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 ››
In my previous post
, I presented a number line model for adding fractions. Now, I'd like to offer an updated Web Sketchpad fraction model below (and here
) with two new pieces of functionality:
- You can subtract as well as add fractions.
- You can divide the number line into equal parts and choose the … Continue Reading ››
In previous posts, I've presented fraction-related Web Sketchpad
models 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 … Continue Reading ››
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 ››
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 ››
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 ››
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 ››
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.
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 ››
Attention Sketchpad fans: If you're a Mac user and would like to give the new Mac Sketchpad a spin, go ahead and contact me so that we can add you to our beta test.
Several weeks ago, Apple released MacOS Catalina and brought an end to all 32-bit apps, including Sketchpad 5.06. Luckily, Nick … Continue Reading ››