In Algebra 1, I was the king of solving for *x*. Algebraic manipulation was fun and satisfying, and I was good at it. But my confidence was shaken when I encountered a test question of the variety 4*x* + 5 = 4*x* – 3. After subtracting 4*x* from both sides, I was … Continue Reading ››

# Tag Archives: Web Sketchpad

# Exploring Scaled Polygons

Below are some common methods that geometry curricula offer for constructing scaled polygons:

- Place a polygon on the coordinate plane, pick the origin as the center of dilation, scale each vertex by some specified amount by using its coordinates, and then connect the scaled vertices.
- Draw rays from the … Continue Reading ››

# Injecting Surprise Into the Triangle Midline Theorem

Pi Day 2022 is now over, but I'm still thinking about a tweet from 10-K Diver: Take two random numbers *X* and *Y* between 0 and 1. What is the probability that the integer nearest to *X*/*Y* is even? The answer—spoiler ahead—is (5 – π)/4. (You can run my Web Sketchpad … Continue Reading ››

# A Paper Folding Investigation from Connected Geometry

In a prior post, I shared some good news: The *Connected Geometry* high-school curriculum authored by Education Development Center (EDC) is now available for free. I could easily devote every future blog post to a tasty *Connected Geometry* morsel, but I'll restrict myself to just a few. The * *investigation … Continue Reading ››

# Symmetry Challenges

In his online article *Simply Symmetric*, Michael de Villiers observes that symmetry is a powerful but often overlooked tool for formulating proofs:

Most primary geometry curricula around the world introduce the concept of line symmetry fairly early, and sometimes also that of rotational, translational and glide reflective symmetry. … Continue Reading ››

# 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 ››

# A Follow-Up to the Interior Angle Sum

This post is a follow-up to Sarah Stephens' guest post of a week ago, in which she described a lesson using embodied cognition to help students make sense of the interior angle sum theorem for triangles, not just as an abstract concept, but as a property grounded in their concrete physical experiences.

# Protect the Sheep

A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.

# Adding and Subtracting Fractions on a Number Line

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 ››

# Adding Fractions on a Number Line

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 ››