The Math Education Blog
When I was child, I loved to solve the brainteasers in logic puzzle magazines. You probably know the type: Ruth, Phyllis, and Joan each bought a different kind of fruit (orange, apple, pear) and a different vegetable (spinach, kale, carrots) at the supermarket. No one bought both an orange and carrots. Ruth didn’t buy an apple or...
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 maligned “new math” of the 1960s. That’s a shame because there is a lot to learn from them, especially when presented as interactive puzzles. Below (and here) are...
For a while now, I’ve been intrigued by the ways in which the study of geometric transformations can provide students with a very effective introduction to function concepts. Daniel and I have written a couple of articles about this topic, and we created a number of activities to take advantage of what can arguably be...
In my prior post, I presented an interactive Web Sketchpad odometer that is a great tool for introducing young learners to place value. Well, technology moves fast these days, and the latest odometers are more powerful than ever. While our prior odometer featured ‘+’ buttons above each digit, our newest innovation in number-tracking technology features ‘+’ and (gasp!) ‘–’...
Below (and here) is an interactive odometer built with Web Sketchpad. Press each of the ‘+’ keys and observe their effect on the odometer’s value. Also notice how your button presses are tracked in the table below the odometer. I built this model as a way to support students’ development of place-value concepts. Here are...
With the World Cup in our hemisphere, and the US squad having started out with a win over Ghana, my thoughts turned to the mathematics of soccer. My friend Henri Picciotto has a nice page about the shooting angle, the angle within which a shot is on goal, so I thought of using Sketchpad to...
For the past eight months, my colleague Scott Steketee and I have collaborated with the authors of the elementary curriculum Everyday Mathematics to design interactive Web Sketchpad models for their next edition. When it came time to create a Sketchpad representation of an isosceles triangle, I built the interactive triangle model below. Try dragging any of the triangle’s three...
Every week, The New York Times challenges its readers to solve a mathematical puzzle in its online Numberplay column. This week’s puzzle was proposed by none other than Dan Bennett, a former editor and author at Key Curriculum Press, and his colleague, Avery Pickford. Here is their puzzle, as described in Numberplay: Dan and Avery love playing...
In this guest post, Nate Burchell describes a sketch he uses with his students to explore parametric functions. In this process students work entirely in a graphical world, manipulating graphs directly rather than by way of equations. (Nate teaches in Seoul, Korea, where I enjoyed his family’s hospitality when I attended ICME in 2012. His...
In several of my earlier blog posts, I’ve written about Sketchpad activities that present factors and multiples in puzzle form (see, for example, When Factoring Gets Personal). Now I’d like to introduce you to another puzzle of mine called Open the Safe that also focuses on factors and multiples. Below (and here) is an interactive safe built...