The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.

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### Susan Baker Empson, Victoria R. Jacobs, Naomi A. Jessup, Ms. Amy Hewitt, D'Anna Pynes, and Gladys Krause

### Emily R. Fagan, Cheryl Rose Tobey, and Amy R. Brodesky

Start with a strategic process to gather and interpret evidence of students' mathematical understandings and misconceptions; then aim your teaching to address identified needs.

### Kimberly Morrow-Leong

Comparing two fractions gives a context for exploring students' flexibility with and understanding of mathematical ideas.

### Jennifer Pfotenhauer, Rick Kleine, Yasmin Sitabkhan, and Darrell Earnest

Students had been learning about integers and fractions on the number line. For a lesson on mixed numbers, they solved an assessment problem at the beginning of the lesson. After the lesson, the authors interviewed two students individually and asked each girl to solve the same problem again.

### Wendy S. Bray

Incorporating a focus on students' mistakes into your instruction can advance their understanding.

### Sarah K. Bleiler and Denisse R. Thompson

Measuring student understanding of math concepts in this manner offers insight into the robustness of their knowledge, particularly of the Common Core State Standards for Mathematics.