The Math Education Blog
The websketch below (and here) provides tools to build six different pattern block shapes. To add a new pattern block to your design, tap its icon. A preview of the pattern block appears with one vertex glowing. Tap to place the pattern block in your design. You can then drag the pattern block wherever you...
Great news statistics fans: A version 3 beta of the Common Online Data Analysis Platform (CODAP) is now available. To quote the CODAP website, “[The new CODAP] is a powerhouse under the hood, handling much larger datasets, drawing graphs and maps faster, animating more smoothly, and responding instantly.” CODAP is the successor to Fathom, both...
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...
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...
It’s a gripe I’ve shared before, but I’ll repeat it—the typical high school geometry approach to introducing transformations is boring. Fresh from learning the definition of a translation, reflection, rotation, or translation, students are whisked off to the safety of the coordinate plane and asked to explore the numerical effect of reflecting a point over...
When I taught a geometry methods course at City College last fall, I devoted an entire class to investigating area. We focused on problems where triangles were sheared, transforming into new triangles, but maintaining their area. The two Web Sketchpad activities that follow introduce shearing and present a problem with a surprising result that can...
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...
In the fall of 2023, I taught a geometry methods course at City College here in New York. While my goal was to make use of Web Sketchpad throughout the semester, I knew that the most effective use of the software required activities that coupled it with hands-on modeling. Two such opportunities arose with the...
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...
What do you get when you cross geometry with the classic murder mystery game Clue? Why, the Mysteries of Polygon Flats, of course! In my prior post, I offered examples of how Web Sketchpad can help students classify special quadrilaterals like squares, rectangles, kites, parallelograms, trapezoids, and rhombuses by providing “dynamic” models of each shape...