How to explain the power of fractional division
a road repair team builds a road, which is 3 / 10 km in the first week, 7 / 20 km in the second week, and 1 / 4 of the road in two weeks. How many kilometers is the total length of the road
you can take 3 / 10 and 7 / 20 as an integer, that is to say, change this question to an integer.
change it to: a road repair team builds a road, which is 3 km in the first week, 7 km in the second week, and 1 / 4 of the road in two weeks. How many km is the total length of the road
students should understand it very well
Tip 1: "whose": "format," who "is the unit" 1 ". How many kilograms did a bag of rice eat? Then "the quality of this bag of rice" is the unit of "1"
tip 2: "more or less than who:" format, "who" is the unit "1". For example, Canghai fishing team caught 2400 tons in May, more than in May in June, how many tons in June? Then "tons of fishing in May" is the unit of "1"
extended materials:
analysis method of applied problems:
1, graphic analysis method: This is actually a simulation method, with strong intuition and pertinence, which is widely used in mathematics teaching. For example, engineering problems, itinerary problems, deployment problems, and so on, drawing is often used for analysis. Through diagrams, students can understand the meaning of the topic, so as to set up unknowns and list the solutions of equations according to the content of the topic 2. Personal experience method: for example, the problem of sailing upstream and downstream. There are many students who have never been in a boat before. It is difficult for them to understand the speed of sailing along and against the water. In order to let students understand, take cycling as an example, students have personal experience, riding along the wind is very easy, riding against the wind is very difficult, this is the impact of wind speed
At the same time, it should be made clear that the speed of sailing along the water is equal to the speed of the ship in still water plus the speed of the water flow; The speed of sailing against the current is equal to the speed of the ship in still water minus the speed of the current< br />1. In order to solve the practical problems of fractions by using the quantitative relation, it is often necessary to analyze the "central sentence" in the questions, find out the unit "1" and "two related quantities" from the "central sentence", clarify the relationship between the "two related quantities", and write the relation according to the meaning of fractional multiplication. For example, in the activity of "extending life", the fifth grade students of our school donated 3500 yuan, while the sixth grade students donated
, how many yuan did the sixth grade students donate? In this paper, the "donation amount of grade five students" is regarded as the unit "1". Grade five and grade six are two related quantities, and their relationship is "donation amount of grade five students" × = The number of donations made by sixth grade students. It's easy to know how to calculate this problem from the formula
in fact, the more complex problem is also a combination of simple application problems. As long as students learn to analyze, the problem will be solved. At ordinary times, teachers can orally train such a relationship so that students can master it skillfully. In this way, they will get unexpected results and get twice the result with half the effort. The practical problems are flexible and changeable. In mathematics learning, if students blindly focus on the formulas and examples in the book, solve the problems in a stylized and mechanical way, lack of a thorough grasp of knowledge, and do not make a specific analysis of the quantitative relationship of the problems, it is impossible for them to learn the practical problems well. But we need to make a specific analysis of the specific topic, otherwise it is easy to make mistakes
2. Solve the problem with the help of line diagram
The mathematician Hua Luogeng once said: "people have long had the impression that mathematics is dry, tasteless, mysterious and difficult to understand. One of the reasons is that it is divorced from reality." The thinking method of the combination of number and shape is the organic connection between theory and practice, the starting point of thinking, and the basic method for children to construct mathematical models. The idea of combination of number and shape is to make full use of "shape" to make the complex quantitative relationship and abstract mathematical concepts vivid and intuitive, which can enrich students' representation and trigger Association. In the teaching of fraction multiplication and division problems, we often draw a line diagram or an area diagram to clarify the meaning of the problem, analyze the quantitative relationship, and broaden the thinking of solving the problem, which can guide students to quickly find a way to solve the problem"line diagram" is intuitive and clear, which can make students clearly see the relationship between the two quantities. It is easy for students to judge and cultivate their judgment ability. Teachers should be patient when teaching students to draw. When students just come into contact with line diagram, they have a lot of difficulties. What to draw first, what to draw later, and which line segment should be divided into "several" parts equally, which is easy to be confused. When teaching, students should try to find problems, and teachers should guide and correct them, so as to make students have a deep impression. For example, the two passenger and freight cars start from a and B at the same time and run in opposite directions. They meet 20 kilometers away from the midpoint. At this time, the freight car runs the whole journey
2. Learning method guidance:
the first category: A is the word problem: divide by the number after the word; B word comparison: (big number small number) divide by the number after the word comparison. This method requires teachers to make students fully understand the relationship between score and division when teaching scores, and understand that the number as denominator refers to unit one
the second type: in the title, it is said that the fraction of "who" is the unit one; in the title, it is said that the fraction of "who" is more or less than "who" is the unit one; if the unit one is known, multiplication is used; if the unit one is unknown, division is used. (here, we can explain it to students in combination with the equation). The title with the word "Bi" is (1 +...) in more than parentheses and (1 --...) in less than parentheses. According to the above method, we can list these formulas: Yes, word title: a × Fraction, a ÷ A: A: A: B: A: B × 1 + fraction), a × 1-fraction), a ÷ 1 + fraction), a ÷ 1-fraction). Of course, the percentage mentioned above can also be changed into a percentage
in this way, we can make the topic right without fully understanding the topic. Of course, we also need teachers to try their best to learn how to get the teaching method in teaching, so that we can understand it reasonably and deal with complex problems easily
the above methods are years of teaching experience, hope to adopt!
2. Xiaohong weighs 42 kg and Xiaoyun weighs 40 kg. Xiaoxin's weight is equal to the total weight of Xiaohong and Xiaoyun. How many kilos does Xiaoxin weigh
3. The fifth grade students collected 42 kg of tree species, and the fourth grade students collected less than the fifth grade students. How many kilograms less tree species are collected in grade four than in grade five? How many kilograms of tree species do you collect in Grade Four
4. There are 128 students in the fifth grade of Xinguang primary school, accounting for 80% who have reached the standard of physical exercise. And the students who "reach the standard" are female students. What is the percentage of male students who "reach the standard" in the total number of fifth grade students< There are 36 students in the fifth grade who participate in the mathematics group. The number of students in the Chinese group is higher than that in the mathematics group, and the number of students in the sports group is higher than that in the Chinese group. How many people are in the sports group Let's talk about who we regard as the unit "1" in each step of calculation
6. The typist type a manuscript and finish it every day. What percentage of the book is finished in five days
7. The school canteen used 640 tons of water in September. The planned water consumption in October was the same as that in September, but the actual water consumption in October was less than the original plan. How many tons of water will be saved in October
8. There is a stack of 120 pieces of paper. The first time I used it, the second time I used it. How many parts of the stack of paper were used in the two times? How many sheets of paper were used in the two times
9. Insects often vibrate their wings ring flight. Locusts can vibrate their wings 18 times per second, bees can vibrate their wings 236 times per second
(1) how many times per second do locusts vibrate their wings
(2) how many times does a bee vibrate its wings per second than a locust
10. The students of three classes in grade five help to repair books in the library. 54 copies were repaired in class one, and the number of copies repaired in class two was twice that of class one,
the number of copies repaired in class three was twice that of class two. How many books are mended in class three
11. (1) a steel pipe is 12 meters long and cut off by 8 meters. What percentage of the total length is cut off? What's the rest of the length
(2) a steel pipe is 12 meters long. How many meters are left after cutting off the steel pipe
(3) a steel pipe is 12 meters long. How many meters are left after it is cut off
(4) for a steel pipe, the total length of the steel pipe is cut off and there are 3 meters left. How long is the steel pipe
12. Hongxing primary school paid 204 yuan for water in October, which was less than that in September. September is 40 yuan more than August. How much is the water charge in August
13. A car will deliver goods from place a to place B, traveling 45 kilometers per hour and delivering goods every hour. Return is the speed is the original, how many hours can return
14. The price of a set of desks and chairs is 60 yuan, of which the price of chairs is that of desks. What's the price of the chair
15. Pine seedlings cover an area of 5 hectares, and cypress seedlings cover less hectares than pine seedlings. These two kinds of seedlings account for half of the whole nursery. How many hectares of land is there in this nursery
16. Yimin food factory proces 3 tons of children's biscuits, more than juice biscuits. How many tons of biscuits are proced
17. For a job, it takes 6 hours for Party A to do it alone and 4 hours for Party B to do it alone. After a is finished, how many hours will it take for them to work together
18. A train goes from station a to station B. Six hours, 480 kilometers, the whole journey. At this speed, how many more hours to reach station B
19. There are two tanks of goldfish. If you take 15 goldfish out of the first tank and put them into the second tank, the goldfish in the second tank is exactly the same as that in the first tank. It is known that there are 35 goldfish in the second tank. How many more goldfish are there in the first tank than in the second tank
20. An engineering team built a section of highway. Those who built this section of road in the first week and those who built it in the second week. The first week was 2 kilometers more than the second. How many kilometers is this highway
21. The school brought a pile of sand. It takes tons to build a wall, tons to build a sports ground, and tons left. How many tons will it take? How many tons of sand is there
22. Divide six apples of the same size equally among eight children, and each child gets a big piece and a small piece. How is it divided? How much is it for each child
23. The canteen of the factory used 13 tons of coal in the first quarter, less than the first quarter in the second quarter, and more than the second quarter in the third quarter. How many tons of coal are used in the third quarter
24. Li Lin drank a glass of milk, then filled it with water, drank another glass, then filled it with water, drank half a glass, then filled it with water, and finally drank all of it. Does Li Lin drink more milk or water
25. To build a canal in Shengli village, kilometer will be built on the first day, kilometer will be built on the second day, and kilometer will be left. How long will the canal be after completion
26. To build a road, the first day the whole road is built, the second day the whole road is built, and how many parts of the whole road are not built
27. In a class, students spend hours doing experiments, teachers spend hours explaining, and the rest of the time students do their homework independently. Given that each class is an hour, how many hours does it take for students to do their homework independently
28. Xinhua primary school held a sports meeting, and each student only participated in one event. The fifth grade students take part in track events, field events and group gymnastics. What percentage of the students in the whole grade take part in group gymnastics
29. A mathematics competition was held in a city with several first, second and third prizes. Those who won the first and second prizes account for the total number of winners, and those who won the second and third prizes account for the total number of winners. What percentage of the total number of people won the second prize
30. Forestation in Piedmont Bay is carried out on a mountain. It is planned to use the total area to grow fruit trees, bamboo and pine and cypress. What percentage of the total area is planted with fruit trees and bamboo? What percentage of the total area is the area planted with pines and cypresses
1. Xiaohong is 156 cm tall and Xiaofang is 1.52 m tall. How much higher is Xiaohong than Xiaofang
2. 50 kg of rapeseed can extract 15 kg of oil. According to this calculation, how many kg of oil can be extracted from 5 tons of rapeseed
3. Xiaoming's home is 1.5km away from the school, Xiaonan's home is 1km and 60m away from the school, whose home is close to the school? How much is it
4. One African ostrich weighs about 150kg 500g, and one pig weighs about 123.06kg. How many kg does an ostrich weigh more than a pig? Then write the result as a compound number
5. The sowing width of a seeder is 3 meters, and the seeder runs 5 kilometers per hour. According to this calculation, how many hectares can be sown in 2 hours
4. The road repair team built 1.078 kilometers on the first day, and 0.456 kilometers more on the second day than on the first day. How many kilometers did the road repair team build in two days? 4. The students of hope primary school saved 40.25 yuan in repairing desks and chairs, and 3.7 yuan less in binding books than repairing desks and chairs. How much money is saved by binding books
5. Xiaoliang's father bought him a set of computer desk and chair. The price of a chair is 45 yuan, which is 12.5 yuan cheaper than a desk. How much is a table
6. In the long jump competition of the sports meeting, Xiaohong's score is 2.85 meters, Xiaoming jumps 1.25 meters more than Xiaohong, and Xiaohong jumps 0.23 meters more than Xiaoju. Who won the first place in the long jump? Why
7. The students of Zhangzhuang primary school spent 40.25 yuan on repairing desks and chairs, 3.7 yuan more than binding books. How much did it cost to bind the books Xiao Hu had to walk 1.3km from home to school in the morning. After walking 0.3km, he found that he didn't bring his math exercise book and went home to get it. In this way, he walked more kilometers than usual to school
9. Su Guo supermarket transported 0.31 tons of Hami melon, and watermelon 2.75 tons more than Hami melon. How many tons of the two kinds of melons
10. Aunt Zhang packed a basket of vegetables to sell at the farmers' market. The basket and vegetables weighed 7.4kg originally. After selling some vegetables, she went home and weighed 3.6kg. How many kilos of vegetables did she sell
1. Wang village builds a canal, which is 8.5km in the first day, and 3.5km more in the second day than in the first day. At this time, the finished canal is 4km less than the one not repaired. How many kilometers are left
2. The passenger car is 24 km faster than the freight car per hour. After 5 hours, the distance between the two cars is 720 km. How many kilometers can the freight car travel per hour There is a triangle experimental field with a bottom of 250m and a height of 180m. The total grain yield in the whole year is 4.5t. How many tons of grain are proced per hectare on average
4. A pile of coal is transported from the school canteen. It is planned to burn 50kg of coal every day, and it will be finished in 6.5 days, but it will be finished in 10 days. How many kilos less coal is actually burned per day than planned
5. Buses and trucks travel from two places 852km apart and face each other at the same time. When they meet, the distance of buses is 189km less than twice that of trucks. How many kilometers do buses and trucks travel When reading a story book, it takes 24 days for my sister to read a complete book, and 32 days for my sister to read a complete book. It is known that my sister reads 4 pages more than her sister every day. How many pages does my sister read every day? Give 1 kg of sugar to 3 children. The first child and the second child have a total of 5 / 11 kg, and the second child and the third child have a total of 2 / 3 kg. How many kg of sugar does the second child have? 1. There are 100 points in a regular octagonal paper. How many triangles can be cut out with the 100 points and the 8 vertices of the octagonal? How many triangles can you cut at least
2. Divide a pile of apples, 3 for each, and there is one left at last; How many apples are there in this pile at least
3. After sawing a 5 cm wide strip from a square board, the remaining area is 750 square cm. How many square centimeters is the area of the sawn wood
4. Party A and Party B run the 100 meter race. When Party A reaches the finish line, Party B is 20 meters behind Party A. if the speed of Party A and Party B remains unchanged, how many meters does the starting line of Party A have to move backward to make Party A and Party B reach the finish line at the same time
5. There is a batch of original stock in the warehouse, and then the goods are transported into the warehouse one after another, and the same amount of goods are transported into the warehouse every day. At present, the goods in the warehouse are transported out by cars with the same carrying capacity. If four cars are used every day, the goods will be transported out in nine days. If five cars are used, the goods will be transported out in six days. How many days does it take to transport the original goods out of the warehouse with a car every day
6. A city holds a long-distance running activity. The long-distance running team advances at the speed of 6 kilometers per hour. At the beginning of the long-distance running, two reporters, Xiao Zhang and Xiao Wang, March to the middle of the team at the same time from the beginning and the end of the line to report and interview. Both Xiao Zhang and Xiao Wang rode motorcycles, traveling 10 kilometers an hour. They met 900 meters from the midpoint of the team. How many meters is the long distance running team
7. Party A, Party B, Party C and Party D take the same amount of money to buy several pieces of goods of the same specification. After the goods are bought back, Party A, Party B and Party C take 3, 7 and 14 more pieces of goods than party D. at the final settlement, Party B pays Party D 14 yuan, so how much should Party C pay Party D
8. When Party A and Party B sell eggs, Party A has 10 more eggs than Party B, but the income after all the eggs are sold is 15 yuan. If Party A's eggs can be sold for 18 yuan at the price of Party B, how many eggs do Party A and Party B have
9. Grandfather and granddaughter walk along the square pond with a side length of 100 meters, as shown in the picture. It is known that granddaughter walks 50 meters per minute and granddad walks 46 meters per minute. How many minutes does it take granddaughter to see granddad
10. There is a number 2003 written on the blackboard for Party A and Party B
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