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In this unit, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4). They use appropriate tools to explore the effects of transformations on graphs of exponential and logarithmic functions. They notice that the transformations of a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3). Students identify appropriate types of functions to model a situation (i.e. based on the context, is an: exponential, linear, quadratic or sinusoidal the most appropriate). They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions” is at the heart of this module. In particular, through repeated opportunities in working through the modeling cycle (see page 61 of CCSS-M), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations. Notes: Lessons attached in a separate document, along with Do Nows. Vocabulary words are embedded in the lessons, as well as posted on the classroom “word wall,” following instruction for the day. Technology is used through a PowerPoint in class to present the work, the use of calculators during some lessons and the doc cam to show student work. Differentiation in the class occurs through the use of a separate graphic organizer for notes, in addition to shortened assignments, strategic seating and targeted circulation in class. All students also have access to the answer key on google classroom and we will review almost all answers in class, through presentation of student work.
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