Protect the Sheep
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.
Category: Math Software
Revisiting the Hundred Chart
With a few adjustments, we can make the Hundred Chart more intuitive and more useful for students. This post explains why the improvements are needed and describes how students can build a physical model that more accurately corresponds to the number system.
A New Twist on Arranging Addends
Of all the original games I’ve designed, Arranging Addends is among my favorites. On page 1 of the Web Sketchpad model below (and here), you’re given five addends—1, 2, 4, 8, and 16—and asked to arrange them in the circles so that the sum of the numbers in each circle matches the values in the...
Tanton’s Two-Pan Balance Puzzle
I’m a big fan of pan-balance puzzles in which you’re given a two-pan balance and asked to use it to uncover a counterfeit coin or determine the weight of a coin. One classic example is the following puzzle: You have 12 coins that all look exactly the same. One is counterfeit and is either heavier...
Splitting Arrays
In last month’s Construct a Building post, I presented any array model in which students construct the rooms and floors of a building as a way of representing multiplication. Now I’d like to follow up with a similar array model that allows students to take a problem they don’t know, like 8 × 7, and break...
Construct a Building: Modeling Multiplication with Arrays
When Scott Steketee and I developed activities for the Dynamic Number project, we thought about ways that dynamic array models could help children to conceptualize multiplication. Rather than presenting children with arrays that were fully formed, we thought it would be instructive for them to build these arrays themselves. That design goal led to the...
Visual Models for Adding and Subtracting Fractions
How can we visualize the process of adding or subtracting fractions with unlike denominators? The Web Sketchpad model below (and here) offers tools for representing fraction addition and subtraction on a number line as well as a parameter (called “divisions”) that allows you to find a like denominator through visual inspection rather than calculation. And...
A Plethora of Hyperbola Constructions
In my prior blog posts, I’ve presented methods for constructing ellipses and parabolas using both Web Sketchpad and paper folding. Now it’s time for me to finally turn my attention to hyperbolas. All of the Web Sketchpad models below (and here) are based on the distance definition of a hyperbola: the set of points P...
Constructing the Pi-Petal Rose
When I was introduced to radian measure in high school, I knew just one thing: How to convert between radians and degrees. Had you asked me to illustrate a radian on a circle or to explain why radian measure was useful, I would have been stumped. In this post, I’ll describe a Web Sketchpad activity...
Tweaking the Expanding Circle Construction
In last month’s blog post, I described a parabola construction technique dating back to the work of Persian polymath Ibn Sina (c. 970 – 1037). After I published the post, my colleague Scott noted that my construction could be more robust to allow for parabolas that are downward facing as well as upward facing. Such...