Mathematics/Physics

 

What Does Greatest Common Factor Mean to Me?

 

Stephen Ha

Lloyd Elementary School

2103 North Lamon Avenue

CHICAGO IL 60639

773-534-3070

 

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 pre-marked 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 pre-marked 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.