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4.2 TeachingStudents should recognize that different types of numbers have particular characteristics; for example square numbers have an odd number of factors and prime numbers have only two factors. NCTM Standards 2000, page 151Design an activity which uses tiles and the rectangular model for products to help school students discover that square numbers have an odd number of factors and prime numbers have only two factors. Use diagrams to explain how your activity will help students to see why each of these statements is true. 4.2 Concepts A teacher used the following activity to give one of his elementary school students a reason why 1 should not be considered a prime number. Using colored tiles he designated the following values: a red tile is worth 2; a yellow worth 3; blue worth 5; and green worth 7. He then asked the student to select a few tiles without letting him see them and calculate the product of their values. The student’s product was 90 and the teacher was able to determine the student had 1 red tile, 2 yellow, and 1 blue. How was the teacher able to determine the number of each type of tile? Explain by giving examples why it is not possible to determine the numbers and colors of tiles if 1 is allowed to be a prime number and assigned a colored tile. 4.2 Concepts Some calculators designed for middle school students have a function for determining if a fraction is in lowest terms, and if it is not in lowest terms, it factors out the smallest common divisor of the numerator and denominator and prints the resulting fraction. This process can be continued to obtain all the common factors of the numerator and denominator. Explain how such a function can be used to determine if a number with four digits or less is a prime number. Show some examples of how your system works. Then write a description for using such a function to show whether or not numbers with ten or fewer digits are prime numbers. |