Knowledge points of "Mathematics Wide Angle-Tree Planting Problem" in the first volume of fifth grade mathematics in a primary school
1. method: make it smaller or simpler, draw a list, and then summarize the application. 2. Planting trees:
(1), both ends should be planted:
Interval number = total length ÷ spacing; Total length = spacing × number of intervals;
Tree number = interval number+1; Number of intervals = number of trees-1
(Similar problems include: erecting telephone poles and putting flags at both ends ...)
(2), both ends are not planted:
Interval number = total length ÷ spacing; Total length = spacing × number of intervals;
Number of trees = number of intervals-1; Number of intervals = number of trees+1
Similar problems are: sawing wood, cutting wires ...
(3) Plant one head and not plant the other: interval number = total length ÷ spacing;
Total length = spacing × number of intervals; Number of trees = number of intervals; Number of intervals = number of trees
(Similar questions include: ringing the bell to listen to the sound, the time to go upstairs ...)
3. Sawing problem: number of segments = times+1; Times = number of segments-1 total time = time per time × times.
4. Square matrix problem: the outermost layer is: side length × 4-4 or (side length-1) × 4;
Unilateral length = (outermost number +4)÷4
The total number of the whole square matrix is: side length × side length.
5, closed graphics (such as circle, ellipse):
Total length ÷ spacing = interval number; Number of trees = number of intervals.
6. The total length of bridge crossing problem = body length+vehicle distance × vehicle distance+bridge (road length)
Speed = total length ÷ time
7, taxi billing (letter postage, photo printing) and other issues.
The calculation is divided into two parts. (1) standard parts. If you already know the total price, it doesn't count. If you don't know the total price, it counts.
(2) Excess. Excess quantity × excess unit price. Finally add it up.
Wide-angle exercises of mathematics in the first volume of the fifth grade of the second elementary school-planting trees.
1. Plant trees around the oval fish pond. The circumference of the fish pond is 1000 meters. If every 50m species 1 tree, how many trees will be planted in a * * *? 1000 ÷ 50 = 20 (tree)
A * * * can plant 20 trees.
There is a square flower bed in the school, with a side length of 50m. Now we should plant trees around the flower bed, in four corners, with a distance of 5m between every two adjacent trees. How many trees will be planted?
50× 4 ÷ 5 = 40 (tree)
A * * * can plant 40 trees.
3. The construction team needs to pile on the foundation with a length of 150m and a width of 60m. Piling should be done at all four corners, and one pile should be driven every 2.5m How many piles should be driven around the foundation of this building?
(150+60)×2=420 (m)
420 ÷ 2.5 = 168 (root)
A: 168 piles need to be driven around the foundation of this building.
4. The school gymnastics team performed in the phalanx. There are 16 people on both sides of the outermost layer. How many people are there in the outermost layer?
(16- 1) × 4 = 60 (person)
There are 60 people on the outermost floor.
5. One table seats 8 people, two tables sit together 12 people, three tables sit together 16 people ... So, how many people can sit in a row of eight tables? If there are 48 people in a * * *, how many tables do you need to sit?
4× 8+4 = 36 (person) (48-4) ÷ 4 = 1 1 (Zhang)
A: You need 1 1 table to sit down.
There is a square flower bed in the center of the square. The outermost layer of the flower bed has 1 16 potted flowers. How many pots of flowers are placed on each side of the outermost layer? How many potted plants are there in this flower bed?
116÷ 4+1= 30 (basin)
30× 30 = 900 (basin)
A: There are 30 pots of flowers on each side of the outermost layer. There are 900 pots of flowers in this flower bed.
7. A square plot, around which a tree is planted every 8m, has planted a total of 100 trees. The corn planted in this field harvested 28 tons. How many tons of corn is harvested per hectare in this field?
100×8=800 meters
800÷4=200 (m)
200×200=40000(㎡)
40000 square meters = 4 hectares
28 ÷ 4 = 7 (t) A: The average yield of corn in this land is 7 tons per hectare.
Wide-angle exercises of mathematics in the first volume of the fifth grade of the third grade primary school-planting trees.
Find the number of trees first: 1. There is an 800-meter-long highway. How many poplar saplings does it take to plant a poplar every 20 meters from beginning to end on one side of the expressway? ?
2. Erect telephone poles on one side of the 2500m-long highway, and erect one every 50m. If both ends of the expressway are not erected, how many wires are needed? ?
On both sides of the 3.50-meter-long runway, a colorful flag is inserted every 5 meters from beginning to end. A * * *, how many colorful flags?
4. How long is the expressway in front of the park gate? 80? Rice and poplar should be planted on both sides of the expressway, every other tree? 8? Rice (planted at both ends). How many trees does the gardener need to prepare?
5. Is there a long highway? 1000? Rice, plant a weeping willow every 5 meters on one side of the road. How many weeping willows can you plant?
6. What is the distance between the two buildings? 56? Meters, every other? 4? A cedar is planted in rice. How many trees can be planted in a row?
Second, find the distance:?
1. The boulevard in Red Scarf Park is 800 meters long. From beginning to end, there are 4 1 trash cans equidistantly placed on its side. How many meters are there between every two trash cans?
2. On one side of a boulevard, there are fixed telephone poles from beginning to end, and 86 telephone poles are used. This boulevard is 1700 meters long. How many meters are there between every two telephone poles?
A tunnel in downtown park is 200 meters long. Canna was planted equidistantly on both sides of the tunnel from beginning to end, with a total of 82 canna plants. How many meters are there between every two cannas?
4. In a long? 250? Planting trees on both sides of the rice road, the starting point and the end point are planted, and a * * * is planted? 10 1? Trees? The distance between every two trees is equal. Do you know how many meters it is? ?
Third, the total length:
1. On both sides of an expressway, a telephone pole is erected every16m, and 52 telephone poles are used. What is the total length of this highway?
2. Planting on one side of a section of highway? 95? Trees are planted at both ends. What is the distance between every two trees? 5? How long is this road?
3. Is there? 320? A few pots of chrysanthemums, have you arranged them? 8? Ok, what is the distance between two adjacent chrysanthemums in each row? 1? What is the length of each row of rice and chrysanthemum?
Fourth, closed graphics:?
1, a circular pond with a circumference of 300 meters, how many saplings do you need to plant a willow every 5 meters?
2. Around the circular pool, 40 poplars are planted every 2 meters. What is the circumference of the swimming pool?
A round fish pond is 200 meters long. Now 25 poplars are planted around the pond. How many meters can I plant?
There is a square flower bed in front of the school library. The outermost layer of this flower bed is placed on both sides? 12? Potted flowers, how many potted flowers are put on the outermost layer? How many potted plants does this flower bed need? ?
In the program, there is a square flower bed in the center of the square. The 1 floor outside the flower bed is chrysanthemum. Is it the outermost layer? Put it on both sides? 10? Washball, a * * *? How many pots of chrysanthemums have you bought? What if you put one on each side of the outermost layer? 20? Pot, how many pots of chrysanthemums are put in a pot?
6. Uncle Zhang planted trees around the contracted square pond. How long is this pond? 60? Rice is planted every 5 meters, one at each corner. Uncle Zhang bought it? 50? Are there enough seedlings?
7. existing? 60? A child besieged a square to play games, and then what? How many students are there on each side? What if the siege is pentagonal? How about a hexagon? ?
8. There is a circular pool every other week? 2? Rice planted a willow, while * * * planted 40 trees. What is the circumference of the swimming pool? ?