How to have a good math class

In the face of the new curriculum reform, the mathematics teacher standing on the platform was at a loss. So we went into other classes and saw such a scene: the teacher kept clicking the mouse, playing flashing pictures and soothing music, making a lot of noise, replacing all blackboard writing and experiments. Students could not see the teacher's demonstration

How to have a good math class

1、 Reading textbooks: reading textbooks is a basic skill for teachers, and reading textbooks is the basis of using textbooks and effective teaching. (1) reading textbooks from the perspective of overall connection; (2) reading textbooks with the concept of curriculum reform; (3) reading textbooks with questioning attitude; (4) grasping the essence of mathematics to understand

A car goes from place a to place B at 60 km / h for 3 hours. It goes back at 90 km / h?

60 × 3 = 180 (km), 180 ／ 90 = 2 (H), 180 × 2 ／ (3 + 2), = 360 ／ 5, = 72 (km / h), a: the average speed of this car is 72 km / h

Given that f (x) = x + AlN (x-1) - alnx, when x1. X2 ∈ [2, + ∞), if the inequality [f (x1) - f (x2)] / (x1-x2)

f'(x)=1+a/(x-1)-a/x =1+a/[x(x-1)]
When x1. X2 ∈ [2, + ∞), the inequality [f (x1) - f (x2)] / (x1-x2)

The passenger car and the freight car are running from the two places at the same time. When they meet, the passenger car runs 80 kilometers more than the freight car. It is known that the speed ratio of the passenger car and the freight car is 7:5, so the distance between the two places can be calculated

Because the distance of multiple lines is equivalent to (7-5) / (7 + 5) = 1 / 6 of the total distance
So the total distance = 80 / (1 / 6) = 480km

If point a (2. - 3) is known and the projection of line AB on the coordinate axis is 5, then the coordinate of point B is

Let the coordinates of point B be (x, y), then:
｜x-2｜=5
｜y+3｜=5
So the solution is x = - 3 or 7, y = - 8 or 2
So there are four kinds of coordinates of point B, which are (- 3, - 8), (7, - 8), (- 3,2), (7,2)

Party A and Party B are facing each other from a and B, which are 36 kilometers apart. When Party A starts from a and arrives at 1 kilometer, he finds something left in place a, and immediately returns. After taking things, he immediately moves from a to B, so that they meet at the midpoint of ab. it is known that Party A walks 0.5 kilometers more per hour than Party B. what are their respective speeds?

Let B's speed be XKM / h, then a's speed is (x + 0.5) km / h. from the question meaning: 18 + 2x + 0.5 = 18x, the solution is: x = 4.5, x = 4.5 is the solution of the original equation, 4.5 + 0.5 = 5, answer: B's speed is 4.5km/h, then a's speed is 5km / h

Factorization factor a square (B-C) + b square (C-A) + C square (a-b)

a^2(b-c)+b^2(c-a)+c^2(a-b)
=(a^2b-b^2a)-(a^2c-b^2c)+c^2(a-b)
=ab(a-b)-c(a-b)(a+b)+c^2(a-b)
=(a-b)(ab-c(a+b)+c^2)
=(a-b)(ab-ac-bc+c^2)
=(a-b)(a(b-c)-c(b-c))
=(a-b)(b-c)(a-c)

Li Wei rides a motorcycle from home to the railway station. If he travels 30 kilometers per hour, he will be 15 minutes earlier than the train. If he travels 18 kilometers per hour, he will be 15 minutes later than the train's departure time. If Li Wei plans to arrive at the railway station 10 minutes before the train leaves, what's the speed of his motorcycle at this time?

Let the departure time of the train be x hours. From the meaning of the question: 30 (x-1560) = 18 (x + 1560), the solution is x = 1. Let Li Wei's cycling speed be y kilometers per hour, y = 30 × (1 − 1560) 1 − 1060 = 27. Therefore, Li Wei's cycling speed is 27 kilometers per hour

Given: A-B = - 3, find the value of: 4 (a-b) - 5A + 5B + 5

Original formula = 4a-4b-5a + 5B + 5 = - A + B + 5, ∵ A-B = - 3, ∵ original formula = - (- 3) + 5 = 8

How to have a good math class