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Challenges |
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Elana and Matt have decided to compete
in a "challenge" to see whose powers of observation are the strongest in
relation to figures drawn on a coordinate plane.
You will be acting as the judge (and
supreme keeper of the correct answer) during this challenge. Your task
is to prepare a proof showing the correct result for each question and
to keep track of Elana's and Matt's scores to determine the winner.
Let the challenge begin!
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Figure |
Elana's prediction |
Matt's prediction |
| 1 |
Quadrilateral A(1,2),
B(2,5),
C(5,7) and D(4,4) |
ABCD is a rhombus |
ABCD is a
parallelogram, but not a rhombus |
| 2 |
Triangle A(1,1), B(4,4),
C(7,2) |
ABC is a right
triangle |
ABC is not a right
triangle |
| 3 |
Quadrilateral A(3,1),
B(5,6),
C(7,6), D(10,2) |
The diagonals are not
perpendicular. |
The diagonals are
perpendicular. |
| 4 |
Quadrilateral A(0,-2),
B(9,1), C(4,6), D(1,5) |
ABCD is an isosceles
trapezoid |
ABCD is a trapezoid,
but not isosceles |
| 5 |
Line segment A(1,5) B(2,3)
and
line segment C(4,4) D(-2,1) |
The segments are
perpendicular |
The segments are not
perpendicular. |
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Score Card |
| Problem
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Elana |
Matt |
| 1 |
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| 2 |
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| 3 |
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| 4 |
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| 5 |
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The winner is
________________.
Note to teacher: There
are many variations on this activity.
1. You can use this activity as it is presented with Matt and
Elana.
2. You can choose two students to play the parts of Matt and Elana.
Draw the five figures on graph paper and let the two students "see" the
graphs (no touching). Then have each student record on a piece of paper what
he/she "observed" regarding the figure in relation to the specifications
listed above (is it a rhombus, are the lines perpendicular, etc).
Then have the class (individually or in groups) prove what the actual
answers are and score the two students.
3. You can have everyone take on the parts of Matt and Elana.
Show the graphs to the entire class and ask each student separately to
write down their "observed" truth. Have the class (individually or
in groups) prove each "truth".
4. Have each group of students prove a different question and then
pool answers.
5. Have one class challenge another class.
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