Teaching objectives:

1. Learn how to solve the unknowns in wide-angle problems.

2. Learn how to apply known conditions to solve problems.

3. Learn how to understand and apply concepts and formulas such as angle and proportion.

Teaching resources: whiteboard, teaching materials

Teaching process:

Step 1 introduction

Teacher: Students, when you finish your math problems, you will often encounter some wide-angle problems. Today we will look at a wide-angle tea making problem.

Lead to the problem: there is a fountain with a height of 1 and a tea maker with a height of 1.8. The base of the teapot is connected with the center of the fountain into a line segment. The bottom of the pot and the fountain mouth are at both ends of this line segment. After boiling water is brewed, the tea leaves flow out of the teapot and still flow back to the fountain through the curved position of the bridge. When the water level in the fountain rises to the height of the cooking spout, the water level in the fountain increases by 1cm. The velocity of water at the bending position of the bridge is 65438+ 0/6 of the original velocity (assuming that the bending position of tea in the middle of the bridge remains unchanged). Ask how long it takes to make tea.

The second step is to analyze the theme

By observing the conditions in the topic, we can know the height of the tea maker and fountain, the water flow speed at the bridge and the rising height of the fountain water level. The topic requires us to solve the time taken to make tea. Therefore, we need to solve the unknown with known conditions.

Clear your mind

The time we need to make tea can be calculated by calculating the sum of the time when water flows from the boiling pot to the fountain center and the time when water flows from the fountain center to the boiling pot. To calculate these two times, it is necessary to convert the velocity of water in the process of two-stage flow, and then multiply the velocity by the distance to get the time used.

The fourth step is to calculate the flow rate.

Because the speed of water at the bridge is 65438+ 0/6 of the original speed, then we can write the original speed as V, and the speed at the bridge is v/6. Next, we can use a similar triangle to calculate the speed at which tea leaves flow from the boiling pot to the center of the fountain.

According to similar triangles, the distance from the kettle mouth to the fountain center is 1.8- 1 = 0.8m, and the time from the kettle to the fountain center is the distance divided by the speed, namely:

t 1=0.8/(v*5/6)

Similarly, the speed of tea leaves from the center of fountain to the boiling pot is V, the distance from the center of fountain to the boiling pot is 0.2m, and the time from the center of fountain to the boiling pot is:

t2=0.2/v

The fifth step is to calculate the required time.

Finally, we can add t 1 and t2 to get the total time required for tea leaves to flow from the boiling pot to the fountain and back to the boiling pot:

t = t 1+T2 = 0.8/(v * 5/6)+0.2/v

summary

According to the mathematical formula, we can get: v = (32/3) (1/5), so:

T=2.744 seconds (three decimal places reserved)

So it takes 2.744 seconds to make tea.

summary

Through this exercise, we can find that in the wide-angle problem, we turn the problem into an unknown by applying the known conditions, and then use the concepts and formulas we have learned to calculate. Only by combining knowledge with practice can we better understand and master mathematical knowledge.