## Wednesday, September 13, 2006

### Next Lesson: Compound Inequalities and Interval Notation

After reviewing the homework and the results of the last quiz (mean: 76%, not great, not terrible), we will dive in to a little guided instruction time.

We'll start with a quick review of inequalities - students will add, subtract, multiply, and divide the inequality 4 < 8 by both 2 and -2 to see which operations cause the inequality symbol to reverse. We'll also review the idea that a < b means that a exists to the left of b - some students have problems with this, especially when the numbers are negative. We'll also see why x < a is the same as a > x, and that when graphing, you can't just draw an arrow in the direction that the inequality symbol faces.

Then, I'll show them how to solve and graph both simple and compound inequalities. I'll do a couple of examples, and then they will also.

Finally, I'll hand out a reading that introduces students to interval notation. They will read it and then complete the practice problems on their own, as I walk around and coach them. This topic is not part of the standards, but it is used extensively in Calculus, and I think Algebra 2 is the right place for students to see it. The handout (with problems) is on ILoveMath.org.

Update:
The lesson went fine, but there was not enough time for the students to complete the interval notation reading, so I'm pushing that to the next class. They were asking good questions about inequalities (i.e. why expressions like 3 < x > 6, or -2 > x > 2 don't make sense). These students seem to have retained a lot from Algebra 1, which is always a good sign!