Tag Archives: Sketchpad

Constructing an Ellipse with Web Sketchpad Tools

In a prior blog post, I described the pins-and-string approach to drawing an ellipse: Press two pins into a corkboard, place a loop of string around the pins, pull the string tight with a pencil, and trace the pencil tip's path as you pull the pencil around the taut string. Guaranteeing that the traced … Continue Reading ››

The Broken Stick Puzzle

Several weeks ago, my friend Martin shared the following probability puzzle with me: Two points are chosen independently and at a random on a stick. The stick is broken at those points to form three smaller sticks. What is the probability these three sticks can form a triangle? This is a classic problem, dating back to … Continue Reading ››

A Double Dissection from The New York Times

Did you know that aside from being a source of news, The New York Times is also the place to get your weekly fix of mathematics? Their online Numberplay column features some very clever math puzzles. Last year, in fact, our blog featured a Numberplay puzzle about a flying squirrel-frog from former Key Curriculum … Continue Reading ››

Zooming Integers: Magnifying the Number Line

In my prior post, I presented a "zooming" number line model that allowed students to estimate the location of a point along a number line and then repeatedly magnify that portion of the number line to obtain ever-finer estimates, accurate to tenths, hundredths, thousandths, and beyond. In a sense I got ahead of myself because I … Continue Reading ››

Zooming in on Place Value

One of the aspects I like best about Dynamic Geometry software like Web Sketchpad is its ability to illustrate concepts that cannot effectively be represented with static media. Take, for example, a number line that we draw on a white board. Showing the number line labeled with integers is easy. Adding tenth-mark divisions to the … Continue Reading ››

Exploring Triangle Area with Custom-Built Tools

With Web Sketchpad, it's easy to craft tools that are tailor made for the task at hand. I was reminded of this flexibility several weeks ago when creating an interactive model for the elementary curriculum Everyday Mathematics. My goal was to design a lesson focusing on the triangle area formula, A = bh/2. … Continue Reading ››

Constructing Equal-Area Triangles

The origins of this week's Web Sketchpad model date back to the  Connected Geometry curriculum from the mid 1990s. I was one of the co-authors of the curriculum, working at Education Development Center with a  wonderful team of math educators (Al Cuoco, Paul Goldenberg, and … Continue Reading ››

Solving Simultaneous Equations with Common Sense

Simultaneous equations belong in elementary-school mathematics curricula. That's been my mantra for many years, and I want to examine it now in the context of an interactive Web Sketchpad activity. When I say that elementary-age students should encounter simultaneous equations, I don't mean that they should be instructed in the standard algebraic procedure for solving pairs of equations … Continue Reading ››

Hello Spring!

Today's blog post features a sketch from Anna Nguyen, who's a 9th grade student. Anna observes, "Math is one of my favorite subjects. I'm not a genius or the smartest in my class, but I do enjoy dealing with letters and numbers, which is also why I like chemistry. I think GSP is the most … Continue Reading ››