction of who, and it can also be said that it is the ratio of who to whom. It should be noted that when comparing two quantities, it is necessary to find out who is comparing with whom. Who is in front and who is behind cannot be reversed, otherwise, the specific meaning of comparison will change. (For example, 3 to 2 is the aspect ratio, and 2 to 3 is the aspect ratio. )
Teacher: Students are really smart. They soon learned to compare the length and width of the red flag by "dividing" and "comparing". Please look at the following example again.
(Projection demonstration)
"A car travels for 2 hours 100 km. How many kilometers per hour? "
Teachers ask the following questions to inspire students to think:
(Projection demonstration)
(1) How to calculate the vehicle speed?
[Divided by: 100 ÷ 2 = 50 (km/h)]
(2) What is 100 km in the question? How about two hours? (distance, time)
(3) What is the speed of the car and what is the proportion?
After the students answered, the teacher wrote on the blackboard: the ratio of distance to time is 100 to 2.
Guide students to summarize the significance of comparison;
Teacher's inspiration: As can be seen from the above two examples, what method can be used to compare the multiple relationship between two quantities? What method can be used (by division)? (Ratio method) So what is used to express the division relationship between two numbers? Blackboard writing:
Division of two numbers is also called the ratio of two numbers.
Then help students deepen their understanding of the meaning of ratio (ask the following questions for inspiration):
(l) What is the relationship between two numbers? (division relation)
After the students answer, the teacher points a dot under the word "divided by stages" and then asks the students to read it twice.
(2) What are the similarities between their solutions in the above two cases? (all use division, which can also be said to be a few-to-several)
(3) What is the difference between the ratios in the two examples? (The ratio in the first example is the ratio of the same quantity, and the ratio in the second example is the ratio of different quantities. Different analogies give a new quantity, such as the ratio of distance to time, which is speed. )
2. Teach the reading and writing methods of ratio, the names of each part, the method of finding ratio and the relationship between ratio and division.
(1).
In mathematics, the ratio of two numbers is expressed as follows. After the teacher demonstrates an example, let the students practice writing and reading. ) Write on the blackboard:
Three to two equals three to two. Write 3 first, then ":",and finally write 2. In this case, the teacher writes a reading model. )
2 to 3 are recorded as ().
100 for 2 ().
Ask students to practice writing and reading in these two formulas.
(2) Explain the names of each part of the ratio and the method of finding the ratio.
Let the students learn the textbook by themselves. Take "3:2" as an example to say that the teacher writes on the blackboard:
(3) According to the above formula, help students understand the relationship between ratio and division.
The teacher pointed to the above formula to inspire students to observe and compare: the former term of ratio is equivalent to dividend, the comparison symbol is equivalent to divisor, the latter term is equivalent to divisor, and the ratio is equivalent to quotient.
(After dictation, use the table below)
correlation
differentiate
compare
ancestors
: (check mark)
What followed.
specific value
A relationship
separate
bonus
(except symbols)
divisor
business
operation
mark
molecule
-(fractional line)
denominator
Fractional value
A number
Guide the students to find out that the ratio is a number according to the definition of the ratio. (usually expressed as a fraction, it can also be expressed as a decimal, and sometimes it may be an integer. )
Then guide students to think about the reason why the latter term of ratio cannot be zero according to the relationship between ratio and division.
Exercise 1: Do the two questions "Do" in the middle of page 56 of the textbook. (Let two students perform on the blackboard, the other students do it independently, and the teacher makes a patrol to correct it.)
3. The relationship between proportion and score (provide the following questions for students to explore their own textbooks. )
(l) The ratio of two numbers indicates the division relationship of two numbers, so what number can the ratio be written as? (Fractional form, but can't be written as a fraction. It's still read as several pairs, and you can't see the number of components clearly. )
(2) According to "the relationship between fraction and division" and "the relationship between ratio and division", what is the relationship between ratio and fraction?
After the students answered the above questions in the self-study textbook, the teacher continued to use the above table to express them.
Exercise 2: Do the "Do" problem below page 56 of the textbook.
Let the students do it independently, and the teacher will patrol. When correcting, pay attention to point out that the proportion expressed by the score cannot be written by the score, and the number of components cannot be read, but the number of components should be read.
Summarize the relationship among ratio, division and fraction, and compare their differences in meaning. (The above table inspires students to summarize and compare)
Third, consolidate the practice.
The first layer of training:
1. Do exercises 14 1 questions. (Practice in groups)
When practicing feedback, guide students to understand the characteristics and significance of ratio in various small problems;
The ratio of distance to time in item (1) is "the ratio of different quantities", which means "speed".
(2) The ratio between the total number of models and the number of people making articles is also the ratio of different categories, that is, the average number of models made by each person.
The ratio of weight to weight in item (3) is the ratio of "same amount". The meaning of this ratio is "the ratio relationship between the weight of oranges and the total weight of fruits".
2. Do exercises 14, question 2. (Oral answer finished)
3. Do exercises 14, question 4. (Ask students to discuss and answer)
After the teacher asked the students to discuss and answer, he pointed out that the ratio of Xiao Qiang and his father's height is the same amount, but when the units are inconsistent, we should quantify the two figures to the same unit before comparing them, otherwise it will lose its meaning.
Level 2 Training: (Maneuver Problem)
1. What does "2: 0" often appear in football matches mean, because the latter term of the ratio cannot be 0? Is it a comparison? (Let the students discuss)
After the students discussed and answered, the teacher pointed out that the meaning of "2: 0" recorded in the football match only means the scores of each team and the other team, and it is not necessary to express the multiple relationship between the scores of the two teams. This is different from the meaning of ratio in learning mathematics today. Although it borrows the writing method of ratio, it is not a ratio.
2. Open questions related to actual design: Who will think?
Topic: Xiaoming 12 years old. He is a student in Class 6 (1). There are 42 students in this class. Xiaoming's father is 38 years old and works in an insurance company with an annual salary of 15000 yuan. Xiaoming's mother has a monthly salary of 800 yuan, and the company has 24 employees. See who can use their brains to find the right quantity according to the information provided by the topic, ask various questions by themselves and talk about the ratio between these quantities. )
[Age ratio, annual salary ratio, number ratio, monthly salary ratio, etc. ]
[Note: The purpose of designing this topic is to fully develop students' personalities and specialties, implement the principle of teaching students in accordance with their aptitude, and provide each student with opportunities for success, so that each student can be improved and developed to varying degrees, which will help develop students' creative thinking and improve their ability to analyze problems. Ability to solve problems. 〕
Fourth, the class summary
Today, we are studying the contents of pages 55 ~ 56 of the textbook. What did the students learn?
Then let the students ask questions and ask difficult questions.
Verb (abbreviation for verb) assigns homework.
Exercise 14 question 3