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• Author or Editor: Ryota Matsuura
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## Delving Deeper: Approximating π Using Similar Triangles

This article presents a method for approximating π using similar triangles that was inspired by the author's work with middle school teachers. The method relies on a repeated application of a geometric construction that allows us to inscribe regular polygons inside a unit circle with arbitrarily large number of sides.

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## From Arithmetic Sequences to Linear Equations

Alerting a class to a connection between two familiar topics will help students become more agile with each of them.

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## Illuminating Coordinate Geometry with Algebraic Symmetry

An approach using symmetric polynomials to prove that the medians of a triangle intersect at a single point reveals underlying structure and generalization to higher dimensions.

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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 Search for Hidden Structure

Designing a lesson that uses routine exercises, creates space for language use, and provides a storyline will go far toward supporting mathematical structure.

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## The Inequality of Arithmetic and Geometric Means from Multiple Perspectives

The inequality of arithmetic and geometric means in three variables is developed through algebra, geometry, and calculus.

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## Leaning on Mathematical Habits of Mind

Two high school classroom situations illustrate how routinely promoting the two practices of experimenting and describing in increasingly precise language can support students' modeling.