Double Number Lines and Dynagraphs
2022 NCTM Baltimore Regional Conference
Scott Steketee stek@geometricfunctions.org
21st Century Partnership for STEM Education
Daniel Scher daniel.scher@mheducation.com
McGraw-Hill Education
1. Numberline Addition
2. Numberline Subtraction
Use the two pages of this sketch to explore subtraction using two numberlines.
3. Numberline Multiplication
This sketch is under construction. You are invited to experiment with it, and to come up with your own ideas about students might use it to explore multiplication, ratios, and proportions.
4. Zooming Numberlines
On each of the four pages, estimate the location of the point and then zoom into its neighborhood to get a closer look. Keep making new predictions as you zoom.
5. The Curious Case of the mxb Dynagraph
What do you notice, and wonder, about page 1?
What do you think about the additional clues on the other pages?
6. Guess the Function from its Dynagraph
7. Make Any Function Dynamic
Double-tap the function to edit it.
8. The Cartesian Connection
Be sure to use the Trace Widget to turn on tracing for the connector!
9. Triple-Numberline Solver
On page 1, drag point `x` and observe the behavior of `2(x + 1)` on the second numberline and `3(x – 1)` on the third numberline. How can the numberlines help you solve `2(x+1) – 6 = 3(x – 1)?` Try solving the equations on pages 2 and 3. What is different about them? Create your own equations on page 4.
10. Play the m-x-b Game
Each of the ten challenges describes the motion of a function's dependent variable. Your job is to set `m` and `b` to produce that motion.
11. Other Links
This web site is based in part upon work supported by the National Science Foundation under NCSU IUSE award 1712280 (July 2017 through December 2020) and KCP Technologies DRK-12 award ID 0918733 (September 2009 through August 2013). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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