The Math Education Blog
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...
In the February 1954 issue of Mathematics Teacher, Paul C. Clifford describes an optimization problem from his trigonometry class. Of all isosceles triangles ABC with sides AB and BC of length 12, which one has the maximal area? Clifford told his class that an exact solution to the question required calculus. One student, however, proved...
With nothing but a compass, students can construct a lovely daisy design consisting of seven interlocking circles, all of the same size. I was delighted to see that the U.S. postal service chose to feature four variations of this design in their floral geometry stamps shown below. I even spotted the daisy design on these...
While most numbers lead anonymous lives away from the mathematical spotlight, eiπ occupies hallowed ground. Douglas Hofstadter writes that when he first saw the statement eiπ = −1, “. . . perhaps at age 12 or so, it seemed truly magical, almost other-worldly.” At the risk of deflating the celebrity status of eiπ, what follows is an...
This past semester, I taught a geometry course for teachers at City College here in New York. As you might expect, Sketchpad figured heavily in the course contents. But unlike other semesters when desktop Sketchpad was my tool of choice, this time, I took the plunge and limited myself to Web Sketchpad. Web Sketchpad kept...
This post, inspired by the work of Al Cuoco, uses Web Sketchpad to explore a transformations approach to complex numbers.
When I reached calculus in my senior year of high school, it was clear that it sat atop a mountain that I had been ascending ever since my Algebra 1 class. Without the tools and procedures I had amassed from algebra and precalculus, I could never have performed the symbolic manipulations necessary to differentiate and...
Given two segments and their midpoints, what quadrilaterals can you build using the segments as the diagonals of the quadrilateral?
This post examines the connections between origami and geometry in the context of a new book written by Daniel Scher and Marc Kirschenbaum.