**Inequalities**

Butler, Ben Jr. Gage Park High School

1-312-471-8630

**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.

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