The Powers of 10
Lesson 15 of 21
Objective: SWBAT to compare large and small numbers and understand the context and units associated with some of these numbers
This is my favorite lesson, hands down. For this lesson, I run the "cold open." This means that students are launched right into the lesson within the first minute of class. The setting for this lesson is "the math movies," I print out some type of movie ticket with a few math trivia questions on it. The questions are basic and related to powers of ten. I usually choose common misconceptions that I saw during the unit, but typical questions include stuff like "what does 10^0 equal?" and "does does 10^-2 equal 1/10, 1/100 or 1/1000?" The same questions are posted up as they would be during the beginning of a movie (think of those cheesy trivia questions).
After about a minute, I turn the lights off and say "welcome to our movie. Its time to blow your minds!" I prefer using the IMAX movie "Cosmic Voyage," but this might only be because Morgan Freeman is the narrator. You can also use the classic version.
Both videos will have the same effect, they will amaze your students. Just let the movie run and work its magic. I circulate and make small comments to the students, but I try not to distract them from the film. Instead I make sure they are focused on the film and thinking about the meaning of the images and scale unfolding before their eyes (the films are about 10 minutes).
Sometimes I include a brief presentation of the powers of ten before the movie (it helps some classes focus): Powers of Ten
Here we recap what happened in the video. I start by giving students 2 minutes to transition (get out their supplies, etc). Then I approach the review in different ways, but each seem equally effective. Regardless of the method, it is critical to include units, because that will add context to this discussion. I also make sure that I have meter sticks on each table (for reference).
Method 1: Replay Cosmic Voyage and pause it at key moments. Each time I pause, I ask students what number he mentioned and how they would write that in scientific notation. I ask them to write this number in standard form and scientific notation and sketch a picture or make a remark about the visual that accompanied the number. For example, they might write 1 meter = 10^0 meters and then sketch the hoola hoop at the start of the video with a diameter of 1 meter.
Method 2: I switch to the classic video, but use the website with preloaded slide images. I print these images for students and hand them out for note taking. Here they would write the appropriate number in standard and scientific notation and then make a note about the image, describing what they saw in the picture and labeling the dimensions around the image. For example, they are given a 1 meter square at the start, showing two people laying on the grass. They would label the square sides with 1m and 1m and make a quick note on the side, "people laying in grass."
As we go between powers, I ask questions like, "how many times larger is this measurement?" I want students to clearly recognize that when we go from 10^a to 10^a + 1, we are multiplying by ten and when we go from 10^a to 10^a-1 we are dividing by 10.
Here we play a game. I print out four copies of the images listed in the resource section. I also print four copies of the powers of ten labels. I laminate them so they will last and then place them into puzzle packets. The idea is to create a game in which groups can work together and solve a challenging puzzle.
I give students a number 1,2,3 or 4 and split them up into teams. The rules are simple:
1. You must not talk unless I tell you to (I give them a few 30 second chunks where they can talk)
2. You must respect each other
3. Everyone needs to help
I don't tell students what the task is (that is part of the fun). Instead I give each team a pack and say, "without talking, figure this out." They don't know it, but their task is to sort the images by their magnitude and then match the appropriate scientific notation label to the picture. This is a variation of the zoom books by Istvan Banyai
Students can do this amazingly fast and will surprise you. If some students are done ahead of time, I give them a challenge question, like "Approximately how many light years would we travel if we went 10^100 meters." To solve this they can use the highest card in their puzzle (or any card that mentions light years). They have a chance to communicate without talking. After all groups are finished, we talk about the experience and show things that tripped them up. I show the powerpoint to keep track of our findings.