Elementary school third and fourth grade mathematics problem case analysis encyclopediaThe following is a case study of a third or fourth-grade elementary school math problem:
* * Year 1 and Year 3 Mathematics Case Study **
1. * * 24 points **
- * * Question examples **: 1, 1, 5, 8; 5, 6, 7, 8; 1, 2, 5, 10; 2, 2, 10, 11, etc.
- [Analysis]:
- For the set of numbers 1, 1, 5, and 8, the solution was to first perform a simple combination operation on the numbers. Here, 3 is obtained by 5 - 1 - 1, and then multiplied by 8 to obtain 24, which is (5 - 1 - 1) × 8 = 24.
- There were many ways to solve the set of numbers 5, 6, 7, and 8. For example, if you calculate 8 × (7 - 5) × 6, you first calculate 7 - 5 = 2 in the parenthesis, then divide 8 by 2 to get 4, and finally multiply by 6 to get 24. You can also calculate 8 - 6 = 2 and 7 + 5 = 12 in the parenthesis by (8 - 6) × (7 + 5), then multiply to get 24. You can also use (7 - 8 + 5) × 6 to calculate 7 - 8 + 5 = 4, then multiply by 6 to get 24.
- For the set of numbers 1, 2, 5, and 10, the idea of 10 × 5 div2 - 1 was to first calculate 10 × 5 = 50, then divide by 2 to get 25, and finally subtract 1 to get 24; or 10 × 2 + 5 - 1, first calculate 10 × 2 = 20, then add 5 minus 1 to get 24.
- For the set of numbers 2, 2, 10, and 11, the idea of (2 × 11 - 10) × 2 was to first calculate 2 × 11 = 22, then subtract 10 to get 12, and finally multiply it by 2 to get 24.
2. * * Diagram Area (Cut and Complement Method)**
- [Question example: Find the area of an irregular graph.]
- [Analysis]:
- For example, if there was an irregular pattern, he could use the method of cutting and filling. If it was divided, it might be divided into a square and a rectangular. When calculating, the area of the square was first calculated. If the horizontal side was 4 decimeters and the vertical side was 8 - 4 = 4 decimeters, the area would be 4 × 4 = 16 decimeters square. If the length of the rectangular shape was 10 decimeters and the width was 4 decimeters, the area would be 10 × 4 = 40 decimeters square. Then the area of this irregular figure would be 16 + 40 = 56 decimeters square.
- You could also use the filling method and see it as a big rectangular minus a small rectangular. The large rectangular area was 10 × 8 = 80 decimeters square, while the small rectangular area was 10 - 4 = 6 decimeters long, 8 - 4 = 4 decimeters wide, and 6 × 4 = 24 decimeters square. Therefore, the required area was 80 - 24 = 56 decimeters square.
3. * * Date related questions **
- [Question example: May of a certain year has five Saturday and four Sunday. What day is May 1st?]
- [Analysis]:
- There were 31 days in May. You can draw a simple calendar frame to help understand. Since there were five Saturday and four Sunday, it meant that the 31st was a Saturday. Then, in order, minus seven days, the 24th, 17th, 10th, and 3rd were all Saturday, so May 1st was a Thursday.
* * Mathematics cases in the second and fourth grades (using the Jiangsu Education Press as an example)**
1. * * Integer-Based Operations **
- * * Question Type **: This is a calculation question that tests the understanding and mastery of addition and substitution.
- [Analysis]:
- These questions were designed to help students consolidate their basic knowledge of integral arithmetic and improve the accuracy of their calculations. For example, some addition and substitution formulas for numbers might be given, and students needed to calculate them accurately according to the rules. Students had to master the basic operation rules such as digital alignment, carry, and abdication to avoid calculation errors.
2. * * Area and Perimeter **
- * * Question Type **: Questions involving the calculation of the area and perimeter of a rectangular and square.
- [Analysis]:
- For a rectangular shape, the area is equal to length multiplied by width, and the perimeter is equal to 2 × (length + width). For a square, the area is equal to the square of the side length, and the perimeter is equal to 4 × the side length. For example, if the length and width of a rectangular shape or the length of a square were given, the student would need to use the formula to calculate it accurately. In the process of solving the question, one had to pay attention to the unity of units. If the length and width given by the question were different, one had to first convert the units before calculating.
3. * * Time and Date **
- * * Question Type **: Questions involving calendar, time period, and time conversion.
- [Analysis]:
- For example, calculating the number of days or time intervals between specific dates, as well as converting time (such as hours and minutes). Students needed to understand the basic concepts of having 24 hours in a day and 60 minutes in an hour. When calculating the date difference, one had to consider the difference in the number of days in the big month and the small month, and the difference in the number of days in February in leap years.
4. * * Charts and graphs **
- * * Question Type **: Questions that involve the collection and arrangement of data, as well as the analysis and comparison of charts and graphs.
- [Analysis]:
- For example, if a bar chart or line chart was given, the student would need to read the data from the chart, answer relevant questions, or further analyze the data. This required students to understand the meaning of the horizontal and vertical coordinates of the chart, accurately read the data, and compare and analyze the data, such as finding the maximum, minimum, and the trend of the data.
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What was the position of a general in ancient times?In ancient China, a general was a high-ranking military officer and a military official. It could also be used as a title. Generals in different dynasties had different positions:
- In the Han Dynasty, the ranks of generals were divided carefully. The general was the head of the generals, and his official position was equal to that of the three princes, sometimes above the three princes, sometimes below the three princes; The position of the general of hussars was below that of the general of hussars, and it was equal to that of the three princes. The position of the general of chariots and horses was below that of the general of hussars, and it was equal to that of the three princes. The position of the general of Wei was below that of the general of chariots and horses, and it was equal to that of the three princes. Zhonglang General was one of the ranks of military officers in the Han Dynasty. It was below the general and above the lieutenant. Usually, the highest official position that ordinary military officers could obtain was Zhonglang General. The rank was "Bi 2000 Shi" and was in charge of the royal guards. During the Three Kingdoms period, Zhonglang General gradually became a middle and lower rank officer position. A lieutenant was slightly lower than a Zhonglang general, and his rank was "more than two thousand stones." During the reign of Emperor Wu of the Han Dynasty, eight lieutenants were set up to take charge of the central army. During the Three Kingdoms period, lieutenants became low-ranking officers. Other than that, there were also the Four Army Generals (Front General, Left General, Right General, and Back General), Four Conquest Generals, Four Town Generals, Four Peace Generals, and Four Peace Generals. There were also positions such as Grand Governor (set up by Cao Wei, first grade, not often set up), Governor (set up at the end of the Eastern Han Dynasty), and General.
- In the Tang Dynasty, the ranks of generals varied. The first grade had General Tiance (only Li Shimin); The second grade had General Fuguo; The second grade had General Zhenjun, Grand Governor, Grand Protector, etc. The third grade had many positions such as Champion General, Huaihua General, etc. The third grade had General Yunhui, General Guide, etc. The fourth grade had General Zhongwu, General Zhuangwu, etc. The fourth grade had General Yiwei, General Wei, etc.
- In the Qing Dynasty, among the military officials in the capital, the first grade had positions such as the minister of the imperial guard, the minister of the imperial guard, and so on.(Here are only some examples of the different situations of the general's related positions in different dynasties.)
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