Teaching objectives:
1. Through mathematical inquiry activities such as guessing, experiment and verification, students can initially understand the law of planting trees at both ends, establish mathematical models and solve related problems in real life.
2. Cultivate students' ability to explore laws from simple problems and find effective methods to solve problems through "simplifying the complex", and initially cultivate students' model thinking and transformation thinking.
Teaching focus:
Discover and understand the law of interval number and tree number in the problem of planting trees at both ends.
Teaching difficulties:
Solve practical problems in life with the problem-solving idea of "planting trees"
Teaching preparation:
Courseware, ruler, study paper.
Teaching process:
(A) the creation of situations, the introduction of new courses
Teacher: Do you know what festival March 12 is? What do you know about planting trees? Guide the students to say that there is a certain distance between two trees when planting trees, and these distances are generally equal ... This information is related to the study of this lesson. )
Teacher: Actually, there are many hidden math problems in planting trees! Today, we will learn the math problems in tree planting in this class. (Title on the blackboard: Planting Trees)
(2) Fully experience and explore new knowledge.
1. Bold speculation leads to conflict.
(1) Read and talk.
Taking 1 as an example, the courseware guides students to obtain relevant mathematical information. Ask the students to read the questions and then say their names: What information did you learn from the questions? Focus on helping students understand the meaning of the following mathematical information:
What does it mean to plant a tree every 5 meters?
Let the students make it clear that "planting a tree every 5 meters" means that the distance between every two trees is 5 meters. The distance between every two trees is also called the interval length, which can also be said as "the interval between two trees is 5 meters".
What do you mean by "planting at both ends"? What do you mean "one side"?
Let the students speak first, and then the teacher will show them in kind. For example, ask students to point out where the ends of a ruler point. What do you mean, aside?
(2) Guess and think.
Ask the students to guess how many seedlings will be planted according to the information in the example. Teachers will not comment on students' guesses, and guide students to express their opinions actively.
Teacher: How many trees will be planted? Right? How will you test your guess?
Guide students to verify by drawing line segments.
(Design intention: Help students to clarify the meaning of the question, let students guess the answer, trigger cognitive conflicts, and stimulate students' desire to continue exploring. )
2. Explore the law by operation.
(1) preliminary experience, simplify the complex.
Teacher: We use line segments to represent the path of 100 meters, and plant a tree every 5 meters. You can use your favorite patterns to represent trees, plant a tree every 5 meters, plant a tree every 5 meters, plant a tree at a time ... Is it very troublesome?
Teacher: Why does it feel so troublesome?
Student: Because 100 meters has 20 5 meters, which is too much.
Teacher: That is to say, this question 100 meter is a bit big, so drawing will be more troublesome. For such a complicated problem, we can start with a simple one. For example, you can choose 100 meters to study first.
(2) Teachers' demonstration and intuitive feeling.
The teacher demonstrated the courseware and explained it while demonstrating.
Teacher: We choose 20 meters from 100 meters for research. We use a line segment to represent 20 meters, and plant a tree every 5 meters, which means that the interval between trees is 5 meters. (Teacher writes on the blackboard)
Teachers; Let's have a look. How many segments have we divided this road into on average? How many intervals are there? How many trees have been planted?
Guide the students to say a 20-meter-long road, with an interval of 5 meters. There are four such intervals, and five trees can be planted.
(Design intention: Let students experience the strategy of solving complex problems from simple problems, and demonstrate the drawing method of line segment diagram to students through the demonstration of courseware, so as to prepare for the following students to explore independently. )
(3) Hands-on operation and preliminary experience.
Ask the students to choose a short section of 100 meters, draw a picture and look at this short section. Plant both ends, and how many trees should be planted in one * * *.
Teachers choose representative works for display. Why do they paint like this? Let the students talk about their own ideas: how do you draw? Why do you paint like this? How many trees will be planted?
Teacher: Although these students chose different lengths and planted different trees, their line drawings, especially the methods of analysis and thinking, have something in common. Can you find it?
There is a similarity in guiding students to observe these different painting methods: the number of trees is more than the number of intervals 1.
(4) Reasonably speculate and perceive the law.
Teacher: There is no need to draw a line drawing. If the road is 30 meters or 35 meters long, how many trees will be planted? Please take out your test paper and fill in the form.
Students fill in the form, teachers patrol, and individual students guide and explain.
After the students fill in the form, communicate in groups and report the results.
(5) Summarize and understand the law.
Teacher: Please observe the table carefully. What do you find about planting trees on a line segment (both ends should be planted) and the number of intervals? Talk about your findings in a group.
Students report their findings.
Guide students to find that trees are planted at both ends, and the number of trees planted is more than the number of intervals 1, or the number of intervals is less than the number of trees 1.
Teacher: Why are trees planted at both ends, more than the interval 1 tree?
After the students answer, the teacher helps the students to further understand intuitively with the help of courseware demonstration.
(Design intention: Students will operate by hand and cooperate and communicate. Let students experience the whole process of observation, discovery and feeling in constant operation and communication, and learn the methods to solve problems. )
(6) immediately consolidate and strengthen the law.
Teacher: Students all understand the relationship between the number of trees and the number of intervals when two plants are planted. The teacher asked several questions to test everyone: How many trees were planted in seven sections? How many trees are planted every 20 seconds? How much space is there between nine trees? How much space is there between 20 trees?
(Design intention: Through this little exercise, students can further master the relationship between the number of trees and the number of intervals when planting at two ends. )
3. Applying this law, the example 1 is verified.
Teacher: Let's go back to the example 1 and plant trees along the path of 100 meters, and plant a tree every 5 meters (both ends). How many trees can a * * * plant? Which students guessed right just now?
Teacher (pointing out some students who guessed wrong): Now do you know the reason why you guessed wrong? Tell us about it What do you want to remind us?
Students try to solve problems in columns, teachers patrol and give targeted guidance.
The whole class reports and exchanges, mainly to make students clear: What does 100÷5=20 mean? Why use 20+ 1=2 1 (tree)?
(Design intention: Let students go through the process of guessing, testing and verifying, and let students know the meaning of each step formula, so that students can better understand the mathematical model of tree planting problem. )
(C) return to life, practical application
1. "Do it" question 1.
Teacher: There is no tree planting in this question. Can you solve it in the way we learned today?
Let students clearly apply the law of planting trees, which can solve many similar problems in life. Taking a street lamp as a tree in this topic can also be solved by the law of planting trees.
Teacher: Actually, the problem of planting trees is not only related to planting trees. There are many similar problems in life, such as installing street lamps, telephone poles and setting up stations.
2. Exercise 24 1, 2, 3.
Let students further feel the extensive application of tree planting in life.
3. Exercise 24, question 4.
Teacher: What's the difference between this question and the example?
The teacher guided the students to find out the difference between this question and the example. The example is to know the total length and interval length to find the number of trees, and this problem is to know the interval length and the number of trees to find the total length of the road.
Teacher: How do you calculate it? Why subtract 1 from 36?
(Design intention: Use the mathematical model of tree planting problem to solve similar problems in life, expand the application of tree planting problem, and let students draw inferences from others, so that students can realize the close connection between mathematics and real life. )
(4) class summary, talk about the harvest.
Self-examination/introspection
Through the study of this lesson, let the students know the relationship between the number of trees and the number of intervals when planting at two ends. This part is more abstract. In order to simplify the difficulties, before teaching new knowledge, I used finger games to lead in, which aroused children's interest and initially felt the relationship between the number of trees and the number of intervals. Then extract the simple tree planting phenomenon from life, extract it, establish a mathematical model, and then apply this mathematical model to real life.
First, create a pleasant atmosphere and let the game enter the situation.
Start with puzzles and games that students are interested in, create a relaxed and happy atmosphere, and let students initially perceive the relationship between the number of trees and the number of intervals, so as to lay the foundation for further exploration. This kind of learning situation that students are interested in is conducive to students' active participation in mathematics activities.
Second, pay attention to independent exploration and let experience enter the method.
Experience is the process that students transfer from old knowledge to implicit new knowledge. In teaching, I create situations to provide students with time and space for full thinking, so that students can start with simple questions and explore the law of planting trees at two ends with the help of intuitive charts. With the help of graphics, knowledge representation is established, and the infiltration of the consciousness of combining numbers and shapes is emphasized, so that students can be inspired and know the methods, thus building up their confidence in learning, further solving more complicated problems and infiltrating a kind of reduction thought.
Third, advocate the use of knowledge, so that modeling into life.
"Mathematics comes from life, but it should serve life." Let students realize that as long as they are good at observation, they will find that many examples in life are similar to the problem of planting trees, and guide students to use what they have learned flexibly to solve some practical problems in life.
However, this class also has some shortcomings. I feel that I have not fully grasped the starting point of students' learning, paid no attention to the cultivation of students' reverse thinking, and paid no good attention to all students. In the future teaching, I should also pay attention to the degree of teaching materials, make appropriate choices and arrange teaching time more reasonably.