Today, I saw such a problem in the training of Mathematics 1+2. A cubic casting with a bottom area of 648 square centimeters, what is the remaining three-dimensional graphic area after removing the largest cylinder and taking the opposite side as the bottom?
Seeing this topic, I was very confused and thought: just say a bottom area, how to do it? My mother sitting in the chair looked at it, smiled at me and said, "Hum, she can't even do this problem."
I know my mother used the goad method, in order to irritate my competitive spirit and let me finish this problem. In order to make my mother think that her provocation was successful, I crustily skin of head did it, but I couldn't figure it out. But I'm not discouraged. I persisted and finally succeeded.
According to the drawing (to be drawn), it can be found that when a cylinder is cut off, a hole with the same size as the original cylinder will come out. Although the volume of the hole is the same as that of the cylinder, their surface areas are not the same, but the areas of the two bottoms are smaller than that of the original cylinder.
Therefore, the remaining graphic area should be equal to the area of the six faces of the cube minus the two bottom faces of the cylinder+the side faces of the cylinder.
The formula is 628× 6-628× 3.14 ÷ 4× 2+628× 3.14.
Today is another sunny day. I was wandering in the street when I suddenly saw a lot of people gathered not far away. I ran for a year, and the result was a prize-winning game. "Hum, what's fun about winning the prize?" I was bored when the person next to me quickly said, "It's not fun to grab the prize, but there is a big prize that can attract people." I asked eagerly, "What is it!" "50 yuan money." The man with big eyes said. I'm very excited to hear that. "I have to try anything for such an attractive prize." Then I asked the shopkeeper how to grasp the rules. The shopkeeper said, "This is 24 Mahjong, and it says 12 5, 12 10. You can only catch 12 mahjong at a time. If the total number of 12 mahjong targets is 60, then you can win the 50 yuan Prize. " Without rolling up my sleeves, I took out 5 yuan money from my pocket and gave it to the shopkeeper.
Although I won 10 times, I still didn't win the grand prize.
When I got home, I thought about it and felt something was wrong. I think, to get 60 points, all 12 mahjong should be marked with 5. In the best case, the first 1 second catch 1 5, the second catch of two 5 s and the third catch of three 5 s will cost at least 6 yuan money. But what if the target number of mahjong is 10 or the sum of the two is the same, how many times will it cost?
Finally, after some consideration, I finally figured it out. I rushed to the street to get even with it, but it had disappeared without a trace.
There are two candles with different thicknesses. A thin candle is twice as long as a thick candle. It takes 1 hour to light a thin candle and 2 hours to light a thick candle. Once there was a power failure, two used candles were lit at the same time. When the phone call came in, I found that the remaining length of the two candles was the same. How long was the power outage?
Solution: If the candle length is 1 and the burning speed is (1)1÷ 2 =1/2 (2) 2 ÷1= 2, the formula is: 65438.
Solution: Set the power outage time as x hours.
1— 1/2X=2—2X
X=2/3
A: The power outage time is 2/3 hours.
I saw such a problem in the "two-color class for primary school students" this afternoon.
The bottom radius of the cone is 8 decimeters, and the ratio of height to bottom radius is 3: 2. What is the volume of this cone?
Analysis: This is an application problem that combines the application problem with the cone problem in proportion. To calculate the volume of a cone, you need to know the bottom area and height of the cone. The topic is about the radius of the bottom surface, so we can find the bottom area, but we don't know the height. You can find it according to a condition, and convert the ratio into a number that accounts for a fraction of the known number, so that you can know that the height accounts for 3/2 of the radius of the bottom surface. After calculating the height, calculate the volume of the cone according to "V=SH÷3".
Every time I go to Tomb-Sweeping Day, there will be a sea of people on the giant mountain, so some swindlers come up with some deceptive tricks, such as gambling on something on a plate.
Prop is very simple, draw a big circle on a board, and fix a rotatable pointer in the center of the big circle with a nail. The great circle is divided into 24 equal squares, and the needles in the squares can rotate. The box says 1-24 equal numbers, which are worthless in the odd box, but almost all even numbers are valuable.
The gameplay is also very simple. Set the pointer to 1 first, then you dial the pointer again, and the pointer will start to rotate and finally stop in a grid. Then press the number marked on the grid where the pointer is located and dial the pointer again. N- 1 grid, where n is the number marked on the grid.
This is just a little math game. In fact, no matter which box you dial, you can only lose money, not make money. Because when the pointer turns to an odd cell, the number of cells dialed is odd-1= even, and odd+even is only equal to odd, so it is impossible to turn to an even cell and nothing valuable can be obtained. If the pointer turns to an even grid and the number of grids dialed is even-1= odd, and odd+even = odd, then you won't get anything of value.
Today, I listened to an open class of "prime numbers and composite numbers" taught by multimedia. After listening to this, he felt something. Originally, multimedia teaching is an organizational means to help teachers, which can better serve teaching, increase the novelty, uniqueness and profundity of teaching and make it more attractive. For such a long time, I proposed to carry out quality-oriented teaching for students. But after listening to several multimedia classes, I showed the shadow of injection. On the other hand, multimedia teaching can better arouse students' enthusiasm, and teaching focuses on serving students rather than computers. Whether it can lead to the * * * of the majority of front-line teachers!
Today is a sunny noon. Reading a math newspaper at home, I came across the topic of seeking comparison and simplification. I don't think I learned this last semester. But on second thought, I'd better have a look!
There are differences and connections between "seeking comparison" and "simplifying comparison". Students should pay attention to the following points when studying:
1, the purpose of comparison is to find the result of dividing the previous item by the later item; The purpose of simplifying the ratio is to change a ratio into an integer ratio that is equal to it and the front and back terms are coprime.
2. Calculating the ratio is similar to simplifying the ratio. There are the following:
Basic properties of (1) utilization rate. For example:
5/6:1/2 = (5/6× 6): (1/2× 6) ① The ratio is 5/3; ② The simplified ratio is 5∶3.
(2) The relationship between ratio and division. For example:
6.3∶0.9=6.3÷0.9① The ratio is 7; ② The simplification ratio is 7∶ 1.
(3) Use the relationship between proportion and score. For example:
16: 20 =16/20 = 4/5 ① the ratio is 4/5 or 0.8; ② The simplified ratio is 4∶5.
3. The result of the ratio is a number, which can be an integer, a decimal or a fraction; The result of simplifying the ratio is a ratio, which can be written in the form of true fraction or false fraction (see the example above), but not in the form of integer, decimal or fraction. The result of simplifying the ratio should be read as several ratios, such as 16: 20. The simplified scale is 4/5, which should read: 4: 5.
It can be seen that as long as you read more materials about mathematics, your grades will be improved.