Illustration of multiple solutions to one problem in primary school mathematics, primary school math

It's better to think of multiple solutions.

The two cars drove opposite each other from A and B at the same time and met five hours later. The speed of one car is 55 kilometers per hour, and the speed of another car is 45 kilometers per hour.

Analysis 1] First find the number of kilometers traveled by the two cars, and then find the sum of the distances traveled by the two cars, that is, how many kilometers apart A and B are obtained.

Solution 1] How many kilometers does a car travel?

55 5 = 275 (km).

How many kilometers did the other car travel?

45 5 = 225 (km).

How many kilometers are A and B apart?

275 + 225 = 500 (km).

Composite formula: 55 5+45 5

275 + 225 = 500 (km).

Analysis 2] First find out how many kilometers the two cars travel per hour, and then multiply by the time of the meeting, that is, how many kilometers apart A and B are apart.

Solution 2] How many kilometers do two cars travel per hour?

55 + 45 = 100 (km).

How many kilometers are A and B apart?

100 5 = 500 (km).

Composite formula: (55+45) 5

100 5 = 500 (km).

Analysis 3] The distance between A and B divided by the time of meeting is equal to the sum of the speeds of the two cars. From this, an equation can be drawn to find how many kilometers apart A and B are between each other.

Solution 3] Let A and B be separated by x kilometers.

x÷5=55+45

x=100×5

x=500 analysis 4] The distance between A and B minus the distance traveled by one car is equal to the distance traveled by the other car, which is solved by this equation.

Solution 4] Let A and B be separated by x kilometers.

x-55×5=45×5

x-275=225

x=275+225

x=500A: A and B are 500 kilometers apart.

Multiple solutions or multiple solutions?

Multiple solutions or multiple solutions?

The railway between the north and south cities is 357 kilometers long, an express train runs from the north city, and at the same time a slow train runs from the south city, the two cars go in opposite directions, after 3 hours of meeting, the express train travels an average of 79 kilometers per hour, and the slow train travels an average of how many kilometers less than the fast train per hour?

Solution 1, [357-(79 3)] 3

40 (km).

That is, the average distance of slow trains is 40 kilometers per hour, and the average number of kilometers per hour of fast trains is 79 kilometers is known, and the average number of kilometers of slow trains per hour is less than that of fast trains.

79-40 = 39 (km).

A: Slow trains travel an average of 39 kilometers less per hour than fast trains.

Solution 2, 79-(357 3-79).

39 (km).

Answer: (Ibid.).

Solution 3: Set the average distance of the slow train to X kilometers per hour.

79×3+3x=357

3x=357-237

3x=120

x=40 (km).

79-40 = 39 (km).

Chickens and rabbits in the same cage.

There were a number of chickens and rabbits, and there were 14 clansmen, 48 legs. How many chickens and rabbits are there?

Method 1: Hypothetical method.

Suppose it's all chickens: 2 14 = 28 (only).

Chicken feet are less than the total number of feet: 48 28 = 20 (only).

Rabbit Duan Suixian: 20 (4-2) = 10 (only).

Chickens: 14 10 = 4 (only).

Method 2: Unary Linear Equation.

Solution: If there are x rabbits with grippers, then chickens have (48-x).

4x+2(14-x)=48

4x+28-2x=48

2x=48-28

2x=20x=10

Then there are chickens: 14-10 = 4 (only).

1) C Sakura Burning 2) The purpose of divergent thinking and seeking is to put forward as many ideas as possible to solve problems in a limited period of time, so that problems can be solved faster and better, which is a way of thinking that can effectively improve students' thinking ability. In the process of divergent thinking, it is necessary to comprehensively use convergent thinking, reverse thinking, and the participation of thinking factors such as intuition, imagination and inspiration, so as to truly improve students' ability to think about the pure dimension of the spine.