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.
Ryota Matsuura and Patrick Harless
Alerting a class to a connection between two familiar topics will help students become more agile with each of them.
Ryota Matsuura and Sarah Sword
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.
Ryota Matsuura and Yu Yan Xu
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.
Ryota Matsuura, Sarah Sword and Tatyana Finkelstein
Designing a lesson that uses routine exercises, creates space for language use, and provides a storyline will go far toward supporting mathematical structure.
Richard Askey, Ryota Matsuura and Sarah Sword
The inequality of arithmetic and geometric means in three variables is developed through algebra, geometry, and calculus.
Sarah Sword, Ryota Matsuura, Al Cuoco, Jane Kang and Miriam Gates
Two high school classroom situations illustrate how routinely promoting the two practices of experimenting and describing in increasingly precise language can support students' modeling.