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Real World Performance Tasks
Real World
Real Life, Real Data, Real-Time - These activities put students into real life scenarios
where they use real-time, real data to solve problems. In the Stellar Performance series,
we use data from university astronomy sites and update our data periodically.
Note - some data has been rounded or simplified in order to adjust the math to the appropriate level.
Engaging
Relevant – Students today are very engaged by space travel – both fiction and nonfiction - making these
activities very relevant to student’s everyday lives.
Authentic Tasks - Through these activity sheets students learn how an astronomer uses data, and makes it
easier to understand, and are prompted to form opinions and ideas about how they would solve real life
problems. A glossary is included to help them with the unfamiliar terms used.
Modular
Principal Activity - The activity sheets always start with repeated practice of a core skill matched to a common
core standard, as set out in the Teacher Guide. This principal activity (or Level 1 as it is labeled to students) can
be used in isolation.
Step Up Activity - For the Level 2 questions, students are required to integrate a different skill or set of skills
with increasing complexity. The additional skills used to answer these questions are set out in the Teacher
Guide.
Challenge - This is designed to require critical thinking skills and stretch students to reason with math and data
to come to conclusions. They are matched up with one of the Common Core Standards for Mathematical
Practice. These activities work well with students in pairs or small groups where they can discuss the math.
Cross-Curricular Activity - Every activity sheet also includes a finale that you can use to extend the math lesson
into another subject (usually ELA). These could be assigned in a second lesson or for homework.
Customizable
All of the activity sheets are provided in Word so that they can be differentiated to add remove or edit
questions or even add space for students to show their work. Suggested customizations for each activity
sheet are given in the Teacher Guide.
Community
We would love you and your students to tell us about your experience. Join the conversation on Twitter
starting your tweet with @nextlesson and using #CosmicMath
Updated July 2014
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Operations with Scientific Notation
Teacher Guide
Sound bite for Students: “In the real world we frequently use scientific notation to make working with very
large and tiny numbers easier to manage.”
Skills Practiced:
Principal Activity (Level 1):
- Convert numbers to scientific notation
- Perform operations with numbers in scientific notation
Step Up Activity (Level 2):
- Compare magnitudes of very large numbers
Common Core Math Standards Addressed:
Principal
Activity:
Step-up
Activity
8.EE.A.4
Perform operations with numbers expressed in scientific notation, including
problems where both decimal and scientific notation are used. Use scientific
notation and choose units of appropriate size for measurements of very large or
very small quantities
8.EE.A.3
Use numbers expressed in the form of a single digit times an integer power of 10
to estimate very large or very small quantities, and to express how many times as
much one is than the other.
Differentiation Tips:
You can edit any of the activity sheets to:
- change the numbers or tasks given (e.g. reduce the number of problems)
- add or remove hints for differentiation purposes (e.g. use calculators to learn how to manage
scientific notation – highly recommended, give more examples or explain ways to work out the
answers)
- remove/add questions (have groups, instead of individuals complete the Challenge or Finale prompts
if time is short)
Due to school paper restriction, the spacing provided is only for answers. However, you could modify the
spacing to add room for work if desired.
Updates:
At NextLesson we strive to engage students with data that is real and real-time. This lesson uses data as of
June 2014. Please come back for the most recent updates.
Updated July 2014
© NextLesson 2014
Name: ________________________________
You are an astronomer designing an interactive
exhibit for the local science museum. By
navigating through the various elements of your
exhibit, visitors will learn about relative sizes,
distances, and other interesting facts about the
Milky Way.
Your Challenge: How far away from
us are the planets and stars?
LEVEL 1
You must compile the following data before you can determine the scale of your exhibit.
1.
Convert to Scientific Notation to complete the missing information in the table.
Celestial Object
Category
Distance from Sun (km)
Saturn
Planet
1,426,725,400
Uranus
Planet
2,870,972,200
Neptune
Planet
4,500,000,000
Venus
Planet
108,208,930
Proxima Centuri
Star
39,700,000,000,000
Jupiter
Planet
778,412,020
Earth
Planet
150,000,000
Pluto
Former Planet
5,906,376,200
Mercury
Planet
57,909,175
Mars
Planet
227,936,640
Barnard’s Star
Star
56,700,000,000,000
Scientific Notation
(km)
3.97 x 1013
1
Updated June 2014
© NextLesson 2014
You’ll want visitors to understand the order of the planets and celestial objects as they
move away from the Sun.
2.
Reorder the celestial objects from closest to the sun to the farthest away. You also want to
provide information on how close the planets are to Earth.
3.
Using information from the previous table, write the equation needed to find the distance
from Earth to the planets listed and then find the answer.
Celestial
Object
Distance from Earth (km)
(Equation)
Distance from Earth
(Scientific Notation)
Neptune
4.5 x 109 - 0.15 x 109 =
4.35 x 109 km.
Mercury
Mars
Jupiter
Venus
Saturn
Uranus
2
Updated July 2014
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LEVEL 2
You want to have some facts visible so visitors really understand how much further away different
planets and other celestial objects are.
1.
How many times farther from the Sun is Proxima Centuri than Venus?
2.
Approximately how many times farther from the Sun is Jupiter than Earth?
3.
How much farther from the Sun is Barnard’s Star than Pluto? Proxima Centuri than Pluto and
Uranus? Use powers of ten and estimate.
4.
Come up with three more facts comparing relative distances from the sun between two
different celestial objects.
5.
The museum would like you to add more stars to your exhibit plan. You’ll need to quickly
determine their distances from the Sun and from Earth.
Celestial Object
Distance from the Sun
(km)
Procyon B
107,852,327,387,421.12
Wolf 359
Rigil Kentaurus
Distance from Earth
7.28 x 1013
40,681,141,032,097.445
3
Updated July 2014
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Challenge
One kilometer is equal to 1.05702341 x 10-13 light-years. Determine the distance, in light-years to
the sun and to Earth. Rank the celestial objects in the last column from closest to the Sun (1) to
farthest from the Sun (5).
Celestial Object
(light-years)
Distance to Sun
(light-years)
Distance to Earth
(light-years)
Ranking
Bernard’s Star
Pluto
Proxima Centuri
Uranus
Mercury
Design your exhibit by sketching each of the celestial objects and labeling the relative distance
in km between each one. Try to use a scale and add in the light years for where you can.
4
Updated July 2014
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Finale
You could give students one of the following ideas or have them choose themselves.
1. Draw a diagram that displays the relative distances of the above celestial bodies, using an
appropriate scale to represent one light-year. Take your diagram to a 3rd grade classroom and
explain the relative distances. Alternatively, display with QR codes linking to an audio file of you
explaining your diagram.
2. Research the definitions of one parsec and one astronomical unit, which are more commonly
used in astronomy. Create an infographic for museum visitors that shows these distances in terms
that make sense to them. Design an Excel spreadsheet to prepare the data, using the distances
provided in Stellar Performance. Create two new columns and apply the appropriate formulae to
convert distances to parsecs and astronomical units, and then use this data to create your
Infographic.
3. Research the location of the International Space Station and create a diagram as in #1 that
includes the nearby celestial objects and the distances to launch points on Earth. Add audio QR
codes that give more information about the history and future of the International Space Station.
4. Go to the NASA website for the Jet Propulsion Lab (http://voyager.jpl.nasa.gov/). Look up the
current position of Voyager One. Determine when Voyager One will pass Proxima Centuri and
follow its path beyond.
5. Research how NASA and astronomers determine distances between planets, stars, and the Sun.
Create an Infographic that clearly shows how they do it and what their assumptions are. How
accurate are they?
5
Updated July 2014
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Glossary
Astronomer – an expert in astronomy.
Light year – a way to measure distance in
1.
space, where one light year is equal to the
2. Astronomy - the branch of science that distance that light would travel in one year.
deals with celestial objects, space, and the
Milky Way – this is the galaxy of stars and
universe as a whole.
planets that contains our Solar System.
Celestial object - any of the natural objects
that can be seen in our sky, including stars, Solar System - the collection of eight
planets, moons, asteroids, galaxies, and planets (including Earth) and their moons in
comets
orbit around the sun.
Exhibit – a public display in a gallery or
museum.
Updated July 2014
© NextLesson 2014
ANSWER KEY
LEVEL 1
1.
Note: Depending on the rounding method used or required in your classroom, the answers in the
table may be slightly different from your student’s response.
Celestial Object
Saturn
Uranus
Neptune
Venus
Proxima Centuri
Jupiter
Earth
Pluto
Mercury
Mars
Barnard’s Star
2.
Category
Planet
Planet
Planet
Planet
Star
Planet
Planet
Former Planet
Planet
Planet
Star
Distance from Sun (km)
1,426,725,400
2,870,972,200
4,500,000,000
108,208,930
39,700,000,000,000
778,412,020
150,000,000
5,906,376,200
57,909,175
227,936,640
56,700,000,000,000
Scientific Notation (km)
1.43 x 109
2.87 x 109
4.50 x 109
1.08 x 108
3.97 x 1013
7.78 x 108
1.50 x 108
5.91 x 109
5.79 x 107
2.28 x 108
5.67 x 1013
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, Proxima Centuri, Barnard’s
Star
ANSWER KEY
LEVEL 2
3.
See below:
Celestial
Object
Category
Distance from Earth (km) (Equation)
Distance from Earth
(Scientific Notation)
Neptune
Planet
4.5 x 109 - 0.15 x 109 =
4.35 x 109 km.
Pluto
Planet
5.91 x 109 - 0.15 x 109 =
5.76 x 109
Mars
Planet
2.28 x 108 – 1.5 x 108 =
0.78 x 108
Bernard’s
Star
Star
5.67 x 1013 – 0.000015 x 10 13 =
5.67 x 1013
Venus
Planet
1.08 x 108 – 1.5 x 108 =
0.42 x 108
(Distance is always
positive)
Saturn
Planet
1.43 x 109 – 0.15 x 109 =
1.28 x 109
Updated July 2014
© NextLesson 2014
ANSWER KEY
4.
It is five powers of ten farther from the sun or 10,000 times farther.
5.
Celestial Object
Distance from the Sun (km)
Distance from Earth
Procyon B
Wolf 359
Rigil Kentaurus
107,852,327,387,421.12
72,800,000,000,000
40,681,141,032,097.445
1.08 x 1014
7.28 x 10 13
4.07 x 1013
ANSWER KEY
Challenge
Note: Depending on the rounding method used or required in your classroom, the answers in the table may
be slightly different from your student’s response.

Celestial Object
(light-years)
Distance to Sun
(light-years)
Distance to Earth
(light-years)
Ranking
Barnard’s Star
5.993194729
5.993178874
5
Pluto
6.24687 x 10-4
6.08832 x 10-4
3
Proxima Centuri
4.196293311
4.196277456
4
Uranus
3.03359 x 10-4
2.87504 x 10-4
2
Mercury
6.12 x 10-6
9.735 x 10-6
1
How much farther from the Sun is Barnard’s Star than Pluto? Proxima Centuri than Pluto and Uranus?
Use powers of ten and estimate it!
Students should use powers of ten to estimate. Barnard’s Star is about 10,000 times farther from
the Sun than Pluto. Proxima Centuri is also about 10,000 times farther from the Sun than Pluto and
Uranus.
Updated July 2014
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Job Background
Quick Facts: Physicists and Astronomers
2012 Median Pay
$106,360 per year
$51.14 per hour
Entry-Level Education
Doctoral or professional degree
Work Experience in a Related Occupation
None
On-the-job Training
None
Number of Jobs, 2012
23,300
Job Outlook, 2012-22
10% (As fast as average)
Employment Change, 2012-22
2,400
What Physicists and Astronomers Do
Physicists and astronomers study the ways in which various forms of matter and energy interact. Theoretical
physicists and astronomers may study the nature of time or the origin of the universe. Physicists and
astronomers in applied fields may develop new military technologies or new sources of energy, or monitor
space debris that could endanger satellites.
Work Environment
Physicists and astronomers spend much of their time working in offices, but they also conduct research in
laboratories and observatories. Most physicists and astronomers work full time.
How to Become a Physicist or Astronomer
Physicists and astronomers need a Ph.D. for most research jobs. Many physics and astronomy Ph.D. holders
typically begin their careers in temporary postdoctoral research positions.
Pay
In May 2012, the median annual wage for physicists was $106,840. The median annual wage for astronomers
was $96,460 in May 2012.
Job Outlook
Employment of physicists and astronomers is projected to grow 10 percent from 2012 to 2022, about as fast
as the average for all occupations. Expected growth in federal government spending for physics and
astronomy research should increase the need for physicists and astronomers, especially at colleges and
universities and national laboratories.
Updated July 2014
© NextLesson 2014