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## Exploring Sequences Related to Medial Triangles

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## Developing Property-Based Geometric Reasoning

Recognizing the complex nature of students’ geometric reasoning, we present guidelines and suggestions for implementing a Guess My Shape minilesson that focuses students’ attention on properties and attributes of geometric shapes.

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## Puddle Play!

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## Children’s Games and Games for Children

This article examines the mathematical activity of five-year-old Liam to explore the difference between the mathematics games designed for children and the children's games that emerge through playful activity. We propose that this distinction is a salient one for teachers observing mathematical play for evidence of mathematical sense making.

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## Triangles from Three Points

Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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## Mathematical Explorations: Find the Distance: No Formula Necessary

This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics.

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## The Circle Approach to Trigonometry

A connected introduction of angle measure and the sine function entails quantitative 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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## If Only Clairaut Had Dynamic Geometry Tools

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

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## Using KenKen to Build Reasoning Skills

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.