1. The students planted trees on one side of a 200-meter-long path, one at every 4 meters (both ends). How many seedlings does a * * * need?

Analysis: The key to this problem is to plant a tree at the starting point and then walk 4 meters to carry a tree. There are 50 4 trees in 200 miles, so ***5 1 tree. Teachers can use this question to ask whether there are no seeds at both ends, or think about climbing stairs and chopping wood, and sum up their similarities and differences. (If trees are planted at both ends, add1; If no trees are planted at both ends,1should be subtracted; If you plant trees at one end, you should add and subtract. )

Formula: 200÷4+ 1=5 1

2. The distance between the two buildings is 60m, and a pine tree is planted every 5m. How many trees can be planted between two buildings? Analysis: The 1 question on this question is similar, and it belongs to the kind where no trees are planted on both sides. 1 title plus 1, minus 1 title.

Formula: 60÷5- 1= 13.

A square, if its adjacent sides are increased by 6 cm, can get a new square, and the area of the new square is larger than the original square 120 square cm. Find the area of the original square.

Analysis: This question should be combined with graphics to help children understand. The added part is a rectangle with a width of 6 and a length of 6+ positive side. Therefore, to ask for the area of the original square, we must find the side length of the square, and only ask for the length of the added rectangle.

Formula:120 ÷ 6-6 =14; 14× 14= 196。

4 pages

1, with serial numbers: 2, 5, 8, 1 1, 14,? According to the above arrangement, do you know the number 1995?

Analysis: the difference between two numbers is 3, and the first number is: 3×1-1= 2; The second number is 3×2- 1=5. What is the number? It is three times less than 1.

Formula: Solution: ∫ 2+3 = 55+3 = 88+3 =111+3 =14.

So: the nth =3N- 1.

∴3× 1995- 1=5984

2. There is a triangular land with three sides of 120m, 150m and 80m respectively. Plant a tree every 10 meter at the boundary. How many trees can you plant at most?

Analysis: Triangle is a closed figure, that is, the starting point is also the end point, so we can understand it as a problem of planting trees. Formula: (120+150+80)/10 = 35.

3. One row has 144 young pioneers practicing, and the other row has 12 people, arranged in a square phalanx. Do you know how many young pioneers are standing around this square?

Analysis: A square has four sides, 12 people have 1 sides, so it is 4×12; There are four corners, so subtract: (1×4).

Formula: (12×4)-( 1×4)

=48-4 =44 (person)

The mother is 32 years older than her son this year. Three years later, the mother is five times older than her son. How old is her son this year?

Analysis: Follow the trend and guide children to start with the problem. If you want to ask your son how old he is this year, you should first ask his son three years ago and ask him if he knows his mother three years ago.

Formula: 32+3 = 35; 35÷5=7; 7+3= 10。

6 pages

1 has three natural numbers, and the results obtained by adding or multiplying them are all the same. What are these three numbers? Analysis: These three numbers are 1, 2 and 3 respectively.

2. The quotient of two natural numbers is 47 and the remainder is 3. The sum of dividend, divisor, quotient and remainder is equal to 629. Do you know what the divisor is?

Analysis: According to the two sentences in the question, 629- remainder-quotient = dividend+divisor; Because dividend-remainder =47 divisors; So you can find the divisor.

Formula: 629-47-3 = 579; (579-3)/48= 12

3. Two natural numbers are subtracted, and the sum of the minuend, the minuend and the difference is 360. Can you find out what a minuet is according to what you have learned?

Analysis: Because: minuend+subtraction+difference =360, minuend = subtraction+difference. So: there are two minuets in 360 degrees. Formula: 360/2= 180

Page 8

1. In order to praise good people and deeds, Teacher Zhang wants to investigate who did good deeds. He called Xiao Ming, Xiao Gang and Xiao Hua for questioning. Ming said: Xiao Gang did it. Xiaogang said: I didn't do it. Xiaohua said: I didn't do it. Knowing that only one of the three of them told the truth, he asked: Who did this?

Analysis: There are only three cases of this problem, one is done by Xiao Ming, the other is done by Xiao Gang, and the third is done by Xiaohua. Exclusion can be used. If Xiao Ming did it, then Xiao Ming lied, Xiao Gang told the truth, and Xiao Hua told the truth, which contradicted the condition of "only one person told the truth" in the question, so Xiao Ming didn't do it; If Xiao Gang did something good, then Xiao Ming told the truth and Xiao Hua told the truth, which contradicted the condition of "only one person told the truth" in the title, so Xiao Gang didn't do it. If Xiaohua did it, then only Xiaogang is telling the truth. This situation still exists.

Format: Xiaohua did this good thing. 2. If the width of a rectangle is increased by 2cm or the length is increased by 3cm, their areas will all increase by120cm2. What was the area of the original rectangle?

Analysis: To find the area of the original rectangle, we must first ask its length and width. It can be known from the figure that its length is equal to 120/2 and its width is 120/3.

Formula:120/2 = 60; 120/3=40; 60×40=2400。

10 page

1, 100 people 200 steamed buns, 4 adults, children 1, and the rest 1. How many adults and children are there?

Analysis: Suppose 100 people are adults and eat 400 steamed buns, which is 400- 199=20 1. And every time children are treated as adults, they will eat three more steamed buns, so 20 1/3=67 children are treated as adults. Then adults are 100-67=33. The formula is: (4×100-199)/(4-1) = 67.

100-67=33

Of course, it can also be assumed that this 100 person is a child. The logic is the same. You can have a try.

2. A math test paper consists of 24 questions. Deduct 7 points for a correct answer and 5 points for a wrong answer. A student answered 24 questions, but the total score was zero. Do you know how many questions he answered correctly? Suppose the students answered all the questions correctly. . .

Then the score: 24*7= 168 (points)

Actually, I got zero, but I was missing: 168-0= 168 (points).

Answering a wrong question not only won't add points, but will also deduct 5 points, so you will lose money if you answer a wrong question: 7+5= 12 (points).

The wrong question is: 168÷(7+5)= 14 (Tao). The correct question is: 24- 14= 10 (Tao).

Page 12

1. During the summer vacation, Xiaoming wants to read a story book. If he reads 12 pages every day, it is estimated that there are still 40 pages left. If you read 16 pages every day, you can finish reading it three days ahead of schedule. How many pages are there in this book?

Analysis: This is a profit and loss problem. Read 16 pages every day. Compared with reading 12 pages every day, you can read more pages at the same time: 16*3+40=88 pages. Because you read four more pages every day, you can get the estimated time.

Formula: 88 divided by 4=22 days. Number of pages in the book: 12*22+40=304 pages. Or: 16*(22-3)=304 pages.

2. The sum of the numbers A and B is 540, A minus 120 and B plus 40. At this time, A is exactly three times that of B. How much more is A than B?

Analysis: Now the sum of Party A and Party B is 540- 120+40=460.

So now a is 460×3÷(3+ 1)=345, so the original a is 345+ 120=465 B and 540-465=75.

So the difference between Party A and Party B is 465-75=390.

Page 14

1, the average of five numbers is 43. If five numbers are arranged from small to large, the average of the first three numbers is 35, and the average of the last three numbers is 50. What's the middle number?

Analysis: the sum of five numbers is 43×5=2 15, and the sum of the first three numbers is 35×3= 105.

The sum of the last three numbers is 50×3= 150.

The first three numbers+the last three numbers =255= the first two numbers+the middle number ×2+ the last two numbers.

The median number is repeated, so the median number is 255-215 = 40 2. Six people each put a bucket in front of the faucet, and the time required to fetch water is 1, 2, 3, 4, 5 and 6 respectively. How to arrange their order of fetching water reasonably, so as to minimize the sum of everyone's queuing time for fetching water? And find the minimum value.

Analysis: The order of fetching water is from small to large. The total time for fetching water is the same, but the waiting time is different. The longer the time for fetching water, the longer the waiting time and the shorter the waiting time.

The minimum value is 6×1+5×+4× 3+3× 4+2× 5+6×1= 56.

Page 16

1. The fifth-grade students of Yucai Primary School are going to form a square queue to participate in the radio exercise competition. Because there were too many people, one line and one column had to be evacuated, so 29 people were evacuated. How many students are there in Grade Five?

Analysis: A row and a column were evacuated, and 29 people were evacuated. The original team is a square, so the number of people in the original team is equal, but there is a duplicate person in the corner, so the number of people in each team in the original square is1+1= 29+1= 30 (people). * * * There are 15 rows and 15 columns.

Formula: (29+ 1)÷2= 15 (person) 15× 15=225 (person)

2. At the class meeting, the head teacher investigated 54 students in Class 4 (1). In one month, half of the boys did three good things, and the other half did five good things. Half of the girls did six good deeds, and the other half did two good deeds. Calculate, how many good things did the whole class do in a month?

Analysis 1: Half male 3. Half-male and half-female means that every two men have made 8 pieces on average, and 6 pieces are half-female. Half girl 2. On average, every two women make 8 pieces. 54 divided by 2 times 8=2 16.

It can also be explained that this problem needs to use the learned concept of "average" to find the average of several numbers, which is actually "moving more to make up less" in the title: "Half of the boys did three good things, and the other half did five good things." Because the figures in the first half and the second half are the same, we can imagine that if a good thing done by the boys in the second half is given to the boys in the first half, then all the boys can be considered to have done four good things. In the same way, the good things that girls do can also be regarded as four good things that all girls do. In this way, we can think that everyone in Class Four (1) has done four good things, 4*54=2 16.

Page 18

1.A and B two barrels of oil * * * weigh 24 kilograms. Pour the same amount of oil as B into barrel B for the first time, and pour the same amount of oil as A barrel into barrel A for the second time. At this time, there is as much oil in the two barrels. How many kilograms are there in these two barrels of oil?

Analysis: The key to solve the problem is that the oil in barrel A actually doubled after the second pouring of the same amount of oil from barrel B. At this time, a barrel of oil, 24 divided by 2 = 12kg. It shows that when barrel B does not pour oil into barrel A, only 12 divided by 2 = 6 kg in barrel A ... At this time, barrel B oil is twice as much as barrel B oil, and barrel B crude oil: (24-6) divided by 2=9 kg. A barrel originally: 24-9= 15 kg.

Aunt Wang gave peaches to the children in kindergarten. If each child gets three peaches, there will be 16 peaches. If everyone is divided into five parts, then four parts are missing. How many children are there in this kindergarten? * * * How many peaches are there?

Analysis: This is another profit and loss problem. Compared with splitting peaches twice, each person is divided into five, and each person is divided into three, with a score of * * 16+4=20. This is because everyone gets three, which is 16 more, while everyone gets five. Not only is the extra 16 more, but it is also less. So * * * is 20. Then I thought, if everyone gets two more, how many people get 20 more? 20 divided by 2= 10 people, peaches: 10*2+ 16=46, or: 10*5-4=46.

3. The students in Class 4 (1) of Hongzhi Primary School have a natural experimental class, with 3 students at each experimental table and 20 more students; Five people sit at each experimental table, which has just been set up. Q * * * How many experimental tables are there? How many students?

Analysis: The idea is the same as the above question. One * * * is 20 people short, and each table is 2 people short. There is a table in * * *: 20 divided by 2= 10. Number of people: 10*3+20=50 people.

20 pages

1. Students from experimental primary school travel to Yuanmingyuan. If there are 65 people in each car, 15 people can't take the bus. If there are five more people in each car, there will be only one car left. Q * * How many cars are there? How many students are there?

Analysis: (1) If there are 5 people in each car, that is, 70 people in each car.

(2) the difference between two times is 70+ 15=85 people (3) the difference between each car is 5 people (4)85÷5= 17 (car).

(5) 65× 17+15 =1120 people answer: car17, student 165438.

It can also be considered as follows: if there are 65 people in each car and the second number of cars is used (one less than the first one), 65+ 15=80 people cannot be transported. At this time (each car carries 5 people), it is 80÷5= 16 cars. In this way, it can be calculated that the first planned vehicle is 16+ 1= 17 * 65×17+15 =120 people. A: There are 65,438 vehicles.

2. Xiaoming put a total of 103 flags in two boxes, with 12 in the big box and 5 in the small box. And that's it. How many big boxes are there? How many small boxes are there?

Analysis: The four small boxes of the big box 1 1 are mantissas. 103 has a mantissa of 3 and only? 8+? 5 can appear.

Mantissa 3. (? Numbers indicating vacancies) So 12 * 4 = 48, 5 * 1 1 = 55, which adds up to mantissa.

Column type:

Page 22

1.a plans to finish reading a book in a few days. On the first day, he read the first 40 pages of this book. From the next day, he read 5 pages more than the day before, and he read 70 pages on the last day. Do you know how many pages this book has? Analysis: Find out how many days you have seen first: (70-40)÷5+ 1=7 (days), the first day+the seventh day = the second day+the sixth day = the third day+the fifth day, and the fourth day is the middle of the seventh day = (the first day+the seventh day).

Formula: (70-40)÷5+ 1=7 (days), (40+70)×3+(40+70)÷2=385 (pages).

There is a lighter counterfeit currency mixed with 27 coins. Please use the balance without weight, weigh it three times at most, and check it.

Inspection method: Divide coins into three piles for the first time, with 9 coins in each pile, and pile two coins on two trays of the balance. If the tray is balanced, counterfeit money is in the third pile; If not, the counterfeit money is in the lighter pile.

For the second time, divide the pile of 9 coins with counterfeit money into three small piles, each with three coins, and put the two small piles into two trays of the balance respectively. Like last time, the tray is balanced, and counterfeit money is in the third small pile; If the unbalanced counterfeit money is in a lighter pile. The third time, from the small pile of three coins containing counterfeit money, two coins were taken out and placed on the two trays of the balance. If the balance is balanced, the remaining 1 coin is the lighter one if the counterfeit currency is unbalanced.

Page 24

1. The following questions are selected from the book Comparison of Algorithms in Nine Chapters edited by Jason Wu, a great mathematician in Ming Dynasty. Looking at the towering seventh floor from a distance, the red light doubled.

* * * three hundred and eighty-one, ask how many lights are there on the spire.

This question means: a magnificent pagoda with seven floors. Red lights are hung on each floor, and the number of lights on each floor is twice that of the previous floor, and the total number of lights is 38 1. How many lights are there on the top floor of this pagoda?

Analysis: the number of lights on the seventh floor is the least, and the number of lights on the seventh floor is 1 time; 2 times in the 6th floor, 4 times in the 5th floor, 8 times in the 4th floor, 3 times 16 times, 32 times in the 2nd floor, and 62 times 1 floor. *** 1+2+4+8+ 16+32+64= 127; Once it is 38 1÷ 127=3 (light)

Formula: * * *1+2+4+8+16+32+64 =127; Once it is 38 1÷ 127=3 (light)

There are 48 students in Class Five (1). After the afternoon self-study class, 37 people finished their Chinese homework, 42 people finished their math homework, and no one didn't finish both subjects. How many people have finished their Chinese and math homework?

Analysis: Why are those who finish Chinese homework and those who finish math homework right compared with the class size? Because those who finish Chinese and math homework are added twice here, they belong to those who finish Chinese homework and those who finish math homework.

Format: (37+42)-48=3 1 (person) who has completed Chinese and math homework.

Page 26

1, 1 10 Students participated in the calligraphy and painting competition, 72 students participated in the calligraphy and painting competition, and 24 students participated in the calligraphy and painting competition at the same time. How many people took part in the painting competition?

Analysis: As long as students know that 72 includes 24 people who take part in the painting and calligraphy competition at the same time, this problem is very clear. This is the key to this problem.

Formula: Only 1 10-72=38 (people) participated in the painting competition, and the total number of people participating in the painting was 38+24=62 (people);

Method 2: Only 72-24=48 people participated in the calligraphy competition, and the total number of people who participated in painting was 1 10-48 = 62 (people). 2. The following question was put forward by oakley, a scholar from Harvard University.

Two ferries, A and B, shuttle back and forth between the two sides of a river. They set out from both sides of the river at the same time, met for the first time at a distance of 700 meters from the first bank, then continued to advance at the original speed, returned immediately after reaching the other bank, and met for the second time at a distance of 400 meters from the second bank. How wide is this river?

Analysis: The distance between the banks of Party A and Party B is a whole journey. When Party A and Party B met twice, they cooperated for three times, so it took three times as long as the first meeting. From "the first meeting is 700 meters away from Party A's residence", we can know that when the first cooperation was completed, Party A walked 700 meters at the same time and the same distance, so Party A left at the second meeting.

700×3=2 100 (meters) A * * * travels 400 meters longer than the distance between Station A and bilibili (this problem should be understood in combination with pictures), so the distance between Station A and bilibili is 2 100-400= 1700 (meters): 7000.

Page 28

1 class and class 4 (2) took part in tree planting activities to beautify the campus. There are 10 seedlings today. They plan to plant 4 trees per row. How many rows can they plant at most? Draw your design.

Scheme: You can plant 4 rows, that is, four sides of a square. Explain to the students with pictures. )

30 pages

1. The number of story books in Zhang Lei is six times that in Xin Li. If two people buy two more books each, there are four times as many books in Zhang Lei as in Xin Li. How many stories do they have?

Analysis: Li Xin regards it as 1 time, so if Li Xin buys two more copies, it will be twice as much as 2, while if Zhang Lei buys two more copies, the original 6 times +2= the original 4 times +8= the current 4 times, that is, the original 2 times +2=8. Formula: Li: (2× 4-2)

2. Put a bunch of apples in some boxes. If there are 8 apples in each box, there are 12 apples left. If you put nine in each box, the last box needs three to fill. How many apples are there? How many boxes?

Analysis: 9 boxes per box can be packed 12+3= 15 (box), with more than 8 boxes per box, and the number of boxes = 15÷(9-8)= 15 (box).

Formula: 12+3= 15 (box),15× 8+12 =132 (piece)

Who can make four triangles with six sticks?

Page 32

1, China chess cart, horse and gun represent different natural numbers respectively. If car-horse =2, gun-car =4 and gun-horse =56, what is "car+horse+gun"?

Analysis: In this question, Kyle is regarded as one time, so the car is twice as big as the horse, the gun is eight times as big as the horse, and eight times the horse minus one time the horse equals 56, that is, seven times the horse equals 56 and one time the horse equals 56÷7=8.

Formula: 56 ÷ 7 = 8,8+2× 8+8× 8 = 88.

2. Fold a rope in half, fold it in half, fold it in half again, and then cut it in the middle. How many sections was this rope cut by an arrow?

Analysis: Use this question to cultivate children's hands-on habits and the ability to sum up laws according to practice. Cut the middle of the first fold into 2+ 1, the middle of the second fold into 2×2+ 1, and the middle of the third fold into 2×2×2+ 1. Question expansion: How about a 50% discount? What about six times? Formula: the middle part of the three-fold is cut into 2×2×2+ 1=9.

There are five figures, with an average of nine. If one of the numbers is changed to 1, the average of these five numbers is 8. What should be the number of such changes?

Analysis: the average of 5 is less than 1, that is, the sum is less than 5, which means that this number is less than the principle and should be 1+5.

Formula: 1+5=6

Page 34

1, red, yellow and white flowers, safflower and yellow flower together * * 15, yellow flower and white flower together * * 18, white flower and red flower together ***9. How many flowers are there in each of the three kinds of flowers?

Analysis: 15+ 18+9 is twice (red+yellow+white).

White = (red+yellow+white)-15; Red = (red+yellow+white)-18; Yellow = (red+yellow+white) -9

Formula: (15+18+9) ÷ 2 = 21; White: 21-15 = 6; Red = 21-18 = 3; Yellow =2 1-9= 12

Students A, B and C each have a little sister. Six people play table tennis together and hold a mixed doubles competition, stipulating that brothers and sisters cannot be paired.

The first set: A and Xiaohong play against C and Xiaolan.

The second set; C and Xiaoli are sisters of A and B. Please judge who the sisters of A, B and C are.

Analysis: by: "C and Xiaolan, C and Xiaoli." C's sister is Xiaohong. Xiaolan and Xiaoli are left below.

By: "the second set" in the title; C and Xiaoli are sisters of A and B. "B's sister must not be Xiaoli. Then A's sister is Xiaolan.

Page 36

1. There is a rectangular experimental field, one side is 8 meters long, and its adjacent side is 10 meter long. If it is planned to dig a canal with a width of 1 meter around the outer edge of this experimental field, what is the outer perimeter of this canal?

Analysis: As long as students draw and analyze their own pictures, this problem can be seen at a glance. Ask for the circumference of the outer edge of the canal, first find its length and width, because both sides of a wide river are 1m wide, so the width is 8+2= 10, and the length is 10+2= 12.

Column type: width is 8+2 =10; The length is10+2 =12; Perimeter = (10+12) × 2 = 44 2. An old man is walking at a constant speed on the expressway. It took him 22 minutes to walk from 1 to 12. If the old man walks for 36 minutes, which telephone pole should he walk to? (The distance between two adjacent magnetic poles is equal)

Analysis: the length between two telephone poles is 1, "1 telephone pole to 12 telephone pole" * * 1 1, and the time for the elderly to walk a certain distance is 22 ÷1=

Formula: 22÷ 1 1=2 (minutes); 36÷2= 18 (paragraph); 18+ 1= 19 (root)

A theater has 25 rows of seats, the first row has 28 seats, and each row has 2 more seats than the previous row. How many seats are there in this theater?

Let's start with 38 seats.

38 × 25 = 950

There are two more in each row after the first row.

2+4+6+8+ 10+ 12+04+ 16+ 18+20+22+24+26+28+30+32+34+36+.

Together, the total number of seats is 950+600 = 1550.

Page 38

1. Two trains run in opposite directions from Station A and bilibili at the same time. The first time we met was 40 kilometers away from Station A, and the two trains were still running at the original speed. Return immediately after arriving at the other station, and meet at a place 20 kilometers away from bilibili. How many kilometers away are the two stations?

Analysis: Let's assume that the cars departing from Station A and bilibili are called Car A and Car B respectively, and the distance between the two stations is a whole journey. When Party A and bilibili met, * * * cooperated to complete the whole journey for three times, and the time should be three times as long as the first meeting. It can be seen from "the first meeting is 40 kilometers away from Station A" that Party A walked 40 kilometers when the first cooperation was completed. So when we met for the second time, A walked 40×3= 120 (km), and A * * walked 20 meters more than the distance between A station and bilibili (this question should be combined with pictures to help students understand), so the distance between A station and bilibili is120 =100 (km

Formula: 40× 3 =120 (km); 120-20= 100 (km).

40 pages

1, with 249 flowers, arranged in the order of 5 red flowers, 9 yellow flowers and 13 green flowers. What color is the last flower?

Analysis: 5 red flowers, 9 yellow flowers and 13 green flowers are a group, and the quotient of 249 (5+9+ 13) is used to see the remainder. The last flower is safflower when the remainder is less than or equal to 5; When the remainder of 5 ≤5+9 is yellow flowers; When 5+9 remainder ≤5+9+ 13 is yellow flower.

Formula: 249÷(5+9+ 13)=9 (group)? 6 (flower), so the last flower is yellow flower.

There are 270 red, yellow and blue marbles of the same size. According to the arrangement of two red marbles, three yellow marbles and four blue marbles, how many marbles are there in three colors?

Analysis: Similar to the above question, if "2 red, 3 yellow and 4 blue" are grouped, then ***270÷(2+3+4)=30 (group), and each group has 2 red, 3 yellow and 4 blue.

Formula: 270÷(2+3+4)=30 (group); Red: 2× 30 = 60; Yellow: 3× 30 = 90; Blue: 4×30= 120.

There are seven numbers in a row. Their average is 32, the average of the first three numbers is 28 and the average of the last five numbers is 33. Find the third number.

Analysis: the sum of 7 numbers is 32×7=224, and the sum of the first three numbers+the last five numbers is 28× 3+33× 5 = 236; Because the sum of the first three numbers+the last five numbers has two third numbers, the sum of the first three numbers+the last five numbers is one third more than the sum of the seven numbers.

Formula: 32× 7 = 224; 28×3+33×5=249; 236-224=25