The links on this site are not working. For full access to the new Learning Mathematics through Representations (LMR) website, including introduction to LMR, materials/curriculum (downloadable), please enter the following link in your browser:


Geoffrey Saxe
Professor of the Graduate School
Graduate School of Education
University of California, Berkeley


Kentucky Center for Mathematics is also hosting downloads of the LMR lessons:  Visit the following link to learn more and to take advantage of the excellent and FREE resource!



The links to the lessons indicated below are currently broken. We expect them to be fixed sometime during mid-December, 2018. Please use the links above. Thank you! The LMR Team

Introduction: The introduction to the curriculum provides essential background and orientation to the lessons.

Positive Integers: In this unit students will use Cuisenaire rods to construct number lines with positive integers.  

Negative Integers: In this unit students will use Cuisenaire rods to explore negative numbers. 

Fractions: In this unit students will use the number line in conjunction with Cuisenaire rods to understand and place fractions on the number line.

Download Curriculum: This link provides various options for downloading the LMR teacher guide and associated resources (transparencies, worksheets, and homework masters).

Manipulatives: This page provides options for purchasing Cuisenaire rods for use in LMR lessons.

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