Category Archives: Geometry

Educational Technology, Geometry

The Varied Paths to Constructing a Square

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Using dynamic geometry software, a student can draw what looks like a square by eyeballing the locations of the vertices. However, the quadrilateral will not stay a square when its vertices are dragged. Building a "real" square requires that it stay a square when any of its parts are dragged. This is only possible by baking … Continue Reading ››
Educational Technology, Geometry, Math Software

Pythagoras Plugged In

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If there were an award for 'Mathematical Theorem Most Amenable to a Visual Proof,'  the Pythagorean Theorem would surely win. The title of this post is a nod to the Sketchpad activity module Pythagoras Plugged In by Dan Bennett. Dan's book contains 18 visual, interactive proofs of the Pythagorean Theorem. And there are more:  The Pythagorean … Continue Reading ››
Educational Technology, Elementary Mathematics, Geometry, Math Software

Estimating Angle Measurement

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Angles are a thorny concept to teach because of the fundamentally different ways in which they can be used and understood. In the article What's Your Angle on Angles?, the authors divide the concept of angle into three main groups: angle-as-figure, angle-as-wedge, and angle-as-turn. In the Web Sketchpad game below, we focus on angle-as-turn. Given an angle, students enter an estimate … Continue Reading ››
Educational Technology, Elementary Mathematics, Geometry, Math Software

Exploring Tessellations with Web Sketchpad

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Metamorphosis is a New York-based company that offers professional content coaching to transform the mindset and practice of both teachers and administrators. I recently had the pleasure to collaborate with Metamorphosis staff members Toni Cameron and Kara Levin as well as mathematics coach Ariel Dlugasch from P.S. 276 in a coaching learning community that … Continue Reading ››
Educational Technology, Geometry, Math Software

Putting the Power of a Point Theorem to Work

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The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords AB and CD of a circle intersect at point P, then the product AP · PB is equal to the product CP · PD. You can see an illustration of this theorem in the Web Sketchpad model below. Drag points … Continue Reading ››
Assessment, Educational Technology, Geometric Functions, Geometry, Math Software

Dilation Games: Assessment That’s Fun

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What does dilation feel like? I recently had the opportunity to work with a group of students who were testing activities that treat geometric transformations as functions (what I call geometric functions). I got lots of good ideas for improving the activities not only by watching the students, but also but also from their suggestions and the … Continue Reading ››
Educational Technology, Geometry, Math Software

Tailoring Tools to the Task

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In years past, my colleagues and I at Key Curriculum conducted Sketchpad professional development workshops for teachers. One of our favorite activities challenged participants to  construct a rhombus in as many different ways as possible. This assignment invariably led to great discussions because there are a multitude of ways to build a rhombus, and each method highlights its … Continue Reading ››
Educational Technology, Geometry, Math Software

Fine Tuning Web Sketchpad’s Construction Interface

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When the Web Sketchpad team created the interface for tools, there were lots of design decisions to be made. We made the best choices we could at the time, but after months of daily use, it became clear that at least one aspect of tool functionality needed some rethinking. In the original design of tools (which you can … Continue Reading ››
Educational Technology, Geometry, Math Software

Creating Mosaics Inspired by a Pattern from Sultan Ahmed Mosque

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Mirek Majewski was born in Poland and studied mathematics at the Nicholas Copernicus University in Poland with an M.S. and Ph.D. in non-classical geometries. He is a professor of mathematics and computer science at several universities – PNG University of Technology, Inter-University of Macau (now Saint Joseph University), Zayed University in United Arab Emirates, and New York … Continue Reading ››
Educational Technology, Geometry, Math Software

A Double Dissection from The New York Times

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Did you know that aside from being a source of news, The New York Times is also the place to get your weekly fix of mathematics? Their online Numberplay column features some very clever math puzzles. Last year, in fact, our blog featured a Numberplay puzzle about a flying squirrel-frog from former Key Curriculum … Continue Reading ››