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

NASA’s Supernova NASA’s Supernova MathematicsMathematics

NASA’s Supernova NASA’s Supernova MathematicsMathematics

Janet MooreJanet MooreNASA Educator AmbassadorNASA Educator Ambassador

Janet MooreJanet MooreNASA Educator AmbassadorNASA Educator Ambassador

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NCTM Chicago RegionalNCTM Chicago RegionalNovember 29, 2012November 29, 2012

NCTM Chicago RegionalNCTM Chicago RegionalNovember 29, 2012November 29, 2012

The NASA E/PO Program at The NASA E/PO Program at Sonoma State UniversitySonoma State University

The NASA E/PO Program at The NASA E/PO Program at Sonoma State UniversitySonoma 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

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

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Three Supernova Activities

•Fishing for Supernovae•Crawl of the Crab•Magnetic Poles and Pulsars

Crawl of the Crab

Crawl of the CrabCrawl of the CrabYou have two images of M1, the Crab Nebula, a supernova remnant

1956

1999

Crab Pulsar

Lots of KnotsLots of Knots

The Mystery: Student TaskThe 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.

Stellar evolution made simpleStellar 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 Mo

~8 ~20 Mo

~20 ~100 Mo

Binding EnergyBinding Energy

Core of star collapsesCore of star collapses

Resulting shock disrupts envelope

Resulting shock disrupts envelope Star explodes

Supernova!Supernova!

The result is a pulsar left where the star used to be and a cloud of gas and dust

expanding from the pulsar.

The Universe’s Flip BookThe Universe’s Flip Book1956

1999

Crab Pulsar

Share Your AnswersShare 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.

After hearing your colleagues’ answers …

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)?

Moment for ReflectionMoment for Reflection

What DID I do to introduce/lead this task?

What DIDN’T 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 DIDN’T I do?

What have the effects been of how I have lead this session so far?

Teacher TaskTeacher 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.

Sharing Time!Sharing Time!

Strategy #1: Make a TableStrategy #1: Make a Table

Strategy #2: RateStrategy #2: Rate

Strategy #3: ProportionStrategy #3: Proportion

Strategy #4: Linear Equation - AStrategy #4: Linear Equation - A

Strategy #5: Linear Equation - BStrategy #5: Linear Equation - B

Strategy #6: Coordinate Plane & VectorsStrategy #6: Coordinate Plane & Vectors

Strategy #7: Coordinate Plane & DistancesStrategy #7: Coordinate Plane & Distances

Strategy #8: Non-linear ModelsStrategy #8: Non-linear Models

With all previous strategies, we have made assumptions.

Let’s question some of those assumptions. It’s 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.

Let’s question some of those assumptions. It’s 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.

Strategy #0: Google it!Strategy #0: Google it!

Modifications and Extensions - 1Modifications 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.

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.

Modifications and Extensions - 2Modifications 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.)

Modifications and Extensions - 3Modifications and Extensions - 3

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

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

Modifications and Extensions - 4Modifications and Extensions - 4

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

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

Modifications and Extensions - 5Modifications 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.

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.

Modifications and Extensions - 6Modifications and Extensions - 6

YOUR Ideas?YOUR Ideas?

Common Core Math PracticesCommon Core Math Practices1. 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.

Common Core Math PracticesCommon Core Math Practices1. 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.

Astronomers REALLY do this!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.

Q&A and EvaluationsQ&A and Evaluations

Thank You!Thank You!

Janet Moore

JanetMoore@gmail.com

NASAJanet.com

Janet Moore

JanetMoore@gmail.com

NASAJanet.com