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"Tree planting problem on line segments" Mathematics wide-angle PPT
Part One: Introduction to the topic
Huanhuan and Lele are planting trees on the edge of a 20-meter garden during Arbor Day this year. If one is planted every 5 meters, how many trees can be planted at both ends? Invite students to communicate in groups. You can use line segment drawings to draw pictures.
PPT on tree planting problem on line segments, part 2: new teaching knowledge
【Analysis】
method one:
Draw a line graph and count 5 trees planted.
Method Two:
There are 4 intervals in counting. Just like the little finger we practiced before class, the number of trees planted is 1 more than the number of intervals.
Method three:
To find the number of intervals, divide the total length by the number of meters of intervals, 20÷5=4.
PPT on tree planting problem on line segments, the third part: knowledge sorting
Knowledge point 1: The problem of planting trees at both ends.
Number of intervals = total length ÷ spacing Number of trees planted = number of intervals + 1
Example: The students planted trees on the side of a 150-meter-long path. Plant one every 10 meters (plant at both ends). How many seedlings are needed in total?
[Analysis] This is a "planting at both ends" situation in the tree planting problem. According to the rule "full length ÷ interval length = number of intervals", you can first find the number of intervals, and then use the number of intervals + 1 to equal the required number of trees. The column formula calculation is: 150÷10=15 15+1=16 (trees), so a total of 16 trees are needed.
[Method Summary] When solving tree planting problems, you must fully understand the meaning of the problem, and then use the rules to calculate.
Knowledge point 2: The law of failure at both ends.
Number of trees = number of intervals - 1 number of intervals = number of trees + 1
Example: Use an 18-meter-long rope to cut a skipping rope. Cut one piece every 3 meters. How many times do you need to cut it in total?
[Analysis] This question belongs to the "no planting at both ends" situation in the tree planting problem. 18 meters is the total length, and 3 is equivalent to the number of intervals. According to the regular formula, it can be calculated as: 18÷3-1=5 (times), and a total of 5 cuts are required.
[Method summary] To solve the problem of tree planting, we must connect it with life, analyze specific problems in detail, and apply rules flexibly.
Knowledge point 3: The rule of planting only at one end.
Number of trees = number of intervals
Example: Sanitation workers need to place trash cans on both sides of a 3-kilometer road (one end is secure and the other is unsafe). Place one every 150 meters. How many trash cans are needed in total?
[Analysis] The key words of this question are "both sides" and "one end is safe and the other is uneasy". According to the rule "number of intervals = number of trees", the calculation is: 3000÷150=20 20×2=40 (pieces), a total of 40 trash cans are needed.
[Method Summary] When solving the tree planting problem, it is necessary to analyze which of the three situations the problem belongs to, and then select the appropriate law to calculate and solve the problem.
PPT on tree planting problem on line segments, Part 4: Classroom exercises
1. The community wants to install street lights on both sides of the 300-meter road, one every 10 meters (installed at both ends). How many street lights are needed in total?
[Commentary] This is a situation where both ends are planted in the tree planting problem. According to the rule "full length ÷ interval length = number of intervals", first find the number on one side, and then multiply the result on one side by 2 to get the total number on both sides. Number of street lights required. The column calculation is: 300÷10+1=31 (lights) 31×2=62 (lights), a total of 62 street lights are needed on both sides.
2. Arbor Day is here, and the Young Pioneers have to plant 8 poplar trees between two buildings 72 meters apart. If neither end is planted, what is the average distance between two trees?
[Commentary] This question is about finding the spacing distance. To find the spacing distance, you need to know the number of spacings. The question tells you to plant 8 poplar trees, and they are planted between two buildings, so the number of spacings is 8+1= 9, then the separation distance = 72÷9=8 (trees).
3. Sawing a steel pipe into small sections took a total of 28 minutes. It is known that it takes 4 minutes to saw each section. How many sections did the steel pipe be sawed into?
[Commentary] The question tells the time for sawing once, so we first find the number of saws, which is 28÷4=7 times, and the number of sawing segments is 1 more than the number of saws, so 7+1=8 part.
PPT on tree planting problem on line segments, part 5: homework
1. Write the number directly.
100－63＝ 3.2＋1.68＝ 8×0.4＝
14-7.4＝ 1.92÷0.04＝ 0.32×500＝
0.65＋4.35＝ 0.51÷17＝ 32.8＋19＝
5.2÷1.3＝ 1.6×0.4＝ 4.9×0.7＝
1÷5＝ 6÷12＝ 0.87－0.49＝
2. Telephone poles are erected on one side of a 2500-meter-long road, one every 50 meters. If there are no telegraph poles erected at both ends of the road, how many telephone poles are needed in total?
Answer: 2500÷50-1=49 (root)
3. A corridor in the street park is 200 meters long. Cannas are planted equidistantly from beginning to end on both sides of the corridor. A total of 82 cannas are planted. How many meters are there between two cannas?
Answer: 82÷2-1=40 200÷40=5 (meters)
4. A boulevard in the Red Scarf Park is 800 meters long. There are 41 trash cans placed equidistantly from beginning to end on one side of it. How many meters are there between each two trash cans?
Answer: 41-1=40 800÷40=20 (meters)
PPT on tree planting problem on line segments, part 6: knowledge expansion
A telephone pole is erected every 16 meters on a road. Not counting the 54 poles shared at both ends of the road, how many meters is the total length of the road?
Answer: (54+1)×16=880 (meters)
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