Prime and Composite Numbers

Charlotte Goldwater            Kenwood Academy
                               5015 S. Blackstone
                               Chicago, Illinois 60645
                               312-536-8909

Objective:

     The main objective is to have a systematic method of deciding if a number 
is prime or not.  This project is geared to fifth through ninth grades.

Materials Needed:

     Large translucent container filled with water
     Roll of masking tape 
     Pennies
     Any permanent marker
     Pencil
     One or two vis-a-vis non-permanent markers
     Three charts of numbers 1-100 on transparencies
     A classroom set of the same chart on paper
     A classroom set of an empty 10x10 grid
     An overhead projector 

Strategy:

     The mini-teach is directed toward fifth through ninth grades.  You give 
students the definitions of prime and composite numbers.  You allow students 
systematically to go through the numbers crossing out or eliminating multiples 
of two, multiples of three, multiples of five, multiples of seven, etc.  You 
continue until you reach the square root of the last number you are testing. 
When you are done, the remaining numbers are prime.  Have students make a list 
of the numbers.  For effect cut out the numbers from 1 to 100 from an acetate 
copy of a Sieve of Eratosthenes.  Put them on the overhead projector.  Take a 
pencil with a loop of masking tape and systematically remove the composite 
numbers.  The remaining numbers are primes. 
     Take fifty to one hundred pieces of masking tape, each about one inch in 
size.  Fold them in half so that the sticky side is together.  In half of them, 
put a penny.  With your permanent marker, write the prime numbers on the pieces 
of tape that have no pennies.  Write the composite numbers on the pieces of tape
that have pennies inside them.  Throw these numbers into a container of water. 
The composite numbers will sink, and the prime numbers will float.  You can have
the number 1 off to the side. 
     Take an empty 10x10 grid.  In row six column five, place the number 11.  
Then begin wrapping the numbers 12 through 110 around 11 in a clockwise fashion.
You will find many primes on the right diagonal of the line of numbers.