On the Traditional Festival of Mathematics in Primary Schools

Team members: Chen Shuying, Hong Yutong and Liu Jinwen.

Name of activity: How big is 100 million?

Activity time: Sunday, September 23rd at 20: 0012.

Activity theme: In groups of three, we started to do a small math experiment of "How big is 100 million". This time we chose a box of colored balls. First, we calculated how many balls a small box can hold, and then through reasoning and calculation, we got how many boxes of the same size are needed to hold 654.38 billion balls.

Activity steps:

1, measuring ball diameter: 0.6 cm.

2. Measure the volume of a box: 2.3× 2.5×1.75 =10.0625 (cubic centimeter).

3. Test how many balls can be put in a box: 45 balls.

4. Calculation: Can a box with a volume of 10.0625 cubic centimeter hold 1000 small balls with a diameter of 0.6 cm?

( 1) 1000÷45=22.222

(2) Because there is surplus, it takes 23 boxes to hold, and how many balls can be held in the last box:

(3)22×45=990; 1000-990= 10, so 1000 balls need 23 boxes, and the last box contains 10 balls.

5. Calculation: 10.0625 cubic centimeter box can hold 10000 small balls with a diameter of 0.6 cm?

( 1) 10000÷45=222.222

(2) Because there is surplus, it needs 223 boxes to hold, and the last box can hold several balls:

(3)222×45=9990; 10000-9990= 10, so 10000 balls need 23 boxes, and the last box contains 10 balls.

6. Calculation: 10.0625 cubic centimeter box can hold 1 100 million balls with a diameter of 0.6 cm?

( 1) 100000000÷45=2222222.222

(2) Because there is surplus, 2,222,223 boxes are needed, and the last box can hold several balls:

(3)22222222×45=99999990; 1 00000000-9999990 = 10, so1100 million balls need 222223 boxes, and the last box contains10.

Conclusion:

65,438+billion balls with a diameter of 0.6 cm need 2,222,223 boxes with a diameter of 65,438+00.0625 cm, and the last box contains 65,438+00.

Through this math activity, the students learned what volume is, how to calculate it and the basic calculation methods. The measuring tools used are: ruler and calculator.

Comprehensive practice course

Yang Ming, Class 6 (5) of Songping Primary School

Last Thursday, our class had a special comprehensive practice class. The content is to measure the volume of eggs.

Before class, Mr. Zhu divided us into six cooperation groups. Each group prepares a bottle of water, a cuboid container and an egg.

Start class. First of all, I wish the teacher showed us pictures of crows drinking water with multimedia, and then asked us, "You all learned a text called" Crows Drinking Water "in your lower grades. So, how do crows drink water? " We all say that the crow threw stones into the bottle, and the stones occupied the space in the bottle, causing the water surface to rise. The crow just drank water. I hope the teacher will praise us for being right. Then, I wish the teacher a bottle with a little water. Then throw some stones into the bottle, and the water level in the bottle will gradually rise with the increase of stones. Teacher Zhu asked again, "Students, can we measure the size of eggs by the principle that crows drink water?" We all agreed. Therefore, I hope the teacher can let us do experiments and measure the size of eggs. After some discussion, our group first determined the operation plan, and then began to measure.

The steps of our measurement are:

Step 1: Pour a proper amount of water into a cuboid container. Step 2: Add eggs, measure and calculate their volume. Step 3: Take out the egg, measure and calculate its volume. Step 4: The difference between the first measured volume and the second measured volume is the volume of the egg. In the operation, some students in our group measure, some calculate and some take notes. After a while, we found that the volume of an egg is 48 cubic centimeters.

After a while, all the groups finished the experiment. The teacher asked me to talk about the operation process, methods and results of our group on behalf of our group. So I wrote the operation flow of our group on the blackboard, and our method was affirmed by the teacher. The teacher summed up the methods of each group and told us: "Everyone uses the principle that crows drink water to measure the volume of eggs. So, what did you gain today? " The students all expressed their feelings. Inspired by the teacher, the students agreed to use this principle to calculate the volume of irregular objects, such as tomatoes and potatoes.

After class, the students are still talking to each other and pouring out their feelings about this course. I am also very emotional. I understand that everything is connected. For example, the text "Crow Drinking Water" in our Chinese class is also closely related to mathematics, but when we finished learning this text, we didn't understand it so thoroughly. Therefore, through this lesson, I not only know the method of measuring the volume of irregular objects, but also deeply realize that the text of Chinese class contains rich philosophical and scientific knowledge. When learning Chinese in the future, we should not only pay attention to learning the language and characters of Chinese, but also carefully analyze the connotation of the text, closely link Chinese lessons with other disciplines, and make what we have learned comprehensive.

Magic subtraction formula

Nanshan Experimental School Nantousi (2) Ban Huang

Instructor: Ceng Weiming

There are many mysteries in mathematics. Today, I found a magical law in the subtraction formula, which is so amazing that people can't believe it!

You must really want to know! Let me tell you something. An ordinary subtraction formula, you only need to add the minuend, subtraction and difference and then divide by the minuend, and the result must be equal to 2. Do you find it hard to believe? Call me a liar? Don't worry, you'll be dumbfounded soon.

Now let's verify it. "5-4 = 1" is a simple formula, but it has three important conditions: minuend, subtraction and difference. If the minuend, subtraction and difference are added up and then divided by the minuend, that is, (5+4+ 1)÷5, the result is equal to 2. You won't believe this. You think it's a coincidence, so let's try again.

For example, 64-38 = 26, (64+38+26) ÷ 64 = 2;

150-90=60, ( 150+90+60)÷ 150=2;

4839-276 1=2078, (4839-276 1-2078)÷4839=2;

…………

The above examples are enough to prove that the law of "(minuend+subtraction+difference) ÷ minuend = 2" does exist in the subtraction formula. "Why?" You will ask if you are in a hurry. In fact, the principle is amazing and simple. Everyone knows that "minuend-minuend = difference". According to the relationship between the parts of subtraction, we can get "difference+subtraction = minuend". From this relationship, we can see that the sum of "difference+subtraction" equals "minuend". When the minuend, subtraction and difference are added, the sum is equivalent to two minuends. When it is divided by the "minuend", it means to ask how many "dividends" there are in the total (the sum of two "dividends"), so it must be 2.

This ingenious rule is hidden in the subtraction formula. If you know the relationship between them very well, you can understand the mystery.

Using this law, we can also solve some math "problems" quickly.

For example, in the subtraction formula, the sum of the minuend, the minuend and the difference is 48. How much is the minuet?

Analysis and solutions:

Because (minuend+subtraction+difference) ÷ minuend = 2,

So (minuend+subtraction+difference) ÷ 2 = minuend,

So the minuend = 48 ÷ 2 = 24.

Jia Kai rice noodle store

Class 6 of Haibin Primary School (1) Li Jingyu

200 thousand can be said to be more or less, but you can open a rice noodle shop and do business with peace of mind.

(1) Buy a small shop with 1.5 million first.

(2) The remaining 50,000 yuan is used as the working capital for the first month.

The monthly fee is as follows:

Hire 8 employees and buy a monthly salary. 800 yuan, * * *:

8 * 800 = 6400 (yuan)

Rice flour raw materials, each bowl 1 yuan, about 500 bowls per day, monthly * * *:

1 * 500 * 30 = 15000 (yuan)

Total monthly expenditure:

6400+ 15000 = 2 1400 (yuan)

Residual working capital of 50,000 yuan:

50000-2 1400 = 28600 (yuan)

(3) The working capital is 28,600 yuan.

Monthly income:

The price of each bowl of rice noodles is 6 yuan, and 15000 bowls are sold every month. Monthly income * * *:

15000 * 6 = 90000 (yuan)

Monthly profit:

90000-21400 = 68600 (yuan)

Time for cost recovery:

200000/68600 =~ 3 (month)

The cost can be recovered in about 3 months. Doing this business will not involve too much risk, explosion or loss.

Instructor: Liu Yongguo

2004-5-9

Do you have to know the step size?

Guo Jiahong, a student from Class 4, Nantou, Nanshan Experimental School (1).

Instructor: Ceng Weiming

At the end of the seventh book of mathematics, we learned the step test. Because of the large number of steps, the complex quantitative relationship and the aggregation of length units, students feel trouble and make many mistakes in solving the application problems of step measurement. Is there a simpler way to solve the problem? In solving problems, I found many application problems related to step size measurement, in fact, it is not necessary to calculate the step size step by step and then calculate the final result.

For example, Exercise 7 13 Question 4:

Xin Li walked four times along the 80-meter-long straight road, the first step 124, the second step 125, the third step 126 and the fourth step 125. At this speed, he walked 500 steps from school to home. How far is his home from school?

According to the problem-solving ideas introduced in the book, this problem should be solved like this:

1, first find out what the step size is.

(124+125+126+125) ÷ 4 =125 (step by step)

80 m =8000 cm

8000÷ 125=64 (cm)

Then figure out how far his home is from school.

500*64=32000 (cm) = 320m

His home is about 320 meters away from the school.

In fact, I found a simpler way to solve this problem. The solution is as follows:

1, first find out how many steps xin li takes on average in 80 meters.

(124+125+126+125) ÷ 4 =125 (step by step)

2. Find out how many times 500 steps are 125 steps.

500÷ 125=4

Then find out how far his home is from school.

80*4=320 (meter)

His home is about 320 meters away from the school.

In this way, the solution does not need to be summarized in length, and it is correct, fast and very convenient.

From the thinking of this problem, I found that as long as I think positively and use my brains diligently, I will definitely find the best way to solve the problem.

How old can a turtle live?

Class 4 (2) of Nanshan Experimental School, Tang Bijun, Yao Chen.

Instructor: Ceng Weiming

Everyone thinks turtles are mascots for longevity, because their life span is really long. It is said that turtles can live 1000 years. However, when I read the exercises about the turtle's age in the math textbook, I found that the turtle can only live 180 years old. I think it's strange. People often say that turtles live long. Why does the book say that turtles can only live 180 years old? Is there a mistake?

I walked into the teacher's office with a big question mark, trying to find out.

I didn't expect the teacher's answer to surprise me more. The teacher said that turtles generally don't live to be 150 years old.

I have more questions about this answer. Who is right? I decided to try to find the exact answer by myself.

In the information class, I turned on my computer and couldn't wait to type the words "tortoise, longevity" from Baidu search engine, and then click "search". In the blink of an eye, hundreds of pieces of information about the life span of turtles immediately came to my face. According to the data, the world's longest-lived turtle recorded in Guinness World Records is only 152 years old.

I moved to China Children's Encyclopedia of all kinds of creatures, Children's Animal Encyclopedia and Children's Encyclopedia ... and rummaged through these books. All the above books think that turtles can only live for about 100 years.

Indeed, not only is the legend that turtles can live for a thousand years groundless, but the data in textbooks are also wrong.

So I verified the ages of lions and elephants in this exercise. It is found that the ages of lions and elephants in the problem are also quite different from the facts. The exercises in the textbook say this:

"Lions can live for 40 years, elephants live twice as long as lions, turtles live twice as long as elephants, and elephants live for 20 years. How many years can a turtle live? " (People's Education Edition, Title 1 on Page 20, Volume 8 of Primary Mathematics. )

Through calculation, it can be concluded that lions can live for 40 years, elephants can live for 80 years, and turtles can live for 180 years. It stands to reason that this generally refers to the average age, but various data show otherwise.

About lions:

-Young lions are sexually mature after 2-3 years, and adult lions live independently in solitary camps. Life expectancy is about 20 years. (Encyclopedia of China-Biology Volume)

In Wuhan Zoo, a lion named "Zhongzhong" has celebrated its 30th birthday, which means it is an 85-year-old man. The life span of wild lions is mostly around 17 years old, and the normal life span of lions under artificial feeding conditions is between 20 and 25 years old. Lions are old when they reach the age of 20. At present, "Zhongzhong" is the oldest lion that humans can observe. (:Beijing Youth Daily Xiao Yangjia Hong Bing)

About elephants:

-Asian elephant, 12 ~ 15 years old, sexually mature, with a life span of about 60 years old. African elephant, the age of sexual maturity is about 15 years old, and its life span is 60 ~ 70 years old. (Encyclopedia of China, Teaching Biology for Middle Schools)

The Royal Society for the Prevention of Cruelty to Animals ... recently completed a report showing that the life span of zoo elephants has been greatly shortened. According to this research report, the life span of elephants raised in European zoos is only about 15 years, while the life span of wild elephants is as long as 60 to 65 years.

About turtles:

The longest life span of tortoise can reach 152 years, and it is a well-deserved longevity animal among animals. (Guinness World Records)

The life span of turtles is quite long, and some of them can live to 100 years old.

It can be seen that under normal circumstances, the life span of a lion is about 20 years, generally not more than 30 years; The life span of elephants is generally between 60 and 70 years old; The longest life span of sea turtles is about 150 years, generally about 100 years.

I think it was originally an application problem, which allowed us to understand mathematics and biology at the same time, but there were errors in the data, which would have a bad influence on students. I hope that all the uncles and aunts who compile books must be cautious, and they can't ignore the accuracy of knowledge in order to calculate a good topic.

Skillfully calculate the size of eggs

Songping School Class 6 (5) Xia Hao

On Thursday morning, in the tense moment of preparing for the final review, we had an interesting comprehensive practice class in the sixth year (5) class.

Before class, the teacher cut one side (the smallest side, of course) of more than a dozen milk cartons, and then let us wash the milk cartons.

"Ding Lingling ..." Accompanied by the crisp and pleasant bell, the students came into the classroom one after another, sat in their seats and quietly waited for the teacher to come to class. When the teacher revealed the content of this lesson-measuring the volume of eggs. The student asked in a low voice, "Is there a formula for calculating the volume of eggs?" "Even if it counts, it must be very complicated." "The teacher must have a trick!" "Yes, there must be." Just when we were at a loss, the teacher told the story of "crow drinking water" and made a demonstration with real objects. Then ask us why the crow threw stones into the bottle, and the water level rose. The students scratched their cheeks and touched their ears, making it difficult to answer. The last classmate casually said, "The stone occupies the space of the bottle." The teacher said, "Yes!" He picked up a small bottle from the podium, which contained only half a bottle of water. He grabbed a handful of stones from the side and put them in the bottle carefully and orderly. The water in the bottle rose slowly and finally almost overflowed the bottle mouth. The teacher said humorously, "Now even sparrows with small mouths can drink water." One sentence made everyone laugh.

Inspired by the story of crows drinking water, the teacher asked us to prepare these cuboid containers and water before class. I have some ideas about how to measure the size of eggs. When the teacher asked us to measure in groups, I was the first to say my measurement method. Hearing this, the students all agreed. As a result, the classroom was boiling. Some people poured water, some measured, some calculated and some took notes. Our group has the fastest calculation. We use the water level drop method. The method is as follows:

Step 1: Put the eggs and water into a cuboid milk box, so that the eggs are completely immersed in the water, and calculate their volume.

Step 2: After taking out the eggs, calculate the volume of water in the cuboid milk box.

The third step is to subtract the volume of water from the volume of eggs with water, and the difference is the volume of eggs. When the teacher asked about the operation process and calculation results of each group, Yang Ming gave an incisive explanation on behalf of our group, which won unanimous praise from teachers and students. The teacher sitting at the back of the classroom also cast an approving look. We are like eating honey, our hearts are full of joy, and our sense of accomplishment rises from scratch.

After each group reported, the teacher went on to say, "The water level fluctuation method you just did can measure the volume of eggs, but sometimes water is stopped or water is scarce. What substance can you use instead of water? " The students whispered to each other. "By the way, you can use sand!" A classmate said loudly, as if he had discovered a new continent. Then the teacher made a demonstration for us with sand. Experiments have proved the feasibility of sand.

Finally, the teacher asked us what we learned in this class. Guo first replied: "The volume of irregular objects can also be calculated in this way in the future." Yes! The volume of apples, tomatoes and other irregular objects can be calculated in this way. Nature is full of infinite mysteries, waiting for us to discover and explore.

A lively and interesting comprehensive practice class ended happily.