Mathematics is a subject based on numbers and quantities. The quantity sense will affect students’ understanding of mathematics. The new curriculum criteria in 2022 have increased the discussion and requirements on the sense of quantity. The author analyses the significance of the sense of quantity, and investigates the situation of primary school students’ sense of quantity through questionnaires and interviews. The results show that the students’ overall mastery of the quantity sense is poor, especially in the estimation of volume unit. In view of the above problems, the article puts forward the strategies of cultivating the sense of quantity of primary school students under the background of the new curriculum standards, mainly including integrating quantity sense elements, enriching quantity sense accumulation and developing quantity sense reasoning to provide reference for relevant researchers.