This blog post features a sliding ruler approach to modeling the addition and subtraction of integers. Rather than memorizing rules for solving problems like 9 + (–14) or -2-(-7), students can develop completely general methods that focus on conceptual understanding.
Category Archives: Elementary Mathematics
Pattern Block Puzzles
Several days ago, I was reminded of an interactive pattern block puzzle that I designed during the pandemic in collaboration with Toni Cameron of Reimagined. It provides an engaging opportunity to promote proportional reasoning in the context of geometry.
On page 1 of the websketch below (and Continue Reading ››
Virtual Cuisenaire Rods
I was happy to collaborate on this blog post with Dr. Stavroula Patsiomitou, a researcher at the Ministry of Education and Religious Affairs in Greece. Dr. Patsiomitou received her PhD from the University of Ioannina and has written extensively about the field of dynamic geometry environments, including Sketchpad and Web Sketchpad. … Continue Reading ››
Introducing Web Sketchpad at the 2021 NCTM Annual Meeting
Protect the Sheep
A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.
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 … Continue Reading ››
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 … Continue Reading ››
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 … Continue Reading ››
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 … Continue Reading ››