Smarter Balance has released several items for the fast approaching Common Core assessments. One really caught my eye as a dynamic context: safe following distance. I can't find a way to link to the specific item, but it is #43060 at
http://sampleitems.smarterbalanced.org (CCSS: F-BF.1a, F-LE.1b). The sketch is
on GeoGebraTube, as well.
How far should you drive behind the car in front of you?
GeoGebra notes: With the spirit of Jennifer Silverman hanging over my shoulder, I got real car images to use. The trickiest thing was sizing the images to look right since the scale was not 1:1. I like the flexibility of looking for feet (sigh, USA) or for car lengths or for time separating the vehicles.
The actual assessment question:
Pretty complex problem, as illustrated by the rubric:
Just a quick post to encourage you to think about using some dynamic visualization with your math work. Many of the released items have a little gif like animation instead of text.
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Interesting, since the 2-second rule is a common rule of thumb, but also wrong. Stopping distance goes up as the square of the speed (see, e.g., http://www.direct.gov.uk/prod_consum_dg/groups/dg_digitalassets/@dg/@en/@motor/documents/digitalasset/dg_188029.pdf). However, adding in the human response distance, which is linear with speed, means the true stopping distance is less than a squared relationship, though not by much.
ReplyDeleteAccording to the graph cited above, speeds above 30mph take more stopping distance than the 2-second rule, if the car in front were to stop suddenly (such as a head on collision).
What do we make of rubrics that don't allow for responses completely beyond the scope of the question?
Granted, having any rule of thumb is better than none at all. And answering the questions asked, instead of out-thinking the problem's author, is probably a good approach.