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# How far is that?

Lesson 15 of 22

## Objective: SWBAT to describe relative distances of objects using scientific notation and the distance formula

## Big Idea: It is easy to write numbers for amazing distances, but it is a challenge to find a way to make sense of these quantities.

*60 minutes*

#### Start Up

*5 min*

The basic question that we ask in this lesson is "how far is that?" We find different ways to quantify "far" by looking at time, distance, rate, and cost. We examine different objects in space and calculate how far that object is by understanding how long it would take to get there.

We start with a quick review of the formula **distance = rate * time** by asking a simple question:

An object is 100 kilometers away and you are driving 5 kilometers per hour. How long would it take you to get there?

The conversation is not just about the answer here, but about the relationship between distance, rate, and time. Students need to recognize that d = rt and t = d/r and r = d/r. Having this flexibility and understanding this fact family will help them navigate the questions we will ask them in this lesson.

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#### The Andromeda Galaxy

*10 min*

Here we combine science and make believe. I show the class this image of the andromeda galaxy and then show them the image of this road bike. I ask, "how long would it take to ride this bike to that galaxy?"

Here the conversation takes on the imagined parts of this question, where students need to imagine that there is a way to simply ride your bike in space and we need to imagine that the speed on that journey has some type of average. I tell the class that a fast average speed accomplished by Tour de France riders is 28 mph or about 45 kph. Together we create the imaginary scenario for this problem and agree upon the imaginary speed the bike would take on to get there.

Whatever the speed, we know that the andromeda galaxy is about 2.5 million light years or 2.4 x 10^19 km from Earth. I give the students around 3 minutes to solve the problem and then we share.

I start with the bicycle problem because it avoids the need to calculate fuel. But I use the problem as an opportunity to start discussing variables in cost.

- What if we drove?
- What if we included the cost of food and gear?
- How does the problem change with each new parameter?

The goal is to get students ready for a future project in which they will model the cost of a trip to a far away place.

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#### Cars in Space

*25 min*

In this part of class, students pick two vehicles and one new object in space. They need to figure out how long it would take to drive to the Andromeda Galaxy and to new object with either vehicle. I also give them opportunities to calculate cost in terms of food, gas and repairs.

I print the vehicles and objects in space on cards and tape them to the board. Students pick one object and pick two vehicles. The cards are taped with the image side down. These keeps the choices somewhat random. The cards contains photos and distances in light years. The vehicles contain images and speeds in kilometers per hour.

**The instructions for the activity are simple:**

- How long would it take for your vehicle to "drive" or "travel" to each space destination?
- Round your speeds down by 1 km/h. Predict how much longer it would take to get your destination.
- Calculate how much longer it would take if you slowed your vehicles down by 1 km per hour. Compare this to your prediction. What are your thoughts?
- Could you figure how much this trip would cost?

Before the students begin, I ask them how they will solve these problems and what they need to know in order to be successful. When they mention something like, "we need to know how far a light year is," I give them the print out with that information. I give them a print out because I like to give them a sheet that I can collect.

**Resources**

- The sheet usually just has this image on it: Light Years to Kilometers
- For each object that is traveling, I save the speeds values in the file name. For example, the Thrust SCC travels at 1228 km per hour: 1228 km:h ThrustSSC
- I used these two sites to get all the objects (I have about 16, enough for each partnership in my class). All the objects are in the resource section.
- I used this list of fastest production cars:Fasted Production Cars
- I also used this list for vehicle speeds:Vehicle Speed Records
- The space destinations are also all included in the resource bin, with file names giving the name of the destination and the distance in Light Years. For example, the Orion Nebula is 1500 Light Years from Earth, so that file is saved as:1500 Ly Orion Nebula

I use about 8 destinations, but print out 16 copies so that each partnership can work on their own destination.

**Resource Note**: I tried to pick images that aren't heavy on black ink, but since each image is intense, I print out one set for all the classes to use and laminate the images. I set the printer to print at a reduced darkness to save ink as well. If ink is a major issue, just give them the numbers on the cards and display the digital images on the projector when you do your summary.

**Sources for Eye Candy and other fun things**:

- You can find wonderful images on the wired space photo series here. Many of the images don't include distances, but those are easy to search online.
- The Hubble Site is also fantastic and the source of many of our best in space images.
- My other "go to" source for space images is the NASA site

##### Resources (26)

#### Resources

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#### Summary

*20 min*

The goal here is for the students to share their findings. I have few groups present and display the photos of their vehicles and space destinations and share results. I record their findings on a table for all to see and talk about the impact of speed on time.

Students are surprised to see the time differences in vehicles fairly close in speed. The idea is that these *incredible* distances magnify the impact of a small change in speed. This is a sharp contrast to our daily lives. If we are driving 5 miles with an average speed of 40 mph versus 50 mph, how much time would we save? Does this small change in speed have a big impact?

I end the discussing by discussing the resources I used to find these images (mentioned in the previous section here) and ask student to start thinking about their own comparisons for one of the projects in this unit (described in another lesson section here. The project is called "Long Distance Relationships.")

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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: Units and Vast Systems of Measurement
- LESSON 2: Adding and Subtracting in Scientific Notation
- LESSON 3: Mad Libs and Math Libs
- LESSON 4: Yuck! Word Problems...
- LESSON 5: The World of Microns
- LESSON 6: 100 People: An Assessment
- LESSON 7: Khan Academy and Scientific Notation Intuition
- LESSON 8: Khan Academy and Scientific Notation Conversions
- LESSON 9: Khan Academy and Orders of Magnitude
- LESSON 10: Khan Academy and Multiplying and Dividing with Scientific Notation
- LESSON 11: Khan Academy and Computations in Scientific Notation
- LESSON 12: Khan Academy Patterns in Zeros
- LESSON 13: Delta Math and Scientific Notation
- LESSON 14: Video Quiz (Alternative Assessment)
- LESSON 15: How far is that?
- LESSON 16: Long Distance Relationships Project
- LESSON 17: Long Distance Relationship Follow Up
- LESSON 18: How big is that?
- LESSON 19: The Universcale (A Project)
- LESSON 20: Universcale Project Follow Up
- LESSON 21: The Digital Scientific Notation Worksheet
- LESSON 22: The Cost of the Death Star