Under the background of the new curriculum, by designing diversified high school math homework, we can cultivate students' good habit of autonomous learning, constantly stimulate students' interest in learning, enlighten students' mathematical thinking, cultivate students' ability to use their hands and brains, develop students' specialty and personality, and continuously improve students' mathematical learning ability.

Keywords: mathematics teaching, diversified design of high school mathematics homework

First, design hierarchical homework to improve students' mathematical ability.

The so-called hierarchical homework refers to the stratification of homework according to different learning time and students' different learning levels, so as to meet the learning needs of students at different levels and make senior high school students better adapt to the new curriculum reform. The research group arranged six different levels of homework in the form of test papers: the first part is pre-class preparation homework, the second part is autonomous learning homework, the third part is foundation consolidation homework, the fourth part is ability improvement homework, the fifth part is extended inquiry homework, and the sixth part is student evaluation. Students must choose one, two and six assignments, and others according to their own abilities. This kind of homework aims to have a clear understanding of students' high school mathematics knowledge, let different students learn different mathematics knowledge, cultivate students' good mathematics learning habits and autonomous learning ability through preview and autonomous learning homework, let students see their own shortcomings through process evaluation and diagnostic evaluation, and constantly inspire students' self-confidence through the evaluation of other students and teachers to overcome their fear of learning mathematics. Through the questionnaire survey, about 80% students think that "thematic" homework is of great help to them, which not only cultivates their thinking ability, but also improves their mathematics learning ability.

Second, design activity-based homework to stimulate students' interest in mathematics