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 =11*19 = 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.
2.300 words and 5 articles math diary 1. Today's math class is a practical activity, and we are divided into groups of 8 people.
Then the members of each group work together to figure out how many soybeans there are in 1 kg. According to the estimation method introduced in the book, it seems not difficult, but it is necessary to be careful to minimize the error. I originally suggested that our group would use more cups accurately.
But I can't find the cup. Later, this group of people chose the method of grasping by hand.
Team member Luo Guangyuan is responsible for catching. Oh, dear! Luo Guangyuan's little hands are quite big! One catch is 180 grains, and 30 consecutive catches have just finished 1 kg of soybeans.
Finally finished. 30 180 equals 5400 capsules.
So I know there are about 5400 1 thousand soybeans. This practical activity inspired me. I might as well try melon seeds, candy and peanuts.
In fact, math problems are closely related to life. There is a problem in today's math homework to weigh a pair of shoes.
So I went to my mother and asked for a scale. Mom said she didn't have weighing scale.
What shall we do? However, as the saying goes, "Nothing is difficult in the world". I think there must be a way.
So, I used my clever brain and came up with a homemade balance. I cut off the paper covers of the empty moon cake box piece by piece, put on transparent tape, folded one of the paper covers into a regular triangle and put it on the table.
Another piece of paper is made into the left and right disks of the balance and placed on the triangle in a balanced way. Then find something with weight at home as a weight.
For example, my mother bought toothpaste, lipstick and other items, including 120g, 40g, 18g, 3g. I'm very excited to say that the shoe activity has started.
I put the shoes on the left side of the homemade balance and the "weight of goods" on the right side. It is best to balance the weight on both sides. Then the sum of the weights is the weight of my shoes.
Exactly 86 grams. Hard work pays off! I finally finished my math homework.
Mom praised me when she found out. Also jokingly said to me: "In ancient times, there was a clever Cao Chong as an elephant, and in modern times, there is a clever Hung Hung as a shoe!" " "Say that finish, everyone laughed.
It turns out that there are scales everywhere in life! The annual math contest began. The forest is very lively.
This year's contestants are: cotton seed, turtle, tiger and lion. The game has already started.
Teacher Swan first gave each of these candidates a test paper, and then said to them, "Whoever can calculate correctly and quickly in a certain period of time will win the Wisdom Cup Award." As soon as Mr. Swan finished.
These candidates began to write. Rabbits run fast and do fast.
I saw that she was very clever and soon finished more than half of it. Come on, let's have a look at its test paper.
"dizzy! ! ! "You see: 80-70= 150, 20 ÷ 4 = 80 ... What a mess! I didn't even see the operation symbols clearly. Look at lions and tigers.
Hey! Why don't you see lions and tigers? I only saw a lot of manuscripts. Before I left, I saw lions and tigers busy! It turns out that every time a lion does something, he has to take out the manuscript paper to calculate.
The more manuscripts are piled up, the more lion heads are hidden. Really simple-minded, developed limbs.
Tigers are more exaggerated. Every time I finish a question, I will take out my manuscript and check it.
No wonder you are sweating. Finally, let's look at the tortoise! The tortoise is usually slow-tempered, but this time its thinking is not slow at all.
See how wonderful this question is: 3456-999 = 3456-1000+1= 2457. The tortoise uses a simple algorithm to finish the test paper quickly, and it is right and fast! Finally, the tortoise won the wisdom prize.
4. In the evening, I saw a difficult 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.
5. Time, a thing of "a good horse doesn't eat grass again". Mathematics, an interesting subject.
It's incredible that the two can be combined into one now. Mathematics is a paradise for numbers, and time is a paradise for moments.
Today, I will introduce mathematics to you in time. Firstly, the rectangular moment is introduced. The moments at right angles are 3 o'clock sharp and 9 o'clock sharp.
Next, I will introduce the moment of "three against two". This moment is 9: 30: 30, 10: 00 sharp, 2: 00 sharp, 7: 40: 40 ... then let's introduce the moment when the original needle is motionless.
This moment is 10: 5: 10, 8: 6: 9, 15: 25: 1, 6: 00: 15: 20 ... Finally, I introduce it to you. Isn't it amazing? This moment is exactly 12 o'clock. How's it going? Interesting! Time, you are amazing! Math, you are great.
3. An article by math diary
Length, area and volume (volume) are all units, and their advancing speeds are different, so are their unit names. The unit names of length are meters and centimeters, and their frankness is 100. Unit of volume's name is cubic meter, cubic decimeter and cubic centimeter, and the forward speed between them is1000; Of course, the unit of volume also has a name, but unit of volume is generally used to measure the volume, but the volume of liquid is usually measured in liters and milliliters, and the forward speed between them is also 1000. The relationship between the unit of volume and the unit of volume is as follows: 1 liter = 1 cubic decimeter 1 ml = 1 cubic centimeter, so what unit is it? A 250-word composition by math diary (/)
4. math diary 2 articles (more than 400 words) 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.
5. Who will give me 20 math diary? Talk less, not too much. It will be cloudy on Wednesday, February 23rd. Today, after I signed up for school and went home, I wrapped the book cover and began to calculate the cost of this semester.
The first is tuition. Tuition fee is 4 10 yuan, plus drinking water fee in 20 yuan, 430 yuan.
Next, the charge of the Olympic Mathematics School is 180 yuan. It is estimated that the bus fare is in 20 yuan and ***200 yuan. There is also money to buy exercise books: 2 copies of "Classpass" 2 1.5 yuan; English practice 1 9.9 yuan; 2 copies of Examination Paper Course Pass 15.9 yuan; "Jiangsu Big Test Paper" 3 copies 2 1 yuan.
21.5+9.9+15.9+13+21= 81.3 (yuan). Study fee: 430+200+81.3 = 711.3 (Yuan).
Living expenses: I will drink about 5 cases of milk this semester, 5*30= 150 (RMB). Every meal is about 2~3 yuan, including 2.5 yuan, 2.5*3*30*5= 1 125 (yuan).
"What else?" I bit my pencil and said to myself, "and your school supplies." Hey, mom's home.
Yes, and school supplies. School supplies: a pencil-box 8 yuan, a pencil-box 3 yuan (very cheap, clearance goods), six pencils 3 yuan, an eraser 0.5 yuan, two triangular rulers 1 yuan, two mechanical pencil 5 yuan, 8+3+0.5+ 1+5=20.5 (yuan).
Total expenditure: 711.3+150+1125+20.5 = 2006.8 (yuan). Wow, I didn't expect that I, who usually don't spend much money, would let my parents spend 2006.8 yuan this semester.
It seems that I will save money! Saturday, September 3, 2005 Weather: Cloudy Day He Jiahong Our new math teacher had a golden September, and the new semester began. I was lucky to meet a new math teacher-Zheng Yang. When you hear this name, don't think it's a man. In fact, she is a female teacher.
Tall, with big eyes, he looks like a middle school student. The first lesson she gave was: multiplication and division.
She not only drew pictures when analyzing math problems, but also quoted examples from life over and over again until we fully understood and nodded to her. Teacher Yang taught me so well that the first class left me with endless memories.
Saturday, September 17, 2005 Weather: Rainy When He Jiahong is in class, why do we like to talk? Yesterday, Teacher Yang asked us to discuss why some students like to talk. I don't think the reason for this kind of thing is unique. I remember one time when I was a foreign teacher, a classmate sitting next to me didn't like English class and couldn't understand what the American teacher said.
So he talked to me secretly. I "discussed" with him because I couldn't stand the temptation of his Disney topic.
Later, it was criticized by the teacher. I think: Talking in class will not only affect your own study, but also affect others' study.
We must get rid of these bad habits. Weather on Sunday, September 25th, 2005: It's raining. He Jiahong said shoes. Today, there is a problem in math homework called a pair of shoes.
So I went to my mother and asked for a scale. Mom said she didn't have weighing scale.
What shall we do? However, as the saying goes, "Nothing is difficult in the world". I think there must be a way.
So, I used my clever brain and came up with a homemade balance. I cut off the paper covers of the empty moon cake box piece by piece, put on transparent tape, folded one of the paper covers into a regular triangle and put it on the table.
Another piece of paper is made into the left and right disks of the balance and placed on the triangle in a balanced way. Then find something with weight at home as a weight.
For example, my mother bought toothpaste, lipstick and other items, including 120g, 40g, 18g, 3g. I'm very excited to say that the shoe activity has started.
I put the shoes on the left side of the homemade balance and the "weight of goods" on the right side. It is best to balance the weight on both sides. Then the sum of the weights is the weight of my shoes.
Exactly 86 grams. Hard work pays off! I finally finished my math homework.
Mom praised me when she found out. Also jokingly said to me: "In ancient times, there was a clever Cao Chong as an elephant, and in modern times, there is a clever Hung Hung as a shoe!" " "Say that finish, everyone laughed.
It turns out that there are scales everywhere in life! Thursday, September 29th, 2005 Weather: Sunny He Jiahong Happy Math Class Yesterday, Teacher Yang told us about "going to the playground". Because this is an interesting project, the students are very active in asking questions.
I am no exception. After thinking about it, I raised my hand and asked such a question: "Is 200 yuan enough for 16 people to finish three projects?" Teacher Yang praised me for asking extremely difficult questions.
However, at the prompt of Teacher Yang, I also helped my classmates to answer the questions. I remember a scientist said, "It is often more difficult to ask a question than to solve it."
In this math class, we not only raised many questions, but also solved many problems. How amazing we are! Sunday, June 2, 2005 Weather: Sunny He Jiahong I'm fine. Today, we went to Happy Valley. The adult entrance ticket price of Happy Valley is: 140 yuan; Half a ticket for children.
While waiting in line to buy tickets, my mother asked me to calculate how many tickets we need to buy. I blurted out, "I want 700 yuan."
My mother asked me in surprise how I calculated so fast. Actually, I think so: four half-price tickets for children are equal to two adult tickets, plus three adult tickets are exactly five adult tickets, and five tickets for 140 are exactly equal to 700 yuan.
Mom praised me for being great! Thursday, June 65438+10/October 65438+March 2005 Weather: How many times does Shenzhou VI circle the earth every day? Today, when the director of Beijing Aerospace Control Center told the reporter interviewed, "Shenzhou VI needs 90 minutes to orbit the earth." After listening to it, I thought, "So how many times can Shenzhou VI circle the earth in one day? So I quickly calculated with my brain: there are 24 hours in a day, 1 hour is 60 minutes, that is, 24 times 60 is a day 1440 minutes.
Then divide 1440 minutes by 90, which is equal to 16 laps. Also, Shenzhou VI will explore in space for five days, that is, 80 times around the earth.
Astronauts are really amazing! Weather on Thursday, June 20, 2005: It's sunny. Today's math class is a practical activity. We were divided into groups of eight people. Then the members of each group work together to figure out how many soybeans there are in 1 kg. According to the estimation method introduced in the book, it seems not difficult, but it is necessary to be careful to minimize the error.
I originally suggested that our group would use more cups accurately. But I can't find the cup.
Later, our group chose to use hands.
6. How to write a good composition in the fifth grade? First, improve the ability to understand and express things. Mr. Ye Shengtao, a famous educator in China, pointed out: "Writing anything depends on knowledge and experience. What kind of knowledge and experience can you write? On the other hand, without the ability to express knowledge, you can't write a good composition. " Second, take the cognitive structure as the core of the composition, including learning knowledge, observing and accumulating, and memorizing to train thinking. From talking about writing, scrutinizing and revising, reading and writing more. Third, set up a big composition concept and combine listening, speaking, reading and writing organically. The second is to make clear the purpose of writing and be innovative; Third, the selection of materials should be based on evidence; Fourth, we should pay attention to writing skills and arrange the structure of the article; Fifth, we should pay attention to the segmentation of the article and list the subheadings and composition outlines in advance; Sixth, we should pay attention to the writing and usage of the article; Seventh, we should use language skillfully and deploy language with ideas. We should learn five methods of conception: praise people with things, express our thoughts directly, understand things with things, touch the scene and express our feelings. Fourth, the big goal of composition should be graded year by year, with first-level words, second-level sentences, third-level fragments, fourth-level chapters, fifth-level synthesis and sixth-level improvement. Fifth, according to the principle that understanding is the core of composition, five trainings should be implemented. Contact your own life reality; Connecting with the learned language and word knowledge, we use the method of "ten quotations" to combine word learning with speech training. The "Top Ten Quotations" are: 1, analyzing glyphs; 2. Use teaching AIDS; 3. Look at the pictures and learn words; 4. Word formation and expansion; 5. Choose words to fill in the blanks; 6. collocation of words; 7. Adjust the word order; 8. Words used to move the scene; 9. Word classification; 10, conjunctions into sentences. Enrich the content of oral training, let me accumulate a large number of words that I can speak and use, and lay a solid foundation for writing. (2) Sentence training. As long as it is a sentence, it includes two aspects: one is people, things, scenery, and the other is purpose. But some teachers don't rely on pictures and things well when guiding students to say a sentence. Take out a picture or something casually and let the students say and write a sentence. Students don't know why to say and write a sentence, how to say and write a sentence, and what sentence pattern to say and write, which leads to a single, dull and lifeless composition tone. On the contrary, students can practice speaking and writing a sentence, including four elements of time, place, people and events, four sentence patterns and nine sentence patterns based on pictures, things and dialogues. Express different thoughts, feelings, attitudes and purposes. (3) Paragraph training. Combine the eight sections: in the order of things development, time and space transformation, summarize and describe the structural section, causal section, turning section, progressive section and parallel section, so as to understand the occurrence and development law of objective things. No matter which paragraph, it is a narrative thing. It is also a description of people, things, things and scenery, and also an expression of a meaning. Just make a sentence clearer and deeper. (4) Text training. A chapter consists of paragraphs. The knowledge and methods of reviewing topics, conceiving, selecting materials, planning articles, defining methods and using words can be expressed in four ways: narration, description, lyricism and discussion. Detailed and appropriate narrative and practical writing. (5) On-site training. Use on-site training to better understand writing from the content. Through various composition teaching activities, such as "centering", "selecting materials", "composition consultation meeting", "small Zhuge grading meeting" and "witty quiz meeting", we can learn composition knowledge vividly and concretely in the activities. Carry out voluntary labor inside and outside the school and learn how to write labor scenes; Hold poetry recitals and lectures to learn how to write conference scenes and experiences; By visiting places of interest, you can learn how to write travel notes and travel notes, learn observation methods, and pay attention to things around you. "You can learn everywhere, and you can write articles if you are knowledgeable." Through on-site life composition, we can further realize that life is fertile ground for composition, so as to learn things, express true feelings, cultivate the sentiments of truth, goodness and beauty, and cultivate a good style of writing. Cultivate students' thinking independence and creativity. After students write their compositions, organize group comments. Learn the advantages of other people's compositions first, and then point out the shortcomings in their own compositions with critical eyes and suggestions for improvement. On this basis, write again. Therefore, students can learn something from every article they write. Writing honest words about yourself was said by Mr. Ye Shengtao, an old educator, in order to create a colorful "independent" composition world. The so-called "independence" means that students can write freely and are not restricted by rules and regulations. "Independent" composition means "from the heart", acting spontaneously and showing one's own style.
7. In the sixth grade of math diary 400-word primary school, math diary wrote that one day I met a practical question that I could answer with my mathematical knowledge. Well, most of them are made up.
Date: Week: Weather:
Title:
In life, we often apply mathematics. For example, we have to calculate money when we go shopping, which is the most realistic. For another example, when we queue up for practice, we should arrange the team reasonably according to the class size. Therefore, there is mathematics everywhere in life!
Today, I saw a round flower bed downstairs, in which many colorful flowers were planted. Some of them are in full bloom, like a bright smiling face, some are half open, like a shy little girl, some are in bud, like an unopened umbrella.
There are three kinds of flowers in the flower bed, magnolia, rose, peony and azalea. There are 400 flowers in a box. The uncle who watered the flowers said that magnolia accounted for 1/4 of all the flowers, roses accounted for 1/3 of the total flowers after magnolia was removed, and peony accounted for 1/2 of the total flowers after magnolia and roses were removed. Finally, it is.
Magnolia grandiflora: 400* 1/4= 100 (flower)
Rose: (400-100) *1/3 =100 (flowers)
Peony: (400-100 * 2) *1/2 =100 (flower)
Rhododendron: 400- 100*3= 100 (flower)
From it, I found that although every answer is the same, the expression is different, the amount of the first unit is different, and the score of each flower is different.
Uncle also said that the radius of this flower bed is 5m, so I did another calculation on the area of the flower bed and got:
S circle =πr2
=3. 14*52 (where 2 stands for square, well, you should know)
=3. 14*25
=78.5 square meters
Today, I found that mathematics is used very frequently in my life, so I must learn it well! (the finishing touch, the teacher's purpose is here, be sure to write! )