"Tree planting problem on closed graphs" Mathematics wide-angle PPT

Description

"Tree planting problem on closed graphs" Mathematics wide-angle PPT

Part One: Introduction to the topic

Huanhuan's neighbor Uncle Zhang, although he is old, is an out-and-out environmentalist. Every year he goes back to the countryside to plant trees during Arbor Day. He plans to plant trees around the circular pond. The perimeter of the pond is 120m. If one tree is planted every 10m, how many trees need to be planted in total? Can you help him do the math?

PPT on tree planting problem on closed figures, part 2: new teaching knowledge

【Analysis】

method one:

Represent the pond as a circle, reducing the perimeter of the pond. Assume that the perimeter is 40 meters and one tree is planted every 10 meters. How many trees can be planted? The result obtained by drawing is 4 trees.

Method Two:

After choosing 40 meters and straightening the graph, we came to the conclusion that the tree planting problem on a closed figure is equivalent to the tree planting problem on a line segment where only the ends are planted.

Method 3: Use the list method to display the tree planting situation, and find that the number of trees planted corresponds to the number of intervals.

Method 4: Calculate directly based on the found rules, 120÷10=12 (trees), 12 trees need to be planted.

[Method Summary] The tree planting problem on a closed graph is equivalent to the tree planting problem on a line segment where only one end is planted. The number of trees planted corresponds to the number of intervals. You only need to find the number of intervals to find out. The number of trees planted.

PPT on tree planting problem on closed graph, part 3: knowledge sorting

Knowledge point: Tree planting problem on closed graph.

The tree planting problem on a closed graph is similar to the tree planting problem on a line segment in which only one end is planted, so only the number of intervals is required. The number of intervals = perimeter (full length) ÷ spacing, the number of trees planted = the number of intervals.

Example: A bracelet is 18 centimeters long and there is an agate every 3 centimeters. How many agates are there in total on this bracelet?

[Analysis] This is a tree planting problem of closed figures in life. According to the conditions given in the question, if you want to find out how many agates are shared, you need to find the number of intervals. You need to divide the circumference (full length) by the number of intervals. The circumference is 18 cm and the spacing is 3 cm, so The formula is: 18÷3=6 (pieces). There are a total of 6 agates on this bracelet.

[Method Summary] When solving the tree planting problem on a closed figure, you need to find the perimeter of the figure and then find the number of intervals. Sometimes the perimeter of a figure is directly told in the question, and sometimes it needs to be calculated.

PPT on tree planting problem on closed graph, part 4: classroom exercises

1. There are spotlights every 20 meters in the circular gymnasium. A total of 45 spotlights are installed. How many meters is the circumference of this gymnasium?

[Commentary] This question is a reverse thinking question on the tree planting problem on a closed graph. In the question, 20 meters is the separation distance, 45 spotlights is the number of intervals, and the perimeter is equal to the separation distance × the number of intervals, 20×45=900 (meters).

2. The students gathered in a square to play a game, with 10 people standing on each side. How many people are needed to play this game?

[Commentary] A square is a closed figure. The number of intervals in a closed figure is equal to a tree, which is equivalent to the number of people. You only need to find the number of intervals on one side to know the number of intervals on the four sides. Therefore, the column formula is calculated as (10-1) × 4 = 36 (people).

3. There is a square pool with a side length of 50 meters. If you want to plant a rose every 2.5 meters around the pool, how many roses will be used?

[Commentary] The length of one side is given in the question, so you can first find the perimeter, and then find the number of intervals, that is, the number of flowers to be planted. The column formula calculation is 50×4÷2.5=80 (trees).

PPT on tree planting problem on closed graph, part 5: homework

1. Write the number directly.

100－63＝ 3.2＋1.68＝ 2.8×0.4＝

14-7.4＝ 1.92÷0.04＝ 0.32×500＝

0.65＋4.35＝ 10－5.4＝ 4÷20＝

3.5×200＝ 1.5－0.06＝ 0.75÷15＝

0.4×0.8＝ 4×0.25＝ 0.36＋1.54＝

2. Before the school holds a sports meeting, a colorful flag should be placed every 10 meters on the outside of the 100-meter straight track. If there is an original colorful flag at one end of the track, do I need to prepare another colorful flag?

Answer: 100÷10=10 (face)

3. It took a total of 15 minutes to saw a log into 2-meter-long sections. It is known that it takes 3 minutes to saw each section. How many meters long is this log?

Answer: (15÷3+1)×2=12 (meters)

4. A circular fish pond is 200 meters long. Now, 25 poplar trees are planted around the pond. How many meters apart should one be planted to plant them all?

Answer: 200÷25=8 (meters)

Keywords: free download of PPT courseware for mathematics in the first volume of the fifth grade of the People's Education Press, download of tree planting problem on closed graphics PPT, download of wide-angle mathematics PPT, .PPT format;

For more information about the PPT courseware "Tree Planting Problems on Mathematics Wide-angle Closed Figures", please click on the Mathematics Wide-angle PPT Tree Planting Problems on Closed Figures PPT tag.

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Update Time: 2024-09-08

This template belongs to Mathematics courseware People's Education Press Fifth Grade Mathematics Volume 1 industry PPT template

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