Towards the end of December, I posted about my interactive notebook pages for our Algebra 1 unit on Linear Graphs and Inequalities. However, we didn't start linear inequalities until AFTER Christmas. Here are our notebook pages for linear inequalities.
Here is a graphic organizer I designed to summarize the steps for graphing linear inequalities. It is a re-design of a graphic organizer I designed during my very first year of teaching.
Step 1: Rearrange the equation into slope-intercept form.
Step 2: Use the slope and y-intercept to create a graph.
Step 3: Determine whether you should use a solid line or broken line.
Step 4: Determine which way the graph should be shaded.
I know that many teachers opt to have their students test a point to determine which way to shade. I've tried this before, and it hasn't worked well for my students. I also find that the method gets confusing when you are trying to go backwards. For example, if students are given a graph and asked to write the inequality, figuring out which way the inequality symbol should face.
Another huge factor in this decision is that I teach a primarily low-level population that has historically struggled in mathematics. Most of them enter Algebra 1 without a strong understanding of integer operations. I try to remediate this area as we go, but I don't have time in our schedule to re-teach integer operations from the beginning. When I have taught shading by point-testing before, many students ended up getting the shading wrong because of small errors with positives and negatives. As a result, I now make my students graph each inequality in slope intercept form so we can shade above for greater than inequalities and shade below for less than inequalities.
My students found my Includes/Excludes posters super-helpful during this part of the unit!
Next, I made a really silly mistake. Since the first step I have my students do to graph inequalities is to rearrange them into slope-intercept form, I decided to do a bit of practice. But, here's my silly mistake. I should have made these inequalities to rearrange so we could practice remembering to flip the inequality symbol when we multiply or divide by a negative number. But, I made them a practice booklet with equations to rearrange. Oops... I have already made myself a note to change this to inequalities for next year.
Here's my note for next year. :)
Next we did two practice books.
And, this is what I get for picking random problems. Did you notice that all of the graphs ended up being greater than except the last one? I was SO frustrated when I realized this! Here's my note to fix this as well for next year.
The second practice book featured graphing inequalities that involved horizontal and vertical lines.
Our last skill of the unit was to write an inequality given a graph. I was super-sick this day, so I let students take turns coming up to the board and walking the class through one of the problems. I didn't have to do much at all because the students caught most of the mistakes of their peers.
I wasn't super careful when picking graphs for this activity which meant I ended up with a graph where my students couldn't determine the slope. Oops...
Files have been uploaded here.