Title
Translations with Conic Sections
Skill
Responding to Counterarguments
EBA Activity
Counterarguments Table Debates
Claims
If the earth was in the path of two asteroids that shared a common trajectory, it
would be best to perform a translation if the path was in the shape of a
hyperbola in order to minimize future collisions.
Procedure
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Timing/Pacing
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Notes
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Follow Up
Activity
Text
Students should prepare a visual with two equations, one a translation
of the other, graphed on the same sheet that is supposed to represent
Earth avoiding an impact from an asteroid.
Proceed with a standard Counterarguments Table Debate Activity.
Before this lesson students will have learned how to write equations for
and graph ellipses, parabolas, and hyperbolas. To engage in this lesson
students must be comfortable with perfect squares, evaluating rational
equations, and using a graphing calculator to make formulaic
adjustments. After this lesson students will continue to practice
applying translated conics to real-life problems.
This activity will take 10 minutes.
This lesson would occur near the end of class. Before this activity
students would have a mini-lesson and practice with writing and
graphing the equation of a translated conic. After this activity students
would begin independent practice that they could finish as homework.
While the person affirming the claim will have to argue that a shifting a
hyperbola will be the best option, the other side could argue that
ellipses, which include circles, or parabolas are the best to perform a
translation on.
When arguing this claim, students should keep in mind the fact that the
earth is moving as well and that the two asteroids may be any distance
between each other and could offer interesting possibly for a hyperbola
given it’s asymptotic behavior.
To add a writing component, follow up with a Defeating The Critic Paragraph.
Standard Pre-Calculus Text.
Boston Debate League © 2012
Name:____________________________________ Class:______________ Date:______________
Counterargument Table-Debate
Claim 1A:
Claim 1B:
If the earth was in the path of two asteroids
that shared a common trajectory, it would be
best to perform a translation if the path was in
the shape of a hyperbola in order to minimize
future collisions.
If the earth was in the path of two asteroids that
shared a common trajectory, it would be best to
perform a translation if the path was in the
shape of an ellipse in order to minimize future
collisions.
Boston Debate League © 2012
Counterargument Table Debates
Before the Table Debate write the two reasons you believe your claim is true. If you have time, start
forming counterarguments for your opponent’s claim.
Claim 1A/1B
Warrants
My Claim
( ):
My
Opponent’s
Claim ( ):
Boston Debate League © 2012
Round 1
Counterarguments
and/or Responses
Warrants
Round 2
Counterarguments
and/or Responses