The "magic digital black hole" is "Do you know?" The content of this section appeared after students learned cyclic decimals and used calculators to explore the law. The knowledge point of "digital black hole" is very interesting and occasionally appears in some interesting exercises. I think it is necessary for students to have a preliminary understanding of it, and at the same time, it can stimulate students' enthusiasm for mathematics learning, so as to feel the wonder and mystery of mathematics knowledge!

As the saying goes, there are methods in teaching, but there is no fixed method. The key is to find the right method. In this lesson, I will first introduce what a "cosmic black hole" is, and then slowly lead to a "digital black hole". Then the teacher told the students an ancient myth and legend-"The String of Sisyphus", and finally led the students to explore the digital black hole in mathematics. There are four activities in class, one is to simply understand the digital black hole "123" (odd and even sum), the other is to explore the four-digit black hole "6 174" by teachers and students, the third is to explore the three-digit black hole "495" by students themselves, and the fourth is to read the extracurricular material "Hail conjecture: 3x+65438".

Classroom questioning-classroom record

Teaching content:

People's Education Edition Unit 3 P38 "Do you know?"

Teaching objectives:?

1. Learn about interesting phenomena such as digital "black holes" in mathematics and explore the mysteries of mathematics.

2. Expand extracurricular knowledge of mathematics, publicize the charm of mathematics culture, and cultivate students' interest in learning mathematics.

Teaching focus:

Understand the four-digit black hole "6 174" and explore the three-digit black hole "495".

Teaching difficulties:

Explore the three-digit digital black hole "495" independently.

Teaching preparation:

Courseware.

Teaching process:

First, talk about it?

Teacher: Students, have you ever heard of "black holes"? (Show PPT) Introduce "cosmic black hole": Black hole is a concept in astronomy. It is a very mysterious celestial body in the universe. It's small, but its density is amazing. As long as something is sucked in by it, it never wants to climb out again. Even the strongest x-rays want to escape the gravity of black holes. If we want the earth to be a black hole, we need to compress it to the size of a pea. ) Transition: In the mysterious mathematics kingdom, there is also a mysterious black hole phenomenon similar to astronomy-digital black hole. So, let's take a look at the interesting digital black hole in this class today. (Camera Blackboard: Magic Digital Black Hole)

Second, the new curriculum professor

Introduction of Sisyphus string (123 black hole).

Teacher: In ancient Greek mythology, Sisyphus, king of Corinth, angered the gods by kidnapping the god of death and was punished for pushing a boulder up the mountain. But no matter how hard he tried, the boulder inevitably rolled down before reaching the top of the mountain, so he had to push it again and endlessly. The famous String of Sisyphus is named after this story.

Teacher: Then the students will definitely ask what is a Sisyphus string? Show PPT, that is, take any number, such as 35962, count the even number, odd number and all numbers in this number, and you can get 2(2 even numbers), 3(3 odd numbers) and 5 (five digits in total), and use these three numbers to form the next number string 235. Repeat the above process for 235 to get 1, 2, 3. Repeating the sequence of 123 will still get 123. 123 is a digital black hole for this "universe" composed of programs and numbers.

? The teacher questioned: Can each number finally get 123? Try with a large number. For example: 88883377499222, in this number, the number of even numbers, odd numbers and all numbers are 1 1, 9 and 20 respectively. Add these three numbers to get 1 1920, which is 1 1920. This is the mathematical black hole "Sisyphus string".

For example: any number string, count even numbers, odd numbers and the total number of all digits contained in this number, for example: 1234567890.

Even number: Count the even numbers in this number, in this example, 2, 4, 6, 8, 0, and there are five in total.

Odd number: Count the odd numbers in this number. In this case, it is 1, 3, 5, 7, 9, a total of five.

Total: Count the total number, in this case, 10.

New number: arrange the answers in the order of "odd and even total", and the new number is: 55 10.

Repeat: Repeat the operation of the new number 55 10 according to the above algorithm to get the new number: 134.

Repeat: Repeat the operation of the new number 134 according to the above algorithm to get the new number: 123.

? Third, explore the "capra Carr Action"

1. Understanding "Digital Black Hole 6 174"

What is a "digital black hole"? What are the interesting "black hole numbers" in mathematics? Self-study textbook page 38.

Organize students' feedback and ask: How did the black hole number 6 174 come from?

Keywords: Choose four different numbers, arrange them into the largest four digits and the smallest four digits, and subtract the smallest four digits from the largest four digits to get a number. Then repeat the above operations and finally get 6 174.

Teacher: Encourage students to give examples (try to write them on exercise paper).

Name the students to answer.

2. Inspire students to explore the three-digit digital black hole "495" independently.

3. Students report the results in groups according to the requirements of the exercise sheet.

4. Teachers and students comment together.

? Fourth, reading extension.

The most famous digital black hole: 3x+ 1- hail conjecture

1976 One day, Washington Post reported a math news on the front page. This article tells a story: In the mid-1970s, on the campuses of famous American universities, people were frantically playing a math game day and night. The game is simple: write a natural number n at will and transform it according to the following rules: if it is odd, the next step is 3N+ 1. If it is an even number, the next step becomes N/2. Not only students but also teachers, researchers, professors and pedants have joined in. Why is the charm of this game enduring? Because people find that no matter what number n is, it can't escape and return to the bottom of 1. Accurately speaking, we can't escape the 4-2- 1 cycle that fell to the bottom, and we will never escape such a fate.

This is the famous "hail conjecture".

For example, starting from 7: 7× 3+1= 22 22 ÷ 2 =11? 1 1×3+ 1=34 34÷2= 17? 17×3+ 1=52 52÷2=26? 26÷2= 13? 13×3+ 1=40? 40÷2=20 20÷2= 10 ? 10÷2=5 5×3+ 1= 16

16÷2=8 8÷2=4 4÷2=2 2÷2= 1

After reaching the peak for five times, it will be 1 1 times, and the bottom will be 1.

The greatest charm of hail lies in its unpredictability. John conway, a professor at Cambridge University in England, discovered a natural number of 27. Although 27 is an unremarkable natural number, if you follow the above method, its rise and fall will be extremely violent ... You can boldly guess how many times it takes to reach the bottom "4-2- 1"?

Fifth, emotional sublimation.

Class summary: Students, these black holes in the mathematics we studied together in this class today are conjectures, some of which have been proved and some of which have not yet been proved. Prove them here when you grow up. In fact, many great inventions are all guesses at first. With bold speculation, step-by-step proof and practice, human beings will make progress! Our life will be better! Ok, that's all for today's class. Goodbye, class!

Feeling after class-reflection on teaching

In mathematics, the teaching purpose of reading "reading", "Do you know" and other materials is mainly to broaden students' horizons and broaden their knowledge. The content of the materials is generally lively, interesting and challenging. I mainly organize students to read this reading material from the following two aspects.

1. Read from the perspective of broadening students' knowledge. For example, reading ancient legends such as "Cosmic Black Hole" and "Sisyphus String" not only enriches students' knowledge, but also is very interesting to read. At the same time, it stimulates students' desire to explore and gradually attracts students to try to verify the correctness of "123 black hole".

2. Reading from the perspective of improving students' inquiry ability. Generally speaking, activity requirement is a necessary link to complete the query task. In order to make students understand the activity requirements correctly, I invited a classmate to read the activity requirements, start with the whole, understand the key words, and then lead everyone to break them one by one. For example, the material mentioned "choose four different numbers at will", and my camera asked students to distinguish, distinguish and understand the similarities and differences between "numbers" and "numbers". Immediately, some students blurted out: "Numbers are composed of numbers, and the numbers are only 0~9", which made me feel very gratified.

In class, after students deeply understand the activity requirements, I will organize students to choose four numbers and try to verify the laws mentioned in the materials by themselves in groups. Although it took a lot of time to pave the way, in the end, each group can accurately get the number of black holes "6 174", thus effectively avoiding the repeated intervention of teachers in each group to help them understand. Through the teacher's guidance on reading methods, students have achieved quality and quantity in the inquiry session of this class. Judging from the classroom effect, this class has achieved the following points: First, students have active thinking, a strong atmosphere of inquiry and high learning efficiency. Second, students are easy to learn, like to learn, and have a high degree of classroom participation. Students of different levels can give one or several examples to try to verify according to their own understanding of the materials.

As we all know, reading ability is the core ability of learning. With the increasing penetration of modern science and technology into all aspects of life, the digital phenomenon of society is becoming increasingly obvious. It is not enough for students to have Chinese reading ability. Therefore, as mathematics teachers, we should also attach importance to the teaching of mathematics reading, make full use of the forms of reading materials, and cultivate students' reading ability. In this way, students can not only learn knowledge-explore laws-exercise their thinking in the process of mathematics reading, but also feel the infinite charm of mathematics by exploring mathematical laws, so that the beauty of reading can shine in mathematics classroom!