Author:
Christopher Danielson

To answer common student questions about slope and first differences.

This brief packet consists of a short video using student questions and responses to an in-class task to address common questions about slope and first differences.

Tutorial

In class, I occasionally ask students to list out things they know, things they want to know and things they have learned about a topic (this is referred to as a "KWL" among educators, for **K**now, **W**ant to know, **L**earned).

We recently did a KWL on slope in College Algebra. I noticed that various students did an excellent job of addressing each others' questions in the "want to know" part through their "know" and "learned" responses.

This brief packet consists of a video showing students' questions and answers; the video concludes with a final answer from me.

Learners should be familiar with the concept of "first difference," which is a quick tool for analyzing change in function tables. The idea is not explained in this packet, but it is demonstrated at the end of the video.

This video uses student responses to a classroom task to ask and answer each others' questions. It finishes with a brief instructor explanation of the relationship between first differences and slope.

So slope is a rate of change (such as velocity). Slope is the ratio of the change in y to the change in x. And first differences analyze change in y. When the change in x is 1, then the first differences and the slope are identical.

First differences are a particularly useful tool when presented with a table of data. And they are especially helpful when the table is non-linear. Non-linear functions technically do not have slopes. But we can still compute first differences and look for patterns that tell us about the behavior of the function.

And first differences are an important precursor to the calculus topic of derivative.