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.
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 … Continue Reading ››
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 … Continue Reading ››
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 … Continue Reading ››
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 … Continue Reading ››
- You can subtract as well as add fractions.
- You can divide the number line into equal parts and choose the … Continue Reading ››
In previous posts, I've presented fraction-related Web Sketchpad models from the Dynamic Number project. Several of these activities—specifically Dividing and Subdividing and Deducing the Mystery Fraction —focus on a number-line representation of fractions. Below (and here) is another such websketch, with students constructing segments of fractional length that can be … Continue Reading ››
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 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. … Continue Reading ››