Instructional Note
This lesson requires students to engage in mathematical reasoning and works best if instructed in conjunction with the mathematics teacher.
Investigation 1: Considering Scale
Preparation:
Prior to class, instruct students to research how far their homes are from school.
Materials:
Copies of Readings
Instructional Sequence:
Begin by asking students to share how far their homes are from school. You can draw a rough map on the board, or create a simple Google Map.
After students have had the chance to share their data point, select one of the farther points on the class map, and ask âIs this home far from school?â Ask students how they judged whether the point was far or not. Record their answers on the board. Next, add an additional data point that is much farther than the one you originally selected. Ask students if they would still consider the original point âfarâ from school. Ask students why their thinking did or did not change.
After eliciting student responses, have students do a quick write on the following prompt âWhat information do we use to judge how far objects or places are from one another?â Use this quick write to assess student thinking and prior knowledge.
Now, begin to introduce the concept of scale. Ask students where they might have heard the term scale before. Possible responses might include a scale used to measure weight, a music scale, or a rating scale of 110. Based on the studentsâ responses, begin to craft a working definition of the term âscaleâ. Tell students that scales are important in helping us make sense of information. Refer back to the example of distance between home and school. The distance of the homes never changed, but depending upon what scale we were using, whether or not the distance seemed âfarâ might have changed.
You can post the working definition of âscaleâ in the classroom, and then have students refine it as they make sense of the term throughout the lesson.
Break students into small groups, and using a jigsaw strategy, provide each group with a reading about a different type of scale. Tell students that scale is a concept that is utilized to make sense of information in across a variety of STEM fields. Each group will be responsible for sharing responses to the following questions with the rest of the class.
Sample Scale Contexts
Geologic time scale
Architectural models
Scale maps
Atomic scale
Guiding Questions
Describe the scale you read about.
What information does the scale make sense of?
What types of tools are needed to gather the information?
What types of relationships does the scale reveal?
You can revisit the different contexts throughout the lesson to help students connect their thinking to disciplines beyond planetary scale.
Investigation 2: Categorizing Objects in Our Solar System
Materials:
 Chart paper
 Solar System Fact Sheets or Sorting Cards (*teacher must create)
 Paper/notebooks and pencils
 Computers with internet access
 NASA website: http://www.nasa.gov
 An example of a physical representation such as a Globe or Volcano with pictures of the real counterpart (if concrete examples are not on hand, a split screen pictures of model and real object should suffice)
Preparation:
Construct a set of classroom âPlanet Factsâ cards. You should make enough so that every team of two has at least one Planet Fact card for each planet. Great resources to use to create these cards:
http://spacefacts.com/planets/
http://mars.nasa.gov/allaboutmars/facts/
http://www.ride.ri.gov/Portals/0/Uploads/Documents/InstructionandAssessmentWorldClassStandards/Assessment/NECAP/ReleasedItems/G8ReferenceSheet0708.pdf
Also it may be helpful to get familiar with models and their limits for classroom discussion. Here are some resources:
http://www.nsta.org/publications/news/story.aspx?id=50431
http://www.britannica.com/EBchecked/topic/387006/scientificmodeling
For students who might be struggling, there are a number of great simulations that could be used to augment this lesson. Here are examples of NASA vetted simulations:
https://solarsystem.nasa.gov/multimedia/interactive.cfm
http://space.jpl.nasa.gov/
Additionally, when creating the Planet Fact cards, you can use images to help students who might struggle with reading.
Instructional Sequence
Transition by telling students that scale is very important in helping us better understand relationships between objects in our solar system. Inform students that the thinking they did in the previous exercise will now be used as a foundation for thinking about scale in the context of the solar system.
Have students thinkpairshare the following prompt: What are different objects that we find in our solar system?
 Planets
 Moons
 Comets, Asteroids, Meteors
 Sun
 Stars
After students have come up with a list of objects, ask students to use their science notebook to jot down some ways that the objects are similar and different. You can use this to assess student thinking and prior knowledge.
Next, let students know that they will be given a set of Solar System Fact cards. Allow them time to observe and read the information on each card. Then, provide students with the prompt: What are different ways we can sort, categorize, and group objects in our solar system? Encourage students to make a list and to draw from the similarities and differences they just brainstormed. Some ideas/variables they may come up with include:
 Size
 Distance from sun (and each other)
 Composition: chemistry, color, gases/atmosphere, etc.
 Planetary motion: Length of day, year
 Gravitational pull
 Possibility of Life
 Moons
Allow students to share their ideas on categorization. Create a studentgenerated list. Tell students that they will be working on ways to better understand one of the variables mentioned today.
Ask students how we can study the different variables listed. Using their responses, begin to transition to a brief discussion about models with the students. Possible prompt: What is a model in science? Why are models used? Allow students to share their thoughts.
You can add to student thoughts by discussing how scientists and engineers both use models as tools to help represent and communicate ideas, make predications, understand relationships, and generate (or produce) data for arguments and explanations. Models can take many different forms (diagrams, drawings, physical replicas, mathematical representations, analogies, and computer simulations), however, we will be focusing on physical replicas and measurements will be used to develop model design. Our models will help us understand relationships between objects in the solar system.
Show an example of a physical representation to students along with its real counterpart. For example, you can show them a globe and then a satellite picture of planet Earth. Engage in a discussion on models and their limits. Have them consider these items:
 What makes [the globe] an effective model, i.e., how does it resemble that which it represents (planet Earth)?
 What makes [the globe] an insufficient model, i.e., how does it differ from that which it represents (planet Earth)? (Share with students that these are considered limitations of the model.)
 How could the globe be used to make predictions, understand relationships, or produce data? If so, how?
 How could we improve [the globe] as a model?
Second example: If the students are familiar with geological phenomena (volcanic activity), a teacher can also use the everpopular clay volcano with a screen shot of a real one and ask:
 How is the model volcano like a real volcano?
 What are the limitations of this model?
 Can it be used to make predictions, understand relationships, or produce data? If so, how?
 How could we make it more like a real volcano?
Refer to the studentgenerated list of solar system categorizations. Remind students that they will be working on ways to begin the foundational work of modeling one of the variables mentioned today. You may want to use the following prompts:
 How could we make models of some of your ideas, using resources in and the space of this classroom, to understand some of these variables better?
Begin to focus in on one variable: Distance of each planet from the sun (and each other).
Ask students to work individually to create an annotated drawing of how they would represent the distances between planets and the sun. Use this drawing to assess studentsâ prior knowledge about distances in the solar system as well as their thinking about how to represent that information. For students who may struggle with this task, you can create a scaffolded worksheet that includes the names and images of the planets. Alternatively, you could have students work in small groups to complete the drawing, but you will lose some of the richness of an individual assessment activity.
Investigation 3: Technology and Models
Materials:
NASA webpage printouts: http://www.nasa.gov/audience/forstudents/912/features/telescope_feature_912.html
https://www.youtube.com/watch?v=ki6kQT7YPQY
Instructional Sequence:
Ask students how their annotated drawing might help them determine what next steps need to be taken to continue building their model. Using their responses, transition to having students think about how people obtain data that is used to build models. Ask students to work in small groups to brainstorm some examples of tools that can be used to gather data about objects in the solar system. Record student responses on the board.
After this short discussion, ask students to think about when each of the tools/technologies that they listed were developed. Which do they think came first? Why? What do they think prompted each advance?
Split students into small groups, and have them use the short article and/or video to create a minitimeline of advances in telescopes. They should include dates when possible, but also focus on what new information was accessible with each new telescope.
Remind students that a telescope is just one tool used to learn about the solar system, but it provides a great example of how scientific discovery and technological advances go together. Engineers develop advances in technology that allow us to make increasingly more accurate models. Ask students how they might use information gathered by complex technology to take the next step in building their models. Using student responses about what data might be available, begin to transition to the next investigation.
Investigation 4: Establishing a Distance Scale for Planets
Materials:
 Solar System Fact Sheets or Sorting Cards (*teacher must create)
 Paper/notebooks and pencils
 Computers with internet access
 NASA website: http://www.nasa.gov
 Various everyday round objects (e.g. cheerios, tennis balls, coins, DVDs, basketballs, frisbees, hula hoops, etc.)
 Yardsticks, rulers, measuring tapes
Instructional Sequence:
Remind students that theyâll be focusing on a single variable: distance. In order to do this theyâll first have to tease out only the data they need. Using the Planet Facts cards, have the students compile their data using the table below. Again, remind students that the information on these cards comes from technology that has been refined over time.
Planet 
Distance from the Sun 
Mercury


Venus


Earth


Mars


Jupiter


Saturn


Uranus


Neptune


Once the students have filled out the table, explain to them that youâve mocked up a model not for distance, but for planetary size, and that that may help them in the planning of their distance models.
Inform them that youâll be using Pluto as a reference point to figure out how you could model the size of the Earthâs diameter. (This is a great time to talk about why we no longer consider Pluto a planet). Use the following steps as guides:
 Give every student 10 cheerios.
 Have everyone hold one cheerio in the air. Inform them that that cheerio represents a scale model of Pluto.
 Write the â2,300 kmâ on the board. Tell them that Pluto is approx. 2,300 km in diameter, and in our first scale model one cheerio will represent that diameter. For reference, Plutoâs diameter is roughly the distance from Boston to Miami. Seems long, but thatâs an entire planet.
 If weâre using the scale of 1 cheerio = 2,300 km, how many cheerios would we need to represent the diameter of the Earth? Have students show their work and complete the Earth calculation on their own, and then pass it in. Remind them to refer to their Planet Facts card to find the diameter of Earth. (Itâs 5.5 cheerios)
Use this as an opportunity to assess studentsâ math skills. If you see that students are struggling, you can do a few more examples together or provide a worksheet to support their calculations.
 Have students work in small groups to complete the chart. After students have had time to work, use the following questions to guide a classroom discussion.
 What are the limitations of this model?
 Can it be used to make predictions, understand relationships, or produce data? If so, which of these can you use the model for and how?
Now that theyâve examined a way in which to use small objects to make a scale model of much larger ones, explain that their challenge is now to work in small groups to figure out a way to use a different object to construct a scale model of the average distances the eight planets are from the sun. (At this point you could choose to have some students come up to measure the various objects youâve amassed, or simply list the measurements). Remind them that the entire solar system model must fit within the confines of your ___ x ___ classroom.
To get students started, you can hold up two of the objects available to them. Select one of the larger objects and one smaller objects. Ask students to talk with their group about which object might make for a better basis for their scale and why. Also, prompt students to think about how many of each object is available to them. What amounts of each object will they need and how might this affect their selection? As students discuss, walk around the room and listen to the discourse. They should also jot notes in their science notebook as they discuss. This conversation is a way for you to assess student understanding and to redirect their thinking if needed.
Have your students fill in the following table with the data theyâll be using in order to construct their model:
Planet 
Distance from the Sun 
Scaled Distance from The Sun 
Mercury


1 (whatever object they choose)

Venus



Earth



Mars



Jupiter



Saturn



Uranus



Neptune



Things to remind students as they construct their scaled table:
 They are not attempting to represent the size of the planets
 Regardless of the total number of the objects they choose, their equivalency from The Sun to Neptune must fit within their classroom. Inform them that theyâre more than welcome to use yardsticks and/or measuring tapes during the construction of their table so as to ensure a good classroom fit.
 If they need to, they should refer back to how we scaled the Earth using one cheerio to represent Pluto. We are essentially doing the same thing but using the object of their choice to represent the distance from The Sun to Mercury.
Ask students to add the âLength of a Yearâ column shown below to their data chart:
Planet 
Distance from the Sun 
Scaled Distance from The Sun 
Approx. Length of a Year 
Mercury


1 (whatever object they choose)

88 days

Venus



224 days

Earth



365.25 days

Mars



687 days

Jupiter



4333 days

Saturn



10592 days

Uranus



30681 days

Neptune



60193 days

Ask students to compare the data in the columns in their table to see if they can find any patterns or trends. In their groups, ask students to discuss the relationship between a planetâs distance from the sun and its length of a year. They should be ready to discuss the relationship with the class when they share their scale and model.
At this point, you could ask students with high interest to return to the other variables they listed in investigation 2 and begin to think about how they might model those relationships. How would those models differ from the distance model they just created? Why wouldnât the model they just created work for properties such as gravitational pull?
Alternatively, you could ask these students to apply their thinking about scale to different disciplines. For example, you could return to the example of a geological time scale and ask them to investigate how that relationship could be represented.
For students who are struggling, provide opportunities for peer or teacher reviews while they are developing their own scale model. This will allow for targeted questioning and redirecting as needed.
Oral Presentations
To culminate the lesson, have each team create short oral presentations. Review the Presentation Rubric with students so they know how they will be assessed. Allow students to ask clarifying questions and provide examples of what a presentation that meets the rubric would include. Be sure that students know that they are not only sharing what they chose to use for their scale but also why they chose to use it.
As students work on their oral presentations, provide opportunities for teacher checkins. This will allow you to better support or redirect students who may not be on target to meet the rubric.
To add to the presentations, place The Sun on the board (or in a corner) and use that as the starting point for the teams to demonstrate the scale they created. During one of the presentations ask the class to think about and then share how their model could be modified to capture information about the length of the year. Ask the students how these models help them understand the relationship between the distance from the sun and length of the year.
WrapUp
Once the students have had a chance to experience the scales derived by their classmates, lead the group in a discussion about the benefits, challenges, and limitations of the scales theyâve created. During the discussion, students should take individual notes to create a recap of what theyâve done, what theyâve learned, and how they could improve upon these new understandings moving forward.
Key question prompts:
 How did our scale models help us to better understand the relative distance of the planets from the sun?
 What kind of data did we need to build our models? Where did that data come from? What did our scale models help us see that more easily than just looking at the raw data?
 What were the limitations of our calculations?
 What (if anything) would you have done differently if instead of using our classroom we used our gym? Or playground?
 Could we improve our model by having the planetâs sizes also be appropriately scaled? Why or why not?
 What did you like about this activity? What didnât you like?
 Letâs return to the definition of Scale that we originally created. Is there anything you would change now that youâve thought more deeply about this topic?
 Returning back to our original example, do you have new ideas about how we could model the distance between home and school?
 Can you think of any similar systems or sets of objects that we could better understand through the creation of a similar scale? This will help surface other cases where students might apply this learning and create a transition to the next lesson.
Finally, ask students âWhat canât our scaled calculations help us to better understand? What other information might we need to include in our model?â This will provide a transition to the next lesson where students can continue to build upon their understanding of interactions between objects in the solar system.