"Factors"

Edwina R. Justice              Gunsaulus Scholastic Academy
                               4420 South Sacramento Ave.
                               Chicago IL   60632
                               (312) 535-7215

Objectives:

     Demonstrate a phenomenological approach to teaching mathematics

     Inspire others to use the approach

Objectives (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 numbers

Materials Needed:

     paper coins (actual coins??)

     worksheet for analyzing first moves

Recommended 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 numbers

Performance 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.