Thinking Methods for Solving Practical Problems 5

The arithmetic methods used to solve practical problems are analytical and synthetic, focusing on how to guide students to learn and apply. Illustrate with examples of teaching practice.

According to your topic, the main object: application questions.

Central Thesis: Approach to Thinking.

Around this answer, touch the analogy, draw inferences, and activate thinking.

First of all, the question should be examined.

Then set the unknowns according to the question.

Finally, the unknown number is solved.

Examples of the correct format for answering first-grade questions are as follows:

Solution: It is known that an apple weighs 1kg.

Then the weight of 5 apples is 5*1=5 (kg).

A: 5 apples weigh five kilograms.

Multiplication: Find how many are the numbers.

Find out what are multiples of a number.

Find the area and volume of the object.

Find out what fractions or hundredths of a number are.

Division: Divide a number into several parts and find one of them.

Find how many other numbers there are in one number.

Knowing what fractions or hundredths of a number are, find this number.

Find how many times one number is another.

Vocabulary questions

It is to use Li Zao's language or writing to describe relevant facts, reflect some kind of mathematical relationship (such as: quantity relationship, position relationship, etc.), and solve an unknown number of problems. Each word problem includes a known condition and a desired problem.

In the past, Chinese application problems usually required the description to meet three requirements: no contradiction, that is, there should be no contradiction between conditions, conditions and problems; Completeness, i.e., the conditions must be sufficient to ensure that the value of the unknown quantity is obtained from the condition; Independent regression, i.e. several known conditions cannot be pushed to each other.

Primary school math problems are usually divided into two categories: simple problems that are solved by only adding, subtracting, multiplying, and dividing one step; It is called a compound problem that needs to be solved with two or more steps.

The first thing to do is to solve the problem, and if you don't remember the formula, no one can help you.

Memorize the formula, and then put the known conditions in, and set the unknown conditions to x, in fact, remember the formula, and you will find that the application problem is quite simple, what kind of formula do you want?

1.Methods and steps to solve problems.

1) Examination of the question: It is necessary to clarify what is known, what is not known and its interrelationship, and use x to represent a reasonable unknown in the question.

2) Find an equal relationship that can represent the full meaning of the problem according to the meaning of the question. (Critical step).

3) According to the equality relation, the equation should be listed correctly, that is, the equation listed should satisfy that the quantities on both sides of the equal sign should be equal; The units of the algebraic equation on both sides of the equation should be the same.

4) Solve the equation: find the value of the unknown.

5) Write out the answer clearly and completely after the test. The test should be that the solution obtained by the test will not only make the equation true, but also make the application problem meaningful.

2.The types of application problems and the basic quantity relationships used for each type:

1) The basic relationship of equal-area application problems: volume before deformation (volume) Volume (volume) after deformation

2) The characteristics of the deployment application problems are: the quantity relationship before the deployment, and a new quantity relationship after the deployment.

3) The basic relationship of interest problems: principal, interest rate, interest, principal, interest, principal and interest.

4) Commodity profit margin: commodity profit margin, commodity profit, commodity selling price, commodity purchase price.

5) The amount of work in engineering problems is not a specific quantity, so the total amount of work is often regarded as a whole1, where the work efficiency and the total amount of work are worked.

6) The basic relationship between the itinerary application questions: distance, speed, and time.

Encounter Problem: A and B are walking in opposite directions, then: the distance A travels The distance B travels The total distance.

Chase the problem: A and B are in the same direction and different places, then: the distance traveled by the pursuer The distance traveled by the former The distance between the two places.

Circular Runway Question:

A and B set off in the same place and direction at the same time on the circular track: the faster one had to run one more lap to catch up with the slow one.

A and B start in opposite directions at the same time and in the same place on the circular runway: the total distance traveled when they meet is the length of one lap of the circular runway.

Flight problems, basic equivalence relations:

Downwind speed No wind speed Wind speed.

Headwind speed No wind speed Wind speed.

Navigation problems, basically equivalence relations:

Downstream velocity hydrostatic velocity Water velocity.

Reverse water velocity Hydrostatic velocity Water velocity.

7) Proportional application questions: If the ratio of A and B is 2:3, you can set A to be 2x and B to be 3x

8) The basic relationship of numerical application problems: if a three-digit number, a hundred digit is a, a ten-digit number is b, and a single digit is c, then these three-digit numbers are:

If you look at 1 share of the apples that A gets, B is 2 times as much as A, C is 2 times as much as B, and C is 4 times as much as A.

Think of 1 basket of apples as "1".

A took 1 7 of the basket of apples

B took 2 7 of the basket of apples

C gets 4 7 of this basket of apples

Consider "the weight of the apples that B gets to be shared" as 1 part, and the weight of the apples that A gets is 1 2 parts, and the weight of the apples that C gets is 2 parts.

There are 1+1 2+2 = servings.

A gets 1 2

B gets 1 and C gets 2

Method 1: Columnar operation algorithm.

Read the question first, find the known quantity, find the unknown quantity, then perform the operation of the unknown quantity in turn, and finally find the question asked.

Method 2: Solve the column equation.

Read the question first, find out the known quantity, and according to the meaning of the question, find out the balance relationship, set direct unknowns or indirect unknowns, and follow the sequence of the question (climb along the pole), and finally solve.

Note: If you want to use the column equation solving method, you must pay attention to what the problem is when answering the question, and do not use indirect unknowns as the answer!

I think it is related to the attainment of the language, there is a certain logical relationship, first understand the logical relationship of the question, and list the expressions according to the requested items!

1.If you don't understand, just ask.

2.Learn to understand the meaning of the question.

3.It is necessary to clarify the relationship between quantities.

4.If the equation solution is overused, then the forward thinking is used; If the solution is solved by arithmetic, then the reasoning is carried out by reverse thinking.

5.You need to memorize the formula and learn to use it flexibly.

6.Practice in areas where you are deficient.

7.Learn to transform, to transform one type of problem into another.

8.Have an abstract mindset.

Mastering the steps is the first step in solving practical problems, and in order to master the skills and skills of solving practical problems, you also need to master the basic methods of solving practical problems. Generally, it can be divided into comprehensive method, analysis method, ** method, demonstration method, elimination method, assumption method, reverse deduction method, enumeration method, etc. The main purpose of introducing these methods here is to help students master how to think and how to open the door of their wisdom when they encounter practical problems.

None of these methods are isolated, and in actual problem solving, two or three methods are often used at the same time, and there are many problems that can be analyzed in one way or another. The problem is that after mastering the various methods, you can flexibly use them according to the quantitative relationship in the problem, and you must not memorize and mechanically apply the problem-solving method.