Irrational Numbers

1
Irrational Numbers

• Investigation 5
• Looking for Pythagoras
• Hope Harris, Melanie Wrenn,
• Suzanne Batchelor

2
Essential Vocabulary

• Pythagorean Theorem
• hypotenuse
• leg (of a right triangle)
• Square root
• Irrational numbers
• Rational numbers
• Real numbers
• Terminating Decimals
• Repeating Decimals

Previous Investigations
This Investigation
3
Where is the

• In your journal explain where you would estimate
  . Describe the strategies you used to find
  your estimation.

Movie
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5
Wheel of Theodorus

• Named for Theodorus of Cyrene, a Pythagorean and
  a teacher of Plato
• Begins with a triangle with legs of length 1 and
  winds around counter clockwise
• You only need to know how to draw right angles
  and segments of length 1.

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• Analyzing the Wheel of Theodorus
• Use the Pythagorean Theorem to find the length of
  each hypotenuse in the Wheel of Theodorus.

• Label each hypotenuse with its length.
• Use the radical symbol to express lengths that
  are not whole numbers.

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Analyzing the Wheel of Theodorus

• Measure each hypotenuse on the Wheel of
  Theodorus, and label the point on the ruler that
  represents its length.

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Analyzing the Wheel of Theodorus

• For each hypotenuse length that is not a whole
  number, give the two consecutive whole numbers
  between which the length is located.

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Analyzing the Wheel of Theodorus

• 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.

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Analyzing the Wheel of Theodorus

• Now, use your calculator to find the value of
  each square root, and compare the result to the
  approximations you found from your ruler.

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Follow-up Problem

• When Joey used his calculator to find v3 he got
  1.732050808. Geeta says that Joeys 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.

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Summary of 5.2 5.3

• 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.

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Essential Vocabulary Follow-up

• Pythagorean Theorem
• hypotenuse
• leg (of a right triangle)
• Square root
• Irrational numbers
• Rational numbers
• Real numbers
• Terminating Decimals
• Repeating Decimals