Teaching Compound Inequalities.

 I am getting ready to help my Algebra I students learn compound inequalities.  We've been through learning to solve one step, two step, multistep inequalities.  They had to learn when the direction of the inequality changes and I think they've got it all but now we hit a topic that can be quite difficult to learn. 

I think the hardest thing about compound inequalities is that they have two different solutions.  Up to now, they have been working on solving inequalities that result in one answer such as x < -5.

It has been suggested that one start with or type inequalities because the student solves two different equations and gets an answer for each problem.  This is similar to what they have been doing except it is for two problems, not one.

In addition, it is good to have students fill out compound inequality graphic organizers so they have a quick reference for or versus and. The first part of or should be filled out as students are learning how to work with the or so they become familiar with it.  

After they are comfortable with doing or, introduce the and so they understand that although there are two equations, the answers overlap more so than any with the or.  Add what they've learned to the graphic organizer for and so they have complete notes.  

No matter which is being taught - or, or and, there needs to be some sort of visual representation such as the use of a number line.  Rather than just shading in the number line, one should use two different colors so that students connect the visual representation with the equation.  In fact, if you want to solve one half in one color and the other half in a second color, you can then draw the answers on the lines with matching colors.  This provides a visual connection with the eye.

This can be re-enforced by having students watch videos by Khan Academy, Math Mashup or any other reputable site.  Khan academy usually walks students through the process but their language might be of a higher level than where your students are at.  However, Khan Academy usually has quizzes and such to help assess their understanding.

Furthermore, one can explore Desmos, or Geogebra as both have activities that can be used for this topic.  Geogrebra has several graphing activities designed to specifically to practice graphing of inequalities.  So have fun teaching compound inequalities.  Let me know what you think, I'd love to hear.  Have a great day.