Teaching plan:
Teaching presupposition in teaching links
First, the problem situation
1. The teacher took out his key and pulled out the combination lock. Tell me where or where you have seen combination locks and how many numbers you have seen combination locks.
Teacher: Students, look at what the teacher has in his hand.
Health: Keys.
Teacher: Yes, these are the keys to the lock. In real life, there is another kind of lock that doesn't need a key. Do you know what the lock is?
Health: password lock
Teacher: Who knows where password locks are often used?
Students may say: safe, safe, suitcase, etc.
Teacher: It seems that the students know a lot, so who can tell me how many digital locks have you seen?
Students may say:
I have seen a three-digit combination lock on the suitcase.
I have seen a six-digit combination lock on the safe.
● The combination lock on some safes is 8 digits.
2. Ask Dr. Rabbit questions and communicate with teachers and students. Teacher: Then who knows why the combination lock is used on the suitcase instead of the key lock?
Students may say:
● Not afraid of losing keys.
● Can be kept secret. If others don't know the password, they can't open it or copy it.
……
Teacher: Another important reason is that when a password consists of a certain number of numbers, there will be many changes, that is, many passwords can be formed. Even if you know what the password lock is, it is difficult to judge which password it is. Today, we will learn the secret of digital password lock.
Blackboard: digital password lock
Second, explore the password lock
1. This paper puts forward the question of how many passwords two numbers make up, and requires students to write passwords consisting of 0 and 1 respectively.
Teacher: Now, let's study the simplest case first. If the password of a digital lock is composed of two numbers, think about it. How many passwords can ten numbers make up: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9? Write it yourself in this book. How many passwords can be formed starting from 0?
Students write down the password and then communicate, and come to the conclusion:
Starting from 0, the passwords of 10 are 00, 0 1, 02, 03, 04, 05, 06, 07, 08 and 09.
Blackboard writing: starting from 0- 10
Teacher: Let's start with 1 How many passwords can you write?
Students communicate after writing and draw the following conclusions:
Starting from 1, the passwords of 10 are 10,1,12, 13, 14 and/kloc-0 respectively.
Blackboard: 1- 10.
Teacher: Think about it. How many passwords can be formed starting from 2?
Health: 10.
2. Put forward separately: How many can 3, 4, 5, 6, 7, 8 and 9 make up? How many can one * * * make up? Students discuss and draw a conclusion: 10× 10= 100 (teacher): How about starting with 3, 4, 5, 6, 7, 8 and 9 respectively?
Health: It can be composed of 10 respectively.
Teacher: A *** 10 number, and each number can form 10 passwords. How many passwords can a * * * form?
Health: A * * * can add up to 100.
Teacher's blackboard writing: 10× 10= 100 (sheets)
3. The teacher told the students to use three numbers to form a 1000 password, encouraging students to cooperate in calculation. Teacher: Just now, by writing several groups of passwords, we worked out a two-digit password consisting of 10 numbers from 0 to 9, which can add up to 100. Do you want to know how many passwords this 10 number can make up?
Teacher's blackboard:10×10×10 =1000 (Zhang)
Teacher: It can be composed of 1000. Do you know how to calculate this result? Students cooperate and try to calculate.
Students do their own calculations first, teachers patrol and give individual guidance.
4. Communicate students' calculation methods and explain the accuracy of the results. Give students ample opportunities to exchange different ideas. Teacher: Who will report it? How did you work it out?
Students may have the following statements:
● The numbers that make up the password can all be ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. If the first digit is 0, the second digit is 0 and the third digit is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, that is, 000,001,002,003, ... 009 * * 65438.
If the first digit is 0, the second digit is 1, and the third digit is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, namely: 0 10/65438,06544. ....., so the passwords with the first digit of 0 * * are 10× 10= 100 (pieces).
Similarly, the first digit is 1, with 100, the first digit is 2, with 100 ... the first digit is 9, with 100, so the password consisting of three digits * * has10× 650.
● Use 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to form 100 two-digit passwords, and add a number after each password to form 10 passwords, so a * * can form10 passwords.
● If you start with any of the ten numbers of 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, you can form (10× 10) two-digit passwords, then a * * can form/kloc-0.
As long as students can speak their reasoning process boldly, whether it is correct or not, teachers should encourage them first, and then teachers should participate in communication. Xiaojingling children's network
5. Briefly explain the relationship between 1000 passwords and the password box, and then ask the students to calculate how long it takes to secretly open a three-digit password box. Communicate after calculation. Teacher: Students use different methods to calculate the password consisting of three numbers: 1000. As we all know, a password box has only one password, that is, a three-digit password lock is only one of 1000 passwords. So it is easy for people who know the password to open it, and it is difficult for people who don't know the password to steal the box. Do you know what the difficulty is?
Health: He has to try one by one.
Teacher: Yes, you have to try one by one, so it may take 1000 times to open it. Please calculate, if it takes 10 second to try a password, how long will it take to try 1000 times?
After the students finish the calculation, exchange the calculation results.
1000×10 ÷ 60 ÷ 60 ≈ 2.7 (hours)
6. Tell the students that there are 1000000 passwords composed of six numbers, and ask the students to calculate how many days it takes to open such a password lock. Teacher: I don't know the password. It takes nearly three hours to open the three-digit combination lock. Important file boxes are all password locks composed of six digits. There are 1 0,000,000 such passwords (blackboard: 1 0,000,000). People who don't know the password will spend more time trying to open the box. Please calculate it. If it takes 10 second to try once, how many days will it take to open the six-digit password lock?
Students report the calculation results.
1000000×10 ÷ 60 ≈16666 (point),
16666÷60≈277 (hours),
277÷24≈ 1 1 (days)
Teacher: It can be seen that the security of digital password lock is very strong, because it takes a long time to open a lock without knowing the password, which increases the security of password lock. Therefore, people often put valuables or important documents in a safe and reliable password box to prevent leakage or loss.
Thirdly, the issue of car license plate.
1. Let students read and answer by themselves. When communicating, talk about how it is worked out.
Teacher: The problem of digital password that we learned just now actually used the knowledge of the composition of numbers in mathematics. Please open page 79 of the book and look at the problem of car license plate. Try to figure out how many license plates can be added.
Students try to calculate, and teachers patrol.
Teacher: Who can tell me what you think? How is it calculated?
Health: There are four numbers:10×10×10 =10000 (pieces). Adding a letter before these numbers can increase 10000.
Fourth, the telephone number problem.
Put forward the telephone number problem and encourage students to cooperate to solve it. When communicating, give students the opportunity to express different opinions.
Teacher: With the improvement of people's living standards, not only private cars have developed rapidly, but also the number of telephones in the world has increased at an unprecedented speed. Please solve the problem of telephone number increase on page 79 of the book. This question is very difficult, try it! We can discuss it at the same table.
Discuss at the same table and have a try.
Teacher: Who can tell us how you did it? What was the result?
Students report the situation and teachers participate.
Students may have the following results:
● It consists of five numbers:10×10×10×10 =100000. Adding a number to each of the 65438+ million numbers can increase 6544. Therefore, a * * * can increase 1 ten thousand, that is,10000×10 =100000 (pieces).
● The telephone number does not start with zero, so zero should be removed. So the five-digit telephone number is10×10× 10×65438 = 90000 (units), and it becomes10× 65438 after it becomes six digits.