Learning Mathematics through Representations (LMR) is a research-based curriculum unit for the teaching and learning of integers and fractions in the elementary grades, using the number line as the principal representational context. The curriculum builds on two core ideas: mathematical representations are fundamental to mathematical communication and learning, and curriculum units should be designed as well-orchestrated lesson sequences that support insight and understanding of representational forms.

The members of the LMR staff bring expertise in developmental and educational research, curriculum development, pre-service education and professional development, and elementary classroom teaching. The LMR team is led by Geoffrey B. Saxe and includes additional faculty and graduate students in the Graduate School of Education, University of California, Berkeley.

Use the menus above to explore the following links:

  • Research & Dev: Provides background information and the design principles, which guided the development of the LMR curriculum.
  • Curriculum: Offers various ways of exploring and downloading the LMR curriculum.  To browse information about specific units or specific lessons please use the submenu options.
  • Publications: Includes lists of recent publications and presentations related to the LMR curriculum.
  • Staff: Includes a list of the researchers, developers, and designers who contributed to the LMR curriculum.


Who can use the LMR curriculum materials?  The LMR curriculum is free for non-commercial use.  Please send any inquiries about commercial use or derived works to lmr@berkeley.edu.

For questions about LMR or for further information, contact lmr@berkeley.edu.