Inequalities






Butler, Ben Jr.                       Gage Park High School 
518 E. 42nd St.                       1-312-471-8630
Chicago, IL 60653-2716
1-312-268-3947 or 285-8625

Objectives

Students will learn how to transform inequalities and find their sets. 

Apparatus Needed:

Math balance, and two rings connected to several rubber bands. 

Recommended Strategies

The procedure starts out with a discussion on the usefulness of numbers. It should be 
pointed out that a number is a very abstract concept and we talk about them in 
solution sets. Its usefulness can be reflected on a number line to indicate quality 
and operation. 

In the sciences, positive and negative numbers can be used in connection with 
temperature readings, linear forces, clockwise and counterclockwise motion, 
positive and negative charges of electricity, acceleration and deceleration, etc. 

In the directional sense they are useful in indicating north and south, east and 
west, above and below sea level, left and right, and up and down. 

The stock market uses them to show changes in prices. They are used in everyday 
statistics to indicate changes such as the increase and decrease in the cost of 
living,and to show deviation from the normal - as in weather reports. Statistics 
in sports and scoring of games often require the use of signed numbers. 

This particular math model is constructed by dividing a horizontal bar into equal 
parts. A point of division is taken as the starting point or origin and labeled 
zero. Each point to the right of the zero is labeled with a positive number:  +1 
representing the first unit, +2 the second unit etc. Every point to the left of 
zero is labeled with a negative number beginning with -1. There is a hook at each 
point to help identify the number. 

To emphasize the ideas of oppositeness, position and direction, students realize that 
the direct value of a number is its absolute value along with the element of 
direction. 

Now we work with examples. We add on the number line until we are able to perform the 
operation readily. 

Next I asked what happens when each member of an inequality is multiplied by a 
nonzero number? Multiplication by a positive whole number is presented as repeated 
addition. Multiplication with negative numbers are motivated by algebraic laws. 

Finally, we motivated the method for solving linear inequalities.