When is it better to use equations to solve problems?

Reflection on the Teaching of Encounter Problems.

The content of this lesson is elementary mathematics.

The teaching content of the fifth grade encounter problem in the first volume, through this lesson, students should learn to analyze simple practical problems, find out the equivalent relationship in the problem, learn to use equations to solve simple practical problems, the textbook presents speed, time, distance and other information through the situation map, closely follow where to meet, the time used when encountering, and how far away the encounter point is from the site park to carry out teaching. After the class, I felt that I did a good job in the following aspects:

1. Review the old knowledge and set up the foreshadowing.

Before the start of the class, I guide the students to review the relationship between speed, time, and distance, arouse the students' old knowledge to find the student's recent development period, so as to prepare for the next link, and find out the quantitative relationship through the situation map.

2. The creation of situations is close to life, starting from the reality of life, and guiding students to transform life problems into mathematical problems.

In order to motivate students to learn mathematics, I first use the textbook creatively, transfer the life situation to the classroom, and use the diagram on the textbook to create a problem situation to attract the children's attention. By taking students on stage to meet with their own demonstrations, students quickly understand the "encounter", and can analyze and try to solve problems independently, in line with the idea of "starting from life - abstracting into mathematical problems--- trying solutions - applying the generated knowledge to solve more problems". It is conducive to cultivating students' ability to find mathematical problems from life and try to analyze and solve practical problems.

3. Highlight the key points and break through the difficulties.

In the teaching of this link, I use the more commonly used method in mathematics - the graphic schematic method to present abstract mathematical problems on the ** paragraph diagram, and after the students have an understanding of the word encounter, let the students say what the encounter here refers to? Students will soon be able to find the equivalence relation on the graph, i.e., the distance traveled by the van and the distance traveled in the mini-tutorial is 50 km.

Based on the equiquantity relationship, the student quickly lists the equations. And answered. The second part is well completed.

4. The diversification of algorithms is reflected in the teaching, and the students continue to ask the students after solving the equations, do you have any other methods? Students were quick to say that they could use arithmetic methods, thus demonstrating the diversity of algorithms.

5. In the process of teaching, I also pay attention to the implementation of differentiated teaching. The level of students is different, some solve problems faster, some are slower, and even some have difficulties with what they have learned, so I require students who have completed the exercises early to implement a gang of mutual inspection and counseling with their classmates next to them, so that students can learn in a good atmosphere of mutual assistance and cooperation, and at the same time, when implementing evaluation and feedback, teachers pay attention to capturing and discovering the sparks of students' thinking, encourage and affirm in a timely manner, greatly mobilize students' enthusiasm for learning, and form an equal and harmonious learning atmosphere.

Answering a question with an equation is to set an x, right?

Then find an equation about x and solve x.

In general, when the relationship between x is complex, for example, the difference between 3 times x and half of the whole process is equal to 5 times the difference between x and all of them.

When this is a complex relationship that is not easy to list directly, it is more convenient to use x to represent the unknown quantity.

i.e. = 5x -1

2x=x=In short, when the equation relationship about x is complicated, it is easier to solve it with equations. Arithmetic is usually deduced from the problem to the condition, which is a kind of reverse thinking, and it is difficult to solve the problem. The emergence of equations is a kind of transformation of mathematical thinking, which is derived from conditions to problems, and it is easier to think in the direction of thinking, which improves the accuracy of doing problems, and the solution of equations that only need to be followed by thinking is more in line with students' learning ideas.

Both methods have their advantages and disadvantages. Arithmetic is more difficult to solve some more complex problems and is not easy to analyze, but because of this, it also exercises people's thinking ability and logical analysis ability. In the Olympiad, arithmetic is often used to solve problems.

The equation thinking process is relatively simple, the problem solving is fast, and the accuracy is high, which is suitable for solving problems in life.

Pear x, apple y: 6x ten 6y =

3x+9y=

x ten y=x= y=

Coarse beam rock difference slag silver price rock royal (6x-3 )+9y-6y)=x=

y=x=

Set the original price of this dress is x, the shopping mall is 80% off, that is: 80% x, "discount 15 yuan", after the discount** is less than the original price contains 15 yuan, that is: the original price - after the discount **=15, this is the equivalent relationship of this question:

Therefore: the solution to the old stop is as follows:

Solution: The original price of this dress is X yuan.

x-80%x=15

x=15 x=75A: Omitted.

This is a change of the balance of the question to read the travel calculation:

Let the original price of the clothes be x yuan, and list the equation according to the question

x x 75 So, the original price of the clothes is 75 yuan, and the discount is 60 yuan.

The steps to solve the problem are:

1) Review the topic. 2) Set the unknowns, and the column is only on the land route.

3) Solve this equation.

3) Test the rationality of the root potato mountain chain.

4) Conclusion. Solution: Set this piece of Sun clothes x yuan, according to the title.

x（1-80%）=15

x=75 so this dress is 75 yuan.

The original price of the clothes is x, then the 20% discount is 20%, and the Fangxin Li program is, x 75, then the actual support is 75-15 60 yuan.

Remove parentheses, move items, merge similar items, find unknowns.

The original price of this simple search clothes is x yuan. Burn the cha.

x - = 15

x = 75 yuan tomato.

The current price is $75 - 15 = $60.

Untie the clothes key and serve the original price x yuan manuscript Huizhi.

The available equation is as follows.

0 2x=15

x=15 x=75 clothes, the original price is 75 yuan.

Wangbilun, thank you.

Set the clothes to be x yuan, and the equation is (stove waiter (attack Zheng x + 15) 15, x 60 yuan to pat the argument.

So the clothes are 60 yuan.

The discount is 15 yuan, and the preferential money divided by the preferential Pei Song Lu discount Peiqing is the original price, so 15 divided by (75 yuan for cherry blossoms.

You can use the equation to solve, let the original price is x, and the 20% discount is 80% of the original price, and the shed is cultivated to have, and the solution is x 15. That is, the original price is only 75 yuan for the chain book.

The original price of the clothes is x, then the 20% discount is a discount of 20% for renting dates, and the equation is, x 75, and the actual payment of the disadvantage is 75-15 60 yuan.

Solution: The original price of this dress is X yuan.

x-80%x=15

20%x=15

x = 75 answer socks: pure lead this dress turned out to be 75 yuan clear pants.

Solution: Set this dress x yuan Xunbi, then.

x=15 x=75 Answer: This piece of clothing is 75 yuan.

15 (1-80%)=15 yuanweiqi).

Set the price of this clothes to the original Bird Mountain trace is a dollar.

x=75 (yuan).

Assuming that this dress is X yuan, 20% off is 15 yuan for Yukai.

x=75 (yuan).

This garment is 75 yuan.

Solution: The original price of this dress is X yuan.

x-80%x=15

x=15÷20%

x=75

In the original problem, the number of products made by the two people is unknown, that is, there are two unknowns, so the binary equation is used.

It will be convenient to solve the law.

However, the primary school will also encounter this type of problem in the first year of junior high school, because during this period, I have not learned the binary one-time equation, so I can only use the one-dimensional one-time solution to solve it, if the one-dimensional one-time equation is used.

To solve, the way to set the unknown is to "let one count one", because: the problem tells the two people that the total number of processed products is 360, so we let one of them be x, then, the other is (360-x), and then list the equation according to the meaning of the question, and solve it.

When setting, only one can be set, because the other is calculated according to assumptions, so it is necessary to pay attention to the expression format, which is usually "set." Rule.

It should also be noted that the calculation based on the assumptions must be accompanied by parentheses, so as to avoid errors in the calculation, such as: let one of them be x, then, the other is（360-x）Piece.

Solution: Let Xiaoli do x, then Xiaojuan is (360-x), and the equation can be obtained according to the meaning of the problem:

x-（360-x）=40

x-360+x=40

2x=40+360

2x=400

x=200 is: Hand 360-x=360-200=160 (pcs).

A: Xiaoli made 200 pieces, and Xiaojuan made 160 pieces.

If Xiaojuan produces x pieces, then the number of small grains producing blind leakage circles is x+40 pieces, then x plus brackets search and training x+40 equals the total number of 360. Just solve this collapse equation.

That's the kind of topic it should be. Set up a person, such as Xiao Sun Qili. It's done, x pieces, then Xiaojuan is 360 -x pieces. Then because of the title, Xiaoli made 40 more pieces than Xiaojuan. The column equation is.

x minus the parentheses of 360 -x. Equal to 40.

That's 2x- 360=40.

2x= is equal to. Xiaoli produced 200 pieces, and Xiaojuan produced 160 pieces of Lao Xun.

It can be set that Xiaoli made x pieces, and then Xiao Juan did (x-40) pieces after Min searched.

Then we can list the equation as x+(x-40)=360, from which we can calculate that x is equal to 200

So Xiao Jian Kuli made 200 pieces, and Xiao Juan made 200-40 = 160 pieces.

Solution: Set Xiaoli to make x pieces of finches to accompany Lu, according to the question, it is intended to be chaotic.

x+(x-40)=360

2x-40=360

2x=400

x=200200-40=160 (pieces).

A: Xiaoli and Xiaojuan made 200 and 160 pieces respectively.

Set Xiao Rotten Yeli to make x pieces, and Xiao Juan to make Y pieces. Hunger shouts.

x+y=360

1+2, 2x=400

x=200y=160

So Xiaoli made 200 pieces, and Xiaojuan made 160 pieces.

Set Xiaojuan to make x ruler pants.

x+x+40=360

2x=320

x=160x+40=160+40=200

Xiaoling brother Jian Li made 200, and Xiaochen Jinjuan made 160.

x÷25＋x÷5＝x－19

Solution: Go to the denominator, multiply both sides of the equation by 25, and rent Hui late.

x+5x=25x-19 25, the transfer item is combined with the same kind of term, 19 25=19x, Bichan.

Solution x=25