Introducing Web Sketchpad at the 2021 NCTM Annual Meeting

NCTM’s Virtual 2021 Annual Meeting ran from April 21 through May 1, and in Session 299 Daniel Scher, Karen Hollebrands, and I presented an on-demand video workshop to introduce Web Sketchpad (WSP). Even if you weren't able to attend the conference, you can still take … Continue Reading ››

Revisiting the Hundred Chart

With a few adjustments, we can make the Hundred Chart more intuitive and more useful for students. This post explains why the improvements are needed and describes how students can build a physical model that more accurately corresponds to the number system.

A New Twist on Arranging Addends

Of all the original games I've designed, Arranging Addends is among my favorites. On page 1 of the Web Sketchpad model below (and here), you're given five addends—1, 2, 4, 8, and 16—and asked to arrange them in the circles so that the sum of the numbers in each circle matches the values … Continue Reading ››

Splitting Arrays

In last month's Construct a Building post, I presented any array model in which students construct the rooms and floors of a building as a way of representing multiplication. Now I'd like to follow up with a similar array model that allows students to take a problem they don’t know, like 8 × 7, and … 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 … 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 … 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.

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 … Continue Reading ››