Guiding ideology and theoretical basis of simple equation teaching plan of People's Education Press.
"Understanding Equation" is one of the teaching contents of senior mathematics in primary schools? Traditional topic? . The educational concept embodied in my design of this course is to enable students to understand and master the meaning of equations, understand the relationship between equations and discriminate them in a wide range of exploration time and space and in a democratic, equal and relaxed atmosphere by using existing knowledge and experience. Make students learn to use equations to express concrete and even equivalent relationships in situations, and further feel the close relationship between mathematics and life. At the same time, improve students' ability to observe, analyze and solve practical problems. Initially establish the idea of classification.
Analysis of teaching background
Teaching content: Simple equation is the basis for students to solve problems with arithmetic thoughts after four years of study, and it is also an important basis for learning to solve integer, decimal, fraction and percentage problems with equations in the future. The intention of compiling teaching materials is to introduce from equations. First of all, through the demonstration of the balance, it is explained that the condition of balance is that the objects placed on the left and right sides have the same mass. At the same time, it is found that an empty cup is exactly100g, and then water is poured into the cup, and the water weight is set to x grams. Through gradual attempts, it is concluded that the cup and water weigh 250 grams. Thus, from inequality to equality, equations with unknowns are called equations.
The meaning of equation is a brand-new mathematical concept course for children, which is an improvement of arithmetic thinking and a leap in digital understanding. On the basis of using letters to represent unknowns, students' mathematical tools for solving practical problems have developed from listing the solutions of formulas to listing the solutions of equations, from seeking the results of unknowns to participating in operations with unknowns, and their thinking space has increased. This is another leap in mathematical thinking method, which will improve students' ability to solve practical problems by using mathematical knowledge. This part of teaching is helpful to cultivate students' abstract thinking ability, and it is also a process to cultivate students' abstract generalization ability, which lays a good foundation for learning to solve equations and solve applied problems in the future.
Student situation: Grade five students have mastered the understanding of integers, decimals and fractions, and can skillfully calculate the four operations of integers and decimals. Students' knowledge and experience in logarithm and algebra have accumulated to a considerable extent, so they need to learn mathematical knowledge and mathematical thoughts in Grade One. But equation, as an important knowledge and thought in the field of mathematics, is also an important thought and method for students to learn middle school mathematics and physics. As an equation with special significance in mathematics, it is basically unfamiliar to primary school students.
Teaching method: discovery
Teaching methods: scene introduction, formula presentation, observation and comparison, and application expansion.
Technical preparation: multimedia presentation
Teaching objectives (content framework)
1. Knowledge and ability: enable students to understand the concept of equation, build the model of equation by using equivalence relation, and experience the relationship between equation and equation, so as to cultivate students' ability of observation, analysis, comparison, abstraction and generalization.
2. Process and method: Through the learning process of observation, exploration and generalization, the order and generality of thinking are trained, and dialectical materialism from practice is infiltrated.
3. Emotion, attitude and values: guide students to know themselves and build self-confidence. It is a positive emotional experience for students to acquire mathematics, and they can use their own experience to discover and re-create.
Schematic diagram of teaching process (optional)
Distinguish the formula with the help of blackboard writing.
Question 1
Question 2
Question 3
Fourth, connect with practice and expand application.
Second, experience feelings and observe accumulation.
Third, refine and summarize, compare and summarize.
With the help of balance, dynamic presentation
Derive the mathematical formula of subtraction.
With the help of balance, dynamic presentation
Derive the mathematical formula of addition.
An activity
Activity 2
Understanding equations with the help of blackboard writing.
Understanding equations with the help of blackboard writing.
Teaching process (written description)
First, introduce the scene and understand the balance:
Show me the balance. Students, did you see it? Do you know how to use it? (Left and right balance) You see, where do you know that left and right are equal? [Pointing to the middle] Because the object is too small, do you want to use courseware?
Second, experience feelings and observe accumulation.
I have a pear and an apple here. If you put them in trays on both sides of the balance, guess what will happen? (Perfect language, three situations: the quality of a pear is greater than that of an apple, and the balance is tilted to the left; Balance equal to balance; Less than a balance tilted to the right)
Because we don't know the uncertain quality, the result will be different. Now I'll tell you their quality: pear 60g, apple110g. What will the balance be like at this time? (tilt to the right, that is, the left and right are not equal) Can this state be expressed by a formula? (60< 1 10) How nice! Mathematical language is concise.
Teacher: What if you put a peach on the left? (Because the quality of peaches is unknown, there are three possible situations. ) Well, now I tell you that the quality of a peach is one gram. Express your balance in mathematical language and write it down in this book. Teacher's blackboard writing: 60+a
Teacher: You see, several simple mathematical expressions express three different situations, which is the beauty of simplicity of mathematical language. Ok, let's put it on. What do you see? [Courseware Demonstration] (Balance Balance) Can you explain it? The weight of pears plus the weight of peaches is exactly the weight of apples.
Teacher: Let's see which formula represents this situation. Read the formula together. Tell me what this formula means. (left and right sides are equal)
Design intention: Make students feel unbalanced by presenting the weight of pears and apples, and then guess by presenting the uncertain quality of peaches, so as to get three mathematical formulas by adding a quantity.
(2) It is the same balance. You just found your balance. Now I have a glass of 500g juice and a can of125g milk. What if you put them on both sides of the balance? (Bottom left) Why? (Juice is heavier than milk) So can you balance this balance? Two people talking together can also be expressed mathematically.
Scheme 1: put 3 more cans on the right.
Teacher: Is that all right? Who can make it clear? Teacher blackboard 500= 125? 4 or 500 =125+125+125+125.
This is a strategy to change the quality on the right. Is there any other way to be inspired by him?
Option 2: I just heard a classmate say that 375 grams is enough. Can everyone talk? But someone did take a sip, but we don't know how many. What shall we do (can be expressed in letters), and what will happen if so? Use mathematical expressions to express instructions and write them in a notebook.
Name the exhibitor on the blackboard: 500-X.
Design intention: From the weight of a glass of juice and a can of yogurt, it is concluded that the transformation process of the balance from imbalance to balance is on one side of the equation. When there are unknowns in the process of change, the equation is called an equation, but when there are no letters, the equation exists but is not an equation. At the same time, let students realize that subtracting an uncertainty may also present three relationships.
(3) Summary: What states do two formulas like this represent? The following two formulas also indicate that the balance is equal to the left and right. What's the difference? (There are no unknowns in the formula) A formula like this is the equation we are going to study today. Writing on the blackboard: understanding of equations
Teacher: How many conditions do you think are needed to judge the equation?
1. Equality equation. Teacher: We call this formula equation.
2. Must contain letters (unknown).
The teacher concluded: An equation with unknown numbers is called an equation. Write on the blackboard.
Design intention: Reveal phenomena, throw the essence to students to study, discover and summarize, and cultivate students' abstract generalization ability.
(4) Give it a try and see if the balance judgment equation can be written and explain the reasons. (Combined with situational diagram)
(1) displays the balance of 30+30+30 = 120 one by one. Why not an equation? Could it be that there are too many numbers on the left?
(2)50+y, the balance shows 50+y on the left, is it because it is not X, so it is not an equation? Then why? Show me 80 grams of watermelon. What about now? (50+y=80)
(3) Presentation 2b
Q: Why not? You mean that as long as the two sides of the balance are balanced, you can definitely write the equation, right? (Wrong) Why? (There are unknowns in the equation) Oh, I see, that is to say, not all equations are equations, right? Then all equations must be equations, right? Talk to each other and let me know the result. (Yes, it must be an equation. )
Then give 30 grams of strawberries. Can you write this equation? (2b +30= 140)
(4) Situation: weight of fox and bear, weight of deer.
Teacher: Can you list the equations according to the information in the picture? Why? (No, 50+x & gt；; 80 contains letters but is not an equation)
Design intention: Students can deepen their understanding of the equation by directly observing the balance or the seesaw. It is further clarified that the equation is based on the situation that one part of the equation is known and the other part is unknown, and it is represented by letters.
Third, the combination of practice, application and expansion.
Small scales help us to understand and understand this equation. In real life, not everything can be put on the balance to find equality, right? Who can use today's equations to express the mathematical problems that we have solved before?
1. Show them in turn: Xiaohong's age is X, and the teacher is 30 years older than Xiaoming.
Q: Do you have a formula in your head now? (x+30)
Let me see again: the teacher is 38 years old. Who thought of this equation?
(x+30=38 or 38-x =30) Once the students appear 38-30= x, the teacher will first affirm, but this is the same as the arithmetic method we have learned before. Think about it? We all know this method, but you can see that x+30=38 is listed directly according to the teacher's step-by-step description, which is the convenience of the equation.
2. Give away three soccer balls in turn, each at one yuan, at a cost of * * * 180 yuan. Can it be expressed by an equation? (3a= 180)
Continue to give away 2 basketballs, each 90 yuan. Teacher: The price of three footballs is exactly the price of these two basketballs. See if you can list an equation this time. (3 a =2？ 90)
Teacher: Not bad! You used football and basketball, and the total price was equal. Inspired by him, can you use the relationship between total price, quantity and unit price to list other equations? (3a？ 2=90) Why, what do you think? (total price? Quantity = unit price)
Teacher: Great! Well done, the human brain is really more flexible with more use! I hope everyone will think more.
3. Show: Use equations to express the following quantitative relations.
(1) Run 2.8km a week and S meters every day.
(2) A box of fruit candy * * *, distributed to 25 children on average, 3 each, just finished eating.
4. In fact, all the previous math problems are equivalent. Think about it. How many equations can you list from the following information? Show me the open questions: 60 stamps collected by Xiao Fang and 48 stamps collected by Xiao Ming. After Xiao Fang gave Xiao Ming X stamps, they had the same number of stamps.
60-2x=48 60-x=48+x (60-48)？ x = 2 ^ 48+2x = 60
According to different equivalence relations, different equations can be listed, and we can solve more complicated problems in life through them in the future.
Design intention: Let students look for equivalence relations in real situations, from the first-level operation to the second-level operation, and then to the twice-calculated equations without the support of scales. In-depth, make students understand the universality of equation application step by step, and lay the foundation for solving practical problems in the next step.
Fourth, summarize and improve.
History of Mathematics: More than 3,600 years ago, Egyptians used equations to solve mathematical problems. In ancient China, Nine Chapters Arithmetic, written about 2,000 years ago, recorded the historical data of solving practical problems with a set of equations. It was not until 300 years ago that Descartes, a French mathematician, first advocated the use of letters such as X, Y and Z to represent unknowns, and the present equation was formed.
Teacher: Students, everyone is thinking actively in this class today. What did you learn from it? What else do you want to know about the equation?
Blackboard Design: Understanding of Equation
Equations with unknowns are called equations.
60+a= 1 10
500-x= 125
60+a & lt； 1 10、60+a & gt； 1 10 60 & lt； 1 10
500-x & lt； 125 500-x & gt； 125, equation
500= 125? four
500= 125+ 125+ 125+ 125
The reflection on the teaching of unary equation in People's Education Publishing House this year is my first contact with the teaching of the first volume of mathematics in grade five. The reform of the equation part in the new curriculum standard and the presentation form of the equation in the textbook really aroused my great interest in inquiry.
When I understand the meaning of the equation, I will show the balance directly, so that students can contact the equation more intuitively. First, I put a 20-gram weight on each side of the balance, and let the students use formulas to express the relationship between the two sides of the balance. The students wrote the equation at once? 20=20? Then I changed one of the plates into two 10g, and the students immediately wrote it again? 10+ 10=20? Then I let the students do it by themselves, but I ask that no matter how the weight is changed, it should be balanced. Students operate the experiment by themselves and come to the conclusion that in order to balance the balance, the weights on both sides of the balance must be equal. At this time, I put a100g weight on the right side of the balance, and a 50g weight and a glass of water on the left side, and proposed to use it? Use letters to represent numbers? Knowledge means equivalence. And come to the conclusion that, generally speaking, in letters? x？ Expressing the unknown, drawing? An equation with an unknown number is called an equation. ? This conclusion. Let students understand a special equation. Only equations and unknowns are equations. Students can be said to have accepted the new concept of equation with relish.
In the process of training new textbooks, I learned that the previous teaching of this part of knowledge, including the solution of the equation in the impression, was based on the relationship between the parts of the formula, that is, the inverse operation relationship of addition, subtraction, multiplication and division. Now, under the guidance of the new curriculum standard, students are required to explore and understand the basic properties of the equation in the process of solving the equation, and then apply the basic properties of the equation to solve the equation. At first glance, I'm not used to it, even as a student. People ask me from time to time. Teacher, X+5= 1 1, X= 1 1-5, X=6? Is this solution ok? I first affirmed the students' solutions, and then introduced the methods in the book from the balance principle to solve the students' doubts. It seems complicated to use the properties of the equation, but this method can be integrated with the methods of our junior middle school and lay the foundation for students' subsequent study. After a period of consolidation practice, I found that students have a good grasp of this method, and they are willing to use the properties of equations to solve them. However, among them, I also feel a little confused:
Elephant? 45-X=23、56？ 7=8? Although this type of topic does not appear in the textbook, students can still encounter it in the actual calculation process. It is more troublesome to solve with the properties of the equation. Obviously, this method has some limitations. For good students, we will let them try to accept the solution of the equation with X behind it, that is, add X to both sides of the equal sign, then change the position left and right, and then subtract a number from both sides. It's a bit of a problem. It is still difficult for some students to master this method. But it is easier to solve the problem with the relationship between subtraction and division.