Author: MaryAnn Moore
My students tested on Monday-Wednesday of this week. For me, the worst part of testing is the lack of teaching. All day long I'm in the same room with my students, but can't teach them, talk with them, or laugh with them. It had a seriously negative impact on my happiness levels. Thank goodness for Thursday! As always, I didn't cover the entire 8th grade core before the test. The next item on my teaching agenda was Scientific Notation. I didn't want to dive into it too deeply on Thursday, though, since several students would be missing my class to finish testing. Enter my very favorite introduction to scientific notation and powers of ten: Cosmic Zoom.
Cosmic Zoom is an iMAX movie narrated by Morgan Freeman. It's about 30 minutes long, but I never watch the whole thing with my students. About seven minutes into the movie, they start zooming out by powers of ten to the furthest limits of the known universe. Then they zoom in on a single-celled paramecium and continue to zoom in to quarks - the smallest known building blocks of matter. I usually stop the video at this point.
Of course with Morgan Freeman narrating, he could be reading the phone book and I could just press play and watch my students slip into a peaceful trance. However, I like to milk this video for all it's worth so I created some warm-up viewing guides to go along with it.
I love watching and listening to my students react to this video! What is most interesting to me is that I usually get the strongest reactions from some of my lowest performing students. They seem astounded to realize how very small they are in comparison to the rest of the universe. And they ask some of the very best questions during the movie! They wanted to know how light can exist in space. They wanted to know how long it would take to travel to the edge of the solar system. One girl asked how long a light-year was and I realized from the way she stated the question that she was considering light-years to be a unit of time. We talked about how we could create a unit of measure called a Lexie-Year by setting Lexie out on the road and asking her to keep moving for an entire year and then using that distance as our new unit. This seemed to be a very acceptable answer. As we've worked with Estimation 180 warm-ups this year, my students have gotten much more flexible in their thinking about units of measure. In fact one of my classes has started using one of their classmate's heads as a unit of measure. "I think that'd be about 2.5 Lucas-heads." So it wasn't too big of a stretch to jump from thinking about Lexie-years to light years both as a unit of length.
After watching the video, I asked my students if we were zooming out at the same speed at the end of the cosmic zoom as we were at the beginning. Almost all students agreed that the speed increased as we zoomed out, but there was some confusion about what happened as we zoomed in on the paramecium. Eventually they agreed that if zooming out meant increased speed, then zooming in must mean decreased speed.
And because I can't help myself, I had my students turn their viewing guides over and we created a graph of the speed on the back. Interesting conversations about how to label the axes! What are the variables? Which label goes on the x-axis? Why? Once we got them labeled, I asked all of the students to trace in the air the shape the graph would make. Almost unanimous:
And of course, one has to make zooming sound effects when tracing this graph in the air. :) There was also some disagreement about where to place the y-intercept. At the beginning, my students placed it at zero, but then weren't sure what to do for the negative powers of ten. How can you have negative speed? Eventually they agreed to move the y-intercept up a little bit on the y-axis.
Inventing Scientific Notation
The next day, when I had the majority of my students back in class, we dived into the nuts and bolts of scientific notation, using this lesson by Dan Meyer. To make it easier to present, I created my own set of google slides based on the slides in Dan Meyer's post. Feel free to use the google slides, but lease read Dan Meyer's blog post, or they won't make sense at all. (Let me tell you, it's a pretty fun thing to see the looks on your students' faces when you tell them to get out their math notebooks and write down the word New Hampshire.)
My favorite adaptation to this lesson came from a question that student asked, "Why does it have to be 5.12 x 10^7? Why couldn't we write it as 51.2 x 10^6?" I explained that both were mathematically accurate but that using one digit to the left of the decimal is just an agreed upon norm - sort of like how driving on the right side of the road is an agreed upon norm. There wouldn't be anything wrong with driving on the left side - and some countries do - but if everyone decided to drive wherever they wanted, mass chaos would ensue. In fact, in later classes, I specifically asked students to give me alternate but mathematically correct ways to write 5.12x10^7 just so we could talk about this issue. Hence the slide about which side of the street is the correct one to drive on.