# Adding and Subtracting on a Dynamic Number Chart

Below (and here) 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 reach the end of a row. This movement corresponds to adding one.  Similarly, the other three arrows correspond to movements of -1, 10, and -10.

Paul Goldenberg in the December 1970 issue of The Arithmetic Teacher (now Teaching Children Mathematics) notes that the number chart is good for posing challenges like the following: Imagine that you start at 68 and then move ↑↑→→↓←←←. Where do you land? Make a prediction before modeling the problem with the chart.

You might wonder why the chart on page one start at 0 rather than 1 and why it’s numbered from the bottom to the top. There are several pedagogical reasons for this choice:

1. The numbers are arranged in the way students talk about them: “higher” numbers are above “lower” numbers, and students move “up” to larger numbers and “down” to smaller numbers.
2. The rows are more coherent than number charts that begin at 1. Each row contains numbers related both by words and by their tens-place digit. The first row contains the single-digit numerals, the next row has the “teens,” the next the “twenties,” and so forth.
3. The chart has a starting place of zero for “counting on.” A student can use “counting on” for both parts of a problem, like 3 + 5: start at 0, count 3 to the right, and then count 5 more to the right.

The short video at the end of this post shows how students might model 27 + 24 as 27 + 3 + 20 + 1,  and 51 + 39 as 51 + 40 – 1.

An annotated list of all our elementary-themed blog posts is here.