# The Varied Paths to Constructing a Square

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 ››

In my very first Sine of the Times blog post from January 2012, I wrote about the paucity of fractions that young learners typically encounter in their math classes. While they might construct visual representations of 1/2, 2/3, and 8/12, it's unlikely they'll create models of 7/31, 36/19, or 5/101. That's a shame because without … Continue Reading ››

# Estimating Angle Measurement

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 ››

How challenging can single-digit addition be? That's the question I asked myself when my friend Hung suggested that I download Chisla, a mobile game for iOS and Android. From its description alone, the game seemed suitable for young learners practicing their addition. Take a look at the image below. The game presents you with an array of 25 random digits. … Continue Reading ››

# An Equivalent Fractions Game

In my recent posts, I've introduced interactive models for comparing fractions and multiplying fractions. To continue the fraction theme, below is a Web Sketchpad model in which the need for equivalent fractions arises naturally through the rules of a game. The model displays two arrays. Dragging the four points changes the arrays' dimensions. The goal is to drag blue squares into the blue array … Continue Reading ››

# A Compendium of Elementary Web Sketchpad Activities

Below is a complete list of all the interactive elementary-themed activities we've offered on our Sine of the Times blog. Most of these activities grew out of the work that we did during our NSF-funded Dynamic Number project. The list includes links to our original blog posts as well as links that take you directly … Continue Reading ››

# Exploring Tessellations with Web Sketchpad

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 ››

# Connecting Functions in Geometry and Algebra

News alert! Scott and I wrote the cover story, Connecting Functions in Geometry and Algebra, in this month's Mathematics Teacher. You can read the article in print, but better yet, go to the free online version. This is the first time Mathematics Teacher has incorporated live dynamic-mathematics figures into its online offerings, allowing readers to manipulate the mathematical … Continue Reading ››

# A Coordinate Plane Logic Puzzle

For the past few years, Scott Steketee and I have collaborated with the author team of Everyday Mathematics to integrate Web Sketchpad deeply into their curriculum. As part of that work, I just completed a websketch that nicely mixes practice with logical reasoning. Students are challenged to find a hidden treasure on the coordinate … Continue Reading ››

# Bunny Times Brings Conceptual Understanding to Multiplication

Four years ago, my colleague Scott Steketee and I set out to develop an interactive game to help students develop strategies for thinking about and solving multiplication problems. As we examined the existing apps on the market, we discovered that most focused on the drill aspect of learning one's multiplication facts. We set our goals higher. We … Continue Reading ››