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| 6.4 Concepts Irrational numbers were the last numbers needed to complete the real number system. The very name suggests that people had difficulty in accepting this type of number. A careful definition of irrational numbers was not obtained for over 2000 years after it was first discovered that not all numbers are rational. Write a brief history of the irrational numbers, beginning with the first evidence that there were numbers that were not rational and ending with the acceptance of irrational numbers by mathematicians. 6.4 Teaching In the middle grades, students should also add another pair to their repertoire of inverse operations – squaring and taking square roots. In grades 6-8 students frequently encounter squares and square roots when they use the Pythagorean relationship. NCTM Standards 2000, page 220The terms “square number” and “square root” should suggest geometric images to students. Use a geometric model to illustrate the square of a number and the square root of a number. Discuss the inverse relationship between the operation of squaring a number and the operation of taking the square root. Use a diagram to illustrate the Pythagorean relationship and describe how the square of a number and square root are involved. 6.4 Concepts The first numbers were whole numbers and this number system was adequate for thousands of years. Then fractions became needed to measure parts of a whole. Hundreds of years later negative numbers became needed to count or measure opposite amounts. The next type of number needed was irrational numbers. Give some reasons why irrational numbers are needed and illustrate your reasons with examples. |