"Countermeasures" Mathematical Wide Angle - Optimization PPT

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"Countermeasures" Mathematical Wide Angle - Optimization PPT

Part 1: Play the game and explore strategies

Students, do you like playing games? So let’s start this lesson with playing games. Have you ever played poker? Let's play a game of size comparison.

Two sets of playing cards 2, 4, 7 and 3, 5, 8.

The rules of the game: Each side plays a card each time to compare the big and small cards. The big card wins the small card. Whoever wins is the winner. A "win-out-of-three" system is adopted.

Some students like to choose the group 3, 5, and 8 because this group has bigger cards and is easier to win.

It seems that the possibility of winning is greater if the card is big, but it is impossible to win if the card is small? Under what circumstances can a small card be used? You take the small cards, and the teacher takes the big cards. Each time, 3, 5, and 8 are played first. Then you play the cards later and take a look. How many different cards are there? Find out which one can win and why?

Using the smallest card against the largest card is a strategy. It is called using the weak to defeat the strong to ensure victory in the other two games. If you want to win with the strategy of using the weak to defeat the strong, there is a prerequisite: the big cards are played first, and the small cards are played later. (Strive to come out last)

Today we will study this kind of game problem, mathematical wide angle - game strategy.

What was the most crucial part of your win? What is the purpose?

Answer: Play the smallest card against the largest card. The opponent's big card has no effect.

Countermeasures PPT, part 2: Consolidate knowledge and apply what you have learned

1. Shooting game.

Which class is worse in terms of overall strength? How can Class Four (2) compete to win?

Class Four (1) Class Four (2)

Xiaojun 180 pieces/minute Xiaoping 160 pieces/minute

Xiaohong 205 pieces/minute Xiaoqiang 190 pieces/minute

Xiaogang 220 pieces/min Xiaoliang 210 pieces/min

Answer: Class 4 (2) is worse, Xiaoping vs. Xiaogang, Xiaoliang vs. Xiaohong, Xiaoqiang vs. Xiaojun.

Game: Grab 10 game.

Rules of the game: Two people work in groups and take turns to report the number. Each time they can only report 1 or 2. Add up all the numbers reported by the two people. Whoever reports the number first and the sum is 10 will win.

Strategic thinking: If you are asked to report the number first, in order to ensure victory, what number should you report for the first time? What should I report next?

Answer: The first time you should report 1 first. Regardless of whether the second person reports 1 or 2, add the sum to 4. Regardless of whether the second person reports 1 or 2, add the sum to 7. Regardless of whether the second person reports 1 or 2, it is OK. add to 10

Countermeasures PPT, the third part: extracurricular games, expansion and extension

There is also an interesting game popular among Chinese people called "Grab 30 Game".

Game rules: Two people work in groups and take turns to report the number. Starting from 1, each person can report one or two numbers at a time (the numbers reported by two people must be consecutive, for example, A reports 1, and B can only report 2 or 2. , 3), whoever can report 30 first will win.

Think about winning strategies and freely combine games after class.

Answer tip: Since counting from 1 to 30, there are 30 numbers in total, and one person can only count 1 or 2 numbers. Since 30 is an integer multiple of 3, the first person to count will lose.

There are 15 matches. A and B take turns to take them. They can only take 1 or 2 at a time. Whoever gets the last match wins. Think about it: If it were you, in order to ensure victory, should you take the matches first, or should you take them last? How to get it?

Answer: Take it later, and you must take out a multiple of 3 each time.

Knowledge sorting

Game theory studies the strategies that each competing party takes to defeat its opponent. The strategy we used today is to defeat the strong with the weak to ensure victory in the other two games. If you want to win this strategy of using the weak to defeat the strong, you must have a prerequisite, and strive to be the last to attack.

Example analysis

Example 1: Two people take turns counting from 1. Each person can report one number, two consecutive numbers or three consecutive numbers each time. Whoever reports 30 first will be the winner. What strategies should be adopted to ensure victory?

Answer tip: Report first, and you must report the numbers 2, 6, 10, 18, 22, 26, and 30.

Countermeasures PPT, part 4: exercises to consolidate

basic exercises

A racquetball game, best of three games. Please see the information of both parties participating in the competition:

Number of shots the opponent takes in 1 minute: 20 for No. 1, 40 for No. 2, 60 for No. 3

Number of balls our side shoots in 1 minute: 10 for No. 1, 30 for No. 2, 50 for No. 3

Question: How can our players win against each other?

Answer: The opponent goes out first, using our No. 1 against the opponent's No. 3, our No. 2 against the opponent's No. 1, and our No. 2 against the opponent's No. 2.

Expand and improve

A game of poker played at the same table: Two sets of playing cards are shown, namely 2, 4, 8 and 3, 6, 9. If you draw 2, 4, and 8, how can you ensure victory in the best-of-three games?

Answer: The opponent plays first, 2→9, 4→3, 8→6.

Rope skipping competition: pairs against each other, elimination round, best of three rounds.

(1) The approximate number of skipping ropes the female athlete usually does in one minute

142 on No. 1, 163 on No. 2, 180 on No. 3

(2) Approximate number of skipping ropes that the male athlete usually performs in one minute

121 for No. 1, 150 for No. 2, and 150 for No. 3? indivual

If the girl jumps first, the boy has a chance to win. How many times must male athlete No. 3 jump at least in one minute? Why? How do the athletes from both sides match up?

Answer: If a boy wants to win, he must use No. 1 → Girls No. 3, No. 2 → Girls No. 1, 3 → Girls No. 2. That is to say, boys have at least more No. 3s than girls No. 2, so male athletes have No. 3. It takes at least 164 jumps per minute.

divergent thinking

2008 empty squares are arranged in a row, with a chess piece placed on the first square. The two play a game and take turns moving the piece. Each person can move 1 to 5 squares forward at a time. Whoever moves the chess piece to the last square first is the winner. Q: What strategy will ensure victory?

Answer: To win, you should move 4 squares first, and then subtract 6 each time according to the number of squares moved by the opponent. Move as many squares as the number you get. This way you can ensure victory.

Keywords: Free download of PPT courseware for fourth-grade mathematics from the People's Education Press, download of strategy PPT, download of mathematics wide-angle optimization PPT, .PPT format;

For more information about the "Mathematical Wide Angle Optimization Countermeasures" PPT courseware, please click the Mathematics Wide Angle Optimization PPT Countermeasures PPT tab.

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Update Time: 2024-07-01

This template belongs to Mathematics courseware People's Education Press Fourth Grade Mathematics Volume 1 industry PPT template

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