The school has a 60-meter-long path, and it is planned to plant trees along the road every 3 meters, with a spacing of (). If a tree is planted at both ends, then * * * needs () seedlings; If you don't plant trees at both ends, then * * * needs () seedlings; If only one plant is planted, then * * * needs () seedlings.
Objective: To explore three situations of planting trees on a line segment and correctly distinguish three relationships between the number of trees planted and the number of intervals.
Answer: 20; 2 1; 19; 20。
Analysis: Use 60 first? 3 find out that there are 20 intervals, and then solve them according to the mathematical models of three cases of planting trees on a line segment: if trees are planted at both ends, the number of trees = interval number+1; If no trees are planted at both ends, the number of trees = interval number-1; If one end is planted and the other end is not planted, the number of trees = the number of intervals.
2. To connect 10 rubber bands into a circle, you need to tie a knot ().
Objective: To study the problem of planting trees on a closed curve (number of intervals = number of trees planted).
Answer: 10.
Analysis: First, it is clear that this problem is a tree planting problem on a closed curve. The rubber band has 10, which is equivalent to the number of intervals 10, and the number of knots is equivalent to the number of trees planted. Because the number of intervals on the closed curve = the number of trees planted, the number of knots is 10.
3. Put 4 pieces on each side of a square, with a maximum of () and a minimum of () on each side.
Objective: To investigate whether planting trees in corners will determine the total number of trees planted in closed graphs.
Answer:16; 12。
Analysis: There are two ways to put four pieces on each side of a square: putting pieces in all corners and not putting pieces in all corners. When there are no pieces in the four corners, the most pieces are placed on the four sides. Can one * * * put four pieces? 4= 16 pieces; When chess pieces are placed in all four corners, the chess pieces on the corner belong to two adjacent sides at the same time. At this time, the total number of pieces placed is the least. If you want to subtract four repeated pieces from the corner, you can place at least four pieces. 4-4= 12 pieces.
Doudou and Lingling live in the same building, with 20 steps between each floor. Doudou lives on the second floor and Lingling lives on the fifth floor. Doudou needs to take () steps to go to Lingling's house from his own home to play with her.
Objective: To explore the reverse application of mathematical model of tree planting.
Answer: 60
Analysis: there are 20 steps between each floor, which is equivalent to an interval of 20; There are three intervals from the second floor to the fifth floor, so how many steps do you need to take, which is the total, so use 20? 3, the answer is 60.
On the problem of wide-angle tree planting in mathematics. 1. Fill in the blanks.
1. There is a 60-meter-long path in the school. Plan to plant trees along the road, one every 3 meters, at intervals (A). If a tree is planted at both ends, then * * * needs seedlings; If you don't plant trees at both ends, then * * * needs (answer) seedlings; If only one end is planted with trees, then * * * needs seedlings.
2. To connect 10 rubber bands into a circle, you need to tie a knot.
3. A square has 4 pieces on each side, and at most four sides can put (answers) and at least (answers).
Doudou and Lingling live in the same building, and there are 20 steps between each floor. Doudou lives on the second floor and Lingling lives on the fifth floor. Doudou needs to walk (answer) from his house to Lingling's house to play with her.
5. As shown below, stick a rectangular colored brick between every two square tiles. In this way, a * * * pastes 50 rectangular colored tiles, so there are (answer) square tiles (the first and last ones are square tiles).
6. 15 Students play games in a circle on the playground. The distance between every two students is 2m, and the circumference of the circle is (answer) m. ..
7. Every floor of a building must go up 18 steps. Wang Fang went home and walked up the 108 steps. Her family lives in the building.
8. Xiaodong arranges some 50-cent coins evenly on a square piece of paper, and the number of coins on each side is equal. The total face value of these coins is 12 yuan. You can put (answer) coins at most on each side.
Second, choose
The total length of bus line 1.7 is 8km, and the distance between two adjacent stops is 1km. How many stations are there? The correct formula is (answer).
A.7？ 1+ 1
B.8？ 1- 1
C.8？ 1+ 1
2. A piece of wood is 10 meter long, which is divided into five sections on average. It takes 8 minutes to saw the next section, and how many minutes does it take to see the next section? What kind of question does this belong to? (answer)
A.it's not about planting trees.
B. Planting trees at both ends
C. plant trees at both ends
3. The construction team shall bury telephone poles every 40m, including both ends, * * * 7 1. This section of road is (answer) meters long.
.40 caliber? (7 1+ 1)=2880
B.40？ 7 1=2840
C.40？ (7 1- 1)=2800
Grandpa Obana went upstairs at the same time, and Xiaohua went upstairs twice as fast as grandpa. When grandpa arrived at the fourth floor, Xiaohua arrived at the (answer) floor.
A.8
B.7
C6
A 20-meter-long rope can be cut into a 2-meter-long short rope, and it needs to be cut (answered) several times.
a . 10； nine
b . 10； 10
C.9 10
Third, answer.
1. There are not enough parking spaces in Xingguang Community. Draw a parking space every 5 meters on one side of the residential road. The signs are separate. /kloc-How many cars can be parked on the 0/00m long roadside at most? How many do you need to draw? Signs?
answer
2. On both sides of a path, plant a tree (both ends) every 5 meters and plant 202 trees. How long is this road?
answer
3. Insert a red flag and two yellow flags every 5 meters around the 400-meter circular runway. How many red and yellow flags do you need?
answer
4. The school nursery is 17m long and 5m wide, with an average of 2 rhododendrons planted per square meter. How many azaleas can one plant grow?
answer
5. During the celebration of June 1st, a string of balloons (with three balloons in a string) was hung every 1m on the outer edge of a rectangular stage with a length of 9m and a width of 3m, but the side against the wall was not hung, and all four corners were hung. How many balloons does a * * need?
answer
Extracurricular development: wide angle of mathematics? Tree planting teaching plan
Teaching objectives:
Knowledge and skills:
(1) Understand the characteristics of planting trees at both ends of a line segment in the tree planting problem, and apply the law to solve the problem.
(2) Explore the problem of planting two trees without planting them through guessing operation, verification and communication.
(3) Find the law of planting trees from the closed curve (square).
Process and method:
Cultivate students' observation ability, operation ability and cooperation ability.
Emotional attitudes and values:
Students explore new knowledge through observation, operation and communication.
Teaching emphases and difficulties:
Teaching emphasis: discover laws in inquiry activities, extract mathematical models, and use the discovered laws to solve some simple practical problems in life.
Teaching difficulties: refining and applying basic laws and methods.
Teaching preparation:
Teaching aid preparation: courseware
Prepare learning tools: workbooks
Teaching process:
First, talk before class.
Students, there is a path 100 meters long next to the school. The teacher is going to plant some seedlings. Would you please ask the little designers to help design it? (OK) Today we will study the mystery of planting trees.
Second, explore the law.
(1) 1. Show the theme.
This path is 100 meter long. Plant a small sapling every 5 meters (plant both ends). How many trees can a * * * plant? Some students may list the formula immediately: 100? 5=20 (tree)
(1) understand the meaning of the problem
A. read the questions by name. What information did you learn from the question?
B, understanding? Two ends? What do you mean?
Say its name, and then demonstrate it in kind.
Point out the position of the end of the stick.
Note: planting at both ends means planting at both ends of the path.
(2) Students begin to operate.
Take out sticks, talk to each other at the same table, draw a picture and pose.
③ After discussing with each other at the same table, the whole class will report and communicate.
Name it: How many sticks did you put?
Put it on the blackboard and show it to everyone.
Count the sticks you just put on. What's the gap between them? How many sticks does a * * * put?
C. what is the relationship between spacing and the number of trees planted?
④ Teacher's Note: Let's start to calculate 100? 5=20, this 20 does not mean that 20 trees can be planted, but that * * * has 20 intervals.
2. Change the subject condition to:
When planting trees along the 20-meter path, please design a tree planting plan according to the requirement of planting trees every 5 meters, and explain the reasons. (Can be represented by line segment diagram)
1. Students try to answer.
Test with a stick
3. Tell me what you think
What is the relationship between the number of intervals and the number of trees planted?
After the students tried to speak, the teacher summarized.
4. Basic exercises: Students do exercises. The distance from the first person to the last person in a vertical line is 24 meters, and the distance between every two people is 2 meters. How many people are there in this line?
5. Improvement exercise: Gardeners plant trees along the roadside, one tree every 6 meters and 36 trees in a row. How far is it from 1 tree to the last one?
(2) Example 2
1, students look at the questions and understand the meaning.
①? A path between two museums? Which paragraph does it refer to?
②? On both sides of the road? How many noodles are you going to plant?
Students cooperate with each other and swing with sticks.
Teacher's Tip: Now we can assume that the distance between the Elephant Pavilion and the Orangutan Pavilion is18m, and other conditions remain unchanged. Let's swing it with a stick first.
Require completion:
(1) How many sticks did you put?
② What is the relationship between the number of sticks per side and the number of intervals?
3, the whole class communication
4. Teacher's summary
This situation belongs to the problem of planting trees at two ends, that is, the number of trees planted = the number of intervals? 1。
(3) Teaching Example 3 by Swinging a Stick
Teacher's summary: The number of trees planted when harvesting at both ends = the number of intervals.
Third, practical application.
1. First, if the wood is 10 meter long, it should be divided into five sections on average. It takes 8 minutes to saw the next section, and how many minutes does it take to see the next section?
2. Plant trees in front of the teaching building, and plant a tree every 4 meters. How many trees can be planted within 20 meters?
Fourth, class summary.