`"Factors"Edwina R. Justice              Gunsaulus Scholastic Academy                               4420 South Sacramento Ave.                               Chicago IL   60632                               (312) 535-7215Objectives:     Demonstrate a phenomenological approach to teaching mathematics     Inspire others to use the approachObjectives (Grades 5-7):     Show and record groups formed by using pennies     Define factor, product, prime, and composite     Write related number sentences     Find the factors of whole numbers     Classify numbers as prime or composite     Identify abundant, deficient, and perfect numbersMaterials Needed:     paper coins (actual coins??)     worksheet for analyzing first movesRecommended Strategy:     Ask: "How many ways can you make change for \$1.00 using only groups of the            same coin?"           Expected responses:  1 group of 100 pennies                               20 groups of nickels                               10 groups of dimes                                4 groups of quarters                                2 groups of half-dollars          "How many ways can you make equal groups of 100 pennies?"           Expected responses:  1 group  of 100 pennies                                2 groups of  50 pennies                                4 groups of  25 pennies                               10 groups of  10 pennies                               20 groups of   5 pennies     Discuss similarities in responses to both questions     Show one penny - Write "1 group of 1 = 1"     Show two pennies - Write "1 group of 2 = 2"     Show three pennies - Write "1 group of 3 = 3"     Show four pennies - Write "1 group of 4 = 4"     Show two groups of two pennies - Write "2 groups of 2 = 4"     Show and record all equal groups for 5 to 12 pennies     Write number sentences: 1 x 1 = 1;  1 x 2 = 2;  1 x 3 = 3;  1 x 4 = 4;                             2 x 2 = 4;  1 x 5 = 5;  1 x 6 = 6;  2 x 3 = 6;                             ...  1 x 12 = 12;  2 x 6 = 12;  3 x 4 = 12     Define factor and product     Analyze number of factors for products 1 - 12     Identify and define prime and composite numbers for products 1 - 20     Play "Factor Game" - List the numbers 1 - 36 as a 6 x 6 grid.           Circle a number.  Students draw a box around each proper factor            of the number. Students select a number and draw a box around it.           Teacher circles proper factors of the number.  Continue process until            no moves are possible.  Add the teacher's and students' numbers.  The            highest total wins.     Analyze first moves for the factor game - List the factors for numbers       1 - 36.  Compare the sum of the proper factors to each number.     Define abundant, deficient, and perfect numbersPerformance Assessment:     Select a two-digit number greater than 50.     Identify its factors.     Write related number sentences using the factors and the number.     Explain why the number is prime or composite.`