**Disclaimer** Some of the images in this lesson are not of my own creation. I have borrowed them from Dan Meyer’s blog…although I am repurposing them.

The lesson began with this slide:

We had a conversation about what we see. My students had to decide what’s important about the car accident and what’s not important about the car accident. Ultimately, the students boiled the question down to whether the van pulled out in front of the car and whether the car was going too fast to stop (just look at those skid marks!).

I asked my students how fast they think the car was going, and they give their guesses. To give my students some extra information, I give my students the following slide:

My students decided some numbers would be nice:

Then they wanted this information:

A very insightful student asked a great question at this point: “Can we just use a proportion to figure out how fast the car was going?”

Another insightful student commented “We can do that if the relationship is linear.”

Needless to say, I was really excited about where the conversation was going.

I asked how could we tell if the relationship is linear. Crickets. I showed them the data again. Someone finally mentioned a graph (imagine…a place where a graph would be useful), so geogebra created us a scatterplot.

Someone yelled “that’s not linear!” I emphasized their point:

My students noticed that there were a lot of options in the dropdown menu for types of relationships and, after a few clicks, they settled on this graph:

As it turned out, the relationship was radical. My students used the equation to estimate a speed in the neighborhood of 70mph and decided that the car was going too fast.

Note: I guess I should note that the goal of this lesson was to graph square root and cube root functions. In all, this opener took about 15 minutes of class time. I feel they were 15 minutes well spent. Now there’s a context to when these graphs may be useful.

Note: I had to set the data up and ask the question that forced the input of the function to the be the length of the skid mark and the output to be the speed…otherwise, this doesn’t work.