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Created with Fabric.js 1.4.5 Cover Letter: Statement of Personal Growth: Baker's Choice Portfolio This is the first paragraph of my POW write-up in which I explained my process for solving the problem. Homework 2: High School Letters The first piece I chose was Homework 2: High School Letters. Homework 2 requires that we analyzegiven variables that have been assigned to a certain meaning. For example, C stands for the numberof classes taken by each student. From these variables we had to create meaningful expressionsand make sure that they all make sense according to the meaning. This was helpful in solvingBakers Choice because we had to read the problem and consider expressions for the given constraintsand make them inequalities. Profitable Pictures The second piece I chose was Profitable Pictures. Profitable Pictures gave us certain constraints and we hadto graph the inequalities as well as their respective solution sets. We then considered the intersection of thesolution sets as the feasible region. The problem required that we find combinations that gave a profit of $500,$600, and $1000. This helped us see that the profit function gives profit lines that are parallel. Through an analysisof the profit lines we were able to conclude that profit increased as the values of x and y increased. These ideashelped us develop ways that we can solve Bakers Choice. Homework 13: The Big U POW:Kick It! The third piece I chose was The Big U. The Big Uwas similar to Bakers Choice in that The Big Uproblem wanted us to minimize (instead ofmaximize) a cost. We were given constraintsand made inequalities. We then found thefeasible region. Unlike Profitable Pictures therewas no support provided in finding the minimalcost of education. Thus we had to find a way toshow that the cost of education decreased acertain way. We checked points and then wecould notice that the cost of education decreasedtoward a certain vertex of the polygon, namely atriangle, which was the feasible region. Thus, TheBig U problem helped us conclude that themaximum or minimum of a function occurs at avertex of the feasible region. This helps to solveBakers Choice. POW: Broken Eggs This image shows some of my work as I continued to explore other solutions to the Broken Eggs problem. Baker's Choice Revisited In Bakers Choice the central problem of the unit was a linear programming problem.We were given information about certain constraints that a bakery had to adhere toand we were asked to help the bakery maximize their profit while satisfying the givenconstraints. The main mathematical ideas from this unit included expressing andinterpreting constraints using inequalities, graphing individual linear inequalities andsystems of linear inequalities, finding the maximum of a linear function over a polygonregion, relating the idea of intersection of graphs to the idea of common solution ofequations, and solving linear equations for one variable in terms of another.The previous mathematical ideas were used to help solve the Bakers Choice problem.We had to consider the given constraints of the problem to create inequalities andthen solve a linear equation for one variable in terms of another in order to graph thatinequality. We had to relate the idea of intersection of graphs to the idea of a commonsolution to the equations and consider the maximum of a linear function over a polygonregion. I will specifically reflect on the following three assignments and how they werepart of the process to develop skills needed to solve Bakers Choice: Homework 2:High School Letters, Profitable Pictures, and Homework 13: The Big U. Here is the graph I used whenrevisiting Baker's Choice as wellas the report that I wrote up forthe Woos. Bakers Choice opened my eyes to a new perspective of mathematics. In high school, mathematics is oftenportrayed as procedural rather than a subject where one can explore to derive new mathematical concepts.In Picturing Cookies Part 1 we were introduced to how we can derive the idea behind graphing inequalities.We had to use two distinct coloring pencils to plot points where one color indicated that the point satisfiedthe inequality and the other color indicated that the point did not satisfy the inequality. This problem lead tothe development of graphing inequalities and considering the solution set of an inequality as a half-plane.Personally I gained a different insight on how to develop the idea of graphing inequalities and as a result thishas given me a new way to consider teaching inequalities in the future. Bakers Choice models a real-worldproblem that requires many mathematical concepts. The structure of the book provides one with the opportunityto develop the mathematical concepts needed in order to solve the big problem. I feel that providing studentswith a big problem can help motivate students to learn because they know that they are learning certainconcepts to solve a bigger problem. As a result this makes the mathematics relevant to the students, whichwill help engage them. This has helped me grow as an educator because I can now consider providing studentswith motivation by explaining that the math they are learning will provide them with the skills to solve a biggerproblem.
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