One Sunday morning, my friends and I went to play basketball.
After a while, we were tired of playing and went to the audience to have a rest. Suddenly I thought of a question and couldn't help but say it: "Xiaoming throws 8 balls a minute, Xiaohong throws 6 balls a minute. After they throw together for 8 minutes, Xiaohong improves the hit rate and throws 8 balls a minute. Xiao Ming only throws six balls a minute because of physical exhaustion. How many minutes later, Xiaohong and Xiaoming threw the same number? "
Probably because my friend is too tired to answer such a simple question. He thought for a while, but didn't come up with it. After a long time, he still didn't figure it out. As time went by, he really couldn't think of it, so he had to say shyly, "It can't be done without a draft." I know that even if he has a draft, he may not be able to do it.
I proudly said, "It turns out that Xiao Ming scored two goals more than Xiao Hong in one point, which is 8×2= 16 (1). Later, Xiaohong, in turn, scored four more goals per minute than Xiaoming. How many minutes does it take for 16? " 16÷4=4 (minutes), it takes 4 minutes to catch up. "He said," You are amazing! " "I am a genius!" I joked. We all laughed.
Through this incident, I found that mathematics is everywhere in life, in life, study and work. Since then, I like math even more.
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Wonderful water level
In life, everything can be changed from an ordinary trivial matter to a vivid and thought-provoking math problem. The applied problems that we often do are the problems that are made from materials in life and then slightly adapted. No, I found an interesting problem when I was doing a math problem: in a swimming pool, there is a boat with many stones on it. Now all the stones are thrown into the water from the boat. Will the water level in the swimming pool rise, fall or remain the same?
At first glance, I am puzzled: this question seems to have nothing to do with mathematics! What should we do now? Not discouraged, I thought hard and soon came up with a clue: when a stone is thrown into the water, the weight of the ship is reduced and the water level will rise and fall, but the stone occupies a part of the space in the water and the water level will rise with it. Because this is the same pile of stones, the fluctuation range should be the same, and the water level must be the same! But dad saw it and said it was a decline. I was not convinced and decided to make a bet with him.
But, with what to prove my guess is correct or not? At this time, the abstract imagination has no real operation. So, with the help of my father, I did an experiment: because of my limited ability, I couldn't move a swimming pool from outside or build a boat, so I had to narrow down the conditions in the problem in proportion. The swimming pool became a plastic basin, the boat became a soap box, and the stone became five erasers. I first poured some water into the plastic basin, then put the soap box with five erasers into the water, and then measured the water level as 20 cm with a ruler. The most critical moment has come. I carefully took out five erasers from the soapbox, put them all into the water, and finally measured the water level with a ruler-oh, my God! Only 18 cm, drop! I was wrong!
Although it turns out that the water level has dropped, I am still a monk-I have no idea at all: how can this water level drop?
I thought hard for a long time, and the draft paper was full of demonstration pictures, but I was still at a loss. I'm in a rash, but the more anxious I am, the more confused my mind is, and I can't think of it. Just when I was about to give up, I suddenly remembered the story of mathematician Chen Jingrun, who worked tirelessly to solve the problem day and night. My blood seems to be full of indomitable strength, and no difficulty can stop me. Sure enough, in less than half an hour, I finally figured out this problem: when the stone is on board, the weight of rising water is equal to the weight of the stone, and the density of the stone is greater than that of water, so the volume of water is greater than that of water and stone with the same weight. When a stone is thrown into the water, the water will reduce its weight, and the stone will occupy space in the water. So after the stone is thrown into the water, the volume of water rising is equal to the volume of the stone. And the same volume of water and stone, the weight of water is less than the weight of stone. To sum up the above points, we can get the following results: after a stone falls, the water level drops more than the stone, and the water level rises less than the stone, that is, the weight of falling water is greater than that of rising water, so the volume of falling water is greater than that of rising water, and the water level naturally drops. In this way, a difficult problem is solved.
In fact, careful observation shows that this problem is inseparable from mathematics, and its volume, weight and density all belong to the category of mathematics. You see, a little thing in life can also become a math problem. Mathematics is everywhere. Let's love mathematics and learn it well.