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

2. 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

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

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. 1u 1u 1u

6. 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.

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

8. 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.

9. 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.

10. 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.

11. Follow-up Problem
When Joey used his calculator to find √3 he got Geeta says that Joey’s answer must be wrong because when she multiplies by , she gets Why do these students disagree? Write your answer in your journal.

12. 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.

13. Essential Vocabulary Follow-up
Pythagorean Theorem
hypotenuse
leg (of a right triangle)
Square root
Irrational numbers
Rational numbers
Real numbers
Terminating Decimals
Repeating Decimals