3-Acts: Quadratic vs. Linear Modeling – Will he stop in time?

PublishingPicDrivers often encounter unexpected reasons to stop.  Will he stop in time?

Students compare a linear gauge of stopping distance with a quadratic gauge.  As an extension, students devise a more accurate linear gauge for faster speeds.

Act 1 video

What questions do you have?  Act 1 is intended to spark an engaging discussion of stopping distances calculated both linearly and quadratically.  Discussion will likely include road conditions, how heavy the vehicle is, etc. but also the fact that the linear model does not fit well with the quadratic model at and beyond 70 mph.  Students will discover they can improve the 3-second rule by writing a piece-function that better fits the quadratic beyond 70 mph.   The focus is not so much this particular scenario, rather a study of different gauges used to predict stopping distances.  Act 2 provides two different gauges for stopping distances for students to compare.  One gauge is linear, and one is quadratic.  The linear gauge is less accurate but certainly more convenient when driving down the road.

Information about stopping distances (Act 2):

driver’s ed   (video)                        breaking distances

Details of suggested approaches for this exploration and CCSS associated with them:  Approaches & Standards

Act 3 Finale (oops):  

 

Commentary:  Thanks to contributions from Megan Schmidt and Jen Sullivan, the initial activity was expanded to include 18 CCSS

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