Large numbers Orders of magnitude and proportional reasoning

One D One D Ten Ds Ten Ds Fifty Ds Fifty Ds How can you represent the length of 100 D’s and make it fit on the screen? How can you represent the length of 100 D’s and make it fit on the screen? Length scale by a power of ten D DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Very large and small distances How do we represent large and small distances relative to each other? How do we represent large and small distances relative to each other? We use models to visualize what we can’t see with the naked eye. We use models to visualize what we can’t see with the naked eye. Representations of atoms, molecules, and planets are a few examples of using this idea. Representations of atoms, molecules, and planets are a few examples of using this idea.

What can you see? Is it possible to see an inch and a mile at the same time? Is it possible to see an inch and a mile at the same time? How about 1 inch and 10 miles? How about 1 inch and 10 miles? How about 1 inch and 100 miles? How about 1 inch and 100 miles? We use scaling to represent large distances so we can make sense of how far a large distance really is. We use scaling to represent large distances so we can make sense of how far a large distance really is.

How far is it…? To Taco Bell? To Tucson? About.5 miles About 100 miles

Relative size Maps use the idea of scaling Maps use the idea of scaling If one inch represents one mile, how many inches would you need from Mesa, AZ to Tucson, AZ? If one inch represents one mile, how many inches would you need from Mesa, AZ to Tucson, AZ? What are the units for this scale? What are the units for this scale? Is this a reasonable size for a useful model? Is this a reasonable size for a useful model? What might be a better representation? What might be a better representation?

How far is it…? To the moon? To the sun? 220,000 miles 93 million miles

Scaling using a proportion If we want to use a dry erase marker to represent the distance from the earth to the moon, what would the scale of the marker be? Remember to include the units!!! If we want to use a dry erase marker to represent the distance from the earth to the moon, what would the scale of the marker be? Remember to include the units!!!

Scaling using a proportion How many markers would be needed to represent the distance from the earth to the sun? How many markers would be needed to represent the distance from the earth to the sun? How many markers to represent a light year (about 5,850,000,000,000 miles)? How many markers to represent a light year (about 5,850,000,000,000 miles)?

Planet size If the Earth (d=7,900 miles was represented using a tennis ball (d=2.5 inches), how big would a ball that represents the Jupiter (d=89,000 miles) have to be? If the Earth (d=7,900 miles was represented using a tennis ball (d=2.5 inches), how big would a ball that represents the Jupiter (d=89,000 miles) have to be? Discuss the technique your group used to solve the problem. Discuss the technique your group used to solve the problem. Do we know of a ball this size that we could use for this model? Do we know of a ball this size that we could use for this model?

The Sun How big would the ball that represents the sun (d=870,000 miles) have to be with the tennis ball representing earth again? How big would the ball that represents the sun (d=870,000 miles) have to be with the tennis ball representing earth again? What ball would you use to represent the sun? What ball would you use to represent the sun? Can you design a better model to compare the earth and the sun? Can you design a better model to compare the earth and the sun?

Your assignment Develop a model for all of the planets in our solar system. Include the Earth’s moon and the Sun, but don’t include Pluto. Make sure the representation you create is to the actual scale. See the handout for actual size of the planets. Develop a model for all of the planets in our solar system. Include the Earth’s moon and the Sun, but don’t include Pluto. Make sure the representation you create is to the actual scale. See the handout for actual size of the planets.

Teacher resources Planet Sizes Planet Sizes Planet Sizes Planet Sizes Galaxy model Galaxy model Galaxy model Galaxy model

How far is far? Length of a ruler,1 foot Length of a ruler,1 foot Distance from floor to the basketball rim, 10 ft Distance from floor to the basketball rim, 10 ft Distance from one end of a basketball court to another, 94 feet Distance from one end of a basketball court to another, 94 feet Distance from campus to Taco Bell and back, 1 mile Distance from campus to Taco Bell and back, 1 mile Distance from campus to Scottsdale Fashion Square, 12 miles Distance from campus to Scottsdale Fashion Square, 12 miles Distance from campus to Tucson, approx. 100 miles Distance from campus to Tucson, approx. 100 miles Distance from campus to Dallas, TX approx 1000 miles Distance from campus to Dallas, TX approx 1000 miles

More on lengths The diameter of the earth at the equator is 7, miles (12, kilometers). The diameter of the earth at the equator is 7, miles (12, kilometers). Halfway to the moon approx 110,000 miles Halfway to the moon approx 110,000 miles To the moon- 384,400 km (220,000 miles) To the moon- 384,400 km (220,000 miles) Travel from the earth to the moon nine times 1 million miles Travel from the earth to the moon nine times 1 million miles To the sun- 149 million km (average) or about 93 million miles (average) To the sun- 149 million km (average) or about 93 million miles (average) One billion miles (from the earth to the sun and back almost 5.5 times) One billion miles (from the earth to the sun and back almost 5.5 times) One light year 5,850,000,000,000 miles—about 6 trillion miles. One light year 5,850,000,000,000 miles—about 6 trillion miles.about 6 trillion milesabout 6 trillion miles Or travel from the earth to the sun and back about 31,500 times Or travel from the earth to the sun and back about 31,500 times Or travel from the earth to the moon and back 13,300,000 times Or travel from the earth to the moon and back 13,300,000 times

Milky Way Galaxy Our galaxy is about 100,000 light years across. If we have a model of the galaxy that is the size of this room (25 feet across), how big would the earth be? Our galaxy is about 100,000 light years across. If we have a model of the galaxy that is the size of this room (25 feet across), how big would the earth be? Milky Way Milky Way

How big is the universe? We can observe only a portion of the entire universe. Because the universe is only about 14 billion years old, light has only had about 14 billion years to travel through it. Therefore, the most distant regions of the universe we can see are about 14 billion light-years away. This is the extent of the "observable universe," but the entire universe is probably much larger. It could even extend infinitely in all directions. -from Hubblesite.org