In this lesson, students were being introduced to linear programming, a real world application of modeling using systems of linear inequalities. This video clip showed the students first look into applying the concepts through a warm-up word problem activity. Initially, I planned to have the students work through the entire problem as small groups without any group instruction to start them off; however, I found that I needed to ease them into the problem by breaking into smaller pieces to review. A volunteer came to the board to explain their process in setting up a linear system of inequalities to explain the constraints for the production problem. After the basis of the system was set up, I went through a few details I felt students would benefit from seeing explicitly, such as constraints requiring students to work in the first quadrant. This is due to products needing to be positive integers in order to be a realistic application. This is the point where we transitioned into the next steps in the linear programming process by showing solutions graphically.
If I were to conduct this lesson again, there were some changes I would make in order to improve the flow and explanations of the content. First and foremost, there were some instances when I began to have a class discussion, but not all of the small group discussions had ended in order to project over the noise. Thus, some of the instruction I was giving went unheard by some of the students. I also noticed after conducting the lesson that there were some slips in important terminology that linked systems to linear programming; since this lesson took place, I have been much more aware of the terminology and phrasing I have used during instruction. Mistaking terms can definitely be confusing for students, especially as they are introduced to new concepts and their applications. Another adjustment I would make for this hook would be the pacing for student work and review. This activity was originally planned to last for about 10 or so minutes, but in actually took about 20 minutes to explain thoroughly. In order to adapt this, I think I would modify the expectations for students to solve. Because the concept of linear programming is so new, I would modify the instructions by placing more guided questions to create a step-by-step process. While our classroom places a focus on student learning through inquiry, I do feel this activity could have utilized more scaffolding to aid student understanding.
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Author20 something year old. Pittsburgh native. Pennsylvania explorer. Graduate student. Aspiring teacher. Archives
March 2016
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