Looking for Pythagoras Unit: Problem 4.1 (Pg 46) Using The Pythagorean Theorem Launch: Introduce the problem by discussing how to find a decimal approximation for a square root. On a dot grid, draw a square with an area of 2 square units on a number line, with the “bottom vertex” at point 0. • What is the length of a side of this square? If we mark off a segment on the number line with the same length as the side, where will the segment end? • So, is approximately equal to 1.4. Is 1.4 exactly equal to ? Suppose we try 1.41. Does 1.41 = ? Try 1.42. Does it equal ? Can you find a number that is closer to than 1.41 and 1.42 are? Display the Wheel of Theodorus. Explore with the class how the wheel was constructed and ask for the lengths of the second and third hypotenuses. Cut out the number-line ruler and demonstrate how to transfer these lengths to the ruler. Summarize: Display the Wheel of Theodorus. Ask for the lengths of the hypotenuses and write them on the wheel. Then, have students come to the front and mark the length of each hypotenuse on the number-line ruler. Ask for approximations to the nearest tenth for each length. As a class, check each approximation by squaring it on a calculator. • Is this estimate too large? Too small? What might be a better estimate? How do you know? Take this opportunity to assess students’ understanding of the ordering of decimals. Ask students to compare their estimates to the numbers they obtained with a calculator. Tell the class that the numbers , , , . . . are called irrational numbers. |