STRATEGIES, AS THEY RELATE TO CCSS-M PRACTICE STANDARDS
In the Rationale Section, I stated that I would incorporate the eight CCSS-M Practice Standards into this unit. As we discussed in our seminar, the Practice Standards are not necessarily meant to be taught explicitly; they are more habits that we want to develop in our students to make them successful. Toward that goal, the carefully planned progression of activities, in the lessons detailed above, will help students achieve the first two Math Practice Standards (MP1 and MP2), "Make sense of problems and persevere in solving them," and "Reason abstractly and quantitatively." By starting with students' prior knowledge, making connections to the vocabulary in other areas of their lives, and from previous math topics, students should have enough confidence to get started. The discussion around inverting functions – getting a clear idea of what invertibility should mean, and the need for one-to-oneness, will require substantial sense-making by students. Students will work collaboratively through most of the unit, always discussing and comparing their observations and results, and making conjectures to test further. These small group discussions and conjectures attend to MP3, "Construct viable arguments and critique the reasoning of others." As students gain confidence within small groups they will be asked to participate in full class discussions, and critique or justify the reasoning of their classmates. The fourth Math Practice Standard, "Modeling with mathematics," is addressed through some of the situations in the tasks and by testing conjectures students make along the way. The next two standards, MP5 and MP6, "Use appropriate tools strategically" and "Attend to precision" are the most strongly addressed. For example, students will use graphing calculators or computer software to make observations and conjectures. Requiring students to state the domain and range throughout the entire unit is one way to "attend to precision." Students will "Look for and make use of structure," according to MP7, in nearly every activity in this unit: connecting definitions to graphs, tables, and formulas, connecting transformations to composition and to geometry, connecting inverse operations and inverse functions, and the structure in graphical representation of functions and their inverses. The last Math Practice Standard, MP8, recommends students "Look for and express regularity in repeated reasoning." This standard states, "As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results." Again, the lesson tree design will help students stay focused on the key understandings for functions, and question whether something new is reasonable based on what they have learned along the way.
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