Engaging learning environments are well-thought out and organized spaces that intentionally promote inclusive mathematical learning for all children. Explore our resources for Inclusion!

This section of our site has printable pdfs of some of the most common materials used in our activities, such as Numeral Cards, Dot Cards, Tangram Puzzles, and more!!


We are creating new digital activities to support young children's math learning. Therefore, we will be phasing out the games currently on LearningTrajectories.organd rolling out a new platform. Help us by trying out Bajillions Early Math! 

Suggested Citation

Clements, D. H., & Sarama, J. (2017/2019). Learning and teaching with learning trajectories [LT]2.
Retrieved from Marsico Institute, Morgridge College of Education, University of Denver.

Special Thanks To

Institute of Education Sciences
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.