Teaching design of product change law
Teaching content: Book 7, Page 58, Example 4, Exercise 9.
Teaching material analysis:
The law of product change is the content of the third unit in the first volume of the fourth grade of primary school. Based on two sets of multiplication formulas, the textbook guides students to explore the change of product and factor when a factor is constant, and summarizes the change law of product. On the basis of mastering multiplication operation, this paper reveals the changing law of product and sum factors, cultivates students' mathematical reasoning ability, and obtains the enlightenment education of dialectical thinking in the process of "changing and unchanging"
Teaching objectives:
Knowledge and skills: Let students explore and master the changing law of product, and use this law appropriately to calculate and solve simple practical problems.
Process and method: Make students experience the discovery process of the law of product change, and initially gain the general methods and experience of exploring and discovering mathematical laws.
Emotional attitude values: 1. By participating in learning activities, we can cultivate students' ability of inquiry, cooperation and communication, and ability of induction and summary, so that students can get happiness of success and enhance their interest and self-confidence. 2. Cultivate students' dialectical thinking of observing things from both positive and negative aspects.
Teaching emphasis: guide students to discover and summarize the changing rules of products themselves.
Teaching Difficulties: Exploring Strategies to Guide Students to Learn the Law of Product Change.
Teaching preparation: multimedia courseware
Pre-class activities: Look at the scale and compare the responses.
1. The teacher gives questions and guesses.
Teacher: What information do you know from the balance? If four chickens are as heavy as several ducks? what do you think?
If six ducks are as heavy as several chickens? Why?
……
2. Do a question and guess.
Teaching process:
First, the calculation area, the initial feeling
Teacher: Just now, the students played the game of changing chickens and ducks, and everyone reacted quickly! There is also such a secret in the multiplication formula. Today's mathematical exploration activity begins with calculating the area of a rectangle. Please calculate the area of the rectangle directly.
6× 4=24 6× 5=30 6× 8=48 6× 16=96
Teacher: What changes did you find in the area calculation just now? The length is constant, the width increases, and the area also increases.
Teacher: Your discovery is very important! We look at these formulas from top to bottom, and it really happened! That is to say, when two numbers are multiplied, one number remains unchanged, the other number becomes larger, and the product also becomes larger.
Teacher: If you look from the bottom up, can you find the changing law between elements and products? When two numbers are multiplied, one factor remains unchanged, the other factor becomes smaller and the product becomes smaller.
Teacher: Just now, I calculated the rectangular area with my mouth, and found that the product sum factor has a certain changing law. What is this rule? Today, we will unveil the changing rules of products together and write them on the blackboard.
Second, observe the formula and explore again.
First explore the law of "two numbers are multiplied, one number remains unchanged, the other number is multiplied by several, and the product is multiplied by several".
1.
Teacher: In order to reveal the changing law of product, we can observe and find it from several special formulas. Ok, let's choose these three formulas to study!
Teacher: Comparing these three formulas, what is the constant factor of 6? Courseware prompts, what's the change? Another factor and product
Teacher: Write on the blackboard with 6× 4=24 as the standard. Compared with 6× 4=24 in the second formula 6× 8=48, what changes do you find between the factor and the product? The courseware board draws icons and images.
Teacher: Compared with the first formula, the third formula is 6× 16=96. What did you find? The courseware board draws icons and images.
guess
Teacher: Who can make a bold guess? When two factors are multiplied, what is the change law between the factor and the product?
verification
Student feedback. How to prove whether my guess is correct? It can be verified by examples, such as the teacher giving an example first. Factor × 4, what is the product? Is it equal to the original product of 24× 4? Sure enough. Ok, let's give an example to verify it, and then communicate at the same table. Feedback, can this formula be completed with examples? Blackboard writing: ... 6× 4× a = 24× a
summary
What do you believe through examples? Courseware presents concepts; Multiply two numbers, one number is constant, the other number is multiplied by a few, and the product is multiplied by a few.
Teachers and students are divided into the roles of reading in sequence and returning to school.
practise
According to 8× 5=40, which of the following formulas is correct?
8×5×2=40×2[] 8×5×6=40×7[ ]
8×3×5=40×3[ ] 8× 10×5=40×5[ ]
8×5+ 1=40+ 1[]
Second, explore the law of "two numbers are multiplied, one number is constant, the other number is divided by several, and the product is divided by several".
1. Discussion
Teacher: If we look at these formulas from bottom to top, with 6× 4=24 as the standard, what is the changing law of factor and product? Communicate your findings with your deskmate, and then verify them with examples.
Student feedback, how many such formulas can you write? Countless, we can use ... 6× 16 ÷ A = 96 ÷ A, where A cannot be equal to 0, why?
summary
What do you understand through examples? Courseware presents concepts; Multiply two numbers, one number remains the same, the other number is divided by a few, and the product is divided by a few. Read back and forth.
deepen
According to 60×8=480, fill in the blanks by using the changing law of product.
60×8÷2=480○□ 60×8÷8=480○□ 60×8○□=480÷4
60÷5×8=480○□ 60÷30×8=480○□ 60-30×8=480○□
read
Read the textbook again. What do you find? Can you sum up these two findings in one sentence?
When two factors are multiplied, when one factor remains unchanged, the other factor is multiplied or divided by several zeros, and the product is also multiplied or divided by several zeros. Except for 0, the whole class reads.
Fourth, the class summarizes.
Design concept and thinking;
The new curriculum standard puts forward that students should "experience, experience and explore". According to the characteristics that children's product change law is abstract, while children's thinking in images is dominant, I creatively adapt the teaching materials, introduce students' existing experience in calculating rectangular area, and combine numbers and shapes to promote students to think deeply and discover the product change law and improve teaching effect. In the teaching of product change law, there are mainly the following ideas:
1 Pre-class activities to pave the way for pregnancy.
Before class, through the game activity of "Look at the balance and see who can react quickly", students' interest in learning is stimulated, the classroom atmosphere is activated, and at the same time, the changing law of multiplication and division is aroused, which effectively resolves the teaching difficulties and accumulates perceptual experience for further study.
2 combination of numbers and shapes, intuitive perception
The presentation of the multiplication formula in this lesson is no longer just a simple formula in the textbook, but based on the area of an intuitive rectangle, so that students can return to the intuitive diagram to confirm and strengthen it in time after observing the changing law of the factor and product of the formula. At the same time, in practice, it is also beneficial to help students understand the mistake of "two numbers are multiplied, one factor adds a few, the other factor remains the same, and the product also adds a few", which breaks through the teaching difficulties. In this way, through the combination of numbers and shapes, it is found that the boring calculation teaching is avoided, and a lively mathematics classroom is constructed, which is conducive to enhancing the teaching effect.
3. Combine support and release, and advocate exploration.
In the teaching of this lesson, I adjusted the two groups of formulas in the original example to a group of multiplication formulas, which helped to popularize and publish through the combination of support and income, and provided students with a space for independent exploration. By asking questions, comparing, summarizing and other "help" strategies, students are guided to explore from top to bottom, and after discovering the changing law of "factor multiplied by several, product multiplied by several", through group discussion, students are allowed to observe, give examples and verify from bottom to top, and discover the changing law of "factor divided by several, product divided by several" by themselves, so as to promote learning by teaching and guide learning.
4 apply what you have learned and improve your practice.
In the exercise design of this lesson, in order to let students get rid of the shackles of verbal arithmetic and really use the changing law of product for reasoning, I turned the obvious into the hidden, and designed the exercise of "writing numbers directly according to the changing law of product according to' 20× A number = 160'", which really allowed students to use the law flexibly. Then, I change the situation, introduce the situations such as distance problem and shopping problem, and let students deepen the application of the law in variant practice. Finally, I echoed the beginning lesson, and created a situation of rectangular area problem, so that students can use the changing law of product in practice for inverse use and reasoning, and then understand that "when two numbers are multiplied, if the product remains the same, the changes of two factors should be just the opposite", expand the changing law of product, deepen understanding, guide students to think deeper and improve teaching objectives.
Lecture draft on product change law
Judges and teachers:
Hello! The content of the lesson I am talking about today is the changing law of product, which is selected from page 58 of the first volume of fourth-grade primary school mathematics by People's Education Press.
First of all, talk about textbooks.
The changing law of product is taught on the basis that students have learned the knowledge of multiplying three digits by two digits and calculating by calculator, which paves the way for students to learn the knowledge of fractional multiplication in the future. In this lesson, students should learn the changing law of products. Through the study of this lesson, it plays a very important role in developing students' computing ability and rational reasoning ability.
As we all know, the fourth-grade students have some experience and can transform new knowledge into existing knowledge, but their abstract thinking is still very weak, so it will be difficult to understand the inquiry process of the law of product change. Based on the above analysis of teaching materials and learning situation, I will determine the changing law of understanding product as the focus of this lesson, and determine the inquiry process of understanding as the difficulty of this lesson. And drew up the following three-dimensional goals:
1. Be able to understand and master the changing rules of products, correctly express the changing rules of products and use them correctly.
2. Experience the exploration process of product change law, learn the methods of observation, conjecture, verification and generalization, feel the changing and unchanging ideas, and develop students' rational reasoning ability.
3. Experience the fun of independent exploration, cooperation and communication, and cultivate the good quality of students' love.
Second, talk about teaching ideas
In order to effectively achieve the teaching objectives, I will strive to achieve the following two points in the implementation of teaching:
1. Pay attention to the experience of inquiry process: the inquiry process of product change law needs to go through the process from intuition to abstraction, from obscurity to clarity. This process requires students to understand the changing law of product and accumulate experience in mathematical activities through observation, conjecture, verification and generalization.
2. Pay attention to the infiltration of changing and unchanging ideas: by changing one factor after another, explore the changing law of products and develop students' rational reasoning ability.
Third, talk about the teaching process
First, create situations and introduce new lessons.
Students, in order to respond to the school's call of "saving pocket money and holding hands with good friends", our class and Hope Primary School 1 class launched the activity of "holding hands and offering love". Please calculate how much it will cost to buy two boxes of 6 yuan's watercolor pens. Buy 20 boxes for 200 boxes? Please take out the draft paper and calculate it. Students will list the formula: 6×2= 12 yuan; 6×20= 120 yuan; 6×200= 1200 yuan. Design intention: By creating a specific situation of "buying stationery", students' original knowledge will be activated, students' enthusiasm will be stimulated, and materials will be provided for exploring the changing law of products.
Second, explore independently and understand the law.
The first level: the law of perception. What do you find by observing this set of formulas? What has changed and what hasn't? Think independently first. After having an idea, discuss with each other in groups of four. After that, the teacher patrolled and gave feedback to the whole class. I will guide students to observe from top to bottom, and students will find that from ① to ②, from ② to ③, one factor remains unchanged, another factor is multiplied by 10, and the product is also multiplied by10; Students will also find that from Formula ① to Formula ③, one factor is constant, another factor is multiplied by 100, and the product is also multiplied by 100. If you look from the bottom up, what will you find? Students will find that from Formula ③ to Formula ②, and from Formula ② to Formula ①, one factor remains unchanged, another factor is divided by 10, and the product is also divided by10; Students will also find that from Formula ③ to Formula ①, one factor remains unchanged, another factor is divided by 100, and the product is also divided by 100. Then who can tell the law you found in a concise sentence? Say it independently first, and then talk to each other at the same table. Let the students say: One factor is constant, another factor is multiplied or divided by several, and the product is also multiplied or divided by several.
The second level: guess. Is the law discovered by students universal? We need to give some more examples to verify whether the same situation will happen. If there are different situations in an example, we can't regard discovery as a rule.
The third level: verifying the law. Ask each student to write three formulas, check each other at the same table, and communicate how the factor and product change. For students who have the spare capacity to study, they can also write some according to other people's formulas. Students will write 7× 12=84, 7×6=42, 7× 3 = 21; Or 6× 150=900, 6×30= 180, 6×6=36 and so on.
The fourth level: inductive conclusion. Students, there are so many formulas on the blackboard. Now, can you talk about the law of this change completely? Speak independently first, and then talk to each other at the same table. Finally, I will name the students to talk about it, so that we can draw the conclusion that one factor is constant, another factor is multiplied or divided by a few, and the product is also multiplied or divided by a few. Can the number divided here be 0? Cannot be 0, because 0 cannot be divided.
The fifth level: expansion and extension. Just now, we all know that one factor is constant, another factor is multiplied or divided by a few, and the product is also multiplied or divided by a few. So if one factor is constant and another factor is added and subtracted, will the product be added and subtracted? Students will find that this is not true, such as 7×12+1≠ 84+1.
The sixth level: interpretation and application. I'll show you a magic eight.
12345679×9= 1 1 1 1 1 1 1 1 1
12345679× 18=222222222
12345679×27=
12345679×36=
12345679×45=
12345679× =
Through the application of this magical missing eight numbers, let students feel the magical mystery of mathematics.
Effective mathematics learning is the unity of students' learning and teachers' teaching. In this link, students can observe, guess, verify and summarize mathematical activities, thus enriching their own experience and deepening their understanding of the changing law of product, thus highlighting key points and breaking through difficulties.
Apply what you have learned and practice at different levels.
I will take doing as a basic exercise to consolidate new knowledge and check whether students understand and master the changing law of products.
I will expand the campus of a primary school, and prepare to change the width of the rectangular playground from 8 meters to 24 meters, with the same length. The area before expansion is 560 square meters. What is the area of the playground after the expansion? As a comprehensive exercise, students' ability to use knowledge comprehensively is cultivated through this question.
24×75= 1800 36× 104=3744
24○6×75×6= 1800 36×4× 104○4=3744
24○3×75○□= 1800 36○□× 104○□=3744
I'll take this question as an extension exercise. By calculating these problems, students can find that one factor is multiplied by several and the other factor is divided by the same number, and the product remains unchanged, thus expanding and developing students' abstract thinking.
Fourth, look back at the classroom and internalize and improve.
The fourth link: classroom review and internalization. At this time, I will ask the students to talk about what you have learned in this class. Is there anything to remind other students? To end the theme of this lesson.