A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.
- 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 ››
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 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.
While the rhombus task works … Continue Reading ››
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.
When students find the nth roots of a complex number, they use de Moivre's Theorem and a fair bit of calculation and trigonometry. In this blog post, I'm going to approach the topic from a more visual perspective and make use of the following geometric way to think about complex number multiplication: To multiply two complex … Continue Reading ››