Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. For example, compare and contrast quadratic functions in standard, vertex, and intercept forms. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Introduction In this task, we create equations (of one to variables) in order to model some realistic phenomena. The structure of this task could, of course, be manipulated to suit the preferences of the teacher. The reasoning for the structure of this task is based on two needs: First, the obvious need to give a narrative structure to the context of the task. Second, and more importantly, while teachers (or students) may question why the task begins with a system of equations utilizing three variables, the task begins here to present (and ask students to evaluate) the types of equations that students will be required to create on their own later. The task covers a number of relationships between variables, including linear, exponential, and quadratic. Materials Pencil Handout Calculator Ted’s Quest for a Tablet Ted has had his eye on a tablet computer for several months, and he’s trying to figure out a way to save enough money so that he can buy one using cash instead of credit. Ted is trying every possible method to build his computer fund he’s looking for change in the couch, he’s – drawn up a savings plan, he’s budgeting in other areas of his life, and so on. But Ted is growing impatient, and he’s afraid that he will resort to using a credit card so that he can get one quickly, but of course that means Ted will have to pay interest on his purchase.
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. For example, compare and contrast quadratic functions in standard, vertex, and intercept forms. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Introduction In this task, we create equations (of one to variables) in order to model some realistic phenomena. The structure of this task could, of course, be manipulated to suit the preferences of the teacher. The reasoning for the structure of this task is based on two needs: First, the obvious need to give a narrative structure to the context of the task. Second, and more importantly, while teachers (or students) may question why the task begins with a system of equations utilizing three variables, the task begins here to present (and ask students to evaluate) the types of equations that students will be required to create on their own later. The task covers a number of relationships between variables, including linear, exponential, and quadratic. Materials Pencil Handout Calculator Ted’s Quest for a Tablet Ted has had his eye on a tablet computer for several months, and he’s trying to figure out a way to save enough money so that he can buy one using cash instead of credit. Ted is trying every possible method to build his computer fund – he’s looking for change in the couch, he’s drawn up a savings plan, he’s budgeting in other areas of his life, and so on. But Ted is growing impatient, and he’s afraid that he will resort to using a credit card so that he can get one quickly, but of course that means Ted will have to pay interest on his purchase.
Algebra-II-Advanced-Algebra-Unit-6.docx