course content
inverse ratio
Textbook comprehension
"The Significance of Inverse Proportion" is the content on pages 47-48 of the second volume of the sixth grade primary school mathematics in the new curriculum standard People's Education Press. The content of this lesson is based on the teaching of proportional quantity, which is the deepening of the knowledge of "proportion" in front and the basis for learning to solve some simple practical problems of positive and negative proportion in the back. It plays an important role in connecting the past with the future, and it is an important content of proportional preparation knowledge teaching in primary schools. Therefore, in teaching, students are first guided to recall the quantitative relations they have learned, and through examples, communication and knowledge transfer, they realize that there are a lot of inverse relationships in life, and on this basis, they explore new knowledge and finally deepen new knowledge.
design concept
In the design of the teaching process, first of all, through the review of positive proportion, we can directly introduce the new class teaching, reveal the topic "inverse proportion", learn examples, guide students to observe the changing laws of the three quantities in the table, summarize the meaning of inverse proportion under the guidance of teachers through students' discussion and independent inquiry, and then further abstract the inverse proportion relationship: xy=k (certain), and then judge the truth of the two quantities by using the knowledge of inverse proportion.
Brief introduction of academic situation
This class is taught on the basis of students' proportional learning. When teaching, we should fully trust and respect students, change the traditional teaching mode, change students' passive learning into active learning, let them actively explore new knowledge and give full play to students' subjective initiative. Let students learn how to explore new knowledge, experience the joy of success and stimulate students' interest in learning. At the same time, the introduction method is adopted to guide students to explore independently and cultivate their ability to solve new problems by using existing knowledge.
Teaching objectives
Knowledge and skill goal: make students understand the meaning of inverse proportion, and correctly judge whether two quantities are inverse proportion according to the meaning of inverse proportion.
Ability goal: cultivate the ability of discovery and generalization through the construction process of inverse proportional meaning.
Emotional attitude goal: understand the relationship between inverse proportion and life, and realize the dialectical materialism view that things are interrelated and transformed.
Emphasis and difficulty in teaching
Key points: Understand the meaning of inverse ratio, and correctly judge whether two quantities are inverse ratio according to the meaning of inverse ratio.
Difficulties: Only by mastering the characteristics of inverse proportion can we correctly judge the inverse proportion relationship.
teaching method
Group cooperation, inductive reasoning, inquiry and communication
Teaching preparation
multimedia courseware
Class arrangement
1 class hour
teaching process
(1) Review and introduce conjectures and questions.
1, what are the characteristics of the proportional quantity? What is a proportional relationship?
2. In life, some of these two related quantities are directly proportional. What can they be? Students naturally think of inverse proportion, stimulate students' desire to learn, ask students what knowledge of inverse proportion they want to learn, and boldly guess the meaning of inverse proportion. This leads to a new lesson.
Achieve the goal: guess the lesson and stimulate the desire to explore.
(2) * * * explore the summary method.
1. Make clear the learning goal of this lesson: (1) Understand the meaning of inverse proportion and correctly judge whether two related quantities are inversely proportional. (2) Experience the learning methods of observation, comparison, reasoning and induction through the inquiry process of inverse proportional meaning.
2, situational introduction, learning and exploring.
(1) Let's look at an experiment first.
Height (cm) 30 20 15 10 5
Bottom area (square centimeter) 10 15 20 30 60
Volume (cubic centimeter)
Question: According to the list, what did you find?
(2) Students discuss and communicate.
(3) Guide the students to answer: The two quantities in the table are height and bottom area.
The height increases, but the bottom area decreases; The height is reduced, but the bottom area is increased.
The product of every two corresponding numbers is 300.
(4) What did you find after the calculation?
The product of every two corresponding numbers is 300, and the product is certain.
The teacher concluded: We say that the height and volume of water are inversely proportional, and the height and volume of water are inversely proportional.
The teacher asked: How to express the relationship between high and low area and volume? Blackboard writing: height× bottom area = volume of water (certain)
(5) If the letters X and Y are used to represent two related quantities, and K is used to represent that their products are certain, what formula can be used to represent the inverse relationship? Blackboard: x×y=k (OK)
Summary: Through the above study, what do you think is the key to judge whether two related quantities are inversely proportional?
(6) Summarize the significance of inverse proportion.
(7) Compare and summarize the similarities and differences of positive and negative proportions.
Achieve the goal: Comparative thinking is a very common mathematical thinking method in primary school mathematics teaching. The inversely proportional amount is the directly proportional amount of the content of the first after-school study. The learning contents and methods of the two classes are similar. Students can find similarities from differences in knowledge, and they can also find differences from similarities. Students can learn new knowledge, deepen development and summarize.
(3) Use methods to solve problems.
1, in life, which related quantities are inversely proportional, for example.
2. Do something after class. Is the tonnage shipped every day inversely proportional to the number of days shipped? Why?
3. Display the reverse scale image and compare it with the forward scale image.
To achieve the goal: students use the understanding of the concept of inverse proportion to judge whether the associated quantity is inverse proportion and learn to analyze and judge.
(D) feedback consolidation, layered practice.
Judge whether the two quantities in each question below are inversely proportional, and explain the reasons.
(1) a certain distance, speed, time.
(2) The speed and time required for Xiao Ming to walk from home to school.
(3) The parallelogram has a certain area, a bottom and a height.
(4) Kobayashi did 10 math problems, what he did and what he didn't do.
(5) Xiao Ming takes money to buy pencils, unit price and purchase quantity.
To achieve the goal: make students realize that mathematics comes from real life, serves real life, and embodies the application of mathematics.
(5) Class summary to enhance understanding.
Summary: What have we learned today? What have you gained? What do you want to remind everyone to pay attention to when studying? Do you have any questions about today's study?
Inverse proportion of blackboard writing design
Height (cm) 30 20 15 10 5
Bottom area (square centimeter) 10 15 20 30 60
Volume (cubic centimeter) 300 300 300 300 300 300 300 300 300
The height increases, but the bottom area decreases; The height is reduced, but the bottom area is increased.
Height × bottom area = volume of water (certain)
Inverse relationship: x×y=k (certain)