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# Astronomical Units

Lesson 16 of 21

## Objective: SWBAT to use scientific notation to create an appropriately scaled model of the solar system

*60 minutes*

#### Start Up

*30 min*

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.

Then I give each group a table: AU Table and print out of a planet: 09_planet_image_cards , card_saturn, card_jupiter

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).

*expand content*

#### The Pluto Files

*30 min*

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:

Credit: YouTube

From there I agree with Krall (the author of the blog). Here is what he wrote for steps to approach the video:

- Show the Intro & Mercury clip
- Get some predictions.
- Reveal just the Mercury solution. Show some of the calculations involved. You can find all the heavenly body sizes from our solar system here or here.

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:

Credit: YouTube

The question about Pluto still remains. First we can find the relative size of Pluto. Again, repeat the process but use this video:

Credit: YouTube

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).

*expand content*

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- UNIT 1: Starting Right
- UNIT 2: Scale of the Universe: Making Sense of Numbers
- UNIT 3: Scale of the Universe: Fluency and Applications
- UNIT 4: Chrome in the Classroom
- UNIT 5: Lines, Angles, and Algebraic Reasoning
- UNIT 6: Math Exploratorium
- UNIT 7: A Year in Review
- UNIT 8: Linear Regression
- UNIT 9: Sets, Subsets and the Universe
- UNIT 10: Probability
- UNIT 11: Law and Order: Special Exponents Unit
- UNIT 12: Gimme the Base: More with Exponents
- UNIT 13: Statistical Spirals
- UNIT 14: Algebra Spirals

- LESSON 1: The Sand Reckoner
- LESSON 2: How High Can You Count?
- LESSON 3: The Mechanics of Scientific Notation
- LESSON 4: Deconstructing Standard Form
- LESSON 5: Fluency with Large Numbers
- LESSON 6: Ongoing Assessment during the Scientific Notation Unit
- LESSON 7: One Quadrillion Yen
- LESSON 8: Fabulous Fab
- LESSON 9: Sand, Stars and Water Drops
- LESSON 10: Strings for Small Numbers
- LESSON 11: Fluency with Small Numbers
- LESSON 12: Homework and Scientific Notation
- LESSON 13: Million and Billions and the Business of Microsoft
- LESSON 14: Don't Eat the Hot Sauce
- LESSON 15: The Powers of 10
- LESSON 16: Astronomical Units
- LESSON 17: The Most Annoying Sound on Earth
- LESSON 18: Products and Quotients in Scientific Notation
- LESSON 19: Study Time (Game)
- LESSON 20: 1.21 Gigawatts
- LESSON 21: Can You Buy the Xbox One?