M.S. and Algebra I - Ideas for Teaching Systems of Linear Inequalities

Teaching linear inequalities typically involves a lot of details for algebra students. In fact, the prior knowledge required is quite extensive, including:
* Inequality symbols (greater than, less than, etc.)
* Solving for a particular variable
* Graphing a linear equation, including vertical and horizontal lines
* A conceptual knowledge of where larger or smaller values occur on a coordinate plane
* Knowledge of a empty vs. solid point on a number line

Using these bits of prior knowledge creates the opportunity to expand into solving systems of linear equations and subsequent expansion into systems of inequalities.

When expanding the concept of inequalities, a comparison should be made between the number line and the coordinate plane. The number line, being in one dimensional space, depicts solutions via a point and a line. If the inequality symbol includes part of the "equal sign", then the point would be filled in, or "solid." These ideas can immediately be extended to the coordinate plane, which lies in two dimensions. The solid dot becomes a solid line as a boundary, and the empty dot turns into a dashed boundary line. Instead of shading a ray on a number line, students shade a two dimensional region bounded by the dashed or solid lines.

After extending the main idea, two methods for doing the actual graphing work well for algebra students. The most inexpensive route, but colorful, is to have students shade with colored pencils, saving the darkest color for the overlapping sections. The second graphing technique is to use a TI-83+ or other graphing calculator. Students really enjoy using technology in their learning, especially if they have never seen shading on a calculator before.

To get the TI-83+ or TI-84 calculators to shade above or below the entered equation, cursor to the far left side of the 'y=' menu. Then press Enter several times until the type of shading is selected. Then graph. To find the intersection point of the two lines, choose 2nd-Calc-Intersect and press enter three times.

Overall, using prior knowledge to make connections and combining them with fun graphing techniques makes learning a difficult concept such as systems of inequalities a manageable task for Algebra I students.

Have you used these techniques? What other methods do you use to teach systems of linear inequalities? Please leave a comment. You may also like to read about creative ways to teach slope in an Algebra I class.

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