Category Archives: Math Software

Construct a Building: Modeling Multiplication with Arrays

When Scott Steketee and I developed activities for the Dynamic Number project, we thought about ways that dynamic array models could help children to conceptualize multiplication. Rather than presenting children with arrays that were fully formed, we thought it would be instructive for them to build these arrays themselves. That design goal led to the … Continue Reading ››

Adding Fractions on a Number Line

In previous posts, I've presented fraction-related websketches from the Dynamic Number project.  Several of these activities—specifically Dividing and Subdividing and Deducing the Mystery Fraction —focus on a number-line representation of fractions. Below (and here) is another such websketch, with students constructing segments of fractional length that can be placed end to … Continue Reading ››

A Plethora of Hyperbola Constructions

In my prior blog posts, I've presented methods for constructing ellipses  and parabolas using both Web Sketchpad and paper folding. Now it's time for me to finally turn my attention to hyperbolas. All of the Web Sketchpad models below (and here) are based on the distance definition of a hyperbola: the set of points … Continue Reading ››

Constructing the Pi-Petal Rose

When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped. In this post, I'll describe a Web Sketchpad activity that … Continue Reading ››

Tweaking the Expanding Circle Construction

In last month's blog post, I described a parabola construction technique dating back to the work of Persian polymath  Ibn Sina  (c. 970 – 1037). After I published the post, my colleague Scott noted that my construction could be more robust to allow for parabolas that are downward facing as well as upward facing. … Continue Reading ››

The Expanding Circle Construction

There can never be enough conic-section construction techniques—at least that's my philosophy, having grown up to think that conics existed purely in the realm of algebraic equations. So to continue my conic section construction series on Sine of the Times, I'll present a parabola construction attributed to Ibn Sina (Avicenna), a Persian polymath (c. 970 – … Continue Reading ››

The Varied Paths to Constructing a Rhombus

In how many different ways can you build a rhombus that stays a rhombus when its vertices are dragged? This assignment, a mainstay of Sketchpad workshops, invariably leads to great discussions because there are a multitude of ways to construct a rhombus, with each method highlighting different mathematical properties of the quadrilateral. While the rhombus task works … Continue Reading ››

A Trio of Parabola Constructions

In my prior blog posts, I've presented methods for constructing ellipses  using Web Sketchpad and paper folding. The other conic sections are feeling a bit left out, so let's explore some techniques for constructing parabolas. All three Web Sketchpad models below (and here) are based on the distance definition of a parabola: The set of … Continue Reading ››