# What Are Factors?

Objective:

To help students learn what factors means to them and how to use this math concept in application.

Materials:

Materials for four groups
- Four 250ml graduated cylinders, four 100ml graduated cylinders, water, six containers of different size with pre-marked volume on each of them.

**Note: All graduated cylinders must be of the same brand so to minimize the percent of error that might be resulted.

Strategy:

Before this hand-on activity, the teacher should already go through the concept of factors through modeling and practice on the board in the previous lesson. The teacher would first explain the activity to students through modeling. Then the students will work on the activity in groups to help themselves understand further the concept of factors and common factors.

Modeling by teacher
- 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 the water is added. For example, if the volume of the container is 150ml, a “based unit” of either 20ml, 30ml, 40ml, and so on, can be used to see which one can exactly fill up 150ml of water into the container (Choose a few volunteers to fill up the same container with different “basic units”).
- Ask students why not all “basic units” being chosen can be used to fill the container exactly up to the mark. Reinforce the concept of factors or even common factors after the discussion.

Student Activity
(1) Each group will use a cylinder being provided to fill a container up with water to the pre-mark label  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 two or more trial, modify the table accordingly..

 Volume of pre-mark label Based unit Successful? Is this a factor? (Y/N) Trial # 1 Trial #2 Trial #3

Performance Assessment:

(1) What is the most efficient way to do this activity?
(2) In what way does it make a difference?

Through the activity and the discussion of the above questions, students should be able to understand precisely the concept of  factors and learn how to use it for application purposes. They should even find out the concept, along with the meaning, of common factors, as well as the greatest common factor.

Conclusions:

The concept of the 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 the 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.

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