Math diary: Write down what you learned in math this day.

Diary must be true.

Therefore, math diary also demands truth.

To sum up, I suggest that your math diary write the following points:

1. Write down what you learned today.

2. Write down what you didn't master today.

3. Establish your own plan to conquer knowledge in the future.

4. Make a long-term plan for your future math study.

First of all, write down what happened today, make up something related to mathematics casually, then say that you think about it (nonsense-it took a lot of effort), then say that you still don't understand, and you are reminded by a casual sentence from others, and finally think of it. Finally, it turns out that mathematics is so useful that it is all around us. end

Math study is really a bit difficult for us girls. But for the dream university and future, work hard!

This morning, I was worried about what math diary wrote. Wandering around Baidu's knowledge, hoping to get some inspiration. Suddenly, an article in the newspaper attracted me:

"Eight-way experimental primary school six (7) class Xu Ruixiang.

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 a proportional application problem ... "

I figured it out on this issue without reading the analysis, huh? I haven't learned how to calculate the area of a cone. Then how can I solve this problem? I sighed, ready to continue to watch the analysis, and then I thought, will I be in the sixth grade soon after this summer vacation? If you can't even do the questions in this course. What kind of Olympics class am I? Is it not worthy of the name? Yes, I have to solve it myself.

As usual, I must build a model in my mind before this kind of problem, but I am very cautious about this problem for fear of making mistakes. I drew a perspective effect of a cone on the paper. Take a closer look, huh? Isn't this figure the same as a triangle if it is a plane figure? Isn't the cubic area of this cone 1 of the area of a cylinder with the same base and height? I am ecstatic. The original cone area is also easy to find. As long as you know the height and bottom area of the cone, can't you get it? Back to this question, its condition tells you the radius of the bottom, which is equivalent to telling the area of the bottom. It says that the ratio of height to bottom radius is 3: 2, which means that the length of bottom radius is two-thirds of height. Isn't that height just radius ×3÷2= height? Therefore, the height is 12 decimeter, the bottom area is 200.96 cubic decimeter, and the cone area is 200.96×12 ÷ 2 =1205.76 cubic decimeter.

"Wow, I finally solved it." I heaved a sigh of relief. Through this question, I also found that there are many things in mathematics, just like the area of a cone and the area of a triangle. In fact, you don't need to know all the calculation formulas, as long as you can understand them, you can also solve problems.

Is it okay? No, modify it!

Also: 1)

Today, my family went to KFC in Longgang for a family meal.

When we get there, people are always crowded. We finally ordered good food and found a seat to sit down. Here comes the food. This is a sumptuous set meal. There are 12 drumsticks in it. I thought: how to divide it equally? Then I remembered the division of 12÷3=4. We each have four drumsticks. Later, I ate my mother's 1 chicken leg and my aunt's two chicken legs. My aunt said, "You can't eat this for free. I ask you, how much did you eat? " How many more servings do you have to eat before you can finish them all? "I thought about it and replied," I ate 7/ 12, and then I ate 5/ 12. I ate all of it. "Fortunately, I learned the knowledge of fractions and can answer the questions correctly.

(2)

Today, my mother gave me 10 yuan to go shopping in the supermarket. I bought a string of firecrackers 2/ 10, four lollipops/10, seven balloons 2/ 10, and finally a comb 4/ 10, a *. There is still one yuan left, and I have to pay it back to my mother.

When I got home, my mother ate 1/4 lollipops, my father ate 1/4 lollipops, I ate 1/4 lollipops, and I gave the other one to my brother Xiao Qiang next door. (Author: Xiao Enling)

(3)

Last week, we studied fractions. Fractions have numerator, denominator and fractional line, for example, 1/3, where 3 is denominator, 1 is numerator and the middle horizontal line is fractional line.

Scores are used in many places in life. For example, a book has thirty pages, and each page is 1/30 of a book. Fractions can also be used to add and subtract! For example, half plus half equals two, which is 1. Why is this happening? If you divide a cake into two parts, each part is 1/2 of the cake, and then put the two parts together, there are two parts 1/2, which is just a cake. When adding and subtracting fractions, if the denominator is the same, only the numerator is added, regardless of the denominator. And 2/2 of the numerator and denominator are the same, which is 1.

I also learned to compare the size of fractions. The teacher taught us the formula: numerator is the same as denominator, the fraction with large denominator is small, and the fraction with small denominator is large; Denominators are the same as numerators, with large numerator scores larger and small numerator scores smaller.

The teacher also reminded us that when writing scores, we usually write the fractional line first, indicating the average score, then the denominator and finally the numerator.

Math diary 4

At noon today, I was doing my math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:

There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.

I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?

Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.

Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.

Finally I got the result, which is 374 cubic centimeters. My formula is: 209 =119 = 2+171× 2×17 = 374 (cubic centimeter).

Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.

I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.

Math diary 6

Saturday, August 6th

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 must they cross the river with this boat at least?

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.

Math diary 7

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 good way to solve the problem.

Math diary 8

I met another math problem today, and it took me a lot of effort to solve it. The topic is: there are 30 birds in two trees, and 4 birds fly away from the second tree first. At this time, tree A flew to tree B with three birds, and the birds on the two trees were just equal. How many birds are there in each tree?

As soon as I saw the topic, I knew it was a reduction problem, so I solved it by the method of reduction problem. But when I checked, I found something was wrong. I will do it again more seriously. I think there are as many as four missing, half of them are 13, and the restored B-tree is14; A tree is 16. The formula is: (30-4) ÷ 2 = 13 (only); 13-3+4 =14 (only); 30- 14 = 16 (only). The answers are: a tree 16 and b tree 14.

By solving this problem, I understand that no matter what I do, I should be careful, otherwise, even if I master the solution to the problem, the result will be wrong.

Math diary 9

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 good way to solve the problem.