When students enter the room, I show them two rendering of the solar system and which one is better?
Image 1: Solar-system
Image 2: The_Solar_System_by_ChiSpaceArt
I ask them questions like, "how could you figure out which one is more accurate without seeing any specific numbers?" Here the idea is that the uniform distribution of the planets in Image 2 somehow doesn't seem believable. Instead, the somewhat random distribution of planets in image 1 seems more natural. It seems to fit the chaos of the universe.
I tell students that they are going to build a model of the solar system as a class with a reference of 1 astronomical unit as 149,597,870,700 meters and is the distance from the Sun to Earth. Here the first question is, how do we want to estimate this number? Students can debate if 150,000,000,000 meters is acceptable and why? I go forward with whatever consensus there is in the class.
Next we think how we can represent this distance with the tools we have and agree on something simple, like 10 inches or 10 centimeters equals 1 AU.
Each group of 4 will be responsible for finding the precise location of their planet on the wall. If they finish early, they can work on the extension questions: AU Extensions
Before they launch into their investigation, I review the one hint in the table. Students need to calculate the AU for each planet and they see the result for Earth as 1. This implies an algorithm (the mean distance of the Earth from the sun divided by itself would give 1 AU). This might help them see that they have to divide the total distance by the Earth distance to find each AU. They might also notice that Pluto is missing, but that is something we come back to at the end.
After they have had a chance to complete their tables, I have each group place their planet on their wall at a distance that they calculated. They present their result to the class and check for agreement. When we are finished we compare our model to the two images at the start and see which model is more like ours (which is certainly pretty accurate).
Neil DeGrasse Tyson is an inspiration for anyone who is into science or math. Fortunately, a great blog called Emergent Math called out an opportunity to bring Tyson's energy into a math lesson.
Here, the idea is to model the size of each planet (something we previously ignored) and the location of each planet. There will also be some excitement because we left Pluto out of our previous calculations and of course there is some controversy as to whether it should be considered a planet.
I would start with their clip from the Pluto files:
From there I agree with Krall (the author of the blog). Here is what he wrote for steps to approach the video:
I would alter the table representing diameters or sizes of planets to be in scientific notation. The students will then be more likely to develop their division algorithm for scientific notation in solving these types of problems.
Once students have a chance to assess the size of the Sun in comparison to the model, they can do the same with Mercury. I would review their results and confirm their numbers with the video (scroll through this link:PBS. You can cue this up to play at the location you need.
Then, you can repeat the process with Saturn. Here is the link to the Saturn video:
The question about Pluto still remains. First we can find the relative size of Pluto. Again, repeat the process but use this video:
As for the location, Tyson mentions that there isn't enough room in the field in the video to fit Pluto (based on the model they built). After we justify this with our calculations, we need to ask, "would Pluto fit on our model?" We finish class by placing Pluto in its original location. Here I want students to understand that we are able to represent the location of Pluto because of our choice of AU (or not able to if our AU is too large).