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NASAs Supernova Mathematics Janet Moore NASA Educator Ambassador Janet Moore NASA Educator Ambassador 1 NCTM Chicago Regional November 29, 2012 NCTM Chicago Regional November 29, 2012

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The NASA E/PO Program at Sonoma State University A group of people working collaboratively to educate the public about current and future NASA high energy astrophysics/astronomy missions. Led by Professor Lynn Cominsky A group of people working collaboratively to educate the public about current and future NASA high energy astrophysics/astronomy missions. Led by Professor Lynn Cominsky Swift Fermi (GLAST) XMM-Newton

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Three Supernova Activities Fishing for Supernovae Crawl of the Crab Magnetic Poles and Pulsars Three Supernova Activities Fishing for Supernovae Crawl of the Crab Magnetic Poles and Pulsars 3 Three Supernova Activities Fishing for Supernovae Crawl of the Crab Magnetic Poles and Pulsars Crawl of the Crab

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You have two images of M1, the Crab Nebula, a supernova remnant 1956 1999 Crab Pulsar

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Lots of Knots

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The Mystery: Student Task Use the two images of the Crab Nebula to determine in what year the supernova explosion occurred. Provide mathematical evidence to support your answer. Use the two images of the Crab Nebula to determine in what year the supernova explosion occurred. Provide mathematical evidence to support your answer.

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Stellar evolution made simple Stars like the Sun go gentle into that good night More massive stars rage, rage against the dying of the light Puff! Bang! BANG! 0.077 ~8 M o ~8 ~20 M o ~20 ~100 M o

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Binding Energy

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Core of star collapses Resulting shock disrupts envelope Star explodes

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Supernova! The result is a pulsar left where the star used to be and a cloud of gas and dust expanding from the pulsar.

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The Universes Flip Book 1956 1999 Crab Pulsar

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Share Your Answers Be ready to share the year in which you think the supernova occurred. Do not tell how you arrived at that answer, though. Be ready to share the year in which you think the supernova occurred. Do not tell how you arrived at that answer, though.

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After hearing your colleagues answers … Do you have any questions for any of the other groups? How should we decide which group is correct (or closest to correct)? Do you have any questions for any of the other groups? How should we decide which group is correct (or closest to correct)?

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Moment for Reflection What DID I do to introduce/lead this task? What DIDNT I do? What have the effects been of how I have lead this session so far? What DID I do to introduce/lead this task? What DIDNT I do? What have the effects been of how I have lead this session so far?

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Teacher Task 3 Strategies for Solving Problem Middle School Mathematics Early High School Mathematics Later High School Mathematics For each strategy, determine what materials and information students would need to complete the task. For each strategy, determine what mathematical concepts and skills students would need to complete the task. 3 Strategies for Solving Problem Middle School Mathematics Early High School Mathematics Later High School Mathematics For each strategy, determine what materials and information students would need to complete the task. For each strategy, determine what mathematical concepts and skills students would need to complete the task.

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Sharing Time!

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Strategy #1: Make a Table

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Strategy #2: Rate

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Strategy #3: Proportion

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Strategy #4: Linear Equation - A

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Strategy #5: Linear Equation - B

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Strategy #6: Coordinate Plane & Vectors

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Strategy #7: Coordinate Plane & Distances

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Strategy #8: Non-linear Models With all previous strategies, we have made assumptions. Lets question some of those assumptions. Its impossible to approach a problem like this without making assumptions, but asking for non-linear models forces our students to identify assumptions and recognize how they affect their mathematical models. With all previous strategies, we have made assumptions. Lets question some of those assumptions. Its impossible to approach a problem like this without making assumptions, but asking for non-linear models forces our students to identify assumptions and recognize how they affect their mathematical models.

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Strategy #0: Google it!

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Modifications and Extensions - 1 Scientific Dispute: Tell students that some astronomers think that the Crab Nebula explosion occurred much earlier than 1054. They think it happened closer to the year 475. The task, then, is to determine whether the data from these pictures could support or contradict that claim.

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Modifications and Extensions - 2 Predictions: How far do you expect the knot to be from the pulsar in the year 2025? 2500? When do you expect the knot to be 17 cm from the pulsar (at this scale on the paper)? Where do you expect knot #1 to be in the year 2025? 2500? (Make a mark on the paper to show where you expect the knot to be.) Predictions: How far do you expect the knot to be from the pulsar in the year 2025? 2500? When do you expect the knot to be 17 cm from the pulsar (at this scale on the paper)? Where do you expect knot #1 to be in the year 2025? 2500? (Make a mark on the paper to show where you expect the knot to be.)

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Modifications and Extensions - 3 True Distances: Given that the Crab Nebula structure is 11 light years in diameter, find thetrue distances for each of the measurements made between objects in the images. Reinterpret any rates/ratios in terms of these true distances.

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Modifications and Extensions - 4 Lookback Time: The Crab Nebula is 6523 light years from Earth. In what year did the explosion actually occur?

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Modifications and Extensions - 5 3-Dimensional Model: Have students build a 3D model to show where each of these knots could be in 3-dimensional space, preserving the way that they look from a position on Earth.

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Modifications and Extensions - 6 YOUR Ideas?

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Common Core Math Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

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Common Core Math Practices 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning.

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Astronomers REALLY do this! Analyze data. Find patterns. Identify assumptions. Formalize models. Draw conclusions. Make predictions. Test according to history and future. Continue the cycle. Analyze data. Find patterns. Identify assumptions. Formalize models. Draw conclusions. Make predictions. Test according to history and future. Continue the cycle.

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Q&A and Evaluations

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Thank You! Janet Moore JanetMoore@gmail.com NASAJanet.com Janet Moore JanetMoore@gmail.com NASAJanet.com

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