Adding and Subtracting on an Open Number Line

For some time now, Scott and I have been thinking about how we might create a Web Sketchpad model of an open number line that could offer functionality not found in the typical hand-drawn variety.

We’re finally ready to share our work. Below [and here] is our Web Sketchpad open number line. This video explains how it operates.

The video offers several ways to represent 17 + 78, with a more complete set of options below. The Web Sketchpad model automatically labels the arcs with the size of your jumps and gives you the option to display a running tally at each arc endpoint.

When representing an addition problem, do students use landmark numbers or jump by tens or split an addend into smaller “friendlier” numbers? Do they use subtraction? Seeing how students decompose and compose numbers can help to assess their understanding of numbers.

Because arc endpoints can be dragged left and right, the values above the arcs can easily be made to represent either addition or subtraction. This gives students a natural entry point for discovering the properties of negative numbers. As an example, if a student starts with jumps of 3, 4, and 5, she can drag all three to the left to show 0 –3 – 4 – 5 = –12.