Teaching design of "pigeon's nest problem" ⅰ. Teaching objectives
Knowledge and skills
Let students understand the principle of pigeon nest through mathematical activities and learn simple analysis methods of pigeon nest principle.
(2) Process and method
Combined with specific practical problems, through experiments, observation, analysis, induction and other mathematical activities, students' ability of independent thinking and cooperative communication to solve practical problems is improved.
(3) Emotional attitudes and values
In the process of actively participating in mathematics activities, let students experience the fun of exploration and the close combination of mathematics and life.
Second, the difficulties in teaching
Teaching emphasis: to understand the principle of pigeon coop, first master it? Average score? , and then adjust the method.
Teaching difficulty: understanding? At least there is, right? The meaning of understanding? At least number = quotient+1? .
Third, teaching preparation.
Multimedia courseware.
Fourth, the teaching process
(A) the introduction of games
Show me a deck of playing cards.
Teacher: The teacher is going to give you a show today? Magic? . Remove the king and Xiao Wang, and there are 52 cards left. We invited five students to come up and each of them drew a picture at will. No matter how they draw, at least two cards are of the same suit. Do the students believe it?
Five students come on stage, draw cards, show cards and count them.
Teacher: This kind of problem is called pigeon's nest problem (blackboard writing) in mathematics. Because the number of 52 playing cards is large, in order to facilitate learning, let's first study several similar problems with a small number.
The design intention comes from what students like. Magic? Starting with setting suspense, we can stimulate students' interest in learning and desire for knowledge, so as to put forward mathematical problems that need to be studied.
(2) Explore new knowledge
1. Teaching examples 1.
(1) Teacher: Is there any way to put three pencils in two pencil cases? Please try in pairs at the same table.
Teacher: Who will tell us the result?
Default: one put 3, one does not put; One put two, one put 1. The teacher draws a picture on the blackboard according to the students' answers and shows two kinds of results. )
Teacher:? Anyway, there is always a pencil box with at least two pencils in it. Is this sentence correct?
Teacher: In this sentence? All the time? What do you mean?
Default: Must have.
Teacher: In this sentence? At least two? What do you mean?
Default: at least 2 pieces, not less than 2 pieces, including 2 pieces and above.
The design intention is to put the example 1 in the textbook? Pen holder? Change to? Pencil box? It is convenient for students to prepare learning tools. Moreover, it is more intuitive to express the results of the above problems by drawing and number decomposition. Okay, okay. At least there is, right? A separate explanation of the meaning of "let students understand more deeply" Anyway, there is always a pencil box with at least two pencils in it. This sentence.
(2) Teacher: Is there any way to put four pencils in three pencil boxes? Please try it in groups of four.
Teacher: Who will tell us the result?
Student: You can play (4, 0, 0); (3, 1,0); (2,2,0); (2, 1, 1)。 The teacher draws a picture on the blackboard according to the students' answers, showing four kinds of results. )
Guide the students to imitate the above example? Anyway, there is always a pencil box with at least two pencils in it. .
Hypothesis (reduction to absurdity):
Teacher: We came to this conclusion through hands-on operation. Think about it, can you find a more direct way to reach this conclusion? Discuss in groups.
Students communicate in groups, then report, and the teacher summarizes:
If you put 1 pencil in each box, you can put up to 3 pencils. No matter which box you put the remaining 1 pencils in, there will always be at least 2 pencils in a box. First of all, through the average score, the remaining 1, no matter which box it is placed in, will definitely appear. There are always at least two pencils in a box? . This is the method of average score.
The design intention starts from the other hand, gradually introduces the hypothesis method to explain the reasons, and rises from the actual operation to the theoretical level to further deepen the understanding.
Teacher: How about putting five pencils in four pencil boxes?
Guide students to analyze? If you put 1 pencil in each box, you can put up to 4 pencils. No matter which box you put the remaining 1 pencils in, there will always be at least 2 pencils in a box. First of all, through the average score, the remaining 1, no matter which box it is placed in, will definitely appear. There are always at least two pencils in a box? .
Teacher: How about putting six pencils in five pencil boxes? How about putting seven pencils in six pencil boxes? What did you find?
Instruct students to draw? As long as the number of pencils is more than the number of pencil boxes 1, then there are always at least two pencils in a box? .
Teacher: What measures have we taken to solve the above problems?
Guide students to draw conclusions through observation and comparison? Average score? The method.
What is the design intention of students through observation and comparison? Average score? The method will raise the experience of solving problems to the theoretical level, further strengthen the method and clarify the thinking.
(3) Teacher: Now let's go back and reveal the results of magic at the beginning of this class. Can you tell us the truth about this magic?
Guide students to analyze? If four people choose four different colors, the remaining 1 person will always be the same as one of the other four people no matter which color they choose. There is always a suit, and there are at least two candidates? .
The design aims at returning to the questions raised at the beginning of the class, revealing suspense, satisfying students' curiosity and making students realize the application value of mathematics.
(4) Exercise textbook page 68? Do it. Question 1 (further practice? Average score? Method).
Five pigeons fly into three pigeon coops, and a pigeon coop always flies into at least two pigeons. Why?
2. Teaching example 2.
(1) Courseware Example 2.
Put seven books in three drawers. No matter how you put it, there are always at least three books in a drawer. Why?
Discuss in groups before reporting.
Guide students to draw imitation examples 1? Average score? How to get it? If you put two books in each drawer, the remaining 1 books will become three in any drawer, so there will always be at least three books in one drawer. ?
(2) Teacher: If you put eight books in three drawers, what kind of conclusion will you have? 10? 1 1? Where is the book of 16?
The teacher wrote on the blackboard according to the students' answers:
7? 3=2 1 No matter how you put it, there are always at least three books in a drawer;
8? 3=22 Anyway, there are always at least three books in a drawer;
10? 3=3 1 No matter how you put it, there are always at least 4 books in a drawer;
1 1? 3=32 No matter how you put it, there are always at least four books in a drawer;
16? 3=5 1 No matter how you put it, there are always at least 6 books in a drawer.
Teacher: What do you find by observing the above formulas and conclusions?
Instruct students to draw? Number of objects? Number of drawers = quotient remainder at least = quotient+1? .
The design intention is to guide students to explore independently step by step, so that students can experience the whole process of problem solving and enhance their enthusiasm and initiative in learning.
(3) Consolidate exercises
1. 1 1 Pigeons flew into four pigeon coops, and at least three pigeons flew into one pigeon coop. Why?
2.5 people sit in four chairs, and there are always at least two people sitting in a chair. Why?
(4) class summary
Teacher: What have you gained from this class?
We learned a simple pigeon nest problem.
You can use drawing to help us analyze, or you can use the meaning of division to answer.
Teaching reflection on "pigeon's nest problem" 1 in sixth grade mathematics, demonstrating and experiencing the inquiry process with intuitive learning tools. Teachers pay attention to let students experience the inquiry process in operation and perceive and understand the pigeon nest problem.
2. Teachers pay attention to cultivating students? Models? Thought. Through a series of operation activities, students have a certain understanding of enumeration method and hypothesis method, compare them, and analyze the advantages and limitations of the two methods in solving the pigeon nest problem, so that students can gradually learn to think with general mathematical methods.