In this article, we report a study on how students learn elementary number theory concepts via pre-constructed activities of curve stitching on a unit circle. By using a dynamic learning approach, students were able to observe and guess the patterns of curve-stitching figures and explore how they were related to the total number of points on the circle and the interval between any pair of connected points. The subjects were pre-service and in-service primary mathematics teachers majored in mathematics or information technology in a BEd programme offered by the Hong Kong Institute of Education. We also discuss some teaching and learning issues related to this topic. Copyright © 2013 The Author. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications.