Earthquakes Part 2 - Circles

I borrowed this lesson from John Stevens.  As a quick side note, this is what I love about the MTBoS community on Twitter.  You build a network of creative educators from literally all over the world and your own lessons improve because of the sharing that happens.

Now, my students and I live in central Pennsylvania.  We have the occasional earthquakes, but they are they type that only the most observant people even notice.  Here is a link to our most recent earthquake.

This is John's original lesson.  On his page, you will find links to his Slides presentation, lesson plan, and student handout as well as notes about how he implemented the lesson.

I started with showing a San Andreas movie trailer.

I asked if anyone had seen the movie.  I asked is any of them felt the earthquake that we had the previous summer.  These questions lead to some lively conversation.

I showed them some maps from the USGS website that show intensity in a variety of ways

http://earthquake.usgs.gov/earthquakes/shakemap/sc/shake/37609552/ 

http://earthquake.usgs.gov/earthquakes/eventpage/ci37609552#general

I asked my students what they noticed and wondered about the images.  I got all sorts of answers but eventually someone brought up circles.  I asked what they thought the concentric circles might represent.  

This part takes some time on the part of the teacher.  You need to find earthquakes that happen inland, far enough away from the coast so that you can see the details on the map.  The maps will not show the circles needed if the epicenter of the earthquake is too close to water.

Next, I put the ShakeMap into Desmos and added a circle equation with sliders (using John's graph as a template).

https://www.desmos.com/calculator/mwfkhxzwxt 

We started with the epicenter circle.  We played with the sliders, one at a time and discussed how the values of h, k, and r change the circle.  Next we adjusted the sliders to line up with each circle of intensity on the map.  Finally, we talked about what each of the equations and each of the graph have in common and how that related to the definition of  concentric circles.

The lesson ended with an exit ticket where students graphed the equation of a circle and wrote the equation of a circle from a graph.  The kids did pretty well with the exit slip.  They will need some more repeated practice, but I think this lesson was a memorable way to hopefully help students remember how to graph and write equations of circles.