Dilation Games: Assessment That’s Fun

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 ››

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 ››

Constructing an Ellipse with Web Sketchpad Tools

In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip's path as you pull the pencil around the taut string. Guaranteeing that the traced … 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 ››

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