Elementary Mathematics, Math Software

Adding Fractions on a Number Line

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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 ››
Conic Sections, Educational Technology, Math Software

A Plethora of Hyperbola Constructions

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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 ››
Elementary Mathematics

Early Childhood Math Routines

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Mathematics is a wonderful game. It's one that can stretch students' minds and expose them to the beauty and unexpected delights that lie behind every good problem. I've always gravitated to colleagues who share my love of math's playful, game-like side, so I quickly made friends with Toni Cameron when we met at P.S. 503 in … Continue Reading ››
Educational Technology, Geometry, Math Software

Constructing the Pi-Petal Rose

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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 ››
Conic Sections, Educational Technology, Math Software

Tweaking the Expanding Circle Construction

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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 ››
Conic Sections, Educational Technology, Math Software

The Expanding Circle Construction

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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 ››
Educational Technology, Geometry, Math Software

The Varied Paths to Constructing a Rhombus

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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 ››
Conic Sections, Educational Technology, Math Software

A Trio of Parabola Constructions

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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 ››
Advanced Mathematics, Educational Technology, Math Software

An Interactive Approach to Finding nth Roots

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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 ››

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