Student Work: Right Hand/Left Hand Experiment Linear Programming Assignment

Linear Programming Assignment

Teacher Commentary: Systems of Linear Equations

The first thing I noticed from Gerardo's paper was that he labeled each section of his paper clearly. He defined the variables and his two equations correctly. Then he chose to find the x-intercepts and y-intercepts in order to graph the equations. I was impressed by the way that he showed all of his work when he substituted 0 for x and then solved for y to get y =91. He then substituted 0 for y and solved for x to get x = 136.5. He also wrote the points in a table of values.

It was so nice to see that Gerardo labeled every part of his graph, labeling the axes as variables x and y and as "the number of two-point shots" and "the number of three-point shots." He also labeled each line with its equation. Gerardo also showed that he knows how to solve a system of two equations in two variables, and that the solution is also the point of intersection of the two lines.

This is the beauty of teaching in this manner, using the IMP program. Students work on a concept for several days, each day adding more complexity. Every three or four days, another part or concept is introduced, and the students are given time to make connections with the concepts they have been studying.

The second piece of student work [the essay] is Alex's cover letter for his unit portfolio at the end of the "Cookies" unit. A portfolio is one of three assessments at the end of each unit. In the cover letter, students are given the opportunity to express what they know in their own words.

I really liked how Alex first introduced the concept of Linear Programming by giving a brief summary of all the skills he had learned to solve linear programming problems, and then going on to explain how one uses variables.

Alex is an emerging English language learner and he still has trouble with his grammar, tenses, and spelling, but I can see that his mathematical thinking is very organized by the way that he organized his paper, by the detail that he gave in explaining how one uses variables, and by the fact that he was able to give an example.

 Next: Teaching Strategies