In the evening, I saw a problem in the Olympiad Book: the number of apple trees in the orchard is three times that of pear trees. Master Lao Wang fertilizes 50 apple trees and 20 pear trees every day. A few days later, all the pear trees were fertilized, but the remaining 80 apple trees were not fertilized. Excuse me: How many apple trees and pear trees are there in the orchard?

I am not intimidated by this question, but it can stimulate my interest. I think the apple tree is three times as big as the pear tree. If two kinds of trees are to be fertilized on the same day, Master Lao Wang will fertilize "20×3" apple trees and 20 pear trees every day. In fact, he only fertilizes 50 apple trees every day, which is 10, and the last 80 trees. Therefore, Master Lao Wang has been fertilizing for 8 days. 20 pear trees a day, 8 days is 160 pear trees. According to the first condition, there are 480 apple trees. This is to solve the problem with the idea of hypothesis, so I think the hypothesis method is really a very good way to solve the problem.

Senior one math diary (2)

I saw a puzzling math problem tonight. The topic is: 37 students want to cross the river. There is an empty boat at the ferry that can only take five people. How many times should they cross the river with this boat?

Careless people often ignore the "empty boat", that is, forget to have a gondola, so they can only take four people at a time. In this way, 37 people subtract one rowing classmate, leaving 36 students, 36 divided by 4 equals 9, and the classmate who worked as a boatman on the other side for the last time also landed 4, so it takes at least 9 trips.

Senior math diary (3)

This morning, I finished my homework and prepared to go out. At this time, my father came over and asked me with a smile: "Son, let me ask you, have you learned to weigh?" "Of course I do!" I answered loudly.

"Well, let me test you." So, dad said, and drew a picture on the paper. Dad said to me, "The actual length of this part is 5 mm, and the distance on the drawing is 10 cm. What do you think is the scale of this painting? " "That's not easy? 10 cm = 100 mm, 5: 100 = 1: 20, "I blurted out at the scale of this picture. Dad smiled and said, "Right?" Think about it, what is the meaning of scale? I thought about it and said, "The scale represents the ratio of the distance on the map to the actual distance." "Is that what you want to ask?" Dad asked.

I suddenly realized and said, "I know what's going on. I have calculated the ratio of the actual distance to the distance on the map. " The distance of parts on the drawing is 100 mm, the actual distance is 5 mm, and the scale is 20: 1. "

"That's right!" This is a special scale, which is greater than the previous term and the latter term. The simplified latter term is generally 1. This ratio should be used after the actual object is enlarged. "Son, you can correct your mistakes in time. I am proud of you. "

I am very happy to hear my father's praise.