1. Looking for Pythagoras Prob. 4.1 1.How do I determine if a number is rational or irrational? 2.How do I estimate the values of square roots that are irrational? 3.How do I estimate lengths of hypotenuses of right triangles? Wheel of Theodorus

2. Bell Ringers 1. The square root of 17 is between what two consecutive whole numbers? 2. Estimate the square root of 17 to 1 decimal place. Approximately 4.1 3. 4 2 = 16, 5 2 = 25; therefore, the square root of 17 is between 4 and 5. Define rational numbers. Any number that can be written in the form of where b ≠ 0. This includes whole numbers, fractions, & decimals both repeating and terminating.

3. Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. c. Recognize square roots as points and as lengths on a number line. Essential Question: How can we use what we know about right triangles to “plot” the lengths of irrational numbers on a number line?

4. What is the area of the square above? Yes, it is 2 sq. cm. What is the length of the side of the square? Yes, it is the square root of 2 which is about 1.4. How long is the square root of 2; where would it “fit” on a number line? We can “copy” that length and mark it on the number line.

5. How do you think the wheel of Theodorus was created? How do we determine the length of the first hypotenuse? How do we determine the length of the second hypotenuse? g 2

6. Now complete your Wheel of Theodorus!

8. Now, let’s check and correct your handout…ready, set, GO!

9. B.

10. radicalwholes betweentenths betweencalculator 1 and 2 1.4 and 1.51.414213562… 1 and 21.7 and 1.81.732050808… 2 and 32.2 and 2.32.236067977… 2 and 32.4 and 2.52.449489743… 2 and 32.6 and 2.72.645751311… 2 and 32.8 and 2.92.828427125… 3 and 43.1 and 3.23.16227766… 3 and 43.3 and 3.43.31662479…

11. How can we use what we know about right triangles to “plot” the lengths of irrational numbers on a number line?