The Story of Fractions
One mathematical story. Seven chapters. A journey from equal sharing to algebraic relationships.
Fractions are not isolated rules assigned to different grades. They are a connected set of ideas about wholes, units, equivalence, operations, and relationships. Follow these ideas as they develop across a child's mathematical education.
Begin the journey → Lead a workshopThe journey map
Choose a chapter
The World of Wholes
What makes a fair share?
Begin chapter →Chapter 2 · Grades 2–3The Many Faces of One Number
Can different fractions name the same point?
Begin chapter →Chapter 3 · Grade 4The Problem of Different Pieces
How do equal units help us combine and multiply?
Begin chapter →Chapter 4 · Grade 5When Parts Act on Parts
What does it mean to take part of a part?
Begin chapter →Chapter 5 · Grade 6The Language of Relationships
How do two quantities compare?
Begin chapter →Chapter 6 · Grade 7The Power of Proportion
Can a relationship predict what comes next?
Begin chapter →Chapter 7 · Grade 8–Algebra IFrom Numbers to Functions
How can we describe change itself?
Begin chapter →Meet the recurring ideas
The Whole
Every fraction needs a reference quantity.
Equal Parts
Fractions require equal-sized units relative to a whole.
The Unit
A unit fraction can be iterated, measured, and located.
Equivalence
Different names can describe the same quantity.
The Relationship
Multiplicative comparison develops into ratio, rate, slope, and function.
Two ways to participate
Independent reading
Read one chapter at a time. Work the investigation on paper, check the mathematical insight, and use the reflection to connect the story to your own grade.
Facilitated PD
Use the 90-minute introduction and two follow-up workshops. The facilitator guide includes pacing, discussion questions, and a collaborative lesson-design task.
Open facilitator guide →Scope note: This is a conceptual learning journey, not a replacement for grade-specific standards, curriculum, or systematic procedural practice. The chapter labels indicate typical emphasis and cross-grade bridges.
Follow the reasoning across grades
Drawing on the Fraction Fix framework, each chapter now traces learning breakpoints through completed solutions, contrasting methods, incorrect-work analysis, partially completed reasoning, and independent transfer. “A Glimpse Ahead” connects today’s idea to its later use. The three-session facilitator guide helps teams study these examples, fade support, and check retention.
Classroom practice collection
Updated October 2026: connected models, chapter-specific teacher decision cues, deliberate practice sequences, and printable delayed checks accompany the worked examples and optional challenges.
Each chapter ends with grade-level student practice and a separate teacher key, formatted for printing with generous workspace and Tower School footers. Grades 6–Algebra I also include an optional “Think Like a Mathematician” extension with nonroutine challenges and worked solutions.
Download worksheets, keys, and delayed checks (ZIP)