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 © NextLesson 2014 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: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific 8.EE.A.4 notation and choose units of appropriate size for measurements of very large or very small quantities Step-­‐up Activity Use numbers expressed in the form of a single digit times an integer power of 10 8.EE.A.3 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
Updated June 2014 Scientific Notation
(km)
3.97 x 1013
1 © 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
Updated July 2014 2 © NextLesson 2014 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
7.28 x 1013
Wolf 359
Rigil Kentaurus
Updated July 2014 Distance from Earth
40,681,141,032,097.445
3 © NextLesson 2014 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
Final your
Partexhibit by sketching each of the celestial objects and labeling the relative distance
Design
in km between each one. Try to use a scale and add in the light years for where you can.
Draw a sketch of the sun and the planets and stars discussed in this
project. The planets and stars should be in order from closet to the Sun
the furthest from the Sun. You should label each planet or star and write
its distance from the Sun in scientific notation. You can use your
creativity on how you would like to display your planets and stars.
Updated July 2014 4 © NextLesson 2014 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?
Updated July 2014 5 © NextLesson 2014 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
universe as a whole.
Milky Way – this is the galaxy of stars and
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 10 – 1.5 x 10 = 0.42 x 108 (Distance is always positive) Saturn Planet 1.43 x 109 – 0.15 x 109 = 1.28 x 109 8
8
Updated July 2014 © NextLesson 2014 ANSWER KEY 4. 5. It is five powers of ten farther from the sun or 10,000 times farther. 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 © NextLesson 2014 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
On-­‐the-­‐job Training
None 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