This research aimed to generate a learning trajectory in an introduction to early mathematics, precisely to measure learning using educational games and Realistic Mathematics Education (RME) and to describe young children's curiosity in learning early mathematics. Children need to have an understanding to take a measurement and use a learning trajectory to learn how to differentiate measurable and countable quantities and to tell the longer and the greater in number. The design of this research involves three phases, namely, preliminary design, experimentation, and retrospective analysis. A Hypothetical Learning Trajectory (HLT) using educational games was developed by collecting data from documentation, observations, and interviews. The results obtained from the implementation in the classroom showed that the educational games were able to help young children get to know early mathematics, particularly on measurements of lengths and volumes. There is an association with several factors in the selection of realistic problems. Communications during the game could stimulate an introduction to measurement. The use of objects in students' vicinity also contributed to their experiments relating to measurement. The results of this research inform policymaking for teachers in designing learning in the classroom in introducing early mathematics based on educational games and Realistic Mathematics Education (RME).