The Math Education Blog
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 left with 5...
Below are some common methods that geometry curricula offer for constructing scaled polygons: To complement these standard approaches, I’d like to present a fourth option, one that allows students to form the original polygon and its dilated image simultaneously rather than starting with the preimage. In the Web Sketchpad model below (and here), begin by...
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 simulation of the problem...
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 below, taken straight from the curriculum,...
The Web Sketchpad model below (and here) shows the function f(θ) = 1 – cos 2θ in both Cartesian and polar form. For each graph, the independent variable appears as a red bar that corresponds to a particular value of x (for Cartesian) or θ (for polar). The red bar has tick marks that show...
In a previous post, I described two different approaches to solving the Burning Tent optimization problem. Now I’d like to offer a related problem that I assigned many years ago to my pre-service mathematics teachers at New York University. A cowgirl wants to give her horse some food and water before returning to her tent....
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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 advantage of this workshop, and we will be glad to...
How can you identify a lover of math? Casually mention a burning tent and notice if her first thought is how to minimize her path to a river and then to the tent to douse the flames. Here is a full statement of this classic geometry problem: Ah, the great outdoors. Camping, the fresh air,...
In a 2018 blog post, I presented George Gamow’s pirate treasure problem, which can neatly be solved by capitalizing on the geometry of complex numbers. There’s more treasure to be had, however, so get ready for another adventure! An island contains a giant boulder, a lighthouse, a cave, and a jail. Among a pirate’s belongings,...
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.