The Standards
6.EE.Reason about and solve one-variable equations and inequalities.
5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
I've taught this to 8th graders before, but never to 6th graders, so I was a little apprehensive, on edge, nervous, and excited. And seeing the word "constraint" in a CCCS 6th grade math standard did add to my apprehension.
Curriculum comparison to standards comparison: I used Pearson EnVision and Carnegie as my curriculum resources, both of which included the inequalities "greater than or equal to" and "less than or equal to." Both of which are not mentioned in the standard.
I asked the students what they thought about the lesson, and here are some of their responses:
"It was one of my favorite lessons, you did a good job presenting it."
"It reminded me and taught me more about the concepts of greater than and less than and it taught me more about the greater than and less than signs."
"It was more than what I had learned in previous grades."
"I liked the inequalities and it was easy."
"I like it because if you don't pay attention, you will totally mess up. Some things I can do without paying attention, but this skill I had to really pay attention."
I asked the student who participated the most during the lesson what he thought about the lesson and he said, "I don't know." That response made me smile.
I'm glad I asked for their feedback, for a couple of reasons. First, I thought the lesson was soooooo boring. I thought it was too heavy with "teacher-talk." Within the "teacher-talk" students had opportunities to talk to their seat partner.
In trying to be reflective, I do see some value in the direct instruction aspect of the lesson and realize that sometimes new concepts require more "teacher-talk" than others. I underestimated the potential of the students to rise to the occasion of a new concept.
As the students got to work and I circulated to see how things were going, I did notice an alarming recurring theme. They graphed the inequality on the number line correctly, but wrote the inequality that went with the graph incorrectly. Many times I said, "Oh, wow, this is interesting because I'm reading two different things. Your graph reads 'm is less than 4,' but your inequality reads 'm is greater than 4.' So which one do you mean?" Every time the student would tell me their graph matched the situation, but their inequality did not.
I was impressed when they started giving me extreme examples of solutions to inequalities. I said, "What is a solution to the inequality, x < -1?" A student excitedly replied, "Negative one million!" #correct
Next steps: I will do a re-engagement lesson from student work to make sure everyone understands it as well as they think they do or have led me to believe... I will look for additional resources. I am hoping to find a good "real-life" inequality situation that I can adapt to a You-We-I Lesson. I will talk to my fellow 6th grade teacher colleagues and see how they have fared with teaching inequalities.
Thank you, kind reader, in advance for any feedback.
The next blog will be about how teaching volume goes.....
