Teaching Design of Finding Defective Products from Wide Angle in Primary Mathematics

In real life and production? Defective products? There are many different situations, some are different from the appearance of qualified products, and some are not up to standard. Next, I sorted out the teaching design of looking for defective products in primary school mathematics from a wide angle. Let's have a look.

Teaching design (1) for finding defective products from a wide angle in primary school mathematics;

New People's Education Publishing House, Unit 8, Book 2, Primary School Mathematics, "Looking for Defective Products in Mathematics with Wide Angle"

Teaching objectives:

1. Through comparison, guessing, verification and other activities, explore problem-solving strategies, infiltrate optimization ideas, feel the diversity of problem-solving strategies, and cultivate the ability of observation, analysis and reasoning.

2. Learn to express the mathematical thinking process clearly and concisely in intuitive ways such as graphics and symbols, and cultivate the ability of logical thinking.

3. By solving simple problems in real life, initially cultivate students' application awareness and ability to solve practical problems.

Teaching emphases and difficulties:

Let the students experience it? Compare? Guess what? Verification? The process of finding the best strategy for finding defective products.

Analysis of learning situation:

? Looking for defective products? What is the teaching content? Olympiad? It happens from time to time in activities, and using graphics to help thinking is good for cultivating students' practical ability and thinking ability. Although it is the first time for students to contact, it is not difficult to master the method of multi-solution through hands-on practice, group discussion and inquiry. The key is the optimal solution strategy. It is difficult for students to summarize methods, and teachers should guide them in time.

Teaching process:

First of all, find out the meaning of the problem and stimulate the desire to explore.

Teacher: In today's class, we will start with the topic of recruiting employees in a company. Suppose you are the applicant. Do you want to accept the challenge of wisdom? (Show courseware)

The problem is: if you have 8 1 glass balls with the same appearance, and one of them is slightly lighter than the others, this is flawed. If you can only judge which ball is lighter with a balance without weight, how many times do you have to weigh it at least to ensure that you can find a lighter ball?

(Think for a minute) Student report: 1 time, 2 times?

Teacher: Please use only 1 student. What do you think?

Health 1:

Health 2:

Teacher: 1 time seems to be rare, but it is only possible, and there is no guarantee that a defective ball will be found. So when we think about this problem, we should not only do the least, but also ensure that we can find it.

Teacher: What if? Promise me to find it? Premise, among so many answers, which one is the least? In this class, we will study this problem together to find out the defective products one by one.

Second, simplify the problem and go through the basic process of solving the problem.

The problem of finding defective products from 8 1 ball is complicated, so how do we carry out our research today?

Health: You can try at least.

Teacher: If we start with the simplest research, how many times should two balls be weighed at least?

Health: 1 time.

Teacher: What if it's three?

Health conjecture: 2 times? Three times? 1 time?

Teacher: Teacher, here are three bottles of chewing gum, one of which is missing three pieces. what do you think?

Health report: first put two bottles on both sides of the balance. If the left side sinks, it means that the right side is defective; If the right side sinks, it means that the left side is defective; If the balance is balanced, it is not called defective. Students talk about the teacher and cooperate with the weighing demonstration. )

While demonstrating the courseware, the teacher leads the students to feel the reasoning process further: although there are three bottles and the balance has only two trays, only two of them need to be placed on both sides of the balance, which may be balanced or unbalanced. What if it is balanced? What if it's unbalanced? Whether it is balanced or not, as long as it is called 1 time, the defective products can be found by reasoning.

Teacher's summary: It seems that although the numbers of 2 and 3 are different, they all weigh only 1 time to find defective products. (Record the query results in the table)

Third, explore again? Key number? , preliminary perception, inductive law

1, explore the situation of four balls.

(1) Teacher: If we add another ball, there are now four balls, one of which is defective. Can you guarantee to find the defective ball once?

Health conjecture: 4 times? 3 times

Teacher: I think the end of the paper is very shallow, and I never know how to do it. Let's explore for ourselves. Please discuss it with your deskmate. You can borrow a small square and put it on it, or you can draw a picture on paper. Either way, write down the thinking process briefly.

(student group study)

Teacher: How many times have you weighed these four balls?

(The branch diagram of the blackboard written by the reporter)

Teacher: There are two different methods to measure four balls, but the results are the same. It takes at least two times to ensure that defective products are found. (Record the results in a table)

Teacher: If the number of balls is more, say, nine, how many times will it take to ensure that defective products are found? Please pose with your school tools and use your strokes.

(Health reporter shows courseware)

Teacher: Why can we find defective products by dividing 9 balls into (3, 3, 3) only twice?

(Guide students to find patterns and fill in the results in the table)

Teacher: It only takes 2 times for 4 balls and 2 times for 9 balls to find defective products. So, let's make a bold guess. 5, 6, 7 and 8 balls between 4 and 9 need at least several times to find the defective products. Now, let's study in groups: 1 group students learn about 5 balls, and learn 6, 7 and 8 balls in turn.

(health report, focus on 8 balls) (fill in the form with the results)

Teacher: Let's make a comparison. We divided the eight balls into three groups (3, 3, 2) and weighed them twice, but we divided the eight balls into two groups (4, 4) and weighed them three times, which exceeded 1 time. /kloc-where is the overweight of 0/times?

Health: When the number of balls is 2 and 3, it is only used once. Divide 8 into (3, 3, 2) three or two balls in each group, and all three or two balls only need to be weighed 1 time to find defective products.

Teacher: Do you understand what he means? You see, weighing (3, 3) or (4, 4) only takes 1 time to determine where the defective products are, but then, the first time I found them in three or two stores, only once, and the second time I found them in four stores, only twice, so I will use them again.

Teacher: We finally have different weighing times. What is the reason?

Student: The number of groups is different, and the number of people in each group is different.

Teacher: Then how to divide it, so as to ensure that the defective products can be found and the times of weighing can be as few as possible?

(Students report after discussion in groups)

Health 1: It should be divided into three groups, because the balance has two trays?

Health 2: There are fewer people in each group.

S3: Try to keep the number of people in each group as close as possible. After each weighing, the defective products will be determined in a smaller range.

Teacher: You are really something. Through our experiment, discussion and communication just now, we not only solved the problem, but also discovered the secret law of grouping.

(Teacher's blackboard: Divide into 3 groups, and try to score equally. )

Fourth, further discover the law.

Teacher: Now let's try this experiment again by applying grouping rules. If the number of balls is 10 (courseware), how should it be divided? How many times?

(Student report, teacher writing on the blackboard:10 (3,3,4) 3 times) (courseware)

Teacher: What if it's 27? (courseware)

(Student report, teacher writing on the blackboard: 27(9, 9, 9)3 times (courseware)

Teacher: This classmate speaks very well. He first divided into three groups, and then used the idea of transformation to turn the problem into the problem of finding defective nine balls that we solved earlier.

It seems that everyone has mastered the grouping rules. The initial recruitment problem, 8 1 ball, can it be solved? Who has the answer? Write the results directly on the blackboard.

(Students discuss and report the results) (Courseware)

Teacher: Can you find out what this has to do with the 27, 9 and 3 we explained earlier?

(group study)

Health Report: How many balls are measured? Multiply it by 3 and weigh it several times. For example, four balls multiplied by three is 8 1, and 8 1 ball only needs to be weighed four times.

Teacher: You are great. You solved the company? Recruitment? Problem, found again? Between the number of tested items and the minimum weighing times? Mysterious law.

Verb (abbreviation of verb) course summary

With the solution of the recruitment problem, today's class will be over. Looking back on our experience in the whole class, from the initial recruitment problem, to solving the problems of 2 and 3, to the grouping law of 8 and 9, until we studied a larger number, such as 27,81,we found some relations between the number of test items and the minimum number of weighing.

In the process of exploring this road, we have been thinking, practicing and discovering. I think we must gain more wisdom as well as knowledge. Finally, there are two words to encourage you: (Courseware)

Explore problems and learn to simplify.

To solve problems, we must have a sense of optimization.