Forging Connections
Introduce Dynagraphs
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This page supports the Introducing Dynagraphs activity from the Dynagraph unit. You will investigate dynagraphs of several different functions. To get a feel for the behavior of each function, you will drag the independent variable and observe the resulting motion of the dependent variable.

1 Explore a Dynagraph


Download the student worksheet.     

2 Play the Dynagraph Game


3 Play the Dynagraph Game with Sliders

  • Use page 1 for practice. Start out by dragging `x` and using the sliders to make `f(x)` and `??(x)` move at the same speed, and then adjust their positions to match.
  • Then use the Animate buttons to make `x` move automatically, and use the sliders again to match mystery function `??(x)`.
  • Finally, go to page 2 and try to score 10 out of 10 on levels 1 and 2.

Notice that you can change the level only at the beginning of a game. To change levels, press Reset and then choose your new level.



The term dynagraph was coined by Paul Goldenberg, Philip Lewis, and James O’Keefe in their study “Dynamic Representation and the Development of a Process Understanding of Functions” published by Education Development Center, Inc., and supported in part by a grant from the National Science Foundation.

Related Activity

In the activity Create a Dynagraph, you can construct your own dynagraph for linear functions, using only geometric transformations (dilation and translation) to accomplish the construction.

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Update History:

08 May 2018: Moved into the Forging Connections project space 29 March 2016: Added the worksheet and refined the sketch.
26 March 2016: Created this page.

Download the teacher notes.