Students always find it difficult to list equations when solving application problems. In fact, the key to solving practical problems by using the equations is to find out the equivalence relation, and then the equations can be listed. So how do you find the equivalence relation?

(1) Master mathematical terms and find equivalence relations.

Quantitative relationship in application problems: general sum-difference relationship or multiple relationship, which is often expressed by terms such as "one * * * has" and "greater than". The key word of this problem is "less than" ..., from which we can find the equivalent relationship: 2 times the number of trees planted in the fourth grade minus 4 equals the number of trees planted in the fifth grade, thus listing equation 2-4 = 50.

(2) Find the equivalence relation according to the common quantitative relation.

Common quantitative relationship: working efficiency × working time = total workload; Unit price × quantity = total price; Speed × time = distance ... When solving problems, we can find equivalence relations according to these quantitative relations. For example, "The retail price of a certain style of clothing is 36 yuan 1 set, and the current price is 2 16 yuan. How many sets of clothes can I buy? " According to the quantitative relationship of "unit price × quantity = total price", equation 36 = 2 16 can be listed.

(3) According to the commonly used calculation formula, find out the equivalence relation.

Commonly used formulas are: rectangular area = length × width; The equivalence relation can be found according to the calculation formula. For example, "the area of a rectangle is 19 square meter, its length is 4 meters, so how many meters is its width?" According to the formula "length× width = area", Equation 4 = 19 can be listed.

(4) Find the equivalence relation according to the literal relation.

For example: "There are 36 students in Class One and 37 students in Class Two in Grade Five; Class one, class two, class three 108, so how many people are there in class three? " The equivalent relationship expressed in words is:

Class One+Class Two+Class Three = Total

Category 1+ Category 2 = Total-Category 3

Category 1+ Category 3 = Total-Category 2

Category 2+ Category 3 = Total-Category 1

According to these literal equivalence relations, the following equations can be listed, for example:

36+37+ = 108

36+37= 108-

36+ = 108-37

37+ = 108-36

(5) Find the equivalence relation according to the graph.

For example, "a farm has 400 hectares of wheat, and 70 hectares of wheat are harvested every day for the first three days, and the rest are harvested in two days." How many hectares of wheat will be harvested on average every day? " Draw a line diagram according to the meaning of the question first.

It can be seen intuitively from the line chart that the total wheat harvest = the wheat harvest in the first three days+the wheat harvest in the last two days. According to this relationship, the equation 70× 3+2 = 400 can be listed.