Understand the number.
Keep the understanding.
Two connected projects: Fraction Fix develops instruction and support. Fraction Audit gathers evidence about understanding and retention. Evidence helps us decide what to teach next.
Fraction Fix
A proposed pathway from equal sharing and the unit to rational-number operations and algebraic transfer. Use selected lessons for support or extension, with a teacher.
Explore the lessonsFraction Audit
A low-stakes check of what is secure, developing, or fragile—and what remains accessible over time. The audit begins with evidence, without assuming the current curriculum is deficient.
Explore the auditFraction Fix
Start with a problem, name the whole and the unit, estimate, and connect a model to an explanation and an equation. Teacher modeling and focused practice help students build efficient procedures from meaning.
Available pilot lessons
All 54 lessons are available in eleven student workbooks. Teacher guides are available for Lessons 11–54, with earlier planning materials in Drive.
Lessons 1–5 Student workbook Available
Lessons 6–10 Student workbook Available
Lessons 11–15 Student workbook + teacher guide Available
Lessons 16–20 Student workbook + teacher guide Available
Lessons 21–25 Student workbook + teacher guide Available
Lessons 26–30 Student workbook + teacher guide Available
Lessons 31–35 Student workbook + teacher guide Available
Lessons 36–40 Student workbook + teacher guide Available
Lessons 41–45 Student workbook + teacher guide Available
Lessons 46–50 Student workbook + teacher guide Available
Lessons 51–54 Student workbook + teacher guide Available
PK–5 Fraction Learning Progression
An evidence-informed framework for curriculum conversation. This progression brings together ideas about how fraction understanding develops across PK–5, recognizing that they may already be addressed through existing instruction. Use it to compare approaches, identify strengths, and consider how learning connects across grades. Grade placements are suggested developmental benchmarks for discussion.
The broader pathway
These strands describe the planned progression, not a completed course.
| Strand | Central idea |
|---|---|
| The whole and the unit | Identify the referent whole and equal shares. |
| Unit fractions | Build a/b from copies of 1/b. |
| Fractions are numbers | Locate proper and improper fractions. |
| Magnitude and benchmarks | Estimate and compare. |
| Equivalence | Connect many names for one value. |
| Composition and decomposition | Connect mixed numbers and improper fractions. |
| Addition and subtraction | Combine quantities with matching units. |
| Multiplication and scaling | Interpret a fraction of a quantity. |
| Division | Connect equal sharing and measurement division. |
| Rational-number languages | Move among fractions, decimals, and percents. |
| Ratio, rate, and proportion | Scale quantities multiplicatively. |
| Signed rational numbers | Connect magnitude and direction. |
| Algebraic transfer | Use fractions in equations and slope. |
Teacher guides and planning materials in Drive · Existing Drive access applies.
Fraction Audit
The current pilot materials cover Grades 3, 5, 6, and 8. They examine meaning, magnitude, equivalence, operations, and connections to decimals, ratios, and algebra.
- Gather initial evidence. Use the grade-specific thinking check with ordinary accommodations and consistent administration conditions.
- Look across the work. Compare accurate computation, explanations, representations, and unfamiliar problems. One incorrect answer is a question to investigate.
- Choose a response. Confirm strengths, clarify language or representations, and select targeted instruction where patterns support it.
- Check again later. The proposed parallel check after 6–8 weeks helps distinguish immediate performance from retention. Form B is not yet listed in the current Drive folder.
A profile, not one total
Number sense and fluency
Magnitude, benchmarks, equivalence, reasonableness, and accurate access to procedures.
Reasoning and transfer
Recognize relationships, analyze an error, and use an idea in an unfamiliar problem.
Comprehension
Interpret mathematical language and contexts; explain connections among quantities and representations.
These are fraction-specific observations, not measures of general intelligence. A claim that understanding was not retained requires earlier evidence and a later comparable check.
For teachers and administrators
Current thinking checks, supplemental measures, and the scoring guide remain in Drive. Use these materials under teacher direction. Individual student results stay private; this site contains no student records or score-entry system.
Open the Fraction Audit materials in DriveExisting Drive access applies. The pilot is a developing measurement approach; it is not an externally normed test.
Connect the evidence to the next lesson
When several responses show an unstable whole or unit, begin with the corresponding Fraction Fix lessons. When those ideas are secure, move ahead to magnitude, equivalence, operations, and transfer. Confirm the pattern with more than one task before choosing support.