In my January 2020 blog post, I presented a collection of Web Sketchpad construction challenges where the goal was to use each handpicked set of tools to build a rhombus. Could you, for example, construct a rhombus with just a Compass and Parallel tool? How about starting with merely the Reflect … Continue Reading ››
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 4x + 5 = 4x – 3. After subtracting 4x from both sides, I was … Continue Reading ››
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 ››
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 ››
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 ››
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.
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 ››