Irrational Numbers Investigation 5 Looking for Pythagoras

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Presentation transcript:

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

Previous Investigations 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

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

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. 1u 1u 1u

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.

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

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.

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.

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.

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