Tag Archives: Dynamic Geometry

Putting the Power of a Point Theorem to Work

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 ››

Tailoring Tools to the Task

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 ››

The Art of Parametric Equations

Can mathematical curves be beautiful? Most certainly! Precalculus students glimpse the connection between mathematics and art when they graph roses, cardioids, limaçons, and lemniscates. But these curves give just a taste of the beauty that can be achieved when graphing equations. In a recent article from the online science magazine Quanta, Pradeep Mutalik reviews a gorgeous new math book, Creating … Continue Reading ››

Fine Tuning Web Sketchpad’s Construction Interface

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 ››

Creating Mosaics Inspired by a Pattern from Sultan Ahmed Mosque

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 ››

A Double Dissection from The New York Times

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 ››

Zooming Integers: Magnifying the Number Line

In my prior post, I presented a "zooming" number line model that allowed students to estimate the location of a point along a number line and then repeatedly magnify that portion of the number line to obtain ever-finer estimates, accurate to tenths, hundredths, thousandths, and beyond. In a sense I got ahead of myself because I … Continue Reading ››

Exploring Triangle Area with Custom-Built Tools

With Web Sketchpad, it's easy to craft tools that are tailor made for the task at hand. I was reminded of this flexibility several weeks ago when creating an interactive model for the elementary curriculum Everyday Mathematics. My goal was to design a lesson focusing on the triangle area formula, A = bh/2. In … Continue Reading ››

Constructing Equal-Area Triangles

The origins of this week's Web Sketchpad model date back to the  Connected Geometry curriculum from the mid 1990s. I was one of the co-authors of the curriculum, working at Education Development Center with a  wonderful team of math educators (Al Cuoco, Paul Goldenberg, and June Mark, … Continue Reading ››

Reflecting on the Annual NCTM Meeting

This Thursday, Scott Steketee and I will be presenting two sessions at the NCTM 2015 Annual Meting in Boston: Functions as Dances: Experience Variation and Relative Rate of Change

Session 52 on Thursday, April 16, 2015: 8:00 AM-9:15 AM in 157 B/C (BCEC)

How better to explore rate of change than as independent and … Continue Reading ››