Tag Archives: Problem Solving

Understanding Fraction Multiplication

Last week, Scott and I attended a fraction symposium at NYU, and it made me realize how long it's been since I've written about our Sketchpad work with fractions. Below is a Web Sketchpad model for displaying and solving fraction multiplication problems. Representing fraction multiplication with an area model is a common approach, but it's challenging to … Continue Reading ››

A Coordinate Plane Logic Puzzle

For the past few years, Scott Steketee and I have collaborated with the author team of Everyday Mathematics to integrate Web Sketchpad deeply into their curriculum. As part of that work, I just completed a websketch that nicely mixes practice with logical reasoning. Students are challenged to find a hidden treasure on … Continue Reading ››

Putting the Power of a Point Theorem to Work

The power of a point theorem is one of the more surprising results in elementary geometry. The theorem says that if two chords AB and CD of a circle intersect at point P, then the product AP · PB is equal to the product CP · PD. You can see an illustration of this theorem in the Web Sketchpad model below. Drag … Continue Reading ››

Arranging Addends Puzzles Revisited

In a prior blog post, I introduced my new puzzle, Arranging Addends, that mixes arithmetic with logical thinking to create an engaging playground for mathematical discovery. Let’s revisit this puzzle and introduce some new variations. Take a look at the puzzle below (and here), built with Web Sketchpad. Your goal is to arrange … 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 ››

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, … 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 ››

Pi Day 2015: Pieces of Pi

For this year’s Pi Day post, I thought I’d continue our Web Sketchpad (WSP) construction theme. But rather than adapting the visualizations from last year’s Pi Day post to the new construction capabilities, I decided to take a different approach. Some time ago, I built a set of custom tools … Continue Reading ››