It was a week ago now that June came in and observed me introduce Inequalities to my 6th grade class. Last week was completely insane with Parent-Teacher Conferences and meetings, plus after school activities. So finally, here is how it went...
I took your advise and assigned the warm-up that asked the students to compare numbers. It was a great lead. Then, all the sudden I felt somewhat unprepared. It threw me through a loop that the students had never seen the symbol "greater than or equal to" and "less than or equal to". Apparently in elementary only "greater than" and "less than" are presented. Once we got passed that hurdle, we began graphing on a number line. We discussed the difference in graphing "open circle" versus "closed circle" and we discussed the direction of the arrow. It got a bit more complicated when I introduced to them Solving the Inequality and Graphing the Solution. My students are still struggling with solving, however, when they did solve correctly they would often use an equal sign instead of the inequality for their answer. They were frazzled because they did not know what to graph. I am catching kids using the equal sign still today.
After the lesson, June and I sat down and discussed the good, the bad and the ugly. We thought about summarizing open and closed circles before moving onto solving, and we discussed using rational numbers instead of all whole number examples.
Since I always take two days on each lesson, the first day to introduce it and have the students try a couple of problems, the second day to remind students of the important points and then let them practice, practice, practice, I thought a good opener for Day 2 would be 3 graphs. On the whiteboard I wrote the sentence x > 5 and graphed it, then x = 5 and graphed it, lastly x > 5 and graphed it. I gave the students 2 minutes to write down what they saw on a peice of scrap paper. Then, without any other explanation, I had students discuss with each other the different observations they wrote down. What I was looking for was x > 5 and x = 5 combine to make x > 5. Since they had never seen the "greater than or equal to" symbol, I wanted to give them a chance to make their own conclusion and do their own thinking on what that symbol means. We discussed what we saw and then every student had to write a sentence summarizing our discussion (a short acitivity that involved writing - go me!).
My students have disappointed me because they are choosing to not do their homework. I worked with several students in class on the 2nd day, but only 1/3 of them came back with the assignment done. I really wish I had an accurate account of how well my teaching affected their learning. For the next observation I will make sure I do.