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## Puddle Play!

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## Seeing Algebraic Structure: The Rubik's Cube

Few high school students associate mathematics with playfulness. In this paper, we offer a series of lessons focused on the underlying algebraic structures of the Rubik's Cube. The Rubik's Cube offers students an interesting space to enjoy the playful side of mathematics, while appreciating mathematics otherwise lost in routine experiences.

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## Algebra Homework: A Sandwich!

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

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## Developing the Area of a Trapezoid

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

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## Improving Student Reasoning in Geometry

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

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## Counterexamples as Starting Points for Reasoning and Sense Making

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.

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## Student-Generated Questions in Mathematics Teaching

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

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## Proofs without Words: A Visual Application of Reasoning and Proof

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