I. Presentation of the Textbook Content:
The "Tree Planting Problem" is a content from the "Mathematical Corner" section in the People's Education Edition Grade 4 Mathematics textbook, which divides the tree planting problem into several levels: planting at both ends, not planting at both ends, circular situations, and square array problems. The focus is on: during the process of solving the tree planting problem, introducing to students an important mathematical thinking method that is very useful in mathematical learning and problem research —— the reduction thought method. Through some common practical problems in real life, allowing students to discover some rules, extract the mathematical model within, and then use the discovered rules to solve some simple practical problems in life. At the same time, enabling students to realize the convenience brought by using mathematical models to solve problems. The teaching of this class is not just about making students proficiently solve practical problems similar to the tree planting problem, but also uses solving the tree planting problem as a learning support point to infiltrate mathematical thinking methods. With the help of the teaching content, develop students' thinking and improve their certain level of thinking ability.
II. Teaching Objectives:
Based on the understanding of the textbook and analysis of students' knowledge level, I have positioned the teaching objectives for this class as follows:
(A) Knowledge and Skills:
1. Utilizing familiar life scenarios, through hands-on practical activities, let students discover the relationship between the number of intervals and the number of trees planted.
2. Through group cooperation and exchange, enable students to understand the rule between the number of intervals and the number of trees planted.
3. Be able to use patterns with the help of diagrams to solve simple tree planting problems.
(B) Process and Methods:
1. Further cultivate students' ability to discover patterns from actual problems and apply these patterns to solve problems.
2. Infiltrate the idea of combining numbers and shapes, cultivating students' awareness of solving problems with the help of graphics.
3. Cultivate students' cooperative awareness, forming good communication habits.
(C) Emotional Attitude and Values:
Through practical activities, stimulate students' love for mathematics, feel the presence of mathematics everywhere in daily life, and experience the joy of successful learning.
III. Key Points and Difficulties in Teaching:
Guide students to explore and discover the pattern between the number of intervals and the number of trees planted through observation, operation, and communication, and be able to apply the pattern to solve practical problems.
IV. Teaching Methods and Learning Strategies:
Modern educational theory advocates that students' learning is not a passive acceptance process, but rather an active construction process. Therefore, in this class, I mainly adopt the teaching process of "finding intervals in life - finding methods in hands-on operations - finding patterns in methods - learning applications in patterns". Let students investigate methods through group cooperation, making each student use their brain, hands, and collaborate in exploration, experiencing the whole process of analyzing, thinking, and solving problems. And assist teaching through intuitive demonstrations of multimedia, guiding students to be interested and inspired, promoting thinking through thinking, participating actively, and promoting comprehensive development of students.
V. Teaching Process
This class is divided into four major parts:
1. Engaging Introduction:
1. Students, do you know? There are mathematical knowledge hidden in our hands, would you like to understand them?
2. Stretch out your right hand, spread it, count, there are how many gaps between the five fingers? In mathematics, we call these gaps "intervals", meaning there are how many intervals between five fingers? Three intervals are between how many fingers? Such mathematical problems can actually be seen everywhere in our lives. (Through finger movements, create a situation, actually the finger problem is the same principle as the tree planting problem. By moving fingers, observing, stimulating students' interest in learning, focusing attention to enter the new lesson.)
2. Creating Contexts, Raising Questions
1. Do students know what day is March 12th every year? It is our country's Tree Planting Day. Do you know what benefits tree planting has? Today, we will study the mathematical problems in tree planting together. Write the topic on the board: Tree Planting Problem.
3. Exploring Communication, Solving Problems
1. Show Example 1: Students plant trees along a 100-meter road on one side, planting one tree every 5 meters (planting at both ends). How many saplings are needed in total?
(1) Ask a student to read the question aloud.
(2) Teacher: Understand what "both ends" means? Ask a student to explain, then teacher demonstrates with a physical object: point where the two ends of this stick are?
Explanation: If we consider this meter ruler as the road, planting at both ends means planting at both ends of the road.
How to solve? (Guide students to use the method of drawing pictures to solve, but the data is too large, so they can simplify the complex problem first, and research the tree planting problem on shorter distances.)
(3) Students explore the tree planting rules on shorter distances.
① If the road length is only 15 meters, how many trees need to be planted? If the road length is 25 meters, how many trees need to be planted? Please draw line segment diagrams to see. (Pay attention to the number of intervals and interval points in the diagram.)
② Draw, simply verify, and discover the pattern. (Fill in the table)
Road Length (meters) Distance Between Adjacent Trees Intervals (number) Number of Trees Diagram
A15
B20
C25
D30
E
Discoveries:
a. First plant 15 meters, still plant one tree every 5 meters, draw and plant, see how many trees were planted? Compare, who drew quickly and planted well. (Write on the board: 3 segments 4 trees)
b. Same as above, plant 20 meters again, this time you divided into how many segments and planted how many trees? (Write on the board: 4 segments 5 trees)
c. Arbitrarily choose a distance and plant again, see how many segments and how many trees you planted this time? What did you discover?
(Write on the board: 2 segments 3 trees; 4 segments 5 trees)
d. What did you discover?
Summary: You are really amazing, discovering a very important rule in the tree planting problem, which is:
(Write on the board: Planting at both ends: number of trees = number of intervals + 1)
③ Apply the rule, solve the problem.
a. Question: Can this rule solve the previous problem? Which answer is correct?
100÷5=20 What does 20 refer to here?
20+1=21 Why add 1?
Teacher: Through simple examples, discovered the rule, applied this rule to solve this complex problem. In the future, when encountering "planting at both ends" and needing to find the number of trees, do you know how to do it now?
(In solving problems, first guide students to analyze the quantitative relationships in the questions. To find the number of saplings required, you must know the number of intervals. Adding one to the number of intervals gives the number of trees needed. The number of intervals is obtained by dividing the total length by the interval distance. Let students clearly express the rules they just learned. Through example problems, students consolidate the newly discovered rules and explain the reasoning, while letting students use the summarized rules to solve practical problems, allowing them to experience the joy of success. On the other hand, recognize that the rules of the tree planting problem are not only used to solve tree planting problems, but also many similar problems in life. Then use the practice exercises on page 118 of the textbook to reinforce. Require students to analyze the quantitative relationships in the questions before listing formulas, cultivating good problem-solving habits. This part of the teaching mainly involves mastering the tree planting rules for planting at both ends through guessing, analyzing, and demonstrating intuitively, and applying these rules to solve practical problems. At the same time, I also use a lot of context creation to strengthen the cultivation of students' mathematical thinking and the ability to solve complex problems.)
4. Consolidating Application, Internalizing Improvement
Basic Practice:
1. Mathematical problems similar to those around us.
School plants trees on one side of the road to the No. 5 bus station, planting one tree every 5 meters, a total of 26 trees. What is the distance from the first tree to the last tree?
Summary: Say, in our lives, what phenomena are similar to the tree planting problem? Group discussions, then report findings. Such as fingers and intervals, railings and intervals, lining up, hanging lanterns, planting cabbage, fence posts, lines in notebooks and intervals...
(In basic mastery of the tree planting problem with planting at both ends, I designed a consolidation exercise. This problem is the reverse calculation of the tree planting problem with planting at both ends, using "total length = interval distance * number of intervals; number of intervals = number of trees - 1".)
Advanced Practice:
1. For Children's Day celebrations, students decorate the classroom by hanging 7 red lanterns, with 2 yellow lanterns hung between every two red lanterns. How many yellow lanterns did the students hang in total?
2. Mr. Zhuo goes to a certain classroom, starting from the first floor, with 32 steps per floor, and a total of 96 steps walked. Which floor is Mr. Zhuo going to?
(Introducing "tree planting problems" in life such as climbing stairs, these questions reflect the mathematization of life and the lifelike nature of mathematical knowledge. These two questions are typical tree planting problems with planting at both ends. This part mainly uses practice to allow students to apply what they have learned to solve problems in life, striving to reflect the value orientation of "everyone learns valuable mathematics.")
Expansion:
A log is 8 meters long, cut into sections every 2 meters. How many cuts need to be made? (Students complete independently.)
8÷2=4 (sections)
4-1=3 (cuts)
Question: Why subtract 1? This type of tree planting problem will be studied more deeply later.
(On the basis of mastering the tree planting problem without planting at both ends, I designed a reinforcement exercise. A log is 8 meters long, cut into sections every 2 meters. How many cuts need to be made? Students analyze the problem independently and solve it. Although this teaching link is not the main teaching goal of this class, in order to further develop students' cooperative investigation abilities and prepare for future tree planting problem studies, I made such arrangements, believing that it will achieve good learning results.)
Five. Review and Reflection
What have you gained from today's learning?
Teacher: Through today's learning, we not only discovered the rule of planting at both ends in the tree planting problem, but also learned a method of studying problems, that is, when encountering complex problems, think about the simpler ones first. There are still many aspects of knowledge in tree planting, we will continue to learn in the future.
Throughout the entire class, we strive to let students' minds fly freely, integrating mathematics teaching into the colorful life, starting from the students' actual situation, creating an environment where "the sky lets birds fly, the sea lets fish leap," making every student the master of the classroom, making every math class a refueling station for students' life journey!