First: You must understand the topic.

What is the unknown quantity? What is the known data? What are the conditions? Is it possible to meet the conditions? Is it a condition to determine the unknown quantity? Still not enough? Or redundant? Or contradiction?

Draw a picture and introduce the appropriate symbols.

Separate different parts of the condition. Can you write it down?

Paulia: How to solve the problem, a new mathematical thinking method.

Second, find out the relationship between known data and unknown quantity.

If you can't find a direct connection, you may have to consider auxiliary topics.

Eventually you will find a solution to the problem.

draw up a plan

Have you seen it before? Or have you ever seen the same topic appear in a slightly different form?

Do you know a related topic? Do you know a theorem that might be useful?

Observe the unknown! And try to put forward a familiar topic with the same or similar unknown.

Here is a topic related to your topic, which has been solved before. Can you use it? Can you make use of its results? Can you use it? Should an auxiliary element be introduced to make its application possible?

Can you repeat the question? Can you describe it in different ways?

Back to definition

If you can't solve the problem, try to find a related topic first. Can you think of a related topic that is easier to start? A more general topic? A more professional topic? Similar topics? Can you work out part of this problem? To what extent can the unknown be determined and how can it be changed? Can you draw anything useful from the known data? Can you think of other suitable known data to determine the unknown quantity? Can we change the unknown quantity or the known data, or both when necessary, so that the new unknown quantity and the new known data are closer? Have you used all the known data? Have all the conditions been used? Have you considered all the key concepts in the topic?

Paulia: How to solve the problem, a new mathematical thinking method.

Third: carry out your plan

Implement your solution and check every step. Can you clearly see that this step is correct? Can you prove that it is correct?

Fourth: Check the answers you have got.

review

Can you check this result? Can you test this argument?

Can you deduce this result in different ways? Can you tell at a glance?

Can you use this result or this method in other topics?