Transcript Irrational Numbers Investigation 5 Looking for Pythagoras Hope Harris, Melanie Wrenn,

Irrational Numbers
Investigation 5
Looking for Pythagoras
Hope Harris, Melanie Wrenn,
Suzanne Batchelor
Essential Vocabulary
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Pythagorean Theorem
hypotenuse
leg (of a right triangle)
Square root
Irrational numbers
Rational numbers
Real numbers
Terminating Decimals
Repeating Decimals
Previous
Investigations
This
Investigation
Where is the 2 ?
In your journal explain where you
would estimate 2 . Describe the
strategies you used to find your
estimation.
Movie
Wheel of Theodorus
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Named for Theodorus of
Cyrene, a Pythagorean
and a teacher of Plato
Begins with a triangle
with legs of length 1 and
1u
winds around counter
clockwise
You only need to know
how to draw right angles
and segments of length 1.
1u
2
1u
1u
Analyzing the Wheel of Theodorus
Use the Pythagorean Theorem to find the
length of each hypotenuse in the Wheel of
Theodorus.
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Label each hypotenuse with its length.
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Use the radical symbol to express lengths
that are not whole numbers.
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Analyzing the Wheel of Theodorus
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Measure each hypotenuse on the Wheel
of Theodorus, and label the point on
the ruler that represents its length.
Analyzing the Wheel of Theodorus
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For each hypotenuse length that is not
a whole number, give the two
consecutive whole numbers between
which the length is located.
Analyzing the Wheel of Theodorus
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For each hypotenuse length that is not
a whole number, use your completed
ruler to find a decimal number that is
slightly less than the length and a
decimal number that is slightly greater
than the length. Try to be accurate to
the tenths place.
Analyzing the Wheel of Theodorus
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Now, use your calculator to find the
value of each square root, and compare
the result to the approximations you
found from your ruler.
Follow-up Problem
When Joey used his calculator to find √3
he got 1.732050808. Geeta says that
Joey’s answer must be wrong because
when she multiplies 1.732050808 by
1.732050808, she gets 3.000000001.
Why do these students disagree? Write
your answer in your journal.
Summary of 5.2 & 5.3
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5.2 – Representing Fractions as Decimals
Students review writing fractions as decimals
and decimals as fractions. Then they are
introduced to the concepts of terminating
decimals and repeating decimals.
5.3 – Exploring Repeating Decimals
Students search a method for writing
repeating decimals as fractions. Then they
are introduced to the concepts rational and
irrational numbers.
Essential Vocabulary Follow-up
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Pythagorean Theorem
hypotenuse
leg (of a right triangle)
Square root
Irrational numbers
Rational numbers
Real numbers
Terminating Decimals
Repeating Decimals