Tag Archives: Modeling

Adding and Subtracting on a Dynamic Number Chart

Below is a collection of four interactive number charts that we first introduced in our NSF-funded Dynamic Number project. Start by asking students to press the four directional arrows and to explore what they do. The right arrow, for example, moves the shaded square to the right, and wraps the square to the next row up when you … Continue Reading ››

A Mathematical Mystery Story with Web Sketchpad

Several years ago, I wrote a blog post about the value that students derive from writing mathematics with Sketchpad. The post included an example of a simple Logo iteration, easily implemented in Sketchpad, that produces some very complex and interesting shapes depending on the values of several input parameters. In the article* where … Continue Reading ››

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 ››

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 for … Continue Reading ››

WCYDWT: A Ball, a Trash Can, and Web Sketchpad

Dan Meyer has posted a number of "What Can You Do With This?" activities on his blog. (Activities is probably too prescriptive a word; they're more in the nature of prompts for student thinking, noticing, and wondering.) One of the first was the image below, which he made by superimposing frames from a … Continue Reading ››

A Quartet of Ellipse Constructions

It's the season for NCTM regional conferences, and I'm presenting sessions on conic section construction techniques in both Richmond and Houston this month. For those of you who can't attend, here's a peek at what I'm demonstrating. The 17th-century Dutch mathematician Frans van Schooten developed "hands-on manipulatives" centuries before the term became popular in math education circles. Below … Continue Reading ››

Logic Puzzles Made Visual

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 kale.Continue Reading ››

The Flying Squirrel-Frog Puzzle

While I enjoy reading The New York Times for its news coverage, I especially look forward to each Monday when they post a new math puzzle online in their Numberplay column. Several months ago, I shared a Numberplay puzzle from former Key Curriculum editor Dan Bennett. Now I'd like to recap the Numberplay puzzle … Continue Reading ››