"Mathematics in Beer Production" PPT courseware 8

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"Mathematics in Beer Production" PPT courseware 8

1. Situation introduction

What do you know about the "football field"?

Player No. 10 took off in the blue area, 1 meter away from the baseline and 25 meters from the right sideline, and scored the first goal.

How many centimeters is the distance between point A and the bottom line on the diagram? What about the right edge?

Player No. 4 kicked off 16 meters from the baseline and 20 meters from the left sideline and scored the second goal.

How many centimeters is the distance between point B and the bottom line on the diagram? What about the left sideline?

What mathematical information do you know from the picture?

What questions can you ask based on this information?

2. Cooperation and exploration

How many centimeters is the distance between point A and the bottom line on the diagram? What about the right edge?

Can you find the distance on the picture? Give it a try!

According to the distance on the graph/actual distance = scale, the equation can be solved.

According to the sense of scale, in this picture, the actual distance is 1000 times the distance on the picture.

10 meters = 1000 centimeters

1000÷1000 = 1 (cm)

25 meters = 2500 centimeters

2500÷1000 = 2.5 (cm)

3. Independent practice

1. A rectangular lawn is 40 meters long and 25 meters wide. Please use a scale of 1:1000 to draw a floor plan of this lawn.

First calculate the distance on the picture:

Solution: Let the distance on the diagram of the length of the rectangular lawn be χ centimeters.

40 meters = 4000 centimeters

x/4000=1/1000

1000χ= 1×4000

χ = 4

2. Fill in the form

3. On a map with a scale of 1:25000, the distance between places A and B is 20 centimeters. If it is drawn on a map with a scale of 1:20000, the distance between places A and B on the map will be How long should the painting be?

Solution: Suppose the actual distance between places A and B is χ centimeters.

1:25000 = 20:χ

χ = 20×25000

χ = 500000

Solution: Suppose the distance on the map between places A and B is y centimeters.

1:20000 = y:500000

2000y = 500000

y=25

Answer: The distance between places A and B on the map should be 25 centimeters.

4. (1) How many meters is the actual length of the living room?

(2) How many square meters is the actual area of ​​the small bedroom?

(3) If the balcony is 1.2 meters wide, how many centimeters should it be drawn on the picture?

(4) What other questions can you ask?

To solve these problems, start by measuring the dimensions of each room.

5. On a map with a scale of 1:20000000, the length of the railway between places A and B is measured to be 6 cm. Two trains leave from places A and B at the same time and opposite each other. It is known that the train leaving from place A travels 125 kilometers per hour, and the train leaving from place B travels 115 kilometers per hour. A few hours later, the two trains Can we meet?

According to the sense of scale, in this picture, the actual distance is 20,000,000 times the distance on the picture.

6×20000000 = 120000000 (cm)

120000000 centimeters = 1200 kilometers

1200÷(125+115)=5(hours)

Answer: The two cars will meet after 5 hours.

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Update Time: 2024-11-20

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