I. teaching material analysis

Optimization is an important mathematical thinking method, which can effectively analyze and solve problems. This unit mainly takes the operation of "finding defective products" as the carrier, so that students can feel the diversity of problem-solving strategies through observation, guess and experiment. On this basis, they can experience the effectiveness of using optimization strategies to solve problems and feel the charm of mathematics through induction and reasoning.

Second, the teaching objectives:

1. Through observation, guessing, experiment, reasoning and other activities, we can understand the diversity of problem-solving strategies and the effectiveness of using optimization methods to solve problems.

2. Feel the extensive application of mathematics in daily life, try to solve simple problems in real life with mathematical methods, and initially cultivate students' application consciousness and ability to solve practical problems.

Third, the difficulties in teaching:

1. Through the activity of selecting defective products, we can understand the diversity of problem-solving strategies and the effectiveness of using optimization methods to solve problems.

2, the method of picking defective products.

Fourth, teaching measures:

This unit is active and operable, and most of it can be taught by students' hands-on practice, group discussion and inquiry. In practical teaching, students can be given more time to fully operate, experiment, discuss and study, and find various strategies to solve problems. Teachers can focus on solving some sexual problems in activities. If some students find defective products when the number of times of weighing is less than at least guaranteed, teachers should remind students to consider all possibilities. After the activity is completed, teachers can ask students to report the results in groups and show them on the blackboard or screen, so that students can feel that there are many solutions to the same problem, and at the same time lay the foundation for research and analysis for seeking the best solution strategy in the future.

Verb (abbreviation of verb) Class division: **2 class hours.

Lesson 65438 +0? The problem of "finding defective products"

Teaching objectives

1, can analyze the problem of "finding defective products" with the help of paper and pencil, sum up the optimal strategy to solve this kind of problem, and go through the thinking process from diversity to optimization.

2. Through observation, guessing, experiment and reasoning, I feel the diversity of problem-solving strategies and the effectiveness of using optimization methods to solve problems.

3. Feel the extensive application of mathematics in daily life and try to solve simple problems in real life by mathematical methods.

Key points: Through the thinking process of observation, speculation, experiment and reasoning, the optimal strategy to solve the problem of "finding defective products" is summarized.

Difficulties: separating from the real thing, using paper and pencil to help analyze the problem of "finding defective products"

Autonomous space of learning guidance process

Autonomous learning

1. What do you know about balance?

2. (textbook example 1 12) 3 bottles of calcium tablets, of which 3 bottles of 1 are missing (defective products). Can you try to find it?

3. Think about it: Can the process of finding defective products be expressed by the principle of balance?

Try to fill in:

Ping? Heng, (? ) defective (fill in quantity)

Unbalanced, (? ) defective (fill in weight)

It is found that it needs to be weighed () times.

Cooperation and mutual learning

1. Communicate the content of autonomous learning in the group, and send representatives to report the communication in the whole class.

If there are 9 items to be tested, and one of them is defective (the defective product is heavier), how many times can it be weighed with a balance to ensure that it can be found out? (Example 2 on page 1 13 of the textbook)

Discussion: What do you mean by "at least several times …"?

(2) For group activities, fill in the table below according to the method you discussed.

The number of times each party is divided is the number of shares to be weighed.

(3) What did you find by observing the completed form?

? Thinking: What is the relationship between the number of points and the method of points and the number of times to find out the defective products?

? How to find out the defective products with the least number of times? What are the characteristics of this division?

(4) Thinking: Use the method you found to find a defective product in 10 and 1 1 parts. Can you guarantee that the number of defective products is also the least?

3. Summarize the best strategy for finding defective products.

I found that when using the balance to find defective products, we should divide the items to be detected into () parts and try to divide them equally. If they can't be evenly distributed, we should only distinguish between more parts and less parts (? ) to ensure that defective products are found and the weighing times must be at least.

Show and guide learning

The whole class shows the controversial problems in cooperative learning, and the groups take turns to show, supplement or ask questions, and ask and answer difficult questions between groups and between teachers and students and give correct comments.

Evaluation promotes learning.

1, page 1 13 "Do it". Complete independently and modify collectively.

2, there are 5 bottles of vitamins, one of which is missing 4 tablets. If you use a balance, weigh 1 bottle at a time, at least (? ) find a bottle with fewer pills; If you weigh 2 bottles at a time, you need at least (? ) double the search.

3. Find out 1 defective products (slightly light) from 9 items, and divide 9 items into (? ) it is more suitable.

4. There are 8 bottles of water, 7 of which are of the same quality. 1 bottle is sugar water, which is slightly heavier than other water. At least () times can guarantee to find this bottle of sugar water.

Teaching reflection