Welcome to the Mathematics Learning Trajectories (MLT) Series

The Equipartitioning Learning Trajectory:
a K-5 Foundation for Rational Number Reasoning

A Massive Open Online Course for Educators (MOOC-Ed)

The Mathematics Learning Trajectories MOOC-Ed series presents Learning Trajectories (LT) as a framework for interpreting and implementing the Common Core State Standards for Mathematics (CCSS-M). Our first course introduces the Equipartitioning LT. Grounded in fair sharing activities that create equal-sized groups (from collections) or parts (from single wholes), Equipartitioning provides a robust foundation for students’ conceptual understanding of division, multiplication, fraction, and ratio. We recommend this course for elementary and middle grades educators seeking a deeper understanding of students’ learning of fundamental mathematics for their own instructional practice.

View Full Series Description Video

Course Information
- Course Series Description
- MLT Team
- Major Course Goals
- Course Outline
- Course Activity Organizer
- The MOOC-Ed Learning Experience
- Acknowledgments
- FAQs

The MLT MOOC-Ed series is brought to you by the GISMO Research Group at the Friday Institute for Educational Innovation at NC State University, led by Dr. Jere Confrey and Dr. Alan Maloney. The MLT team will provide instructions, suggest resources, contribute to discussions, and answer questions from course participants in each lesson in the course.


  • Unit 1 - Recommended Background on Learning Trajectories and the Common Core Mathematics Standards

  • Unit 2 - That's Not Fair! (Or Is It?): Equipartitioning as a Foundation for Rational Number Reasoning

  • Unit 3 - Deal or No Deal? (part 1): Pirate Treasure, Splitting and Reassembly, Naming and Justifying

  • Unit 4 - Deal or No Deal? (part 2): Reallocation and Compensation in Collections through Clinical Interviews

  • Unit 5 - Let Them Share Cake! (part 1): Introduction to Equipartitioning Single Wholes

  • Unit 6 - Let Them Share Cake! (part 2): Strategies and Emergent Properties for Equipartitioning Single Wholes

  • Unit 7 - Pizza(s) for Everyone--Equipartitioning Multiple Wholes for Multiple People

  • Unit 8 - Wrapping it Up: Further Equipartitioning of Multiple Wholes; Learning Trajectory-Based Instruction

Mathematics Learning Trajectories MOOC-Ed course copyright 2013 - Jere Confrey and Alan Maloney