## Constant Difference & the Number Line App

Cynthia Hockman-Chupp

After teaching the Constant Difference strategy for subtraction to at least six different groups of teachers and students in third and fourth grade over the past month, I think I finally hit on a winning tool: the Number Line app. Here’s what I did.

First, I selected a plain number line, no ticks. Then, anticipating two sets of numbers, I added four blank boxes to the line.

I told the class of fourth graders that we were going to first use the Find the Difference strategy for the expression 81 – 47. While the class made their own number line in their math notebooks, I added the numbers to the line I’d already prepared.

Several students shared their thinking (with jumps) at the document camera. We agreed that the difference is 34. I added a single jump to my number line to demonstrate their finding.

Then, moving to Constant Difference, I asked them to think of a number close to 47 that would be friendly and easy to work with. Immediately, students suggested 50. I added that to our number line. I continued by asking them to think about how we got from 47 to 50. How far did we go, and in what direction? A student volunteered—and many agreed—that we moved 3 to the right.

At some point, it’s critical for students—especially English Language learners—to consider what is meant by the word constant. Students might say, “stays the same” or “doesn’t change.” Looking at the work we’d done so far, students thought about what we’d have to do to keep the distance constant. If we previously figured the difference from 47 to 81, what would the difference be if we started with 50? This took a little discussion. When students agreed that we needed to move 3 to the right from 81, we moved our jump.

At this point, several light bulbs went off. Not everyone understood. But it clicked for a significant number. I asked the class which they would rather solve: 81 – 47 or 84 – 50. The verdict for the later was unanimous.

On the next problem, students could choose a strategy. Quite a few gravitated to Constant Difference. Now, with peer modeling, the strategy extends to a broader audience.

Do you have tips for teaching Constant Difference or other strategies? Please comment below.

Cynthia Hockman-Chupp is a curriculum specialist for MLC.