In my numerous blog posts about Exploring Conic Sections with The Geometer’s Sketchpad, I’ve featured an assortment of hands-on and virtual models for drawing conic sections, ranging from pins and string to paper folding to 17th-century linkages. But in order for students to understand why any of these approaches work, they must first grapple with...
In this lesson, one of my favorites from Exploring Algebra 1 with The Geometer’s Sketchpad, students model expressions with dynamic algebra tiles, using the areas of the tiles to see the equivalence of expressions in factored and expanded form. Down below (and here) is a Web Sketchpad model of algebra tiles. To model (x +...
Welcome to Algebra Mazes, my new early algebra puzzle that shares DNA with my earlier creation, Sneaky Sums. Both Algebra Mazes and Sneaky Sums puzzles present you with a grid of shapes. Each shape represents a secret numerical value for you to deduce. Whereas Sneaky Sums puzzles were generated randomly, Algebra Mazes are handcrafted and...
I must admit that I am addicted to triangle shearing problems . I’ve written about them before, and will be revisiting them soon in my City College geometry class. I mention this because several weeks ago, I encountered a problem in the LinkedIn feed of mathematics educator James Tanton that made me wonder whether a...
I was doing some spring cleaning a few weeks ago and came across a stash of old files that were “extra” ideas that never made their way into our Dynamic Number curriculum project. One concept in particular caught my attention—a “scooting” tick mark. Unlike traditional tick marks that dutifully sit in place on a number...
Way back in 2014, I wrote a blog post titled Covering Your Bases that offered an interactive Web Sketchpad experience with various number bases. As I noted then, “There are certain topics in mathematics education not appropriate for polite discussion. Number bases other than 10 fit this category well, perhaps because of their association with the...
For the past eight years, I’ve been engaged in a project that is about as far from mathematics as one could imagine — coediting an English anthology of contemporary Turkish poetry with my good friend, Buğra Giritlioğlu, who is the founder of the queer publishing house obiçim yayınlar. Our anthology, The Pulse of Contemporary Turkish,...
Longtime readers of this blog will know that I get more than just a little excited by devices—both mechanical and virtual—that draw conic sections. I’ve written about the conic section-drawing devices of the 17th-century Dutch mathematician Frans van Schooten as well as other methods of generating conics in a variety of posts. I also wrote...
This blog post features a sliding ruler approach to modeling the addition and subtraction of integers. Rather than memorizing rules for solving problems like 9 + (–14) or -2-(-7), students can develop completely general methods that focus on conceptual understanding.
Below is a problem taken from Dietmar Küchemann’s Algebradabra site. Many problems that mix geometry with algebra invariably shortchange the geometry. For example, the angles of a triangle might be labeled x, 2x, and 3x, and students are asked to find the value of x. Other than knowing that the angles of a triangle sum...