Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.

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### Agida G. Manizade and Marguerite M. Mason

When calculating the area of a trapezoid, students use a range of problem-solving strategies and measurement concepts.

### Bobson Wong and Larisa Bukalov

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

### David A. Yopp

Asked to “fix” a false conjecture, students combine their reasoning and observations about absolute value inequalities, signed numbers, and distance to write true mathematical statements.

### Colin Foster

Exploring even something as simple as a straight-line graph leads to various mathematical possibilities that students can uncover through their own questions.

### Carol J. Bell

Reasoning and Proof is one of the process standards set forth in NCTM's *principles and standards for school mathematics* (2000).