This Thursday, Scott Steketee and I will be presenting two sessions at the NCTM 2015 Annual Meting in Boston:

Functions as Dances: Experience Variation and Relative Rate of Change

Session 52 on Thursday, April 16, 2015: 8:00 AM-9:15 AM in 157 B/C (BCEC)

How better to explore rate of change than as independent and dependent variables dancing together? We’ll vary x and y by doing both real and computer-based dances based on geometric transformations, dynagraphs, and Cartesian graphs of various functions. Bring a laptop or iPad with Sketchpad. Leave with student-ready geometry and algebra activities.

Geometric Transformations and Algebraic Functions: Two Sides of a Coin

Session 245 on Thursday, April 16, 2015: 2:00 PM-3:00 PM in Ballroom West (BCEC)

In grades 7–12, CCSSM expects students to understand transformations as functions. This profound link allows students to build a transformation, drag its input (a point), describe the output’s behavior, restrict the domain to a number line, and voilà!—end up with a linear function and its Cartesian graph. Leave with student-ready GSP activities.

We’re hoping you can come to one or both sessions, but if not, here are two reflection challenges from our presentations that you can try right now with Web Sketchpad.

For the first challenge, your task is to drag the red point so that its reflection, the blue point, reaches the target. But move carefully! Don’t allow the blue point to touch any of the obstacles in its path.

To view the second challenge, press the arrow in the lower-right corner of the sketch. Now, your goal is to drag red point so that its reflection, the green point, follows the border of the blue polygon. Notice that in the sketch, we use the term “range” to reference the path of the green point. By dragging the red point, you’re determining both the domain of the red point and the range of the green point. The terms ‘domain’ and ‘range’ allude to the connections between transformations and functions we’ll be highlighting in our presentations.

You’ll find more material from our NCTM sessions on the Geometric Functions website.

We look forward to meeting some of you in Boston!