The nature of decimals is the basis of the calculation of four decimal places. According to the nature of decimals, we can simplify decimals, add one or remove several zeros at the end of decimals, or rewrite integers into decimals without changing the size of decimals. In teaching, we should help students understand and master the essence of decimals through a series of thinking activities such as comparison, discrimination, abstraction and generalization.
Analysis of learning situation:
This lesson is to learn more about decimals on the basis of students' learning the meaning of decimals. Mastering the nature of decimals can not only deepen the understanding of the meaning of decimals, but also lay a solid foundation for learning the size comparison and four operations of decimals. Students have a better understanding of the knowledge of integers, and have a certain understanding that adding "0" or removing "0" at the end of integers will cause the change of integer size. However, decimals are different in nature from integers. Adding "0" or deleting "0" at the end of the decimal will keep the size of the decimal unchanged.
Therefore, these contents of the integer part will have a certain impact on the learning of decimal properties, which is easy to cause confusion.
Teaching objectives:
1. Guide students to understand and master the nature of decimals, and simplify and rewrite decimals by using the nature of decimals.
2. In the process of solving problems, students can accumulate experience in mathematical activities and develop mathematical thinking abilities such as observation, comparison, abstraction and generalization through independent exploration and cooperation.
3. Cultivate students' preliminary mathematical consciousness and thoughts, and infiltrate the view that things can be transformed into each other under certain circumstances.
Teaching focus:
Let students understand and master the nature of decimals.
Teaching difficulties:
Can apply the properties of decimals to solve practical problems.
Teaching methods:
Creating situational method, Group Discussion and Transfer Induction.
Teaching preparation:
The onion micro-lesson video "The Nature of Decimals" and multimedia courseware
Teaching process:
First, create situations and introduce new lessons.
(Show the onion micro-lesson video to create a situation)
1, Teacher: Dog eggs and friends want to go shopping in the mall and have a crush on a Martian clay. The clerk told them that this product was on sale. The original package is only 0.8kg, and the new package is 0.80kg, and the price is only 0. 1 yuan. The dog egg was so happy that he wanted to pay for it, but he was stopped by a witty hammer and said, 0.8kg and 0.80kg are the same!
Students help to think about it together. Is 0.8kg and 0.80kg the same? Why?
Teacher: Why does the size of 0 after 0.8 remain the same? How many zeros can we add at the end?
In this class, we will learn these knowledge together.
(blackboard title: the essence of decimals)
Second, ask questions and explore new knowledge.
(a) Compare the sizes of 0.8 and 0.80.
Teacher: If you want to know the size of 0.8 and 0.80, you must first know how big they are.
(Introduction to onion micro-course)
The counting unit of 0.8 is 0. 1, and 0.8 is 8 0. 1.
The counting unit of 0.80 is 0.0 1, and 0.80 is 80 0.0 1.
Teacher: Their counting units are different. How do we compare sizes?
(With the help of the grid diagram of onion micro-lesson video, feel intuitively and help students understand)
Students intuitively understand with the help of the grid diagram in the micro-lesson video that although 0.80 has one more zero than 0.8 at the end, the size of the decimal has not changed.
Teacher: Do all decimals have this rule?
(2) Compare the sizes of 0.8 and 0.800.
(With the help of the grid diagram of onion micro-lesson video, help students understand)
0.800 is 800 pieces of 0.00 1, so first divide the square representing 1 into 1000 pieces, each piece is 0.00 1, and 800 pieces is 0.800. So: 0.8=0.800
Teachers guide students to observe and compare the equation "0. 8=0.80=0.800 ",mark the arrow of thinking, let the students observe and compare from left to right first. What did you find?
According to the students' answers, the teacher wrote on the blackboard: This equation only changed the counting unit of decimals, that is, 0.1→ 0.01→ 0.005438+0. The decimal size has not changed.
The teacher stressed: mark the arrow of reverse thinking again and let the students observe from right to left. What pattern did you find?
This equation only changes the counting unit of decimals, namely: 0.1← 0.01← 0.005438+0. The decimal size has not changed.
(3) Find the law and draw a conclusion.
Properties of decimals: Add "0" or remove "0" at the end of decimals, and the size of decimals remains unchanged.
The teacher stressed that if we encounter a "0" after the decimal point, we can generally remove the "0" at the end and simplify the decimal point. The 0 in the middle of the decimal point cannot be deleted.
(Import onion micro-lesson video to deepen understanding)
The teacher questioned: Does that integer have this property?
Students discuss in groups and give examples to prove the conclusion. .
The teacher emphasized the difference between decimals and integers.
Summary of the whole class: According to the nature of decimal, Dog Egg finally realized that the original new packaging has increased in price but not in quantity! So I complained to the merchant and got the corresponding compensation.
Teacher: It seems that mathematical knowledge can help us solve practical problems in life and avoid many sales promotion traps. It's really useful to learn math well!
(4) practice.
Show the courseware and do it: compare the size of 0. Thirty to zero. 3.
Teacher: What do you think of the size of these two numbers?
Let the students guess by applying the conclusion first?
Teacher: Think about how you compare these two numbers. Give students time to think independently and discuss cooperation in groups. )
Report conclusion: 0.3=0.30
The teacher questioned: Decimals range from 0.3 to 0.30. What changes have you seen? What hasn't changed? What did you find out from it?
The teacher guides the students to say that the average number of copies has changed, that is, the counting unit of decimals has changed, but the size of the shaded part has not changed, which is 0.3 = 0.30.
Three, combined with the actual, consolidate the use of
1. Which "0" in the following figures can be removed and which "0" cannot be removed?
3.90m 0.30 Yuan 500m 1.80 yuan
0.70 meters 0.04 yuan 600 kilograms? 20.20 meters
2. Simplify the following decimals:
2.900 ? 0.50600 ? 0.090 ? 10.830 ? 12.000
3. Rewrite the following decimals into decimals with three decimal places without changing the number size.
0.9 30.04 ? 5.4 ? 8. 18 ? 14
Fourth, class summary.
This lesson learned the nature of decimals: add "0" or remove "0" at the end of decimals, and the size of decimals remains the same.
When applying the properties of decimals, it should be noted that the zero in the middle of decimals cannot be removed.
Verb (abbreviation for verb) assignment
Complete "Exercise10"1,2, 3, 4.
Blackboard design:
Properties of decimals
Observed value: 0.8=0.80
? 0.8=0.800
? What pattern did you find?
Properties of decimals: Add or remove "0" at the end of decimals, and the size of decimals remains unchanged. (The 0 in the middle of the decimal point cannot be removed)
Teaching reflection:
This course makes full use of excellent teaching resources such as onion micro-course, and makes students realize that mathematics comes from life and serves life in the situation (new and old packaging and price of goods). In teaching, I try my best to arouse the enthusiasm of students and let them participate in the whole process of solving practical problems. The teaching links are also designed reasonably.
However, in the collective activities of this class, some students can't understand the purpose of the activities well, some students don't have a strong sense of participation, and some students don't listen carefully to others when communicating. I will continue to work hard in classroom teaching organization and learn from excellent teachers with an open mind. When summarizing the nature of decimals, students can't fully express it because of time, so they hurried through this link, and the time control of each link in class should be improved in the future.