Mathematics/Physics
What
Does Greatest Common
Factor Mean to Me?
Stephen Ha 
Lloyd
Elementary School 
2103 North
Lamon Avenue 

CHICAGO IL
60639 

7735343070 
Objective(s):
What
are the factors of a given integer.
Materials:
Materials
for four groups
 Four 250ml graduated cylinders, four 100ml graduated cylinders, six containers of different size with premarked volume on each of them.
Strategy:
The teacher will first show the concept of factors through modeling. Then the students will do an activity that will help them understand further the concept of common factors and greatest common factor.
Modeling by teacher
(1)
Choose
a premarked container and tell students the objective is to fill the
container
with water up exactly to the mark by using a graduated
cylinder.
However, the cylinder must carry the same amount of water, the “basic
unit,”
each time water is added.
For example, if the volume of the container is 300ml, a “based unit” of either 20ml, 30ml, 40ml, and so on, can be used to see which one can exactly fill up 300ml of water into the container (Choose a few volunteers to fill up the same container with different “basic units”).
(2) Ask students why not all “basic units” being chosen can be used to fill the container exactly up to the mark. Explain the concept of factors after the discussion.
Student
Activity
(1) Each group will use the cylinders being provided to fill a container up with water by choosing a “basic unit” they believe that can carry out the task.
(2) Record the “based unit” being used and fill out the related information in the following table.
(3) Repeat step (1) and (2) for 5 trials.
Volume in ml. 
“Basic unit” in ml. 
Number of repetitions 
(Exact?) Success / failure 
Container #1 Volume = 



Container #2 Volume = 



Container #3 Volume = 



Container #4 Volume = 



Container #5 Volume = 



Performance
Assessment:
(1)
What is the
most efficient way to do this activity?
(2)
In what way
does it make a difference?
Through the discussion of
the above questions, students will find out and understand the concept
of
common factors and greatest common factor.
Conclusions:
The concept of
greatest common factor is a useful
tool in some real life applications. For example, if the above activity
turns
into a competition, those who know the concept of greatest common
factor will
have a better chance to win the contest. Another example can be such as
what is
the most efficient way to give an exact change of 50 cents? Two
quarters? Five
dimes? Ten nickels? Or so forth.