Butler, Ben Jr. Gage Park High School

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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