Linear Inequalities

This week is my last full week with my 8th grade algebra students.  One of the topics for the week was linear inequalities.  In the past, I have found that the kiddos have had a lot of trouble understanding why we shade one half plane or the other.  I saw on either a blog or Pinterest (sorry I can't find either one) of a teacher that plotted points that were solutions to the linear inequality.

So, here is my take on the idea.  I made this worksheet to guide the kiddos while they worked.  I asked the student to pick points and determine if they were solutions to the inequality or not.  If the point chosen was a solution, they were to graph it on their graph at the top of the page.  I also gave the kiddos a bank coordinate plan and asked them to plot all of the solutions their group found.

What I found was that the kids immediately noticed linear patterns for the solutions.  They were saying all of the double numbers seem to work, like (2,2).  Others found complete chaos and couldn't figure out how others were finding so many solutions so quickly.  We had to go to a band concert, so I had to cut the exploration time short.  But, I was loving what I was hearing as they tried to find solutions.  When some kids got a line parallel to the boundary line they thought they had found all of the solutions, so there was a great authentic math discussion.  I was so happy with how the activity went.

Next time, I would give each group a different color marker and ask then to plot all of their solutions onto one class graph.  That way we will have a larger number of solutions to observe and draw conclusion.  I would also not do this activity on the day we have a shorten class. 

The graphic organizer is what I used to wrap up the basics of graphing linear inequalities.  It is based on lesson 97 from the Saxon Algebra textbook.