Core competency oriented problem-solving teaching ----Taking "Solving Application Problems with a System of Equations" as an Example

The teaching of Mathematical problem-solving is one of the three key teaching points in junior high school mathematics. Solving applied problems through equations (systems) is an important component of the first module of teaching content, "Numbers and Algebra", and holds a very important position. It is a key focus in junior high school mathematics problem-solving teaching. At present, under the premise of the implementation of the new curriculum reform in the field of mathematics in China, based on the recent publication of compulsory education curriculum standards,the teachers of mathematics should focus on cultivating excellent mathematical core literacy among junior high school students, and ensuring that they can independently cope with and solve problems in  the math teaching of junior high school.   Based on the above background, the author focuses on the newly published mathematics curriculum standards in 2022, and studies the teaching design of "solving application problems for systems of equations". In this paper, we explore the mathematical core literacy elements contained in the teaching of solving applied problems in equations, study the improvement path of mathematical problem-solving teaching, share the teaching design practice and thinking based on core literacy oriented problem-solving teaching, and the important role that this teaching design can play in cultivating students' core literacy .