-From "magic" to "magic number", let children enter the hall of intelligent mathematics.

? Leping city 9 th primary school Jiang

In late March, 2065438+2007, I had the honor to participate in the 17th national seminar on "Meeting famous teachers and focusing on the classroom" in elementary school mathematics teaching, which was jointly organized by the Education Science and Technology Center of Beijing Culture Festival and the National Organizing Committee in the beautiful coastal city of Xiamen. During this period, I was deeply moved by Wu Ruhao, a junior high school math teacher in Taipei, who gave a lecture on "Mathematical Magic Class with Active Thinking".

Mathematical magic is a strange entry point for students to enter the mathematical world, giving them a brand-new feeling, and it is also a new idea and breakthrough for mathematics teachers to teach mathematics. Let students learn mathematics by magic, experience the magic of magic in mathematics, and experience the mathematical scenery hidden behind magic, so as to travel freely in the vast hall of mathematics. Now share some highlights as follows.

First, read the cards according to the dice.

Magic props: a deck of playing cards (excluding kings and kings), a dice and a deformed template (as shown in Figure ①).

The magical process:

1. Ask an audience to be a helper, and the helper will cut the cards prepared in advance at will;

2. The helper rolls the dice at will and reads the upper and lower points (3 points above and 4 points below);

3. The helper shall calculate according to the following requirements, and the magician shall deal cards according to the number (as shown in Figure ②):

On it, if 3× 3 = 9, the magician takes out 9 cards from it;

Up and down as 3× 4 = 12, the magician takes out 12 cards from it;

Multiplied by 4× 4 = 16, the magician will take out 16 cards from it;

Multiplied by, for example, 4× 3 = 12, the magician will take out 12 cards from it;

4. Take one card from the remaining cards and put it aside (as shown in Figure ③);

5. Take out the deformed template and signal the audience to watch it, which is a bunch of unrecognizable garbled codes;

6. The magician deforms the deformed template to obtain the pattern of spades K (as shown in Figures ④ and ⑤);

7. The magician magically reads the card put aside as the K of spades and checks it over (Figure 6).

Figure ①

? Figure ②

? Figure ③

? Figure ④

? Figure ⑤

? Figure 6

Decryption instructions and mathematical principles;

Setting of the six sides of the dice: 1 opposite to 6, opposite to 2 and 5, opposite to 3 and 4. When you roll dice at will, the sum of the top and bottom must be 7, and the sum of the products of the top, top, bottom, bottom and bottom is a fixed value of 49. There are 52 cards in a deck. Before you cut the card, put the K of spades in the penultimate card. The helper cuts the cards at will, and the magician cuts the cards at will, confirming that the penultimate card is the king of spades. The deformation template is set into spades K pattern in advance and converted into garbled code. In the process of magic, the top 49 cards are removed by rolling dice, and then the 50th card, the penultimate card, is put aside (this card is the prepared spades K). Then use the deformation template to pretend to be spades. Finally, turn out the spades and show your magic. If the penultimate card is not the K of spades but another card, remember this card, and cancel the deformation template deformation steps 5-6 in the magic process, and pretend to guess this card before the flop (the penultimate card remembered after cutting the card).

Second, God added seconds to count.

Magic props: 4 sticks (as shown in Figure ① below);

The magical process:

1. Please invite two spectators to go to the stage to be assistants, of which Assistant A is responsible for the operation and Assistant B uses a calculator to calculate;

2. Operator A randomly puts four sticks together to form four four-digit numbers for addition (as shown in Figure ②): 6386+5773+9257+7839);

3. Operator B uses the counter to calculate the results, and the magician uses his heart to calculate the results and compare the results (29255);

4. Operator A randomly flips the bar or randomly changes the position of the bar (as shown in Figures ③ and ④);

5. Operator B and magician calculate and compare the results at the same time;

6. The magician's calculation result is correct and the speed is amazing.

? Figure ①

? Figure ②

? Figure ③

? Figure ④

Decryption instructions and mathematical principles;

In the process of making several sticks, the sum of the numbers 1, 2 and 4 from top to bottom is the fixed value 18, and each side of each stick is the same. In the process of magic mental arithmetic, you only need to subtract 2 from the four digits in the third line to get a digit, and copy the ten digits, the hundred digits and the thousand digits. Ten thousand digits is 2, which is the sum of four four digits. Such as: 6386+5773+9257+7839=29255. The ingenious calculation process is: 7-2=5, make a number, copy the numbers of ten, hundred and thousand, ten is 5, hundred is 2, thousand is 9, and ten thousand is the fixed number 2.

According to the idea of fixed value, in the process of making several sticks, the sum of four numbers on each side of each stick is set as fixed value 19, and its sum is also set as fixed value 2 1 109, which can show charm in magic.

Third, recognize money with your palm.

Magic props: some coins;

The magical process:

1. Invite an audience to help;

2. Ask the helper to put some coins on the table while the magician is standing and observing (as shown in Figure ①);

3. The magician turns his back, and the assistant flips two coins randomly several times with both hands (Figure 2);

4. The helper takes out a coin and holds it in his palm (Figure ③);

5. The magician turned around and observed the coins on the table;

6. The magician can tell whether the coin is "word" up or "flower" up with his palm (Figure 4).

? Figure ①

? Figure ②

? Figure ③

? Figure ④

Decryption instructions and mathematical principles;

(1) If the number of coins is even, the upward numbers of "word" and "flower" are either even or odd. Before the magic begins, the magician should remember whether the number of coins with the word and the flower facing up is even or odd.

If they are all even numbers, after the helper holds down a coin, the magician observes the situation of the coins on the desktop, and whether the odd coins are "characters" or "flowers": if they are "characters", the helper holds down "characters"; If it is a "flower", the helper holds down the "flower".

If they are all odd numbers, after the helper holds down a coin, the magician observes the coin on the desktop, and whether the even number of the coin is "word" or "flower": if it is "word", the helper holds down "word"; If it is a "flower", the helper holds down the "flower".

(2) If the number of coins is odd, the upward numbers of "Zi" and "Hua" must be one.

One is even and the other is odd. Before the magic begins, the magician should remember whether the number of coins facing up is even, whether it is "word" or "flower".

If the number of coins facing up is even, after the helper holds down a coin, the magician observes the situation of coins on the table: if the number of coins facing up is odd, the helper holds down this word; If the number of coins with the word "Shang" is even, the helper holds down "Hua".

If the number of coins facing up is even, the magician observes the situation of coins on the table after the assistant holds down a coin: if the number of coins facing up is odd, the assistant holds down the coin; If the number of coins with "flower" facing up is even, the helper holds down the word.

The core mathematical principle of this magic is that after two coins are flipped randomly with both hands for several times at the same time, the parity of the number of coins with "word" and "flower" up will never change.

Fourth, inspiration guessing words.

Magic props: a calculator and a dictionary;

The magical process:

1. Invite an audience to help; Ask the helper to randomly select three different numbers from the ten numbers of 1 to 9 to form a three-digit number and record it (for example, 861);

2. Write this three-digit number backwards to get another three-digit number (such as168);

3. Subtract these two three digits to get a new three digits (such as 693);

4. Write this new three-digit back to get another three-digit (such as 396);

5. Add the last two three digits to get a new four digits (such as1089);

6. Subtract 1000 from this new four-digit number to get the final result (such as 89);

7. Turn to this page of the dictionary according to the final result. The first word is "when" (when the chest is a punch);

8. The helper opened the dictionary and magically found that the result was true.

? Figure ①

? Figure ②

Decryption instructions and mathematical principles;

The difference (e.g. 297) between a three-digit number composed of any three different numbers (e.g. 9 16) and the anti-three-digit number of this three-digit number (e.g. 6 19) has a characteristic that all ten digits are 9, and the sum of digits and ten digits is also 9. Compare such a three-digit number (such as 297) with its last three digits. Finally subtract 1000 to get a fixed value of 89. As for the first word on page 89 of the dictionary, we know it in advance. If we have a dictionary or other books with pages over 1089, we can directly guess the first word on page 1089 in the last step without subtracting 89.

Magic is a kind of performing art aimed at violating objective phenomena. Magic strengthens the emotional component of mathematical abstract concepts and creates cognitive conflicts while deftly violating objective phenomena. This collision between vision and thinking makes the next exploration and attempt more sensible, and the process of groping with feelings is the most direct experience of students to mathematical methods. Students' knowledge of mathematics should not be just a mess of pieces. The goal of mathematical magic is not only to acquire mathematical knowledge, but also to let students experience mathematical thinking. Professor Hong Wansheng once said: Mathematics is great. It teaches you not to be confused by the appearance of things. Some simple answers are hidden there-and you can find them with the right tools. Mathematical magic will temporarily confuse you with the appearance of things, knowing that there is a simple answer hidden inside, but you can't see it. You should pursue the eternal law behind the chaotic appearance with curiosity and enthusiasm.

In the exploration of mathematical magic, using magic phenomenon can stimulate students' learning motivation and interest, increase students' sense of participation through appropriate hints and tasks, closely link mathematical concepts with gradual explanations, and use designers' thinking to turn a single magic into thousands of infinite possibilities through mathematics and creativity. Therefore, students can experience in participation: curiosity about phenomena → active observation and recording of operation process → finding eternal laws in changing examples → learning to imagine and create after applying laws.

Mathematical magic is a concept of artificial art packaging mathematics, which gives mathematics a different look. Yes, "Why on earth did this happen?" Our doubts and curiosity provide emotional motivation for positive thinking. Teachers can start a series of mathematical magic from the operation of playing cards, scraps of paper, coins, calculators and dice, create opportunities in the impossible, see eternal establishment in the opportunity, light up students' hearts, stimulate and cultivate students' strong interest, let interest be the best teacher, lead students from "magic" to "magic number", and invite them to swim in the knowledge hall of intelligent mathematics world.