Compound Inequalities

My students only worked on compound inequalities that shaded between the two points if it was a "and" inequality and outside the two points if it was an "or" inequality, but I felt that it was misleading.  My kids had recently mastered no solution and all real numbers in the previous section, so why should it not carry through to compound inequalities.  I felt like I had misled them if I didn't show them other compound results.

First, we started off with a review sheet, I had noticed that some kids were struggling.  Thank goodness all my classes had an even number today otherwise my plan may have had more kinks.  There were four sections on the worksheet I had in class.  The first part was just interpreting the graphs.  The kids chose their best friend as their partners as usual.  Before moving to the next section, they had to find another partner.  Typically my low level students don't work with a higher level  math student in fear that someone may find out that they can't solve the equation.  This forced my levels to mix by the third and fourth round.  Haha, math teacher won out.  The kids worked the hardest they have worked in a while.  I praised them and then threw in the monkey wrench...

I started with the statement "Raise your hand if your grandmother is older than 50 years old."  Then, I said "continue to raise your hand if your grandmother is older than 50 and younger than 10."  I had a few "what?!" faces, but the hands quickly went down as I began to explain a no solution equation.

For all real numbers, I asked them to raise their hands if they were older than 14.  Then, I said raise your hand if you are older than 15 or younger than 17.  They all raised their hands.  This was an example for all real numbers, I begin to see ah-ha faces.

We'll see after their homework tonight if they grasped the two concepts.